Deliverable 6.2 Guidelines on the design for end-usersdiswall.dic.unipd.it/Results/D6.2_FINAL.pdf · forces are generally the governing actions, where earthquake forces are high

DEVELOPING INNOVATIVE SYSTEMS

FOR REINFORCED MASONRY WALLS

COOP-CT-2005

CONTRACT N 018120

Design of masonry walls D62 Page 1 of 106

Deliverable 62

Guidelines on the design for end-users

Due date July 2007 Draft submission July 2007

Final submission date January 2008 Issued by TUM

WORKPACKAGE 6 Design of masonry walls (Leader TUM)

PROJECT Ndeg COOP-CT-2005-018120

ACRONYM DISWall

TITLE Developing Innovative Systems for Reinforced Masonry Walls

COORDINATOR Universitagrave di Padova (Italy)

START DATE 16 January 2006 DURATION 24 months

INSTRUMENT Co-operative Research Project

THEMATIC PRIORITY Horizontal Research activities involving SMEs

-50 0 50 100 150 200 250 300

120

150

180

210

240

ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086

Shea

r (kN

)

Moment (kNm)

M-N domain for walls of different length and fixed vertical reinforcement (spacing 780 mm)

TensionCompression

Limit 2-3

Limit 3-4

Limit 4-5

Limit 5-6

Limit 60

50

100

150

200

250

300

350

-10000 -8000 -6000 -4000 -2000 0 2000 4000

NRd (kN)

MRd (kNm)

l=1165 mml=1945 mml=2725 mml=3505 mml=4285 mml=5065 mml=5845 mml=6625 mml=7405 mm

Vd (MdNd) [kN]-5000

-4000

-3000

-2000

-1000

0

1000

0 200 400 600 800 1000 1200 1400 1600

Md [kNm]

Nd

[kN

]

0 30 60

90 120 150

180 210 240

270 Loadings

V-M domain (left) M-N domain (middle) V (M-N) domain for concrete perforated clay and hollow clay unit

reinforced masonry

Dissemination level PU Rev FINAL


INDEX

INDEX 2 1 INTRODUCTION 5

11 DESCRIPTION AND OBJECTIVES OF THE WORK PACKAGE 5 12 OBJECTIVES AND STRUCTURE OF THE DELIVERABLE 5

2 TYPES OF CONSTRUCTION 6 21 RESIDENTIAL BUILDINGS 6 22 SERVICE COMMERCIAL AND INDUSTRIAL BUILDINGS 7

3 DESCRIPTION OF THE CONSTRUCTION SYSTEMS 10 31 PERFORATED CLAY UNITS 10

311 Perforated clay units for in-plane masonry walls 10 312 Perforated clay units for out-of-plane masonry walls 11

32 HOLLOW CLAY UNITS 12 33 CONCRETE MASONRY UNITS 14

4 GENERAL DESIGN ASPECTS 16 41 LOADING CONDITIONS 16

411 Vertical loading 16 412 Wind loading 18 413 Earthquake loading 19 414 Ultimate limit states load combinations and partial safety factors 22 415 Loading conditions in different National Codes 25

42 STRUCTURAL BEHAVIOUR 27 421 Vertical loading 27 422 Wind loading 27 423 Earthquake loading 28

43 MECHANISM OF LOAD TRANSMISSION 31 431 Vertical loading 31 432 Horizontal loading 31 433 Effect of openings 32

5 DESIGN OF WALLS FOR VERTICAL LOADING 34 51 INTRODUCTION 34 52 PERFORATED CLAY UNITS 35

521 Geometry and boundary conditions 35 522 Material properties 39 523 Design for vertical loading 41 524 Design charts 42


53 HOLLOW CLAY UNITS 44 531 Geometry and boundary conditions 44 532 Material properties 45 534 Design for vertical loading 52 534 Design charts 53

54 CONCRETE MASONRY UNITS 54 541 Geometry and boundary conditions 54 542 Material properties 55 543 Design for vertical loading 55 544 Design charts 56

6 DESIGN OF WALLS FOR IN-PLANE LOADING 57 61 INTRODUCTION 57 62 PERFORATED CLAY UNITS 59

621 Geometry and boundary conditions 59 622 Material properties 59 623 In-plane wall design 60 624 Design charts 63

63 HOLLOW CLAY UNITS 68 631 Geometry and boundary conditions 68 632 Material properties 69 633 In-plane wall design 69 634 Design charts 71

64 CONCRETE MASONRY UNITS 78 641 Geometry and boundary conditions 78 642 Material properties 80 643 In-plane wall design 81 644 Design charts 83

7 DESIGN OF WALLS FOR OUT-OF-PLANE LOADING 87 71 INTRODUCTION 87 72 PERFORATED CLAY UNITS 87

721 Geometry and boundary conditions 87 722 Material properties 88 723 Out of plane wall design 88 724 Design charts 91

73 HOLLOW CLAY UNITS 93 731 Geometry and boundary conditions 93 732 Material properties 93 733 Out of plane wall design 94 734 Design charts 95


74 CONCRETE MASONRY UNITS 97 741 Geometry and boundary conditions 97 742 Material properties 97 743 Out-of-plane wall design 98 744 Design charts 98

8 OTHER DESIGN ASPECTS 101 81 DURABILITY 101 82 SERVICEABILITY LIMIT STATE 101

REFERENCES 103 ANNEX EXPLANATORY NOTES FOR THE USE OF THE SOFTWARE 105


1 INTRODUCTION

11 DESCRIPTION AND OBJECTIVES OF THE WORK PACKAGE

The major aim of DISWall project is the proposal of innovative systems for reinforced masonry walls The

validation of the feasibility of the systems as a whole to be used as an industrialized solution involves the

study of the technical economical and mechanical performance The WP3 WP4 WP5 are devoted to this

studies by means of design and production of materials development and construction of reinforced

masonry systems and by means of experimental and numerical simulations The workpackage 6 is aimed at

producing guidelines for end users and practitioners regarding the design of masonry walls with vertical and

horizontal reinforcement including design charts and a software code for the design of masonry walls made

with the proposed construction systems These products of the WP6 are of crucial importance to ensure the

commercial expansion and the exploitation of the intended technology as they provide the potential users

(designer architects and engineers and construction companies) with understandable easy to use and

sound design tools These rules and tools should provide the average user with easy criteria to safely design

masonry walls for most of the expected situations Moreover the interaction and the incorporation of these

recommendations into norms and codes (eg EC6 and EC8) can vanish any mistrust and strongly foster the

use of the intended structural solutions For special cases the designer will be addressed to scientific and

technical reports and the use of more complex software The workpackage 6 is mainly based on the

experience of WP5 through which the understanding of the behaviour of reinforced masonry walls under

service and ultimate conditions subjected to diverse possible actions has been gained

12 OBJECTIVES AND STRUCTURE OF THE DELIVERABLE

These guidelines give general recommendations for the structural design of reinforced masonry walls

They cover the main aspects related to how to calculate and design masonry walls built with perforated clay

units hollow clay units and concrete units and also include design charts They are not intended to cover any

other type of reinforced masonry besides those above mentioned and any other aspect of design such as

acoustic thermal etc The aspect related to the construction are covered by D75

The recommendations in these guidelines are based on literature research and code recommendations and

on the experience gained through the testing and modelling of masonry wall specimens in the framework of

the DISWall project They are intended in particular for those end-users (architects engineers construction

companies etc) that are involved with the conception and the design of the buildings

The guidelines are structured into seven main sections After the introduction there is a short reference to

the type of buildings that can be built with the proposed construction systems and a description of the

systems Following some general aspects of the structural design are reported and the aspects of design

for in-plane and out-of-plane loadings are described Other design aspects related to the structural

performance of the buildings are briefly described Finally some reference publications and relevant

standards are listed


2 TYPES OF CONSTRUCTION

Some typical example of buildings that can be built with the proposed reinforced masonry systems is given in

the deliverable D75 section 8 In the following the different building typologies are divided according to the

typical structural behaviour that can be recognized for each of them

21 RESIDENTIAL BUILDINGS

The common form of residential construction in Europe varies from the single occupancy house (Figure 1)

one or two-storey high to the multiple-occupancy residential buildings of load bearing masonry which are

commonly constituted by two or three-storey when they are built of unreinforced masonry but can reach

relevant height (five-storey or more) when they are built with reinforced masonry (Figure 2) Intermediate

types of buildings include two-storey semi-detached two-family houses (Figure 3) or attached row houses

(Figure 4) In these buildings the masonry walls carry the gravity loads and they usually support concrete

floor slabs and roofs which are characterized by adequate in-plane stiffness The inter-storey height is

generally low around 270 m

Figure 1 One-family house in San Gregorio

nelle Alpi (BL Italy) Figure 2 Residential complex in Colle Aperto

(MN Italy)

Figure 3 Two-family house in Peron di Sedico

(BL Italy) Figure 4 Eight row houses in Alberi di Vigatto

(PR Italy)

In these structures the masonry walls must provide the resistance to horizontal in-plane (shear) forces with

the floor and roof acting as diaphragms to distribute forces to the walls Very often the lateral (out-of-plane)


forces from wind are taken into account in the design by calculating the correspondent eccentricity in the

vertical forces and by reducing accordingly the compression strength of masonry in the vertical load

verifications or can be carryed out directly out-of-plane bending moment verification in the case of

reinforced masonry In case of stiff floors and roofs the out-of-plane verifications for the load bearing walls is

generally carried out separately in the hypothesis of double hinges at the wall bottom and top by comparing

the resisting out-of-plane bending moment with the design bending moment However the in-plane shear

forces are generally the governing actions where earthquake forces are high

In certain cases in particular for low-rise residential buildings such as single occupancy houses or two-family

houses the roof structures can be made of wooden beams and can be deformable even in new buildings In

these cases or in the upper storeys of multi-storey multiple-occupancy residential buildings wall designs

can be governed by resistance to out-of-plane forces

22 SERVICE COMMERCIAL AND INDUSTRIAL BUILDINGS

In service commercial and industrial buildings where masonry walls also reinforced are used as infill walls

with non-structural function their structural design is usually governed only by the resistance to wind and

earthquake forces as the gravity loads are assumed to be carried by the resisting frames In these buildings

the walls must have sufficient in-plane flexural resistance to span between frame members and other

supports Deflection compatibility between frames and walls has to be taken into account in particular if

these buildings are multi-storey buildings In this case the infill walls have to be verified against out-of-plane

earthquake and wind loading to avoid dangerous felt of material that would not compromise the stability of

the building but would prejudice the safety of people

A particular type of building is constituted by the low-rise commercial and industrial buildings generally one-

storey high made with load bearing reinforced masonry instead of infill walls In this case compared to

residential buildings with the same number of storeys the inter-storey height will be generally quite high

(between 5divide8 m) as the inner space has to be used for production or for activities such as sport activities

etc This solution can be chosen for example as it allows obtaining good indoor environmental conditions

suitable for food processing (Figure 5) or for recreational activities (Figure 6)

In this case it is possible to find both deformable (Figure 7) and stiff (Figure 8) roof structures according to

the construction system chosen by the designer The presence of one or the other will influence the

behaviour of the walls If the roof is stiff the horizontal action is mainly distributed to the in-plane loaded

walls The out-of-plane walls in case of seismic action are mainly loaded by the action coming from their

own mass where the roof can be considered a very stiff elastic restraint and act only for its dead-load If the

building is made with deformable roof this is not able to distribute the horizontal load to the in-plane walls In

this case the out-of-plane forces will be dominant In case of seismic action the walls can be tentatively

considered as cantilevers with a vertical load applied at the top and a horizontal load due to the masses of

both the roof and the wall itself The two resulting static schemes of the reinforced masonry walls are

represented in Figure 9


Figure 5 Parmigiano Reggiano factory in Ramiseto (RE Italy) Figure 6 Sport centre in Reggio Emilia (Italy)

Gluelam beams and metallic cover

Precast RC double T-beams

Precast RC shed

Figure 7 Sketch of the three deformable roof typologies

RC slabs with lightening clay units

Composite steel-concrete slabs

Steel beams and collaborating RC slab

Figure 8 Sketch of the three rigid roof typologies


Figure 9 Static schemes for out-of-plane walls with deformable roof (left) with rigid roof (right)


3 DESCRIPTION OF THE CONSTRUCTION SYSTEMS

31 PERFORATED CLAY UNITS

Italy as many other countries facing the Mediterranean basin (Portugal Slovenia Greece etc) is almost

entirely affected by a low to high seismic hazard Load bearing masonry buildings where walls are made of

perforated clay units are largely used for the construction of residential buildings as well as larger buildings

with industrial or services destination Within this project one of the studied construction system is aimed at

improving the behaviour of walls under in-plane actions for medium to low size residential buildings

characterized by low rise walls (about 27m) see sect 311 The second construction system is aimed at

improving the out-of-plane resistance of reinforced masonry walls in the case of slender tall walls (6divide8 m

high) to be used for the construction of large buildings such as gymnasiums industrial buildings etc (see sect

312)

311 Perforated clay units for in-plane masonry walls

This reinforced masonry construction system with concentrated vertical reinforcement and similar to

confined masonry is made by using a special clay unit with horizontal holes and recesses for the

accommodation of the horizontal reinforcement and an ordinary clay unit with vertical holes for the confining

columns that contain the vertical reinforcement (Figure 10 Figure 11)

Figure 10 Construction system with horizontally

perforated clay units Front view and cross sections

Figure 11 Construction system with horizontally perforated clay units Axonometric view of the corner

detail


The wall width in the figures is 300 mm but the width can be increased in a modular way Two types of

horizontal reinforcement can be used ordinary ribbed steel rebars or prefabricated steel trusses of the

Murfor type The mortar to be used with this reinforced masonry system is a premixed M10 cement mortar

with 0divide4 mm aggregate size and additives to improve plasticity and adhesion properties The mortar is

developed to be suitable for both the filling of the vertical cavities and the bedding of the horizontal joints

Figure 10 and Figure 11 show the developed masonry system

The system which makes use of horizontally perforated clay units that is a very traditional construction

technique for all the countries facing the Mediterranean basin has been developed mainly to be used in

small residential buildings that are generally built with stiff floors and roofs and in which the walls have to

withstand in-plane actions This masonry system has been developed in order to optimize the bond of the

horizontal reinforcement to improve durability thanks to the adequate covering provided all around of the

reinforcement and to make easier and more precise the placement of the horizontal reinforcement It is also

possible that the units with horizontally oriented webs can obtain a better shear stress transfer to the

vertical confining columns

312 Perforated clay units for out-of-plane masonry walls

This construction system is made by using vertically perforated clay units and is developed and aimed at

building mainly tall load bearing reinforced masonry walls for factories sport centres etc These types of

structures have to resist out-of-plane actions in particular when they are in the presence of deformable

roofs This system is based on the use of traditional lsquoHrsquo shaped units which are threaded over the top of the

bar and requires one or several bar overlapping along the wall height or of lsquoCrsquo shaped units which can be

easily put in place after the vertical reinforcement has been already placed Figure 12 shows the developed

masonry system

Figure 12 Construction system with vertically perforated clay units Front view and cross sections


The developed lsquoCrsquo shaped unit has also the main objective to allow the uncoupling of the vertical rebars far

from the axis of the wall The un-coupling of the vertical reinforcement guarantees a better out-of-plane

behaviour assuring at the same time an appropriate confining effect on the small reinforced column The

developed premixed M10 cement mortar with 0divide4 mm aggregate size and additives to improve plasticity and

adhesion properties is suitable for both the filling of the vertical cavities and the bedding of the horizontal

joints For the reinforcement traditional ribbed steel rebars can be used and with the lsquoCrsquo shaped units there

is no need of having overlapping even in tall walls Two and three-dimensional prefabricated steel trusses

can be also used for the horizontal and vertical reinforcement respectively They can have some

advantages compared to the rebars for example the easier and better placing and the direct collaboration of

the different longitudinal wires of the three-dimensional truss that brings to a better mechanical behaviour

32 HOLLOW CLAY UNITS

The hollow clay unit system is based on unreinforced masonry systems used in Germany since several

years mostly for load bearing walls with high demands on sound insulation Within these systems the

concrete infill is not activated for the load bearing function

Nevertheless the increased seismic loadings acc to Eurocode 8 and the corresponding national standard

DIN 4149 (2005) made the use of masonry structural elements with higher (shear-) load bearing capacities

necessary Therefore the development focused on the application of reinforcement to increase the in-plane-

shear and also the in-plane bending resistance Out-of-plane loadings are for the mentioned walls in

common types of construction not relevant as the these types of reinforced masonry are used for internal

walls and the exterior walls are usually build using vertically perforated clay units with a high thermal

insulation

For the load bearing capacity vertical and also horizontal reinforcement is necessary (coupling of the vertical

columns and load distribution) Therefore the bricks were modified amongst others to enable the application

of horizontal reinforcement

The system is built on site using thin layer mortar At the end of each row a modified clay unit is used to

avoid leakage The reinforcement is placed as a prefabricated element into the lower row The overlapping of

the horizontal and also the vertical reinforcement is ensured


Figure 13 Construction system with hollow clay units

The amount of reinforcement was fixed for horizontal and vertical direction to 4 d 6mm with a spacing of

25cm ie 425 mmsup2m

Figure 14 Reinforcement for the hollow clay unit system plan view

Figure 15 Reinforcement for the hollow clay unit system vertical section

The fixation and anchorage of the vertical reinforcement into the foundation resp RC storey slabs (base of

the wall) is done by single reinforcement bars with a spacing of 25cm The bars are either integrated into the

RC structural member before or glued in after it At the top of the wall also single reinforcement bars are

fixed into the clay elements before placing the concrete infill into the wall


33 CONCRETE MASONRY UNITS

Portugal is a country with very different seismic risk zones with low to high seismicity A construction system

is proposed for reinforced masonry walls to be used in general masonry buildings located in zones with

moderate to high seismic hazards and to carry out mainly in-plane loadings The construction system is

based on concrete masonry units whose geometry and mechanical properties have to be specially designed

to be used for structural purposes Two and three hollow cell concrete masonry units were developed in

order to vertical reinforcements can be properly accommodated For this construction system different

possibilities of placing the vertical reinforcements and distinct masonry bonds can be used see Figure 16

and Figure 17 The concrete block with three hollow cells is especially formulated to accommodate uniformly

spaced vertical reinforcement If the traditional masonry bond is used the vertical reinforcements (Murfor

RND Z) can be introduced both in the internal hollow cell and in the hollow cell formed by the frogged ends

In this case both continuous and overlapped vertical reinforcements are possible In both cases and due to

the type of masonry units the horizontal reinforcements are to be placed in the bed joints An important

aspect of this construction system is the filling of the vertical reinforced joints with a modified general

purpose mortar instead the traditional grout so that suitable bond strength between reinforcements and the

masonry can be reached and thus an effective stress transfer mechanism between both materials can be

obtained

(a)

(b)

Figure 16 Construction system based hollow concrete masonry units CMU2c with (a) continuous vertical

joints (b) vertical reinforcements placed in the hollow cells


Figure 17 Detail of the intersection of reinforced masonry walls


4 GENERAL DESIGN ASPECTS

41 LOADING CONDITIONS

The size of the structural members are primarily governed by the requirement that these elements must

adequately carry all the gravity loads imposed upon them that are vertical loads related to the weight of the

building components or permanent construction and machinery inside the building and the vertical loads

related to the building occupancy due to the use of the building but not related to wind earthquake or dead

loads [Schneider and Dickey 1980] Wind and earthquake produce horizontal lateral loads on a structure

which generate in-plane shear loads and out-of-plane face loads on individual members While both loading

types generate horizontal forces they are different in nature Wind loads are applied directly to the surface of

building elements whereas earthquake loads arise due to the inertia inherent in the building when the

ground moves Consequently the relative forces induced in various building elements are different under the

two types of loading [Lawrence and Page 1999]

In the following some general rules for the determination of the load intensity for the different loading

conditions and the load combinations for the structural design taken from the Eurocodes are given These

rules apply to all the countries of the European Community even if in each country some specific differences

or different values of the loading parameters and the related partial safety factors can be used Finally some

information of the structural behaviour and the mechanism of load transmission in masonry buildings are

given

411 Vertical loading

In this very general category the main distinction is between dead and live load The first can be described

as those loads that remain essentially constant during the life of a structure such as the weight of the

building components or any permanent or stationary construction such as partition or equipment Therefore

the dead load is the vertical load due to the weight of all permanent structural and non-structural components

of a building such as walls floors roofs and fixed equipment [Schneider and Dickey 1980] Generally

reasonably accurate estimate for preliminary design purpose can be made on the basis of the experience

and of the knowledge of the approximate weights of building materials Table 1and Table 2 give the mean

values of density of construction materials such as concrete mortar and masonry other materials such as

wood metals plastics glass and also possible stored materials can be found from a number of sources

and in particular in EN 1991-1-1

The live loads are also referred to as occupancy loads and are those loads which are directly caused by

people furniture machines or other movable objects They may be considered as short-duration loads

since they act intermittently during the life of a structure The codes specify minimum floor live-load

requirements for various types of occupancies or uses [Schneider and Dickey 1980] The imposed loads

can be modelled by uniformly distributed loads line loads or concentrated loads or combinations of these

loads Table 3 gives the values fixed by the EN 1991-1-1 where the type of occupancy can be inferred by


the following Table 8 Snow also represents a type of live load to be distributed on roofs Snow loads can be

evaluated according to EN 1991-1-3 taking into account the characteristic value of snow load on the ground

sk given for each site according to the climatic region and the altitude the shape of the roof and in certain

cases of the building by means of the shape coefficient microi the topography of the building location by means

of the exposure coefficient Ce and the reduction of snow loads on roofs with high thermal transmittance (gt 1

Wm2K) because of melting caused by heat loss by means of the thermal coefficient Ct The resulting snow

load for the persistenttransient design situation is thus given by

s = microi Ce Ct sk (41)

Table 1 Density of constructions materials concrete and mortar [after EN 1991-1-1]

Table 2 Density of constructions materials masonry [after EN 1991-1-1]


Table 3 Imposed loads on floors balconies and stairs in buildings [after EN 1991-1-1]

412 Wind loading

According to the EN 1991-1-4 wind actions fluctuate with time and act directly as pressures on the external

surfaces of enclosed structures and also act indirectly on the internal surfaces of enclosed structures or

directly on the internal surface of open structures Pressures act on areas of the surface resulting in forces

normal to the surface of the structure or of individual cladding components Generally the wind action is

represented by a simplified set of pressures or forces whose effects are equivalent to the extreme effects of

the turbulent wind

Wind loads can be evaluated according to EN 1991-1-4 taking into account the mean wind velocity vm

determined from the basic wind velocity vb at 10 m above ground level in open country terrain which

depends on the wind climate given for each geographical area and the height variation of the wind

determined from the terrain roughness (roughness factor cr(z)) and orography (orography factor co(z))

vm = vb cr(z) co(z) (42)

To codify wind-load values that may be readily used in design the kinetic energy of wind motion must be first

converted into a dynamic pressure Once defined the air density ρ (with recommended value of 125 kgm3)

and the basic velocity pressure qp

(43)

the peak velocity pressure qp(z) at height z is equal to

(44)


where ce(z) is the exposure factor and is equal to the ratio between the peak velocity pressure at the

corresponding height qp(z) and the basic velocity pressure qp at this point the wind pressure acting on the

external surfaces we and on the internal surfaces wi of buildings can be respectively found as

we = qp (ze) cpe (45a)

wi = qp (zi) cpi (45b)

where ze and zi are the reference heights for the external and the internal pressure and depend on the aspect ratio of

the loaded portion of the building hb and cpe and cpi are the pressure coefficients for the external and the internal

pressure which depend on the size and shape of the loaded area In the definition of the wind load also the size

factor cs which takes into account the reduction effect on the wind action due to the non-simultaneity of occurrence of

the peak wind pressures on the surface and the dynamic factor cd which takes into account the increasing effect from

vibrations due to turbulence in resonance with the structure are used

413 Earthquake loading

Earthquake loading is the force generated by horizontal and vertical ground movements due to earthquake

These movements induce inertial forces in the structure related to the distributions of mass and rigidity and

the overall forces produce bending shear and axial effects in the structural members For simplicity

earthquake loading can be converted to equivalent static forces with appropriate allowance for the dynamic

characteristics of the structure foundation conditions etc [Lawrence and Page 1999]

This operation is carried out by representing the impact of ground motion on vibrating structures by an elastic

response spectrum that is a plot of the peak response (displacement velocity or acceleration) of a series of

SDOF systems of varying natural frequency that are forced into motion by the same base vibration or shock

The resulting plot can then be used to pick off the response of any linear system given its period (the

inverse of the frequency) When the maximum acceleration is obtained from the spectrum the maximum

lateral forces to carry out elastic analysis and the following verifications are obtained The elastic response

spectra given by the codes are obtained from different accelerograms and are differentiated on the bases of

the soil characteristics besides the values of the structural damping To take into account in a simplified way

of the non-linearity of the structure the ordinates of the spectra are reduced by means of the behaviour

factors lsquoqrsquo and the design response spectra are obtained

The process for calculating the seismic action according to the EN 1998-1-1 is the following First the

national territories shall be subdivided into seismic zones depending on the local hazard that is described in

terms of a single parameter ie the value of the reference peak ground acceleration on type A ground agR

The reference peak ground acceleration corresponds to the reference return period TNCR of the seismic

action for the no-collapse requirement (or equivalently the reference probability of exceedance in 50 years

PNCR) chosen by the National Authorities An importance factor γI equal to 10 is assigned to this reference

return period For return periods other than the reference related to the importance classes of the building

the design ground acceleration on type A ground ag is equal to agR times the importance factor γI (ag = γIagR)


where γI is equal to 12 for relevant buildings and 14 for strategic buildings Ground types A B C D and E

described by the stratigraphic profiles and parameters given in the EN 1998-1-1 shall be used to account for

the influence of local ground conditions on the seismic action

For the horizontal components of the seismic action the elastic response spectrum Se(T) is defined by the

following expressions

(46a)

(46b)

(46c)

(46d)

where Se(T) is the elastic response spectrum T is the vibration period of a linear SDOF system ag is the

design ground acceleration on type A ground (ag = γIagR) TB is the lower limit of the period of the constant

spectral acceleration branch TC is the upper limit of the period of the constant spectral acceleration branch

TD is the value defining the beginning of the constant displacement response range of the spectrum S is the

soil factor η is the damping correction factor with a reference value of η = 1 for 5 viscous damping and

equal to for different values of viscous damping ξ

In the EN 1998-1-1 there are two types of recommended spectra Type 1 and Type 2 where the second is

adopted if the earthquakes that contribute most to the seismic hazard defined for the site for the purpose of

probabilistic hazard assessment have a surface-wave magnitude Ms le 55 The following Table 4 and Figure

18 give values of the soil parameter and the vibration periods describing the recommended Type 1 elastic

response spectra and the corresponding spectra (for 5 viscous damping)

Table 4 Values of the parameters describing the recommended Type 1 elastic response spectra [after EN

1998-1-1]


Figure 18 Recommended Type 1 elastic response spectra for ground types A to E (5 damping) [after EN 1998-1-1]

When needed the elastic displacement response spectrum SDe(T) shall be obtained by direct

transformation of the elastic acceleration response spectrum Se(T) using the following expression normally

for vibration periods not exceeding 40 s

(47)

The code also gives the expressions for the evaluation of the elastic response spectrum Sve(T) for the

vertical component of the seismic action

(48a)

(48b)

(48c)

(48d)

where Table 5 gives the recommended values of parameters describing the vertical elastic response

spectra

Table 5 Values of the parameters describing the vertical elastic response spectra [after EN 1998-1-1]


As already explained the capacity of the structural systems to resist seismic actions in the non-linear range

generally permits their design for resistance to seismic forces smaller than those corresponding to a linear

elastic response Therefore design spectra obtained by reducing the elastic response spectra by the lsquoqrsquo

behaviour factor can be used in elastic analysis For the horizontal components of the seismic action the

design spectrum Sd(T) shall be defined by the following expressions

(49a)

(49b)

(49c)

(49d)

where ag S TC and TD are as defined in Table 4 for Type 1 spectra Sd(T) is the design spectrum β is the

lower bound factor for the horizontal design spectrum and its recommended value is 02 For the vertical

component of the seismic action the design spectrum is given by expressions (49a) to (49d) with the

design ground acceleration in the vertical direction avg replacing ag S taken as being equal to 10 and the

other parameters as defined in Table 5 Furthermore for the vertical component of the seismic action a

behaviour factor q up to to 15 should generally be adopted for all materials and structural systems whereas

in the specific case of masonry structures the recommended values of behaviour factor are given in Table 6

Table 6 Types of construction and upper limit of the behaviour factor [after EN 1998-1-1]

414 Ultimate limit states load combinations and partial safety factors

According to EN 1990 the ultimate limit states to be verified are the following

a) EQU Loss of static equilibrium of the structure or any part of it considered as a rigid body


b) STR Internal failure or excessive deformation of the structure or structural members where the strength

of construction materials of the structure governs

c) GEO Failure or excessive deformation of the ground where the strengths of soil or rock are significant in

providing resistance

d) FAT Fatigue failure of the structure or structural members

At the ultimate limit states for each critical load case the design values of the effects of actions (Ed) shall be

determined by combining the values of actions that are considered to occur simultaneously Each

combination of actions should include a leading variable action (such as wind for example) or an accidental

action The fundamental combination of actions for persistent or transient design situations and the

combination of actions for accidental design situations are respectively given by

(410a)

(410b)

where γG is the partial safety factor for permanent actions Gkj γQ is the partial factor for the variable actions

Qki and γP is the partial factor for the precompression P and are given in Table 7 Ad is the accidental action

and ψ0i is the combination coefficient given in Table 8

Table 7 Recommended values of γ factors for buildings [after EN 1990]

EQU limit state (set A) STRGEO limit state (set B) STRGEO limit state (set C)

Factor γG γQ γG γQ γG γQ

favourable 090 000 100 000 100 000

unfavourable 110 150 135 150 100 130 where the verification of static equilibrium also involves the resistance of structural members for γG values of 135 and 115 can be adopted

In the seismic design the inertial effects of the design seismic action shall be evaluated by taking into

account the presence of the masses associated with the gravity loads appearing in the following combination

of actions

(411)

where ψEi is the combination coefficient for variable action i and takes into account the likelihood of the

variable loads Qki not being present over the entire structure during the earthquake According to EN 1998-

1-1 the combination coefficients ψEi introduced in eq (411) for the calculation of the effects of the seismic

actions shall be computed from the following expression

ψEi = φ ψ2i (412)


where the combination coefficients ψ2i for the quasi-permanent value of variable action qi for the design of

buildings is given in EN 1990 and is reported in Table 8 together with the categories of building use and the

the recommended values for φ are listed in Table 9

Table 8 Recommended values of ψ factors for buildings [after EN 1990]

Table 9 Values of φ for calculating ψEi [after EN 1998-1-1]

The combination of actions for seismic design situations for calculating the design value Ed of the effects of

actions in the seismic design situation according to EN 1990 is given by

(413)

where AEd is the design value of the seismic action


415 Loading conditions in different National Codes

In Italy a process of adaptation of the structural codes to the Eurocodes has recently started in the field of

seismic design with the OPCM 3274 (2003) updated till the last version issued in 2005 [OPCM 3431 2005]

The novelties introduced in the seismic design of buildings has been integrated into a general structural code

in 2005 reedited at the very beginning of 2008 [DM 140108 2008] The rationales for the definition of

vertical wind and earthquake loading including the load combinations are the same that can be found in the

Eurocodes with differences found only in the definition of some parameters The seismic design is based on

the assumption of 4 main seismic area (see Figure 20) characterized by values of peak ground acceleration

(with a probability of exceedance equal to 10 in 50 years) equal to 035g (seismic zone 1) 025g (seismic

zone 2) 015g (seismic zone 3) and 005g (seismic zone 4) Actually the basic values for the construction of

the elastic response spectra are given on the basis also of detailed microzonation maps The calculation of

the seismic action for buildings with different importance factors is made explicit as the code require

evaluating the expected building life-time and class of use on the bases of which the return period for the

seismic action is calculated In the microzonation maps anchorage values for the definition of the spectra

are given also with reference to the different return periods and probability of exceedance

In Germany the adaptation of the national structural codes to the Eurocodes started in the field of wind

loadings (DIN 1055-4 Action on structures - Part 4 Wind loads (2005-03)) and seismic loadings (DIN 4149

Buildings in German earthquake areas - Design loads analysis and structural design of buildings (2005-04))

For the design of masonry the partial safety factor concept was introduced into practice in January 2005 with

the new standard DIN 1053-100 Design on the basis of semi-probabilistic safety concept (08-2004)

The wind loadings increased compared to the pervious standard from 1986 significantly Especially in

regions next to the North Sea up to 40 higher wind loadings have to be considered

The seismic design is based on the assumption of 3 main seismic area characterized by values of design

(peak) ground acceleration (with a probability of exceedance equal to 10 in 50 years) equal to 004g

(seismic zone 1) up to 008g (seismic zone 3)

In Portugal the definition of the design load for the structural design of buildings has been made accordingly

to the national code for the safety and actions for buildings and bridges (RSA) In the recent few years a

process to the adaptation to the European codes has also been started The calculation of the design loads

are to be designed according to EN 1991 and EN 1998 Concerning the seismic action a national annex is

under preparation where new seismic zones are defined according to the type of seismic action For close

seismic action three seismic areas are defines with peak ground acceleration (with a probability of

exceedance equal to 10 in 475 years) of 017g (seismic zone 1) 011g (seismic zone 2) and 008g

(seismic zone 3) For a distant seismic load five zones are defined corresponding to a peak ground

acceleration of 025g (seismic zone 1) 020g (seismic zone 2) and 015g (seismic zone 4) 010g (seismic

zone 2) and 005g (seismic zone 5) see Figure 20


Figure 19 Seismic zones and wind zones in Germany [after DIN 1055-4 (2005-03) and DIN 4149 (2005-04)]

Figure 20 Seismic zones in Italy (left after OPCM 3274) and in Portugal (rigth)


42 STRUCTURAL BEHAVIOUR


This section covers in general the most typical behaviour of loadbearing masonry structures In these

buildings the masonry walls and piers usually support concrete floor slabs and the roof structure without

any separate building frame The masonry walls thus have to carry significant vertical loading (dead and live

load) in addition to their own weight and their sizes are usually determined by their capacity to resist vertical

load In other words they rely on their compressive load resistance to support other parts of the structure

The vertical loading can consist in uniformly distributed loads over the top edge of the masonry walls but

there can also be concentrated loads and effects arising from composite action between walls and lintels and

beams

Buckling and crushing effects which depend on the wall slenderness and interaction with the elements the

wall supports determine the compressive capacity of each individual wall Strength properties of masonry

are difficult to predict from known properties of the mortar and masonry units because of the relatively

complex interaction of the two component materials However such interaction is that on which the

determination of the compressive strength of masonry is based for most of the codes Not only the material

(unit and mortar) properties but also the shape of the units particularly the presence the size and the

direction of the holes influences the compressive strength of the masonry [Lawrence and Page 2004]

422 Wind loading

Traditionally masonry structures were massively proportioned to provide stability and prevent tensile

stresses In the period following the Second World War traditional loadbearing constructions were replaced

by structures using the shear wall concept where stability against horizontal loads is achieved by aligning

walls parallel to the load direction (Figure 21)

Figure 21 Shear wall concept and box-type structural system [after Schneider and Dickey]


Lateral forces are therefore transmitted to the lower levels by in-plane shear When combined with the use of

concrete floor systems acting as diaphragms this produces robust box-like structures with the capacity to

resist horizontal load For these structures the walls subjected to face loading must be designed to have

sufficient flexural resistance and the shear walls must have sufficient in-plane resistance The infill masonry

walls in framed buildings are designed for out-of-plane action only [Lawrence and Page 1999]


In buildings subjected to earthquake loading the walls in the upper levels are more heavily loaded by seismic

forces because of dynamic effects and are therefore more susceptible to damage caused by face loading

The resulting damage is consistent with that due to wind or other out-of-plane loading Shear failures are

more likely to occur in the lower storeys where horizontal in-plane forces are greatest and are characterised

by stepped diagonal cracking Still at the lower storeys in-plane flexural failure can occur This failure is

characterized by the yielding of vertical reinforcement (in reinforced masonry) and crushing of the

compressed masonry toes These failure modes do not usually result in wall collapse but can cause

considerable damage [Lawrence and Page 1999] The flexuralshear failure mode is to a large extent

defined by the aspect ratio (geometry) of the wall the ratio of vertical to horizontal load applied and the

strength of the materials [Tomazevic 1999] Because of higher displacement and energy dissipation

capacity in-plane flexural failure mode are preferred and according to the capacity design should occur

first Shear damage can also occur in structures with masonry infills when large frame deflections cause

load to be transferred to the non-structural walls Both plan and elevation symmetry is desirable to avoid

torsional and softstorey effects Compact plan shapes behave better than extended wings If irregular

shapes cannot be avoided then more detailed earthquake analysis may be necessary According to the EN

1998-1-1 for a building to be categorised as being regular in plan the following conditions should be

satisfied

1- With respect to the lateral stiffness and mass distribution the building structure shall be approximately

symmetrical in plan with respect to two orthogonal axes

2- The plan configuration shall be compact ie each floor shall be delimited by a polygonal convex line If in

plan set-backs (re-entrant corners or edge recesses) exist regularity in plan may still be considered as being

satisfied provided that these setbacks do not affect the floor in-plan stiffness and that for each set-back the

area between the outline of the floor and a convex polygonal line enveloping the floor does not exceed 5

of the floor area

3- The in-plan stiffness of the floors shall be sufficiently large in comparison with the lateral stiffness of the

vertical structural elements so that the deformation of the floor shall have a small effect on the distribution of

the forces among the vertical structural elements In this respect the L C H I and X plan shapes should be

carefully examined notably as concerns the stiffness of the lateral branches which should be comparable to

that of the central part in order to satisfy the rigid diaphragm condition The application of this paragraph

should be considered for the global behaviour of the building


4- The slenderness λ = LmaxLmin of the building in plan shall be not higher than 4 where Lmax and Lmin are

respectively the larger and smaller in plan dimension of the building measured in orthogonal directions

5- At each level and for each direction of analysis x and y the structural eccentricity eo and the torsional

radius r shall be in accordance with the two conditions below which are expressed for the direction of

analysis y

eox le 030 rx (414a)

rx ge ls (414b)

where eox is the distance between the centre of stiffness and the centre of mass measured along the x

direction which is normal to the direction of analysis considered rx is the square root of the ratio of the

torsional stiffness to the lateral stiffness in the y direction (ldquotorsional radiusrdquo) and ls is the radius of gyration of

the floor mass in plan (square root of the ratio of (a) the polar moment of inertia of the floor mass in plan with

respect to the centre of mass of the floor to (b) the floor mass)

Still according to the EN 1998-1-1 for a building to be categorised as being regular in elevation the following

conditions should be satisfied

1- All lateral load resisting systems such as cores structural walls or frames shall run without interruption

from their foundations to the top of the building or if setbacks at different heights are present to the top of

the relevant zone of the building

2- Both the lateral stiffness and the mass of the individual storeys shall remain constant or reduce gradually

without abrupt changes from the base to the top of a particular building

3- In framed buildings the ratio of the actual storey resistance to the resistance required by the analysis

should not vary disproportionately between adjacent storeys

4- When setbacks are present the following additional conditions apply

a) for gradual setbacks preserving axial symmetry the setback at any floor shall be not greater than 20 of

the previous plan dimension in the direction of the setback (see Figure 22a and Figure 22b)

b) for a single setback within the lower 15 of the total height of the main structural system the setback

shall be not greater than 50 of the previous plan dimension (see Figure 22c) In this case the structure of

the base zone within the vertically projected perimeter of the upper storeys should be designed to resist at

least 75 of the horizontal shear forces that would develop in that zone in a similar building without the base

enlargement

c) if the setbacks do not preserve symmetry in each face the sum of the setbacks at all storeys shall be not

greater than 30 of the plan dimension at the ground floor above the foundation or above the top of a rigid

basement and the individual setbacks shall be not greater than 10 of the previous plan dimension (see

Figure 22d)


Figure 22 Criteria for regularity of buildings with setbacks


43 MECHANISM OF LOAD TRANSMISSION


Ideally the vertical loadings have to be transmitted directly to the foundation Generally it is recommended to

avoid any secondary support construction eg beams as their vertical stiffness leads to problems especially

under seismic loadings

432 Horizontal loading

The distribution of the horizontal loadings ndash eg from wind or seismic action ndash to the shear walls is deciding

for the behaviour of the structure On the one hand it is necessary to ensure a proper load distribution in

combination with possible redundancies (redistribution) by a stiff slab and on the other hand an in-plane

restraint leads to more favourable boundary conditions of the shear walls Therefore the structural system as

a cantilever beam is generally too unfavourable describing a shear wall in a common construction

The calculated horizontal loadings of each shear wall can be redistributed according to EN 1996-1-1 2005

553 (8) Here a reduction up to 15 is allowed if the load on a parallel shear wall is increased

correspondingly and assuming equilibrium

Figure 23 Spacial structural system under combined loadings


Figure 24 Horizontal system of the shear wall with different restraints into the RC storey slabs

433 Effect of openings

Openings influence the stiffness of in-plane loaded shear walls and the corresponding stress distribution

significantly The effects can be calculated using a finite-element-programme assuming al linear-elastic

behaviour of the material The shear modulus should be fixed to 40 of the E-modulus For the design

process wall can be separated into stripes

Figure 25 Effect of opening on the structural idealization for out-of-plane-loadings

For the out-of plane loaded walls the effect of openings can be handled by idealizing the walls as several

combinations of horizontal and vertical strips Additional constructive arrangements have to be kept eg

extra reinforcement in the corners (diagonal and orthogonal)


Figure 26 Effect of opening on the structural idealization for out-of-plane-loadings [MDG-4]


5 DESIGN OF WALLS FOR VERTICAL LOADING

51 INTRODUCTION

According to the EN 1996-1-1 and to most of the structural codes when analysing walls subjected to vertical

loading allowance in the design should be made not only for the vertical loads directly applied to the wall

but also for second order effects eccentricities calculated from a knowledge of the layout of the walls the

interaction of the floors and the stiffening walls and eccentricities resulting from construction deviations and

differences in the material properties of individual components The definition of the masonry wall capacity is

thus based not only on the compressive strength but also on the slenderness ratio of the walls and on their

typical boundary conditions These consist in walls restrained only at the top and bottom or can be improved

by restrains also on the vertical edges (one or both) Once the eccentricity is known it can be used to

evaluate reduction factors for the compressive strength of the masonry walls and carry out axial load

verifications or it can be used to carry out out-of-plane bending moment verifications of the wall sections



521 Geometry and boundary conditions

Prior to the definition of the design strategy based on the out-of-plane moment of resistance due to the

presence of the reinforcement or on the reduction of vertical load capacity as it is made for unreinforced

masonry in the case of walls with slenderness ratio λ gt 12 it is necessary to define the effective height hef

and the effective thickness tef of the walls where λ = hef tef based on the boundary conditions of the walls

The selected boundary conditions are some of the typical conditions listed in section sect 51 and given by the

EN 1996-1-1 (2005) walls restrained at the top and bottom by reinforced concrete floors or roofs spanning

from both sides at the same level or by a reinforced concrete floor spanning from one side only and having a

bearing of at least 23 of the thickness of the wall and with eccentricity smaller than 025 times the thickness

of the wall walls restrained at the top and bottom by timber floors or roofs spanning from both sides at the

same level or by a timber floor spanning from one side having a bearing of at least 23 the thickness of the

wall but not less than 85 mm (in our case more in general deformable roofs) walls restrained at the top and

bottom and stiffened on one vertical edge walls restrained at the top and bottom and stiffened on two

vertical edges

The effective thickness tef of single-leaf walls should be taken as the actual thickness of the wall t unless

the wall is stiffened by piers In that case the effective thickness is measured as

tef = ρt t (51)

where the stiffness coefficient ρt is found as explained in Table 10 and Figure 27

Table 10 Stiffness coefficient ρt for walls stiffened by piers see Figure 27 [after EN 1996-1-1]

Figure 27 Diagrammatic view of the definitions used in Table 10 [after EN 1996-1-1]


In the analyzed cases the effective thickness of the wall has been taken as the actual thickness The

effective height hef of single-leaf walls should be taken as the actual height of the wall h times a reduction

factor ρn that changes according to the above mentioned wall boundary conditions

hef = ρn h (52)

For walls restrained at the top and bottom by reinforced concrete floors or roofs spanning from both sides at

the same level or by a reinforced concrete floor spanning from one side only and having a bearing of at least

23 of the thickness of the wall and unless the eccentricity is greater than 025 times the thickness of the

wall ρ2 = 075 (otherwise and for wooden floors ρ2 = 10) For walls restrained at the top and bottom and

stiffened on one vertical edge (with one free vertical edge)

if hl le 35

(53a)

if hl gt 35

(53b)

For walls restrained at the top and bottom and stiffened on two vertical edges

if hl le 115

(54a)

if hl gt 115

(54b)

These cases that are typical for the constructions analyzed have been all taken into account Figure 28

gives the slenderness ratios for walls with different height to thickness ratio in case that the walls are not

restrained at the vertical edges In the case of eccentricity of the vertical load due to floors smaller than 025

times it can be seen that λ le 12 for the ALAN masonry system but with deformable roofs λ becomes major

than 12 for the CISEDIL system Figure 29 shows the reduction factors for the evaluation of the effective

height for walls restrained at the vertical edges varying the height to length ratio of the wall The

corresponding slenderness ratios are given in Figure 30 and Figure 31 It can be see that obviously if the

walls are restrained by stiff roofs and are stiffened at one or two vertical edges the slenderness ratio is even

more reduced (case of the ALAN system) In the case of deformable roofs if the walls are restrained on two

vertical edges or are restrained on only one vertical edge but with length of the wall le 35 m the

slenderness is reduced to λ le 12 also for the CISEDIL system This case thus cover most of the practical

application therefore for the design the out of plane bending moment of resistance should be evaluated


Slenderness ratio for walls not restrained at the vertical edges

0

2

4

6

8

10

12

14

16

18

50 54 58 62 66 70 74 78 82 86 90 94 98 102

106

110

114

118

122

126

130

134

138

142

146

150

154

158

162

166

170 ht

λ

λ2 (e le 025 t)λ2 (e gt 025 t)

wall h = 2700 mm t = 300 mmeccentricity of load lt 025 t

wall h = 6000 mm t = 380 mmdeformable roof

Figure 28 Slenderness ratios for walls not restrained at the vertical edges(varying the height to thickness

ratio)

Reduction factors for the evaluation of the eccentricity for walls restrained at the vertical edges

00

01

02

03

04

05

06

07

08

09

10

053

065

080

095

110

125

140

155

170

185

200

215

230

245

260

275

290

305

320

335

350

365

380

395

410

425

440

455

470

485

500 hl

ρ

ρ3 (e le 025 t)ρ3 (e gt 025 t)ρ4 (e le 025 t)ρ4 (e gt 025 t)

Figure 29 Reduction factors for the evaluation of the effective height for walls restrained at the vertical

edges (varying the wall height to length ratio)


Slenderness ratio for walls restrained at the vertical edges

0

1

2

3

4

5

6

7

8

9

10

50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600

l (cm)

λ

h=270 cm t=30 cmh=270 cm t=34 cmh=270 cm t=38 cmh=270 cm t=42 cmh=270 cm t=46 cm

Figure 30 Slenderness ratio for walls restrained at the vertical edges (walls with h=2700 mm varying

thickness and wall length)


0

2

4

6

8

10

12

14

16

18

20

50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600

l (cm)

λ




The design for vertical loading of masonry made with horizontally perforated clay units (ALAN system) has

been based on walls of length equal to a multiple of the unit length (250 mm thus starting from short piers

500 mm long) and thickness equal to that of the studied unit (300 mm) The design for vertical loading of

masonry made with vertically perforated clay units (CISEDIL system) has been based on walls of length

equal to a multiple of the reinforcement interaxis (780 mm + 385 mm of final unit length thus starting from

walls 1165 mm long) and thickness equal to that of the studied unit (380 mm)


522 Material properties

The materials properties that have to be used for the design under vertical loading of reinforced masonry

walls made with perforated clay units concern the materials (normalized compressive strength of the units fb

mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and ultimate strain

εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength fk) To derive

the design values the partial safety factors for the materials are required For the definition of the

compressive strength of masonry the EN 1996-1-1 formulation can be used

(55)

where K α and β are given in relation to the type and class of unit and of masonry Table 11 gives the main

parameters adopted for the creation of the design charts

Table 11 Material properties parameters and partial safety factors used for the design

ALAN Material property CISEDIL Horizontal Holes

(G4) Vertical Holes

(G2) fbm Nmm2 12 93 216 fb Nmm2 132 102 241 fm Nmm2 113 141 141 K - 045 035 045 α - 07 07 07 β - 03 03 03 fk Nmm2 57 393 922 γM - 20 20 20 fd Nmm2 28 196 461 α - 085 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10

In the case of the masonry made with horizontally and vertically perforated units (ALAN system) the

characteristics of both the types of unit have been taken into account to define the strength of the entire

masonry system Once the characteristic compressive strength of each portion of masonry (masonry made

with horizontally perforated units subscript h masonry made with vertically perforated units subscript v) has

been evaluated the overall characteristic compressive strength of masonry can be evaluated on the base of

a simple geometric homogenization

vh

kvvkhhk AA

fAfAf

++

= (56)


where A is the gross cross sectional area of the different portions of the wall Considering that in any

masonry panel the two vertically reinforced columns placed at the edges of the wall cover a length of about

315 mm each (length of one vertically perforated unit 250 mm plus one quarter of the overlapping unit) the

compressive strength of the masonry is thus factored to the length of the wall being analyzed as can be

seen in Figure 32 This has been proven to be realistic by means of experimental testing where values of

experimental compressive strength fexp were derived for the masonry columns made with vertically perforated

units the masonry panels made with horizontally perforated units and for the whole system Table 12

compare the experimental (fexp) and the theoretical (fth) values of the masonry system compressive strength

Table 12 Experimental and theoretical values of the masonry system compressive strength

Masonry columns

Masonry panels

Masonry system

l (mm) 630 920 1550

fexp (Nmm2) 559 271 390

fth (eq 56) (Nmm2) - - 388

Error () - - 0005

Factored compressive strength

10

15

20

25

30

35

40

45

50

55

60

500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500 3750 4000 4250

lw (mm)

f (Nmm2)

fexpfdα fd

Figure 32 Compressive strength (experimental design and reduced design values) factored to the length of

the wall


523 Design for vertical loading

The design for vertical loading of reinforced masonry provided that λ le 12 has been based on the

determination of the design out-of-plane bending moment resistance that divided for possible values of

vertical load eccentricity give the value of the design value of the vertical load resistance of the wall In

determining the design value of the moment of resistance of the walls a rectangular stress distribution as

been assumed for masonry and the ultimate strain of the reinforcement εu has been limited to 001 (see

Figure 33) In the case of the ALAN system the calculations were repeated for wall of different length (from

500 mm to 4250 mm) taking thus into account the factored design compressive strength (reduced to take

into account the stress block distribution) α fd given by Figure 32 Being the reinforcement concentrated

locally in the vertical columns the reinforced section has been considered as having a width of not more

than two times the width of the reinforced column multiplied by the number of columns in the wall No other

limitations have been taken into account in the calculation of the resisting moment as the limitation of the

section width and the reduction of the compressive strength for increasing wall length appeared to be

already on the safety side beside the limitation on the maximum compressive strength of the full wall section

subjected to a centred axial load considered the factored compressive strength

Figure 33 Stress and strain distribution in the masonry section [after EN 1996-1-1]

In the case of the CISEDIL system the calculations were still repeated for different lengths of the wall but in

this case the design compressive strength remains constant Being the reinforcement constituted by 4Φ12

mm rebar placed at 780 mm of interaxis and considering that after the vertical reinforcement position there

are other 385 mm constituted by the mortar cores and the units the typical length of CISEDIL walls can be

calculated by x times 780 mm plus 385 mm Therefore the calculations were repeated for length equal to

1165 mm 1945mm 2725 mm 3505 mm 4285 mm 5065 mm 5845 mm and 6625 mm considered typical

for real building site conditions In this case the reinforcement percentage is that resulting from the

constructive system for out-of-plane loads that is the percentage resulting from 4Φ12 mm 780 mm

Figure 34 gives the design values of the vertical load resistance of the walls (NRd) for the ALAN walls If one

knows the length of the wall and the eccentricity of the vertical load enters the diagram and find the design

vertical load resistance of the wall The top left figure gives these values for walls of different length provided

with the minimum amount of vertical reinforcement The other figures gives the values of NRd for fixed wall

length (1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm) and varying vertical


reinforcement (of steel type Feb 44k) The horizontal reinforcement is the minimum amount required (two

rebars oslash6 mm each 400 mm or 1 Murfor RNDZ-5-150 400 mm) Figure 35 gives the design values of the

vertical load resistance of the walls (NRd) for the CISEDIL walls The diagram works as the previous

524 Design charts

NRd for walls of different length min vert reinf and varying eccentricity

750 mm1000 mm

1250 mm1500 mm

1750 mm2000 mm

2250 mm2500 mm

2750 mm3000 mm3250 mm3500 mm

4000 mm4250 mm

50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm

3750 mm

500 mm

wall t = 300 mm steel 2oslash6 400 mm Feb 44k or 1 Murfor RNDZ-5-

150 400 mm

NRd for walls with fixed length varying vert reinf and eccentricity

50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)


wall l = 1000 mm t = 300 mm steel 2oslash6 400 mm Feb 44k or 1

Murfor RNDZ-5-150 400 mm


50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)





50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash14 mm

2oslash16 mm

2oslash18 mm2oslash20 mm

4oslash16 mm




50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash16 mm

2oslash18 mm

2oslash20 mm

4oslash16 mm




50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash18 mm

2oslash20 mm

4oslash16 mm





50200

350500650

800950

11001250

140015501700

185020002150

23002450

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash20 mm

4oslash16 mm




50200

350500650

800950

110012501400

155017001850

20002150

23002450

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash20 mm

4oslash16 mm



Figure 34 Design charts for ALAN reinforced masonry system Design values of the vertical load resistance

of the wall NRd From top left to bottom right NRd for walls of different length minimum vertical reinforcement

(FeB 44k) and varying eccentricity NRd for walls of length equal to 1000 mm 1500 mm 2000 mm 2500 mm

3000 mm 3500 mm 4000 mm different vertical reinforcement (FeB 44k) and varying eccentricity

NRd for walls of different length and varying eccentricity

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

1165 mm1945 mm2725 mm3505 mm4285 mm5065 mm5845 mm6625 mm

wall t = 380 mm steel 4oslash12 780 mm Feb 44k

Figure 35 Design chart for CISEDIL reinforced masonry system Design values of the vertical load

resistance of the wall NRd for walls of different length with 4Φ12 mm 780 mm (FeB 44k) and varying

eccentricity




The design for vertical loading of masonry made with hollow clay units (System UNIPOR) has been based on

walls of length equal to a multiple of the unit length of 50cm The thickness is fixed to 24cm and the height is

taken typical of housing construction with 25m (10 rows high)

The design under dominant vertical loadings has to consider the boundary conditions at the top and the base

of the wall (out-of-plane restraint with reduced effective height of the wall) Stiffening effects at the vertical

edges are in the following not considered (safe side) Also the effects of partially increased effective

thickness of the wall by considering stiffening piers (EN 1996-1-1 2005 5513) are omitted as the use of

the UNIPOR-system is designated for wall with rectangular plan view

Figure 36 Geometry of the hollow clay unit and the concrete infill column

Analogous to the approach at the perforated clay brick system the effective height hef of single-leaf walls

should be taken as the actual height of the wall h times a reduction factor ρn that changes according to the

wall boundary condition as given in eq 52 According to the restraint at the top and the bottom by RC floor

slabs and no eccentricity greater than 025 the parameter ρn is taken to ρ2 =075



The material properties of the infill material are characterized by the compression strength fck Generally the

minimum strength demand of the self compacting concrete is 25 Nmmsup2 For the design under dominant

compression also long term effects are taken into consideration


Material property UNIPOR

fck Nmm2 SCC 25 Nmmsup2 (min demand)

γM - 15 αcc - 085 φinfin - 20 fcd Nmm2 1416 Nmmsup2

For the design under vertical loadings only the concrete infill is considered for the load bearing design In the

analyzed cases the effective thickness of the wall has been taken to tcolumn = 24cm ndash 24cm = 16cm As the

hollow clay units divide the concrete infill into vertical columns the smeared strength is reduced

corresponding to the geometry of the length of the column (l=20cm) divided by the spacing of 25cm ie with

a reduction of 08

The effective compression strength fd_eff is calculated

column

column

M

ccckeffd s

lff sdotsdot

=γ

α (57)

with lcolumn=02m scolumn=025m

In the context of the workpackage 5 extensive experimental investigations were carried out with respect to

the description of the load bearing behaviour of the composite material clay unit and concrete Both material

laws of the single materials were determined and the load bearing behaviour of the compound was

examined under tensile and compressive loads With the aid of the finite element method the investigations

at the compound specimen could be described appropriate For the evaluation of the masonry compression

tests an analytic calculation approach is applied for the composite cross section on the assumption of plane

remaining surfaces and neglecting lateral extensions

The material properties of the clay unit material and the concrete are indicated in the diagrams from Figure

37 to Figure 40 in accordance with Deliverable 54


0

5

10

15

20

25

30

35

40

00 05 10 15 20 25 30 35 40

compressive stress in Nmmsup2

compressive strain in mmm

0

5

10

15

20

25

30

35

40

00 05 10 15 20 25 30 35 40


compressive strain in mmm Figure 37 Standard unit material compressive

stress-strain-curve Figure 38 DISWall unit material compressive

stress-strain-curve

0

5

10

15

20

25

30

35

40

00 20 40 60 80 100 120 140 160



0

5

10

15

20

25

30

35

40

00 20 40 60 80 100 120 140 160


compressive strain in mmm Figure 39 Standard concrete compressive

stress-strain-curve

Figure 40 Standard selfcompating concrete

compressive stress-strain-curve

The compressive ndashstressndashstrain curves of the compound are simplified computed with the following

equation

( ) ( ) ( )c u sc u s

A A AE

A A Aσ ε σ ε σ ε ε= + + sdot sdot (58)

σ (ε) compressive stress-strain curve of the compound

σu (ε) compressive stress-strain curve of unit material (see figure 1)

σc (ε) compressive stress-strain curve of concrete (see figure 2)

A total cross section

Ac cross section of concrete

Au cross section of unit material

ES modulus of elasticity of steel (210000Nmmsup2 fy = 500 Nmmsup2)

fy yield strength


The estimated cross sections of the single materials are indicated in Table 14

Table 14 Material cross section in half unit

area in mmsup2 chamber (half unit) material

Standard unit DISWall unit

Concrete 36500 38500

Clay Material 18500 18500

Hole 5000 3000

In Figure 42 to Figure 43 the compression stress strain curves which are calculated with equation 1 and

application of the stress-strain-curves of the single materials (Figure 37 to Figure 40) are represented in

comparison with the experimental and the numerical computed curves Figure 44 shows the numerically

computed stress-strain-curves compared with the calculated stress strain-curves according to equation (58)

for the investigated material combinations The influence of the different material combinations on the stress-

strain-curve are to be recognized in the numeric and the analytic solution in a similar way The values

according to equation (58) are about 7-8 smaller compared to the numerical results The difference may

be caused among others things by the lateral confinement of the pressure plates This influence is not

considered by equation (58)

In Deliverable 55 compression tests on 12 masonry walls are described Table 15 contains the substantial

test results The mean value of the concrete compressive strength of the cubes fccubedry (storage according to

standard) which were manufactured with the wall specimens as well as the masonry compressive strength

(single and average values) are given The masonry compressive strength was calculated according to

equation (58) and the material laws shown in Figure 37 to Figure 40 whereas also the steel cross section (4

Ф 12 mmchamber standard reinforcement and 4 Ф 6 mmchamber DISWall reinforcement) was considered

if necessary In Table 15 the calculated masonry compressive strength cal fcmas and the ratio of the

experimental determined and the calculated masonry strength fcmas cal fcmas are specified The calculated

stress-strain-curves of the composite material are depicted in Figure 45

Within the tests for the determination of the fundamental material properties the mean value of the cube

strength of the Normal Concrete amounts to 439 Nmmsup2 (compressive strength of cylinder 383 Nmmsup2) and

the Selfcompacting Concrete to 352 Nmmsup2 (compressive strength of cylinder 407 Nmmsup2) The

compressive strength of the mixtures produced for the individual walls deviate up to 8 Nmmsup2 of these values

(upward and downward) To consider these deviations roughly in the calculations with equation (58) the

stress-strain curves of the concrete were scaled (stretched or compressed) in y-direction (compression

stress) with the ratio of the cube strength tested parallel to the wall specimen and the cube strength

determined within the fundamental tests The ldquoadjustedrdquo compressive strength corr cal fcmas and the ratio

fcmas corr cal fcmas are given in Table 15 The calculated stress-strain-curves of the composite material are

depicted in Figure 46


For the unreinforced masonry walls the ratio of the calculated and the experimental determined compressive

strength amounts for the adjusted values between 057 and 069 (average value 064) The difference

between the calculated and experimental values may have different causes Among other things the

specimen geometry and imperfections as well as the scatter of the material properties affect the compressive

strength of the walls A similar factor can be found for the ratio of the compressive strength of masonry made

of solid units and thin layer mortar masonry and the compressive strength of the used units The higher ratio

for the walls of Selfcompacting Concrete may be generated by a worse compaction of the Normal Concrete

in the wall specimen A similar effect could be identified in the lower modulus of elasticity of the masonry

walls with Normal Concrete within the experimental investigations

For the test series of reinforced masonry the ratio is remarkable larger and amounts to 082 or 084

respectively The higher values can be attributed to the positive effect of the horizontal reinforcement

elements (longitudinal bars binder) which are not considered in equation (58)

Table 15 Comparison of calculated and tested masonry compressive strengths

description fccubedry fcmas cal fc

fcmas

cal fcmas corr cal fcmas

fcmas

corr cal fcmas

- Nmmsup2 Nmmsup2 - Nmmsup2 -

182 SU-VC-NM

136

163 SU-VC

353

168

mean 162

327 050 283 057

236 SU-SCC 445

216

mean 226

327 069 346 065

247 DU-SCC

438 175

mean 211

286 074 304 069

223 DU-SCC-DR 399

234

mean 229

295 078 272 084

261 DU-SCC-SR 365

257

mean 259

321 081 317 082


0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3

unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234FE-Simulationequation

compressive stress σD in Nmmsup2

compressive strain εD in mmm

Figure 41 SU with NC Results of compressive tests in direction of the unit height in comparison with FE-

simulation and analytical calculation (equation)

0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3

unit 1 - M1234unit 2 - M1234unit 3 - M1234unit 4 - M1234unit 5 - M1234FE-Simulationequation


compessive strain in mmm

final compressive strength

Figure 42 SU with SCC Results of compressive tests in direction of the unit height in comparison with FE-



0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35





Figure 43 DU with SCC Results of compressive tests in direction of the unit height in comparison with FE-


0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35

SU-NC (eq)SU-NC (FE)SU-SCC (eq)SU-SCC (FE)DU-SCC (eq)DU-SCC (FE)



Figure 44 Results of FE-simulation in comparison with analytical calculation (equation) bonded specimen


0

5

10

15

20

25

30

35

0 05 1 15 2 25 3 35

SU-VCSU-SCCDU-SCCDU-SCC-reinf (standard)DU-SCC-reinf (DISWall)



Figure 45 Results of analytical calculation (equation) masonry walls

0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35




Figure 46 Results of analytical calculation (equation) with corrected concrete strength masonry walls



The design the under dominant axial forces is performed acc EN 1996-1-1 2005 61 As bending moments

can affect the behaviour these loadings have to be considerer at the top resp bottom and the mid height of

the wall ie M1d M2d and Mmd

The design is performed by checking the axial force

SdRd NN ge (58)

for rectangular cross sections

dRd ftN sdotsdotΦ= (59)

The reduction factor Φ has to be determined at the relevant points ie mid height and top resp bottom of the

wall As in the mid height of the wall creep effects and the slenderness has to be considered the simple

approach is done by taking the maximum bending moment for all design checks ie at the mid height and

the top resp bottom of the wall Therefore an easy and fast use of the diagrams is ensured

Especially when the bending moment at the mid height is significantly smaller than the bending moment at

the top resp bottom of the wall it might be favourable to perform the design with the following charts only for

the moment at the mid height of the wall and in a second step for the bending moment at the top resp

bottom of the wall using equations (64) and 65)

For the following design procedure the determination of Φi is done according to eq (64) and Φm according to

eq (66) in combination with annex G assuming E = 1000fk The difference is shown in the following

comparison


534 Design charts

Figure 47 N-M diagram Load bearing capacity of walls under dominant axial compression with different

geometry and material parameters here different heights h and restraint factors ρ


geometry and material parameters here strength of the infill




The design for vertical loads of masonry walls with concrete units was based on walls with different lengths

proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190 mm + 1 mm of

joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is commonly about

280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of the design charts

Besides the aspect ratio also the amount of vertical and horizontal reinforcement was taken into account in

the design charts

The boundary conditions reinforced concrete walls to be used in residential buildings consists of two top and

bottom restrained edges by the stiff floors or roofs or three or four restrained sides depending on the

capacity of transversal walls to stiff the walls


the wall is stiffened by piers In the analyzed cases the effective thickness of the wall has been taken as the

actual thickness The effective height hef of single-leaf walls should be taken as the actual height of the wall

h times a reduction factor ρn that changes according to the wall boundary condition as already explained in

sections sect 521 and 531 (eq 52) If for the reinforced concrete walls only two restrained edges (safety

side) are considered and if ρ2 is taken with the value of 075 the slenderness ratio of the concrete walls is

105 (lt12)



The value of the design compressive strength of the concrete masonry units is calculated based on the

values of the compressive strength of units and mortar to be used in practice Thus it is desirable to produce

real scale masonry units with a normalized compressive strength close to the one obtained by experimental

tests in the reduced scale masonry units A value of 10MPa was considered in the calculation of the

compressive strength of masonry Table 16 summarizes the mechanical properties and safety factor used in

the calculation of the design compressive strength of concrete masonry


Material properties

fb Nmm2 1000 fm Nmm2 1000 K - 045 α - 070 β - 030 fk Nmm2 450 γM - 150 fd Nmm2 300


The design for vertical loading of masonry made with concrete units (UMINHO system) has been based on

the determination of the design out-of-plane bending moment resistance that divided for possible values of



been assumed for masonry and the ultimate strain of the reinforcement εu has been limited to 001 similarly

to was stated in Figure 33 for perforated clay units The calculations were repeated for wall of different length

(from 160 mm to 560 mm) taking thus into account the factored design compressive strength

Figure 49 to Figure 51 give the design values of the vertical load resistance of the walls (NRd) If one knows

the length of the wall and the eccentricity of the vertical load enters the diagram and find the ddesign vertical

load resistance of the wall For the obtainment of the design charts also the variation of the vertical

reinforcement is taken into account


544 Design charts

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

Nrd

(kN

)

(et)

L=80cm L=100cm L=160cm L=280cm L=400cm L=560cm

Figure 49 Design charts for reinforced concrete masonry system Ddesign values of the vertical load

resistance of the wall NRd for walls of different length

00 01 02 03 04 050

500

1000

1500

2000

2500

3000L=160cm

As = 0036 As = 0045 As = 0074 As = 011 As = 017

Nrd

(kN

)

(et)

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

As = 0035 As = 0045 As = 0070 As = 011 As = 018

Nrd

(kN

)

(et)

L=280cm

(a) (b)

Figure 50 Design charts for reinforced concrete masonry system Design values of the vertical load

resistance of the wall NRd for walls (a) L= 160cm (b) L= 280cm

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

As = 0022 As = 0034 As = 0045 As = 0070 As = 010

Nrd

(kN

)

(et)

L=400cm

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

3500

As = 0022 As = 0034 As = 0045 As = 0070 As = 010

Nrd

(kN

)

(et)

L=560cm

(a) (b)




6 DESIGN OF WALLS FOR IN-PLANE LOADING

61 INTRODUCTION

The shear capacity of reinforced masonry walls is governed by several mechanisms induced by the

presence of the reinforcement The tensioning of the horizontal reinforcement becomes fully effective when

the first shear crack appears by preventing the separation of the cracked portions of the wall The vertical

reinforcement is mainly effective in case of flexural behaviour of the wall However it also gives a

contribution to the shear capacity of the wall by means of the dowel-action mechanism The combination of

vertical and horizontal reinforcement leads to the development of a global mechanism which lies in between

the arch-beam and truss mechanism [Tomazevic 1999 Tassios 1988]

Following these observations the recent formulations proposed to predict the nominal shear strength (VR) of

reinforced masonry walls are based on the idea of calculating the shear resistance as a sum of contributions

These are generally classified as contribution due to the shear strength of unreinforced masonry (VR1)

contribution due to the horizontal reinforcement (VR2) contribution due to the dowel-action of vertical

reinforcement (VR3) as in eq (61)

1 2 3R R R RV V V V= + + (61)

Formulations of this type are proposed by many standards as the Eurocode 6 [EN 1996-1-1 2005] or for

example the Australian Standard [AS 3700 2001] the British standard [BS 5628-2 2005] and the Italian

standard [DM 140108 2007] The New Zealand code [NZS 4230 2004] and the American code [ACI 530

2005] are based on some similar concepts but the expressions for the strength contribution is more complex

and based on the calibration of experimental results Generally the codes omit the dowel-action contribution

that is proposed by the researches [Tomazevic 1999] The single terms in the considered formulation are

reported in Table 17

In Table 17 l and t are respectively the length and the thickness of the walls Asw n and drv are respectively

the total area of the horizontal shear reinforcement and the number and diameter of the vertical bars fd is the

design compressive strength of masonry fvd is the design shear strength of masonry fvd0 is the design shear

strength of masonry under zero compressive stresses fyd and fm are respectively the design yield strength of

the horizontal reinforcement and the characteristic compressive strength of the embedding mortar or grout N

is the design vertical load M and V the design bending moment and shear α is the angle formed by the

applied loads s is the spacing of the horizontal reinforcement C1 is a constant that depends on the

percentage of horizontal reinforcement and C2 is a constant that depends on the MV ratio A different

approach for the evaluation of the reinforced masonry shear strength based on the contribution of the

various resisting mechanisms of the theoretical stereostatic model has been finally proposed by Tassios

(1988) The comparison between the experimental values of shear capacity and the theoretical values given

by some of these formulations has been carried out in Deliverable D12bis (2006)


Table 17 Shear strength contribution for reinforced masonry

Formulation VR1 unreinforced masonry VR2 horizontal reinforcement VR3 dowel-action EN 1996-1-1

(2005) tlf vd sdot ydSw fA sdot90 0

AS 3700 (2001) tlf vd sdot ydSw fA sdot80 0

BS 5628-2 (2005) tlf vd sdot ydSw fA sdot 0

DM 140905 (2007) tlf vd sdot ydSw fA sdot60 0

NZS 4230 (2004) ltfC

ltN

vd 8080tan90

02 sdot⎟⎠

⎞⎜⎝

⎛+

sdotα lt

stfA

fC ydswvd 80)

80( 01 sdot

sdot+ 0

ACI 530 (2005) Nftl

VLM

d 250)7514(0830 +minus slfA ydsw 50 0

Tomazevic (1999) tlf vd sdot ( )ydSw fA sdotsdot 9030 ydmrv ffdn sdotsdotsdot 28060

The bending moment capacity of reinforced masonry walls is generally based on assumption adapted from

those of reinforced concrete where plane sections remain plane the reinforcement is subjected to the same

variations in strain as the adjacent masonry the tensile strength of the masonry is taken to be zero the

maximum strain of the masonry and of the reinforcement is chosen according to the material the stress-

strain relationship for masonry can be taken to be linear parabolic parabolic rectangular or rectangular

whereas the stress-strain relationship of the reinforcement is obtained from EN 1992-1-1




The design for in-plane horizontal load of masonry made with horizontally perforated clay units (ALAN

system) has been based on walls of length equal to a multiple of the unit length (250 mm thus starting from

short piers 500 mm long) thickness equal to that of the studied unit (300 mm) and height typical of housing

construction for which the system has been developed (2700 mm) The study has been limited to masonry

piers 4250 mm long as the Italian Code [DM 140108] requires a maximum distance between vertical

reinforcement of 4000 mm For the analysis it is required to know the boundary condition of the wall ie

whether it is a cantilever or a wall with double fixed end as this condition change the value of the design

applied in-plane bending moment The design values of the resisting shear and bending moment are found

on the basis of the geometry of the wall cross section the amount of vertical and horizontal reinforcement

and the material properties

Regarding the horizontal reinforcement the introduction of two steel rebars with diameter equal to 6 mm

each other course (being the unit height equal to 200 mm it means at a distance equal to 400 mm) has been

taken into account in the following calculations This is equal to a percentage of steel on the wall cross

section of 0042 very close to the minimum 004 fixed by the code [DM 140905 2007] As

demonstrated by the experimental tests [D55 2006] in terms of strength this reinforcement (when steel Feb

44k is used) can be considered almost equivalent to the introduction of a Murfor RNDZ-5-15 truss each

other course (every other 400 mm) with diameter of the longitudinal and transversal wires equal to 5 mm

Regarding the vertical reinforcement a percentage of reinforcement from the minimum 005 [DM 140905

2007] upwards has been taken into account into the calculations When the 005 of the masonry wall

section is lower than 200 mm2 the latter value has been taken as the minimum quantity of vertical

reinforcement [DM 140905 2007]


The materials properties that have to be used for the design under in-plane horizontal loading of reinforced

masonry walls made with perforated clay units concern the materials (normalized compressive strength of

the units fb mean compressive strength of the mortar fm class elastic modulus E yielding strength fyk and

ultimate strain εu of the reinforcement) and the masonry itself (masonry characteristic compressive strength

fk masonry characteristic shear strength under zero compressive stresses fvk0) To derive the design values

the partial safety factors for the materials are required The compressive strength of masonry is derived as

described in section sect 522 using eq (55) and is factored to the length of the wall being analyzed as

described by Figure 32 to take into account the different properties of the unit with vertical and with

horizontal holes Table 18 gives the main parameters adopted for the creation of the design charts



Material property Horizontal Holes (G4) Vertical Holes (G2)

fbm Nmm2 93 216 fb Nmm2 102 241 fm Nmm2 141 141 K - 035 045 α - 07 07 β - 03 03 fk Nmm2 393 922

fvk0 Nmm2 030 fvklim Nmm2 066 157 γM - 20 20 fd Nmm2 196 461 α - 085 micro - 040 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10

For the definition of the characteristic shear strength of masonry fvk it is necessary to know the design

compressive stresses of the wall σd and the EN 1996-1-1 formulation can be used

(62)

with the limitation that fvk le 0065 fb The design value of the shear strength of masonry fvd can be then

inferred from fvk dividing by γM

623 In-plane wall design

The design for in-plane horizontal loading of reinforced masonry made with horizontally perforated clay units

(ALAN system) has been based on the determination of the design in-plane bending moment resistance and

the design in-plane shear resistance

In determining the design value of the moment of resistance of the walls for various values of design

compressive stresses in a range reasonable for reinforced masonry buildings (from 01 Nmm2 up) a

rectangular stress distribution as been assumed for masonry (see Figure 33) The ultimate strain of the

reinforcement εu has been limited to 001 Furthermore the M-N domain of the masonry wall section has

been computed by studying the limit conditions between different fields and limiting for cross-sections not

fully in compression the compressive strain of masonry εmu = -0002 (limitations given by the EN 1996-1-1

for Group 2 and 4 units) The calculations were repeated for wall of different length (from 500 mm to 4250


mm) taking thus into account the factored design compressive strength (reduced to take into account the

stress block distribution) α fd given by Figure 32 A preliminary evaluation of the validity of this calculation

method has been carried out by comparing the experimental values of maximum bending moment in the

tested specimens that failed in flexure (black dots in Figure 52) and the corresponding predicted design

values of resisting moment (light blue dots in Figure 52) As can be seen the design formulation is able to

get the trend of the strength for varying applied compressive stresses and gives value of predicted bending

moment with a safety coefficient equal to 135 It has been thus assumed that the proposed design method

is reliable

The prediction of the design value of the shear resistance of the walls has been also carried out for various

values of design compressive stresses in a range reasonable for reinforced masonry buildings (from 01

Nmm2 up) The shear capacity evaluation has been based on the simplest available concept which is a sum

of the contributions of the shear strength of unreinforced masonry and of the strength of the horizontal

reinforcement However the formulation proposed by the Eurocode 6 [EN 1996-1-1 2005] where the

horizontal reinforcement contribution is reduced by 10 overestimated the experimental values of shear

strength (respectively in light blue dots and black dots in Figure 53) even if it was able to get the trend of the

strength for varying applied compressive stresses Therefore it was decided to use a similar formulation

proposed by the Italian code (see Table 17) that reduces the horizontal reinforcement contribution by 40

[DM 140108] As can be seen this formulation is able to predict the shear capacity with a safety coefficient

of 110 (blue dots in Figure 53)

MRd for walls with fixed length and varying vert reinf

0

50

100

150

200

250

0 50 100 150 200 250 300 350 400

NEd (kN)

MRd (kNm)

2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmExperimental

wall l = 1000 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor RNDZ-

5-150 400 mm

VRd varying the influence of hor reinf

NTC 1500 mm

EC6 1500 mm

100

150

200

250

300

0 100 200 300 400 500 600

NEd (kN)

VRd (kN)

06 Asy fyd09 Asy fydExperimental

wall l = 1500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or 1 Murfor

RNDZ-5-150 400 mm

Figure 52 Comparison of design bending moment of resistance and experimental values of maximum benging moment

Figure 53 Comparison of design shear resistance and experimental values of maximum shear force

Figure 54 gives the design values of the bending moment of resistance of the wall (MRd) when the minimum

percentage of vertical reinforcement is used (Feb 44k) If one knows the length of the wall and the value of

the design applied compressive stresses (or axial load on the wall Figure 54 right) enters the diagrams and

finds the design bending moment of resistance Figure 55 is based on the same concept but gives the value

of the design shear strength where the amount of vertical reinforcement is irrelevant Figure 56 gives the M-


N domains for walls of different length and minimum vertical reinforcement (Feb 44k) If one knows the

length of the wall and the value of the design applied bending moment and axial load enters the diagram

and finds if those values are inside or outside the strength domain of the masonry wall section Figure 57

gives the V-M domain for walls of different length and minimum vertical reinforcement (Feb 44k) varying the

applied design compressive stresses If one knows the design value of the applied compressive stresses or

axial load and of the applied horizontal load by knowing the boundary condition (double fixed ends or

cantilever) can calculate the design values of the applied shear and bending moment At this point heshe

enters the diagram and finds if those values are inside or outside the strength domain of the masonry wall

section Figure 58 and Figure 59 gives the M-N domains and the V-M domains for fixed wall length (500 mm

1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm) and varying vertical reinforcement

(of steel type Feb 44k) The horizontal reinforcement is the minimum amount required (two rebars oslash6 mm

each 400 mm or 1 Murfor RNDZ-5-150 400 mm)


624 Design charts

MRd for walls of different length and min vert reinf

500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm

2250 mm2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm

0

200

400

600

800

1000

1200

1400

1600

1800

2000

00 02 04 06 08 10 12 14σd (Nmm2)

MRd (kNm)


wall t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm


500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm

2250 mm2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 200 400 600 800 1000 1200 1400 1600

NEd (kN)

MRd (kNm)



Figure 54 Design charts for ALAN reinforced masonry system Design values of the bending moment of

resistance of the wall MRd when a minimum amount of vertical reinforcement is used and for varying design

compressive stresses (left) and design axial load (right)

VRd for walls of different length

500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm2250 mm2500 mm2750 mm3000 mm3250 mm3500 mm3750 mm4000 mm4250 mm

100

150

200

250

300

350

400

450

500

550

00 02 04 06 08 10 12 14

σd (Nmm2)

VRd (kN)



500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm2250 mm

2500 mm2750 mm

3000 mm3250 mm

3500 mm

3750 mm4000 mm

4250 mm

100

150

200

250

300

350

400

450

500

550

0 200 400 600 800 1000 1200 1400 1600

NEd (kN)

VRd (kN)


Figure 55 Design charts for ALAN reinforced masonry system Design values of the shear resistance of the

wall VRd for varying design compressive stresses (left) and design axial load (right)


M-N domain for walls of different length and minimum vertical reinforcement

0

200

400

600

800

1000

1200

1400

1600

1800

2000

-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400

NRd (kN)

MRd (kNm) 2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm


500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm2250 mm

2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm

Figure 56 Design charts for ALAN reinforced masonry system M-N domain for walls of different length and

minimum vertical reinforcement (FeB 44k)

V-M domain for walls with different legth and different applied σd

100

150

200

250

300

350

400

450

500

550

0 250 500 750 1000 1250 1500 1750 2000

MRd (kNm)

VRd (kN)

σd = 01 Nmmsup2 σd = 02 Nmmsup2 σd = 03 Nmmsup2σd = 04 Nmmsup2 σd = 05 Nmmsup2 σd = 06 Nmmsup2σd = 07 Nmmsup2 σd = 08 Nmmsup2 σd = 09 Nmmsup2σd = 10 Nmmsup2 σd = 11 Nmmsup2 σd = 12 Nmmsup2σd = 13 Nmmsup2 4000 mm 3750 mm3500 mm 3250 mm 3000 mm2750 mm 2500 mm 2250 mm2000 mm 1750 mm 1500 mm1250 mm 1000 mm 750 mm500 mm lw = 4250 mm


Figure 57 Design charts for ALAN reinforced masonry system V-M domain for walls of different length and

minimum vertical reinforcement (FeB 44k) varying the applied design compressive stresses


M-N domain for walls with fixed length and varying vert reinf

0

10

20

30

40

50

60

70

-400 -300 -200 -100 0 100 200 300 400 500 600 700 800 900

NRd (kN)

MRd (kNm)


wall l = 500 mm t = 300 mmsteel 2oslash6 400 mm Feb 44k or1 Murfor RNDZ-5-150 400 mm


0

50

100

150

200

250

-400 -200 0 200 400 600 800 1000 1200

NRd (kN)

MRd (kNm)




0

50

100

150

200

250

300

350

400

-400 -200 0 200 400 600 800 1000 1200 1400

NRd (kN)

MRd (kNm)




0

100

200

300

400

500

600

-400 -200 0 200 400 600 800 1000 1200 1400 1600

NRd (kN)

MRd (kNm)

2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm



0

100

200

300

400

500

600

700

800

900

-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800

NRd (kN)

MRd (kNm)

2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mm



0

200

400

600

800

1000

1200

-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000

NRd (kN)

MRd (kNm)

2oslash18 mm

2oslash20 mm

4oslash16 mm




0

200

400

600

800

1000

1200

1400

-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

NRd (kN)

MRd (kNm)

2oslash20 mm

4oslash16 mm



0

300

600

900

1200

1500

1800

-600 -300 0 300 600 900 1200 1500 1800 2100 2400

NRd (kN)

MRd (kNm)

2oslash20 mm

4oslash16 mm


Figure 58 Design charts for ALAN reinforced masonry system From top left to bottom right M-N domain for

walls of different length and varying vertical reinforcement (FeB 44k) length equal to 500 mm 1000 mm

1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm

V-M domain for walls with fixed legth varying vert reinf and σd

100

110

120

130

140

150

0 10 20 30 40 50 60 70 80 90 100

MRd (kNm)

VRd (kN)

2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd = 09 Nmmsup2σd = 10 Nmmsup2σd = 11 Nmmsup2σd = 12 Nmmsup2σd = 13 Nmmsup2


RNDZ-5-150 400 mm


100

110

120

130

140

150

160

170

180

190

200

0 25 50 75 100 125 150 175 200 225 250

MRd (kNm)

VRd (kN)

2oslash12 mm2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2


RNDZ-5-150 400 mm


150

160

170

180

190

200

210

220

230

240

250

50 100 150 200 250 300 350 400 450

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


160

180

200

220

240

260

280

300

150 200 250 300 350 400 450 500 550 600 650

MRd (kNm)

VRd (kN)

2oslash14 mm2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2


RNDZ-5-150 400 mm



200

220

240

260

280

300

320

340

360

250 300 350 400 450 500 550 600 650 700 750 800 850

MRd (kNm)

VRd (kN)

2oslash16 mm2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2


RNDZ-5-150 400 mm


220

240

260

280

300

320

340

360

380

400

420

350 450 550 650 750 850 950 1050 1150

MRd (kNm)

VRd (kN)

2oslash18 mm2oslash20 mm4oslash16 mmσd = 01 Nmmsup2σd = 02 Nmmsup2σd = 03 Nmmsup2σd = 04 Nmmsup2σd = 05 Nmmsup2σd = 06 Nmmsup2σd = 07 Nmmsup2σd = 08 Nmmsup2σd ge 09 Nmmsup2


RNDZ-5-150 400 mm


240

260

280

300

320

340

360

380

400

420

440

460

550 650 750 850 950 1050 1150 1250 1350 1450

MRd (kNm)

VRd (kN)

2oslash20 mm

4oslash16 mm

σd = 01 Nmmsup2

σd = 02 Nmmsup2

σd = 03 Nmmsup2

σd = 04 Nmmsup2σd = 05 Nmmsup2

σd = 06 Nmmsup2

σd = 07 Nmmsup2

σd = 08 Nmmsup2

σd ge 09 Nmmsup2


RNDZ-5-150 400 mm


280

300

320

340

360

380

400

420

440

460

480

500

520

650 750 850 950 1050 1150 1250 1350 1450 1550 1650 1750 1850

MRd (kNm)

VRd (kN)

2oslash20 mm

4oslash16 mm

σd = 01 Nmmsup2

σd = 02 Nmmsup2

σd = 03 Nmmsup2


σd = 06 Nmmsup2

σd = 07 Nmmsup2

σd = 08 Nmmsup2

σd ge 09 Nmmsup2


RNDZ-5-150 400 mm

Figure 59 Design charts for ALAN reinforced masonry system From top left to bottom right V-M domain for

walls of different length and vertical reinforcement (FeB 44k) varying the applied design compressive

stresses Length of 500 mm 1000 mm 1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm




The hollow clay unit system UNIPOR is designated for load bearing wall with high vertical and horizontal in-

plane loadings Due to the stiff connection to the RC-slabs relevant restraint effects can be ensured

Figure 60 Structural system of in-plane loaded wall and corresponding bending moment with restraint

effects at the top of the wall (left) and without (cantilever system right)

The thickness of the hollow clay units is fixed due to the developed product to 24cm For typical residential

housing structures the full storey height hwall is between 25 and 275m Usually the length of shear wall in

the relevant direction ndash ie perpendicular to the orientation of the regarded apartment or terraced house ndash is

limited by architectonical demands and does not exceed generally 40 m If longer walls are used in common

residential housing structures (limited number of storeys) the design for in-plane-loading is mostly not

relevant

Regarding the reinforcement in horizontal and vertical direction 4 d6mm s = 25cm are applied The

developed hollow clay units system allows generally also additional reinforcement but in the following the

design focuses only on the basic reinforcement ratio If additional reinforcement is applied (eg in corners

next to opening or at the connection points between wall an RC slabs) it has to be mentioned that the filling

and the necessary compaction of the concrete infill is not affected by this additional reinforcement

significantly



For the design under in-plane loadings also just the concrete infill is taken into account The relevant

property is here the compression strength



fck Nmm2SCC

25 Nmmsup2 (min demand)measured 275 Nmmsup2

εcu3 - -350permil εc3 - -175permil γM - 15 αcc - 085 fcd Nmm2 1416 Nmmsup2

fyk Nmm2 500 Nmmsup2 (measured 560 Nmmsup2)

εuk - 25permil ES Nmm2 200000 γS - 115


The in-plane wall design bases on the separation of the wall in the relevant cross section into the single

columns Here the local strain and stress distribution is determined

Figure 61 Design approach for the UNIPOR-System Separation of the wall in the relevant cross section

into several columns (left) and determination of the corresponding state in the column (right)


bull For columns under tension only vertical tension forces can be carried by the reinforcement The

tension force is determined depending to the strain and the amount of reinforcement

Figure 62 Stress-strain relation of the reinforcement under tension for the design

It is assumed the not shear stresses can be carried in regions with tension

bull For columns under compression the compression stresses are carried by the concrete infill The

force is determined by the cross section of the column and the strain

Figure 63 Stress-strain relation of the concrete infill under compression for the design

The shear stress in the compressed area is calculated acc to EN 1992 by following equations

(63)

(64)

(65)

(66)


The determination of the internal forces is carried out by integration along the wall length (= summation of

forces in the single columns)

Figure 64 Design approach for the UNIPOR-System Resulting internal force in the relevant cross section

634 Design charts

Following parameters were fixed within the design charts

bull Thickness of the system 24cm

bull Horizontal and vertical reinforcement ratio

bull Partial safety factors

Following parameters were varied within the design charts

bull Loadings (N M V) result from the charts

bull Length of the wall 1m 25m and 4m

bull Compression strength of the concrete infill 25 and 45 Nmmsup2

bull Yield strength of the reinforcement 500 and 600 Nmmsup2


Vd (MdNd) [kN]-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250

Md [kNm]

Nd [

kN]

0 10 20

30 40 50

60 70 80

90 Loadings

l = 1 mfyk = 500 Nmmsup2fck = 25 Nmmsup2

Figure 65 Design chart for UNIPOR-System under in-plane loadings

Length = 1m fck=25Nmmsup2 fyk=500Nmmsup2

Vd (MdNd) [kN]-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250

Md [kNm]

Nd [

kN]

0 10 20

30 40 50

60 70 80

90 Loadings




Vd (MdNd) [kN]-3500

-3000

-2500

-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250 300 350 400 450

Md [kNm]

Nd [

kN]

0 20 40

60 80 100

120 140 160

180 Loadings



Vd (MdNd) [kN]-3500

-3000

-2500

-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250 300 350 400 450

Md [kNm]

Nd [

kN]

0 20 40

60 80 100

120 140 160

180 Loadings




Vd (MdNd) [kN]-5000

-4000

-3000

-2000

-1000

0

1000

0 200 400 600 800 1000 1200 1400 1600

Md [kNm]

Nd [

kN]

0 30 60

90 120 150

180 210 240

270 Loadings



Vd (MdNd) [kN]-5000

-4000

-3000

-2000

-1000

0

1000

0 200 400 600 800 1000 1200 1400 1600

Md [kNm]

Nd [

kN]

0 30 60

90 120 150

180 210 240

270 Loadings




Vd (MdNd) [kN]-9000

-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

0 500 1000 1500 2000 2500 3000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings



Vd (MdNd) [kN]-9000

-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings




Vd (MdNd) [kN]-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000 3500 4000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings



Vd (MdNd) [kN]-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000 3500 4000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings




Vd (MdNd) [kN]-14000

-12000

-10000

-8000

-6000

-4000

-2000

0

2000

0 1000 2000 3000 4000 5000 6000 7000

Md [kNm]

Nd [

kN]

0 70 140

210 280 350

420 490 560

630 Loadings




-12000

-10000

-8000

-6000

-4000

-2000

0

2000

0 1000 2000 3000 4000 5000 6000 7000

Md [kNm]

Nd [

kN]

0 70 140

210 280 350

420 490 560

630 Loadings






The reinforced concrete walls consist of a system (UMINHO system) to be used in typical residential

buildings to undergo mostly combined vertical and horizontal in-plane loads In terms of boundary conditions

both cantilever and fixed ended walls are possible according to the stiffness of the concrete slabs

The design for in-plane horizontal load of masonry made with concrete units was based on walls with

different lengths proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190

mm + 1 mm of joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is

commonly about 280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of

the design charts see Figure 77 Besides the aspect ratio also the amount of vertical and horizontal

reinforcement was taken into account in the design charts

Figure 77 Geometry of concrete masonry walls (Variation of HL)

One or two truss-reinforcements were considered in vertical cores according to the vertical reinforcement

ratio The use of two truss-reinforcements should be considered to avoid the disposition of the vertical

reinforcement in all holes of the wall which becomes the construction time consuming

Five vertical reinforcement ratios were also considered to derive the design charts respecting simultaneously

the spacing limits of EN1996-1-1 An example of he variation of vertical reinforcement for wall with HL=100

is presented in Figure 78


Figure 78 Geometry of concrete masonry walls (Variation of vertical reinforcement ratio)

Finally three horizontal reinforcement ratios were also used to create the design charts respecting spacing

limits of EN1996-1-1 An example of the variation of horizontal reinforcement in wall with HL=100 is

presented in Figure 79

Figure 79 Geometry of concrete masonry walls (Variation of horizontal reinforcement ratio)



All properties used in this analysis are referred to the desirable design properties of the real scale units to be

used for structural purposes Thus fixing the normalized compressive strength of the units fb and of the

mortar fm the compressive strength of masonry strength fk can be calculated according to EN1996-1-1

From the definition of the group of the units (group 2) it is possible to take the characteristic shear strength

under zero compressive stresses fvk0 The properties of the reinforcements (yielding strength fyk and ultimate

strain εu) were considered to be the same the ones obtained in the experimental campaign according to the

results pointed out in D55 To derive the design values the partial safety factors for the materials are

required Table 20 gives the main parameters adopted for the creation of the design charts


Material properties

fb Nmm2 1000

fm Nmm2 1000

K - 045

α - 070

β - 030

fk Nmm2 450

γM - 150

fd Nmm2 300

fyk0 Nmm2 020

fyk Nmm2 500

γS - 115

fyd Nmm2 43478

E Nmm2 210000

εyd permil 207



According to EN1996-1-1 the design of in-plane walls can be divided in two steps verification of masonry

subjected to flexure and verification of masonry subjected to shear The evaluation of masonry walls

subjected to flexure shall be based on the following assumptions

bull the reinforcement is subjected to the same variations in strain as the adjacent masonry

bull the tensile strength of the masonry is taken to be zero

bull the tensile strength of the reinforcement should be limited by 001

bull the maximum compressive strain of the masonry is chosen according to the material

bull the maximum tensile strain in the reinforcement is chosen according to the material

bull the stress-strain relationship of masonry is taken to be linear parabolic parabolic rectangular or

rectangular (λ = 08x)

bull the stress-strain relationship of the reinforcement is obtained from EN 1992-1-1

bull for cross-sections not fully in compression the limiting compressive strain is taken to be not greater

than εmu = -00035 for Group 1 units and εmu = -0002 for Group 2 3 and 4 units

The equilibrium of the section should be satisfied as shows Figure 80 according compatibility of strains

(67) constitutive laws (68) and equilibrium of forces and moments (69 612) respectively

Figure 80 Stress and strain distribution in wall section (EN1996-1-1)

xdx i

sim

minus=

minus εε (67)

sissi E εσ = (68)

summinus=i

sim FFN (69)

xtfF wam 80= (610)


svisisi AF σ= (611)

sum ⎟⎠⎞

⎜⎝⎛ minus+⎟

⎠⎞

⎜⎝⎛ minus==

i

wisi

wmfR

bdFx

bFzHM

240

2 (612)

In case of the shear evaluation EN1996-1-1 proposes equation (7)

wwyhshwwvsh btMPafAtbfH )2(90 le+= (613)

σ400 += vv ff bv ff 0650le (614)

where Ash is the area of horizontal reinforcement fyh is the yield strength of horizontal reinforcement fv0 is

the initial shear strength of masonry σ is the normal stress and fb is the compressive strength of unit

Shear strength of walls accounts for the contribution of masonry and reinforcements The contribution of

masonry in shear strength follows the law of Mohr-Coulomb with the initial shear strength considered as the

cohesion of masonry and the friction coefficient equal to 04 see (614) This standard considers also a limit

of 2 MPa to the shear strength This limit probably is defined to consider the possibility of crushing of some

part of wall because the biaxial tensile-compressive stresses Using the analogy of strut and ties this limit

seems to represent the rupture of a strut


644 Design charts

According to the formulation previously presented some design charts can be proposed assisting the design

of reinforced concrete masonry walls see from Figure 81 to Figure 87

These diagrams allow do some observations about the behaviour of reinforced masonry Flexure and shear

capacity of walls decreases with the increasing of the aspect ratio This behaviour is expected because the

reduction of the resistant section of the wall see Figure 81 Shear strength increases with the normal force

only up to a limit This limit is defined sometimes by the compressive strength of the unit or by the shear

stress of 2 MPa

-500 0 500 1000 1500 2000 2500 3000 3500 40000

500

1000

1500

2000

2500

3000

3500

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Mom

ent (

kNm

)

Normal (kN) (a)

-500 0 500 1000 1500 2000 2500 3000 3500 40000

100

200

300

400

500

600

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Shea

r (kN

)

Normal (kN) (b)

0 500 1000 1500 2000 2500 3000 35000

100

200

300

400

500

600

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

She

ar (k

N)

Moment (kNm) (c)

Figure 81 Design charts for UMINHO reinforced masonry system (Variation of HL) (a) M x N (b) V x N and

(c) V x M


As showed by Figure 82 according to EN1996-1-1 the shear strength is directly proportional to the

horizontal reinforcement ratio Increasing the horizontal reinforcement ratio can improve the behaviour of the

masonry walls but the flexure capacity should be take in account

-500 0 500 1000 1500 2000100

150

200

250

300

350

400

450

500

ρh = 0035 ρ

h = 0049

ρh = 0098

Shea

r (kN

)

Normal (kN) (a)

0 100 200 300 400 500 600 700 800 900 1000

150

200

250

300

350

400

450

ρh = 0035 ρh = 0049 ρh = 0098

Shea

r (kN

)

Moment (kNm) (b)

Figure 82 Design chart for UMINHO reinforced masonry system (Variation of horizontal reinforcement ratio

to HL=100) (a) V x N and (b) V x M

According to EN1996-1-1 vertical reinforcement has influence only in flexural behaviour of masonry walls

Figure 83 to Figure 87 showed that increasing the vertical reinforcement there are an improvement in flexural

behaviour of the walls independent of the aspect ratio

-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000

500

1000

1500

2000

2500

3000

3500

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091

Mom

ent (

kNm

)

Normal (kN) (a)

0 400 800 1200 1600 2000 2400 2800 3200 3600

200

250

300

350

400

450

500

550

600

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091

Shea

r (kN

)

Moment (kNm) (b)

Figure 83 Design chart for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio

HL=050) (a) M x N and (b) V x M


-500 0 500 1000 1500 2000 2500 30000

200

400

600

800

1000

1200

1400

1600

1800

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Mom

ent (

kNm

)

Normal (kN) (a)

-200 0 200 400 600 800 1000 1200 1400 1600 1800150

200

250

300

350

400

450

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Shea

r (kN

)

Moment (kNm) (b)



-500 0 500 1000 1500 20000

100

200

300

400

500

600

700

800

900

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Mom

ent (

kNm

)

Normal (kN) (a)

0 200 400 600 800 1000100

150

200

250

300

350

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Shea

r (kN

)

Moment (kNm) (b)




-300 0 300 600 900 12000

50

100

150

200

250

300

ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086

Mom

ent (

kNm

)

Normal (kN) (a)

-50 0 50 100 150 200 250 300

120

150

180

210

240

ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086

Shea

r (kN

)

Moment (kNm) (b)



-100 0 100 200 300 400 500 6000

10

20

30

40

50

60

70

ρv = 0049 ρv = 0070 ρv = 0098M

omen

t (kN

m)

Normal (kN) (a)

-10 0 10 20 30 40 50 60 7090

100

110

120

130

140

150

ρv = 0049 ρv = 0070 ρv = 0098

Shea

r (kN

)

Moment (kNm) (b)




7 DESIGN OF WALLS FOR OUT-OF-PLANE LOADING

71 INTRODUCTION

Out-of-plane loadings occur mainly for wind loaded exterior walls for earthquake loads or for exterior walls

in the basement with earth pressure For masonry structural elements the resulting bending moment can be

suppressed by a high axial force (necessary for unreinforced masonry elements) or the load bearing capacity

can be assured by reinforcement

If the axial force is not too high ndash generally smaller than 30 of the maximum vertical load bearing capacity ndash

the bending is dominant and the effect of additional axial force can be neglected This approach is also

allowed acc EN 1996-1-1 2005



Generally the out-of-plane load bearing walls are full storey high elements connected to rigid floors and are

regarded as simple supported at the top and the base of the wall The height of the wall is adapted to the use

of the system eg in housing structures generally 25 up to 3 m and in industrial buildings from 5 up to 8 m

In the case of the presence in one-storey tall buildings such as industrial or commercial buildings of

deformable roofs made with prefabricated elements or glulam beams as already discussed in deliverable

D52 (2006) the walls can be tentatively considered as cantilevers with a vertical load applied at the top and

a horizontal load due to the masses of both the roof and the wall itself Therefore the possible structural

configurations for out of plane loads are as represented in Figure 88




The materials properties that have to be used for the design under out-of-plane loading of reinforced




fk) To derive the design values the partial safety factors for the materials are required The compressive

strength of masonry is derived as described in section sect 522 using eq (55) Table 21 gives the main



To have realistic values of element deflection the strain of masonry into the model column model described

in the following section sect723 was limited to the experimental value deduced from the compressive test

results (see D55 2008) equal to 1145permil

723 Out of plane wall design

In the out-of-plane direction the reinforced concrete walls should be designed only by flexure since the

effect of shear can be negligible in most cases because the thickness of wall is several times lower than the

other dimensions and on the other hand the shears loads can not be significant According to EN 1996-1-1

the design of out-of-plane walls under flexure can be made with the same formulation used in case of in-

plane walls (section sect 623) see also Figure 93 in the next section sect73Figure 963 This is valid when the

Material property

CISEDIL

fbm Nmm2 12 fb Nmm2 132 fm Nmm2 113 K - 045 α - 07 β - 03 fk Nmm2 57 γM - 20 fd Nmm2 28 α - 085 fyk Nmm2 Feb 44k 430 γS - 115 fyd Nmm2 Feb 44k 374 E Nmm2 206000 εu permil 10


slenderness ratio is less than 12 which is often the case when the wall is connected to rigid floors at both

ends (see also section sect522) or is anyway inserted into ordinary inter-storey height floors

In this case the out-of-plane resistance of reinforced masonry walls can be made based on bending only if

the design vertical loading is lower than 30 of the design masonry compressive strength (σdlt03fd) In any

case for completeness it was decided to obtain the interaction diagrams N-M also for the out-of plane

loading of the CISEDIL system as shown in sect 724

When the slenderness ratio is higher than 12 that can occur for example for tall walls particularly when

they are not retained by reinforced concrete or other rigid floors the design should follow the same

provisions given for unreinforced masonry neglecting the presence of the reinforcement and taking into

account the effects of the second order by means of an additional design moment

(71)

However as demonstrated by the testing campaign on the CISEDIL system by means of cyclic out-of-plane

tests on tall walls (see D55 2008) this design can be too conservative if the reinforced masonry system is

developed with some constructive details that allow improving their out-of-plane behaviour even if the

second order effects due to the vertical load that in the case of the test was equal to 25 kN per linear meter

of wall cannot be neglected as well Furthermore the additional bending moment given by eq 71 is

calculated by assuming an eccentricity for the vertical load equal to hef2 2000 t which take into account

only the geometry of the wall but do not take into account the real eccentricity due to the section properties

These effects and their strong influence on the wall behaviour were on the contrary demonstrated by

means of the cyclic out-of-plane tests on tall walls carried out on the CISEDIL system (see D55 2008)

Therefore the use of a different model was proposed for the calculation of the wall deflection at the top and

the vertical load eccentricity in the particular case of cantilever boundary conditions The model column

method which can be applied to isostatic columns with constant section and vertical load was considered It

is assumed that the deformed shape of the wall axis can be assimilated to a sinusoidal function (eq 72)

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛minus=

Lxvy

2cos1max

π (72)

where x is the ordinate vmax the maximum displacement at the top of the wall L the overall height of the wall

Under the assumed conditions the second derivate of the deformed shape give the curvature and when x=0

(at the base of the wall) it is obtained (eq 73)

max2

2

41 v

LEJM

ry

base

π==⎟

⎠⎞

⎜⎝⎛=primeprime (73)

By inverting this equation the maximum (top) displacement is obtained and from that the second moment

order The maximum first order bending moment MI that can be sustained by the wall can be thus easily

calculated by the difference between the sectional resisting moment M calculated as above and the second

order moment MII calculated on the model column


The validity of the proposed models was checked by comparing the theoretical with the experimental data

see Table 22 The evaluation of the resistant moment of the section is slightly conservative even without

using any safety factor On the base of this moment by means of the model column method the top

deflection was obtained The theoretical and the experimental values are in good agreement (less than 5)

From this value it is possible to obtain the MII which shows the same good agreement and from the

underestimated value of MR a conservative value of MI

Table 22 Comparison of experimental and theoretical data for out-of-plane capacity

Experimental Values Out-of-Plane Compared

Parameters MIdeg MIIdeg MR N kN 50 50 50 M kNm 103 155 118

vmax mm 310 310 310 Theoretical Values

Out-of-Plane Compared Parameters MIdeg MIIdeg MR

N kN 50 50 50 M kNm 702 148 85

vmax mm 296 296 296

The design charts were produced for different lengths of the wall Being the reinforcement constituted by

4Φ12 mm rebar placed at 780 mm of spacing and considering that after the vertical reinforcement position

there are other 385 mm constituted by the mortar cores and the units the typical length of CISEDIL walls

can be calculated by x times 780 mm plus 385 mm Therefore the calculations were repeated for length

equal to 1165 mm 1945mm 2725 mm 3505 mm 4285 mm 5065 mm 5845 mm 6625 mm and 7405 mm

considered typical for real building site conditions In this case the reinforcement percentage is that resulting

from the constructive system for out-of-plane loads which is resulting from 4Φ12 mm 780 mm Besides

these geometrical aspects also the mechanical properties of the materials were kept constant The height of

the walls for the tall walls verification was changed from 5 up to 8 meters considering 1 m differences from

one case to the other In this case also the vertical load that produces the second order effect was changed

in order to take into account indirectly of the different roof dead load and building spans

Figure 89 gives the M-N domain for different length of the wall and for fixed vertical reinforcement positions

Figure 90 gives the resisting moment per linear meter of wall (continuous line) for walls of different heights

taking into account the second order effects (dashed lines) Figure 91 gives the resisting moment found in

the previous diagram in terms of out-of-plane lateral load capacity for walls of different heights taking into

account the second order effects One can enter the diagrams of Figure 89 to make a ordinary out-of-plane

flexural design of the masonry section or in case the slenderness is higher than 12 and the second order

effects have to be taken into account can use directly the diagrams of Figure 90 and Figure 91


724 Design charts


TensionCompression

Limit 2-3

Limit 3-4

Limit 4-5

Limit 5-6

Limit 60

50

100

150

200

250

300

350

-10000 -8000 -6000 -4000 -2000 0 2000 4000

NRd (kN)

MRd (kNm)


Figure 89 Design charts for CISEDIL reinforced masonry system M-N design domain for different length of

the wall and for fixed percentage of vertical reinforcement


Variation of the Moments with different vertical loads

0

5

10

15

20

25

30

35

0 5 10 15 20 25 30 35

N (kN)

MRD (kNm)

rmC-45m-IdegrmC-5m-IdegrmC-6m-IdegrmC-7m-IdegrmC-8m-IdegMRDrmC-8m-IIdegrmC-7m-IIdegrmC-6m-IIdegrmC-5m-IIdegrmC-45m-IIdeg

t = 380 mm λ ge 12 Feb 44k

Figure 90 Design charts for CISEDIL reinforced masonry system Resisting moment (continuous line) for

walls of different heights taking into account the second order effects (dashed lines)

Variation of the Lateral load from MIdeg for different height and different vetical loads

0

1

2

3

4

5

6

7

0 10 20 30 40 50

N (kN)

LIdeg (kN)

rmC-45m

rmC-5m

rmC-6m

rmC-7m

rmC-8m

t = 380 mm λ gt 12 Feb 44k

Figure 91 Design charts for CISEDIL reinforced masonry system Out-of-plane lateral load capacity for

walls of different heights taking into account the second order effects




Generally the mentioned structural members are full storey high elements with simple support at the top and

the base of the wall The height of the wall is adapted to the use of the system eg in housing structures

generally 25 up to 3 m and in industrial buildings analogous The thickness of the regarded element is the

effective thickness of the wall acc top EN 1996-1-12005 5513 resp 663

Figure 92 Effect of flanges to the bending design [EN 1996-1-1] Figure 66

The use and consideration of flanges is generally possible but simply in the following neglected


For the design under out-plane loadings also just the concrete infill is taken into account The relevant

property for the infill is the compression strength



fck Nmm2SCC


γM - 15 αcc - 085 fcd Nmm2 1416 Nmmsup2 λ - 085


γS - 115



The design approach follows the demands in EN 1996-1-1 Here ndash for dominant bending ndash internal force can

be assumed according to following figure

Figure 93 Behaviour of a reinforced masonry structural element under dominant

out-of-plane bending in the ULS

According to EN 1996-1-1 this is allowed only if the axial stress σd does not exceed 03fd If the axial stress

exceeds 03fd the design has to be carried out assuming an unreinforced member according EN 1996-1-1

(2005) 612 and 62 This design has to follow the load type vertical loading (s chapter 5)

The bending resistance is determined

(74)

with

(75)

A limitation of MRd to ensure a ductile behaviour is given by

(76)

The shear resistance for out-of-plane loaded reinforce masonry walls is generally not relevant If high out-of

ndashplane shear loadings appear following failure modes have to be checked

bull Friction sliding in the joint VRdsliding = microFM

bull Failure in the units VRdunit tension faliure = 0065fb λx

If second-order-effects might be relevant for action loadings they can be covered acc to EN 1996-1-1 200

with the formulation already given in section sect723 eq 71


734 Design charts


bull Reference length 1m

bull Partial safety factors 20 resp 115


bull Thickness t=20 cm and 30cm (d=t-4cm)

bull Loadings MRd result from the charts

bull Reinforcement amount 01cmsup2m (per side) op to 10cmsup2m

bull Compression strength 4 and 10 Nmmsup2


Table 24 Properties of the regarded combinations A ndash L of in the design chart

Name t [m] fk [Nmmsup2] A 024 2 B 04 2 C 024 4 D 035 4 E 04 4 F 024 8 G 035 8 H 04 8 I 024 10 J 035 10 K 03 16 L 016 20

0

20

40

60

80

100

120

140

0 2 4 6 8 10 12

as [cmsup2m]

MR

d [kN

mm

]

ABCDEFGHIJKL

Figure 94 Design chart for dominant out-of-plane bending moments in the ULS fyk=500Nmmsup2


0

20

40

60

80

100

120

140

160

0 2 4 6 8 10 12

as [cmsup2m]

MR

d [kN

mm

]

ABCDEFGHIJKL





In spite of reinforced concrete walls are predominantly shear walls resisting to in-plane vertical and lateral

loads it is needed to know its out-of-plane resistance as these walls can also be under this type of action

due to seismic loading Besides the distribution of the vertical reinforcement is in part to address the out-of-

plane resistance of the wall

The design for out-of-plane loads of reinforced concrete masonry walls was made based on the walls with

the geometry and vertical reinforcement distribution already presented in section 64 Walls with different

lengths proportional to the dimensions of the real scale concrete units (400 mm x 200 mm x 190 mm + 1

mm of joint) 08 m 16m 280 40m and 56m Considering that the storey height of the walls is commonly

about 280m height to length ratios of 35 175 10 07 and 05 were taken into the definition of the design

charts corresponding to out-of-plane loading see Figure 77 Besides the aspect ratio also the amount of

vertical and horizontal reinforcement was taken into account in the design charts


ratio Five vertical reinforcement ratios were also used to create the design charts respecting spacing limits

of EN1996-1-1 An example of he variation of vertical reinforcement for wall with HL=100 is presented in

Figure 78 A height of 2800 mm was considered for all masonry walls studied since it is the common value

used in Portuguese buildings

In terms of boundary conditions the walls can be fixed at bottom and top edges by the concrete slabs (2

edges restrained) also by lateral stiffening walls (3 or 4 sides restrained)









required Table 20 gives the main parameters adopted for the creation of the design charts see section

642


743 Out-of-plane wall design



other dimensions and on the other hand the shears loads can not be significant

According to EN1996-1-1 the design of out-of-plane walls under flexure can be made with the same

formulation used in case of in-plane walls (section 623) see Figure 96 For the common applications of the

reinforced concrete walls the slenderness ratio is inferior to 12 The reinforced masonry members with a

slenderness ratio greater than 12 may be designed using the principles and application rules for

unreinforced members taking into account second order effects by an additional design moment

xεm

εsc

εst

Figure 96 ndash Strain distribution in out-of-plane wall section

In spite of according to the EN1996-1-1 the out-of-plane resistance of reinforced masonry walls can be made

based on bending only if the design vertical loading is lower than 03 (σdlt03fd) of the compressive

resistance of the walls it was decided to obtain the interaction diagrams N-M also for the out-of plane

loading as shown in 744

744 Design charts

According to the formulation previously presented some design charts can be proposed to help the design of

reinforced masonry walls These diagrams allow do some observations about the behaviour of reinforced

masonry Flexure capacity of walls decreases with the increasing of the aspect ratio as in case of in-plane

walls This behaviour is expected because the reduction of the resistant section of the wall see Figure 97


-500 0 500 1000 1500 2000 2500 3000 3500 40000

20

40

60

80

100

120

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Mom

ent (

kNm

)

Normal (kN) Figure 97 Design chart M x N for UMINHO reinforced masonry system with variation of HL

According to EN1996-1-1 vertical reinforcement has influence in flexural behaviour of masonry walls

Figure 98 showed that the increasing the vertical reinforcement leads to an improvement in flexural


-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000

20

40

60

80

100

120

ρv = 0035

ρv = 0049 ρv = 0070 ρv = 0091

Mom

ent (

kNm

)

Normal (kN)(a)

-500 0 500 1000 1500 2000 2500 30000

10

20

30

40

50

60

70

80

90

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Mom

ent (

kNm

)

Normal (kN)(b)

-500 0 500 1000 1500 200005

101520253035404550556065

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Mom

ent (

kNm

)

Normal (kN)(c)

-300 0 300 600 900 12000

5

10

15

20

25

30

35

40

ρv = 0037

ρv = 0049 ρv = 0070 ρv = 0086

Mom

ent (

kNm

)

Normal (kN)(d)


-100 0 100 200 300 400 500 6000

2

4

6

8

10

12

14

16

18

20

ρv = 0049

ρv = 0070 ρv = 0098

Mom

ent (

kNm

)

Normal (kN) (e)

Figure 98 Design chart M x N for UMINHO reinforced masonry system (Variation of vertical reinforcement ratio HL=050) (a) HL = 050 (b) HL = 070 (c) HL = 100 (d) HL = 175 and (e) HL = 350


8 OTHER DESIGN ASPECTS

81 DURABILITY

For the durability of reinforced masonry the corrosion of the reinforcement is the relevant issue Generally it

can be solved using corrosion resistant steel (not considered here) or by adequate protection (place in

mortar place in concrete zinc coating) According to the local exposure conditions (climate conditions

moisture) the level of protection for reinforcing steel has to be determined

The demands are give in the following table (EN 1996-1-1 2005 433)

Table 25 Protection level for the reinforcement steel depending on the exposure class

(EN 1996-1-1 2005 433)

82 SERVICEABILITY LIMIT STATE

The serviceability limit state is for common types of structures generally covered by the design process

within the ultimate limit state (ULS) and the additional code requirements - especially demands on the

minimum strength of the materials (units mortar infill reinforcement) and the minimum reinforcement ratio

Also the minimum thickness (corresponding slenderness) has to be checked

Relevant types of construction where SLS might become relevant can be


bull Very tall exterior slim walls with wind loading and low axial force

=gt dynamic effects effective stiffness swinging

bull Exterior walls with low axial forces and earth pressure

=gt deformation under dominant bending effective stiffness assuming gapping

For these types of constructions the loadings and the behaviour of the structural elements have to be

investigated in a deepened manner


REFERENCES

ACI 530-05ASCE 5-05TMS 402-05 (2005) ldquoBuilding code requirements for masonry structuresrdquo Masonry

Standards Joint Committee

AS 3700 (2001) ldquoMasonry Structuresrdquo Standards Australia International Sydney 2001

AMRHEIN JE (1998) ldquoReinforced masonry engineering handbookrdquo Masonry Institute of America amp CRC

Press Boca Raton New York

AAVV (1992) ldquoMasonry Structural Design for Buildingsrdquo Publication Number TM 5-809-3 Departments of

the Army (Corps of Engineers)

BS 5628-2 (2005) Code of practice for the use of masonry ndash Part 2 Structural Use of reinforced and

prestressed masonry

DELIVERABLE D12bis (2006) ldquoData-base of experimental resultsrdquo Issued by UNIPD DISWall COOP-CT-

2005-018120

DELIVERABLE D55 (2007) ldquoTechnical report with the experimental results on materials and masonry walls

the agreement between experimental and numerical resultsrdquo Issued by UMINHO DISWall COOP-CT-2005-

018120

DM 14012008 (2008) Technical Standards for Constructions

EN 1990 (2002) ldquoEurocode - Basis of structural designrdquo

EN 1991-1-1 (2002) ldquoEurocode 1 Actions on structures - Part 1-1 General actions - Densities self-weight

imposed loads for buildingsrdquo

EN 1991-1-3 (2003) ldquoEurocode 1 - Actions on structures - Part 1-3 General actions - Snow loadsrdquo

EN 1991-1-4 (2005) ldquoEurocode 1 Actions on structures - General actions - Part 1-4 Wind actionsrdquo

EN 1992-1-1 (2004) ldquoEurocode 2 - Design of concrete structures - Part 1-1 General rules and rules for

buildingsrdquo

EN 1996-1-1 (2005) ldquoEurocode 6 - Design of masonry structures - Part 1-1 General rules for reinforced and

unreinforced masonry structuresrdquo

EN 1998-1-1 (2004) ldquoEurocode 8 - Design of structures for earthquake resistance - Part 1 General rules

seismic actions and rules for buildingsrdquo

LAWRENCE S PAGE A (1999) ldquoDesign of Clay Masonry for wind amp earthquakerdquo Clay Brick and Paver

Institute Baulkham Hills Australia downloadable from httpwwwthinkbrickcomauindexcfm66F69F44-

EE34-C88B-8B8F-141E78E86E7Aampsearch_option=technical_manuals

LAWRENCE S PAGE A (2004) ldquoDesign of Clay Masonry for compressionrdquo Clay Brick and Paver Institute

Baulkham Hills Australia downloadable from httpwwwthinkbrickcomauindexcfm66F69F44-EE34-

C88B-8B8F-141E78E86E7Aampsearch_option=technical_manuals

NZS 4230 (2004) ldquoCode of practice for the design of masonry structuresrdquo Standards Association of New

Zeland Wellingston

OPCM 3274 (2003) Technical Standards for the seismic design evaluation and upgrading of buildings(and

subsequent updating in Italian)


OPCM 3431 (2005) Technical Standards for the seismic design evaluation and upgrading of buildings (in

Italian)

SCHNEIDER RR DICKEY WL (1980) ldquoReinforced masonry designrdquo Prentice-Hall Inc Englewood Cliffs

New Jersey

TASSIOS TP (1998) ldquoMeccanica delle muraturardquo Liguori Editore Napoli (in italian)

TOMAZEVIC M (1999) Earthquake-Resistant design of masonry buildings ndash vol I Series on Innovation in

structures and Construction Elnashai A S amp Dowling P J


ANNEX EXPLANATORY NOTES FOR THE USE OF THE SOFTWARE

As part of the project deliverable D63 it was foreseen to produce the So-Wall software for the reinforced

masonry walls verification Information on how to use the software are given in this annex as the software is

based on the design rules reported in section from sect 5 to sect 7 The software allows calculating the resisting

parameters of reinforced masonry walls made with the different construction technologies developed and

tested in the framework of the DISWall project ie reinforced masonry with perforated clay units for resisting

mainly in-plane (ALAN system) and out-of-plane (CISEDIL system) load with hollow clay units (UNIPOR)

with concrete units (CampA) The designer on the basis of the analyses carried out and the knowledge of the

design values of the applied axial load shear and bending moment can carry out the masonry wall

verifications using the So-Wall

The Software code is running within the MS-Excel programme using Visual Basic Scripts Therefore for the

use of the software the execution of macros has to be enabled At the beginning the type of dominant

loading has to be chosen

bull in-plane loadings

or

bull out-of-plane loadings

As suitable design approaches for the general interaction of the two types of loadings does not exist the

user has to make further investigation when relevant interaction is assumed The software carries out the

design process in the Ultimate-Limit-State (ULS) according to the rules presented in this report (D62) If the

Serviceability Limit State (SLS) is not covered by the ULS additional investigation have to be performed by

the user The durability has to be ensured by further checks acc EN 1996-1-1 2005 eg climate conditions

or coating of the reinforcement according to what is reported in section sect 8

For the out-of-plane loadings the relevant design action is the bending in vertical direction For the in-plane

loadings the relevant action is the combined N-M-V loading As reinforced masonry is generally not intended

for axial tension forces this type of loading is not covered by this design software

When the type of loading for which carrying out the verification is inserted the type of masonry has to be

selected By doing this the software automatically switch the calculation of correct formulations according to

what is written in section from sect5 to sect7

Then according to the type of loading the length l and the thickness t of the wall has to be entered (in-plane

loading) or the width b the thickness h and the position of the reinforcement d (out-of-plane loading) have to

be entered (see Figure 99) Some minimum limitations on the geometry are already given by the software

and they reflect the configuration of the developed construction systems The amount of the horizontal and

vertical reinforcement has also to be entered If no horizontal reinforcement is applied the corresponding

value has to be set to zero The effect of opening on the behaviour of reinforced masonry structural elements

has to be considered by dividing the whole wall in several sub-elements


Figure 99 Cross section for out-of-plane and in-plane loadings

A list of value of mechanical parameters has to be inserted next These values regard the unit mortar

concrete and reinforcement mechanical properties The symbols used in this section are self-explanatory

and in any case each parameter found into the software is explained in detail into the present deliverable

D62 The compression strength of masonry is calculated according EN 1996-1-1 2005 (pressing the

Calculate f_k button) or entered directly by the user as input parameter For the compression strength of

ALAN masonry the factored compressive strength is directly evaluated by the software given the material

properties and the wall length For the UNIPOR system the approaches from EN 1992 are taken into account

including long term effect of the concrete

The choice of the partial safety factors are made by the user After entering the design loadings the

calculation is started pressing the Design-button The result is given within few seconds The result can also

be checked in the V-N-M-chart Here in the Nd-Md-range the allowable shear loadings VRd are plotted with

different symbols and colours The design action is marked directly within the chart In the main page a

message indicates whereas the masonry section is verified or if not an error message stating which

parameter is outside the safety range is given

For the developers an Admin-Button is available By pressing it all the cells of the worksheet are visible and

can be modified In the end-user version this button and also all worksheets except for the Design- and V-N-

M-Chart-sheets that give the resisting domain of the masonry walls are hidden and protected by a

password


INDEX

INDEX 2 1 INTRODUCTION 5

11 DESCRIPTION AND OBJECTIVES OF THE WORK PACKAGE 5 12 OBJECTIVES AND STRUCTURE OF THE DELIVERABLE 5

2 TYPES OF CONSTRUCTION 6 21 RESIDENTIAL BUILDINGS 6 22 SERVICE COMMERCIAL AND INDUSTRIAL BUILDINGS 7

3 DESCRIPTION OF THE CONSTRUCTION SYSTEMS 10 31 PERFORATED CLAY UNITS 10

311 Perforated clay units for in-plane masonry walls 10 312 Perforated clay units for out-of-plane masonry walls 11

32 HOLLOW CLAY UNITS 12 33 CONCRETE MASONRY UNITS 14

4 GENERAL DESIGN ASPECTS 16 41 LOADING CONDITIONS 16

411 Vertical loading 16 412 Wind loading 18 413 Earthquake loading 19 414 Ultimate limit states load combinations and partial safety factors 22 415 Loading conditions in different National Codes 25

42 STRUCTURAL BEHAVIOUR 27 421 Vertical loading 27 422 Wind loading 27 423 Earthquake loading 28

43 MECHANISM OF LOAD TRANSMISSION 31 431 Vertical loading 31 432 Horizontal loading 31 433 Effect of openings 32

5 DESIGN OF WALLS FOR VERTICAL LOADING 34 51 INTRODUCTION 34 52 PERFORATED CLAY UNITS 35

521 Geometry and boundary conditions 35 522 Material properties 39 523 Design for vertical loading 41 524 Design charts 42
















1 INTRODUCTION



















































(MN Italy)



(PR Italy)












































Precast RC shed



















312)









detail























masonry system























insulation










25cm ie 425 mmsup2m
























obtained

(a)

(b)























given































412 Wind loading






the turbulent wind









(43)


(44)











































(46a)

(46b)

(46c)

(46d)













1998-1-1]






(47)



(48a)

(48b)

(48c)

(48d)


spectra








(49a)

(49b)

(49c)

(49d)























(410a)

(410b)







favourable 090 000 100 000 100 000




of actions

(411)





ψEi = φ ψ2i (412)









(413)



















































beams








422 Wind loading





























satisfied







of the floor area












analysis y


rx ge ls (414b)






















enlargement




Figure 22d)


































51 INTRODUCTION


























vertical edges



tef = ρt t (51)








hef = ρn h (52)






if hl le 35

(53a)

if hl gt 35

(53b)


if hl le 115

(54a)

if hl gt 115

(54b)















0

2

4

6

8

10

12

14

16

18

50 54 58 62 66 70 74 78 82 86 90 94 98 102

106

110

114

118

122

126

130

134

138

142

146

150

154

158

162

166

170 ht

λ

λ2 (e le 025 t)λ2 (e gt 025 t)




ratio)


00

01

02

03

04

05

06

07

08

09

10

053

065

080

095

110

125

140

155

170

185

200

215

230

245

260

275

290

305

320

335

350

365

380

395

410

425

440

455

470

485

500 hl

ρ






0

1

2

3

4

5

6

7

8

9

10

50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600

l (cm)

λ





0

2

4

6

8

10

12

14

16

18

20

50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600

l (cm)

λ


















(55)





(G4) Vertical Holes








vh

kvvkhhk AA

fAfAf

++

= (56)











Masonry columns

Masonry panels

Masonry system

l (mm) 630 920 1550

fexp (Nmm2) 559 271 390

fth (eq 56) (Nmm2) - - 388

Error () - - 0005


10

15

20

25

30

35

40

45

50

55

60

500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500 3750 4000 4250

lw (mm)

f (Nmm2)

fexpfdα fd


the wall



































524 Design charts


750 mm1000 mm

1250 mm1500 mm

1750 mm2000 mm

2250 mm2500 mm

2750 mm3000 mm3250 mm3500 mm

4000 mm4250 mm

50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)


3750 mm

500 mm


150 400 mm


50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)





50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)





50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash14 mm

2oslash16 mm


4oslash16 mm




50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash16 mm

2oslash18 mm

2oslash20 mm

4oslash16 mm




50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash18 mm

2oslash20 mm

4oslash16 mm





50200

350500650

800950

11001250

140015501700

185020002150

23002450

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash20 mm

4oslash16 mm




50200

350500650

800950

110012501400

155017001850

20002150

23002450

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash20 mm

4oslash16 mm








0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)





eccentricity






























a reduction of 08


column

column

M

ccckeffd s

lff sdotsdot

=γ

α (57)












0

5

10

15

20

25

30

35

40

00 05 10 15 20 25 30 35 40



0

5

10

15

20

25

30

35

40

00 05 10 15 20 25 30 35 40




stress-strain-curve

0

5

10

15

20

25

30

35

40

00 20 40 60 80 100 120 140 160



0

5

10

15

20

25

30

35

40

00 20 40 60 80 100 120 140 160



stress-strain-curve




equation

( ) ( ) ( )c u sc u s

A A AE









fy yield strength








Hole 5000 3000












































fcmas


fcmas

corr cal fcmas


182 SU-VC-NM

136

163 SU-VC

353

168

mean 162

327 050 283 057

236 SU-SCC 445

216

mean 226

327 069 346 065

247 DU-SCC

438 175

mean 211

286 074 304 069

223 DU-SCC-DR 399

234

mean 229

295 078 272 084

261 DU-SCC-SR 365

257

mean 259

321 081 317 082


0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3






0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3








0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35







0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35






0

5

10

15

20

25

30

35

0 05 1 15 2 25 3 35





0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35











SdRd NN ge (58)













comparison


534 Design charts













the design charts










105 (lt12)










Material properties















544 Design charts

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

Nrd

(kN

)

(et)




00 01 02 03 04 050

500

1000

1500

2000

2500

3000L=160cm

As = 0036 As = 0045 As = 0074 As = 011 As = 017

Nrd

(kN

)

(et)

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

As = 0035 As = 0045 As = 0070 As = 011 As = 018

Nrd

(kN

)

(et)

L=280cm

(a) (b)



00 01 02 03 04 050

500

1000

1500

2000

2500

3000

As = 0022 As = 0034 As = 0045 As = 0070 As = 010

Nrd

(kN

)

(et)

L=400cm

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

3500

As = 0022 As = 0034 As = 0045 As = 0070 As = 010

Nrd

(kN

)

(et)

L=560cm

(a) (b)





61 INTRODUCTION













1 2 3R R R RV V V V= + + (61)



























NZS 4230 (2004) ltfC

ltN

vd 8080tan90

02 sdot⎟⎠

⎞⎜⎝

⎛+

sdotα lt

stfA

fC ydswvd 80)

80( 01 sdot

sdot+ 0

ACI 530 (2005) Nftl

VLM

d 250)7514(0830 +minus slfA ydsw 50 0

















































(62)






















is reliable













0

50

100

150

200

250

0 50 100 150 200 250 300 350 400

NEd (kN)

MRd (kNm)



5-150 400 mm


NTC 1500 mm

EC6 1500 mm

100

150

200

250

300

0 100 200 300 400 500 600

NEd (kN)

VRd (kN)



RNDZ-5-150 400 mm






















624 Design charts


500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm

2250 mm2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm

0

200

400

600

800

1000

1200

1400

1600

1800

2000

00 02 04 06 08 10 12 14σd (Nmm2)

MRd (kNm)




500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm

2250 mm2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 200 400 600 800 1000 1200 1400 1600

NEd (kN)

MRd (kNm)








100

150

200

250

300

350

400

450

500

550

00 02 04 06 08 10 12 14

σd (Nmm2)

VRd (kN)



500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm2250 mm

2500 mm2750 mm

3000 mm3250 mm

3500 mm

3750 mm4000 mm

4250 mm

100

150

200

250

300

350

400

450

500

550

0 200 400 600 800 1000 1200 1400 1600

NEd (kN)

VRd (kN)






0

200

400

600

800

1000

1200

1400

1600

1800

2000

-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400

NRd (kN)



500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm2250 mm

2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm




100

150

200

250

300

350

400

450

500

550

0 250 500 750 1000 1250 1500 1750 2000

MRd (kNm)

VRd (kN)







0

10

20

30

40

50

60

70

-400 -300 -200 -100 0 100 200 300 400 500 600 700 800 900

NRd (kN)

MRd (kNm)




0

50

100

150

200

250

-400 -200 0 200 400 600 800 1000 1200

NRd (kN)

MRd (kNm)




0

50

100

150

200

250

300

350

400

-400 -200 0 200 400 600 800 1000 1200 1400

NRd (kN)

MRd (kNm)




0

100

200

300

400

500

600

-400 -200 0 200 400 600 800 1000 1200 1400 1600

NRd (kN)

MRd (kNm)




0

100

200

300

400

500

600

700

800

900

-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800

NRd (kN)

MRd (kNm)




0

200

400

600

800

1000

1200

-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000

NRd (kN)

MRd (kNm)

2oslash18 mm

2oslash20 mm

4oslash16 mm




0

200

400

600

800

1000

1200

1400

-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

NRd (kN)

MRd (kNm)

2oslash20 mm

4oslash16 mm



0

300

600

900

1200

1500

1800

-600 -300 0 300 600 900 1200 1500 1800 2100 2400

NRd (kN)

MRd (kNm)

2oslash20 mm

4oslash16 mm




1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm


100

110

120

130

140

150

0 10 20 30 40 50 60 70 80 90 100

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


100

110

120

130

140

150

160

170

180

190

200

0 25 50 75 100 125 150 175 200 225 250

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


150

160

170

180

190

200

210

220

230

240

250

50 100 150 200 250 300 350 400 450

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


160

180

200

220

240

260

280

300

150 200 250 300 350 400 450 500 550 600 650

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm



200

220

240

260

280

300

320

340

360

250 300 350 400 450 500 550 600 650 700 750 800 850

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


220

240

260

280

300

320

340

360

380

400

420

350 450 550 650 750 850 950 1050 1150

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


240

260

280

300

320

340

360

380

400

420

440

460

550 650 750 850 950 1050 1150 1250 1350 1450

MRd (kNm)

VRd (kN)

2oslash20 mm

4oslash16 mm

σd = 01 Nmmsup2

σd = 02 Nmmsup2

σd = 03 Nmmsup2


σd = 06 Nmmsup2

σd = 07 Nmmsup2

σd = 08 Nmmsup2

σd ge 09 Nmmsup2


RNDZ-5-150 400 mm


280

300

320

340

360

380

400

420

440

460

480

500

520

650 750 850 950 1050 1150 1250 1350 1450 1550 1650 1750 1850

MRd (kNm)

VRd (kN)

2oslash20 mm

4oslash16 mm

σd = 01 Nmmsup2

σd = 02 Nmmsup2

σd = 03 Nmmsup2


σd = 06 Nmmsup2

σd = 07 Nmmsup2

σd = 08 Nmmsup2

σd ge 09 Nmmsup2


RNDZ-5-150 400 mm
















relevant






significantly







fck Nmm2SCC



















(63)

(64)

(65)

(66)





634 Design charts











Vd (MdNd) [kN]-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250

Md [kNm]

Nd [

kN]

0 10 20

30 40 50

60 70 80

90 Loadings




Vd (MdNd) [kN]-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250

Md [kNm]

Nd [

kN]

0 10 20

30 40 50

60 70 80

90 Loadings




Vd (MdNd) [kN]-3500

-3000

-2500

-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250 300 350 400 450

Md [kNm]

Nd [

kN]

0 20 40

60 80 100

120 140 160

180 Loadings



Vd (MdNd) [kN]-3500

-3000

-2500

-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250 300 350 400 450

Md [kNm]

Nd [

kN]

0 20 40

60 80 100

120 140 160

180 Loadings




Vd (MdNd) [kN]-5000

-4000

-3000

-2000

-1000

0

1000

0 200 400 600 800 1000 1200 1400 1600

Md [kNm]

Nd [

kN]

0 30 60

90 120 150

180 210 240

270 Loadings



Vd (MdNd) [kN]-5000

-4000

-3000

-2000

-1000

0

1000

0 200 400 600 800 1000 1200 1400 1600

Md [kNm]

Nd [

kN]

0 30 60

90 120 150

180 210 240

270 Loadings




Vd (MdNd) [kN]-9000

-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

0 500 1000 1500 2000 2500 3000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings



Vd (MdNd) [kN]-9000

-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings




Vd (MdNd) [kN]-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000 3500 4000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings



Vd (MdNd) [kN]-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000 3500 4000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings





-12000

-10000

-8000

-6000

-4000

-2000

0

2000

0 1000 2000 3000 4000 5000 6000 7000

Md [kNm]

Nd [

kN]

0 70 140

210 280 350

420 490 560

630 Loadings




-12000

-10000

-8000

-6000

-4000

-2000

0

2000

0 1000 2000 3000 4000 5000 6000 7000

Md [kNm]

Nd [

kN]

0 70 140

210 280 350

420 490 560

630 Loadings







































Material properties

fb Nmm2 1000

fm Nmm2 1000

K - 045

α - 070

β - 030

fk Nmm2 450

γM - 150

fd Nmm2 300

fyk0 Nmm2 020

fyk Nmm2 500

γS - 115

fyd Nmm2 43478

E Nmm2 210000

εyd permil 207



















xdx i

sim

minus=

minus εε (67)

sissi E εσ = (68)

summinus=i

sim FFN (69)

xtfF wam 80= (610)



sum ⎟⎠⎞

⎜⎝⎛ minus+⎟

⎠⎞

⎜⎝⎛ minus==

i

wisi

wmfR

bdFx

bFzHM

240

2 (612)



σ400 += vv ff bv ff 0650le (614)










644 Design charts







stress of 2 MPa

-500 0 500 1000 1500 2000 2500 3000 3500 40000

500

1000

1500

2000

2500

3000

3500

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Mom

ent (

kNm

)

Normal (kN) (a)

-500 0 500 1000 1500 2000 2500 3000 3500 40000

100

200

300

400

500

600

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Shea

r (kN

)

Normal (kN) (b)

0 500 1000 1500 2000 2500 3000 35000

100

200

300

400

500

600

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

She

ar (k

N)

Moment (kNm) (c)


(c) V x M





-500 0 500 1000 1500 2000100

150

200

250

300

350

400

450

500

ρh = 0035 ρ

h = 0049

ρh = 0098

Shea

r (kN

)

Normal (kN) (a)

0 100 200 300 400 500 600 700 800 900 1000

150

200

250

300

350

400

450

ρh = 0035 ρh = 0049 ρh = 0098

Shea

r (kN

)

Moment (kNm) (b)






-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000

500

1000

1500

2000

2500

3000

3500

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091

Mom

ent (

kNm

)

Normal (kN) (a)

0 400 800 1200 1600 2000 2400 2800 3200 3600

200

250

300

350

400

450

500

550

600

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091

Shea

r (kN

)

Moment (kNm) (b)




-500 0 500 1000 1500 2000 2500 30000

200

400

600

800

1000

1200

1400

1600

1800

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Mom

ent (

kNm

)

Normal (kN) (a)

-200 0 200 400 600 800 1000 1200 1400 1600 1800150

200

250

300

350

400

450

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Shea

r (kN

)

Moment (kNm) (b)



-500 0 500 1000 1500 20000

100

200

300

400

500

600

700

800

900

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Mom

ent (

kNm

)

Normal (kN) (a)

0 200 400 600 800 1000100

150

200

250

300

350

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Shea

r (kN

)

Moment (kNm) (b)




-300 0 300 600 900 12000

50

100

150

200

250

300

ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086

Mom

ent (

kNm

)

Normal (kN) (a)

-50 0 50 100 150 200 250 300

120

150

180

210

240

ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086

Shea

r (kN

)

Moment (kNm) (b)



-100 0 100 200 300 400 500 6000

10

20

30

40

50

60

70

ρv = 0049 ρv = 0070 ρv = 0098M

omen

t (kN

m)

Normal (kN) (a)

-10 0 10 20 30 40 50 60 7090

100

110

120

130

140

150

ρv = 0049 ρv = 0070 ρv = 0098

Shea

r (kN

)

Moment (kNm) (b)





71 INTRODUCTION






































Material property

CISEDIL













(71)














⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛minus=

Lxvy

2cos1max

π (72)




max2

2

41 v

LEJM

ry

base

π==⎟

⎠⎞


















N kN 50 50 50 M kNm 702 148 85

vmax mm 296 296 296




















724 Design charts


TensionCompression

Limit 2-3

Limit 3-4

Limit 4-5

Limit 5-6

Limit 60

50

100

150

200

250

300

350

-10000 -8000 -6000 -4000 -2000 0 2000 4000

NRd (kN)

MRd (kNm)






0

5

10

15

20

25

30

35

0 5 10 15 20 25 30 35

N (kN)

MRD (kNm)


t = 380 mm λ ge 12 Feb 44k




0

1

2

3

4

5

6

7

0 10 20 30 40 50

N (kN)

LIdeg (kN)

rmC-45m

rmC-5m

rmC-6m

rmC-7m

rmC-8m

t = 380 mm λ gt 12 Feb 44k

















fck Nmm2SCC




γS - 115











(74)

with

(75)


(76)








734 Design charts












0

20

40

60

80

100

120

140

0 2 4 6 8 10 12

as [cmsup2m]

MR

d [kN

mm

]

ABCDEFGHIJKL



0

20

40

60

80

100

120

140

160

0 2 4 6 8 10 12

as [cmsup2m]

MR

d [kN

mm

]

ABCDEFGHIJKL
































642











xεm

εsc

εst






744 Design charts






-500 0 500 1000 1500 2000 2500 3000 3500 40000

20

40

60

80

100

120

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Mom

ent (

kNm

)





-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000

20

40

60

80

100

120

ρv = 0035

ρv = 0049 ρv = 0070 ρv = 0091

Mom

ent (

kNm

)

Normal (kN)(a)

-500 0 500 1000 1500 2000 2500 30000

10

20

30

40

50

60

70

80

90

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Mom

ent (

kNm

)

Normal (kN)(b)

-500 0 500 1000 1500 200005

101520253035404550556065

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Mom

ent (

kNm

)

Normal (kN)(c)

-300 0 300 600 900 12000

5

10

15

20

25

30

35

40

ρv = 0037

ρv = 0049 ρv = 0070 ρv = 0086

Mom

ent (

kNm

)

Normal (kN)(d)


-100 0 100 200 300 400 500 6000

2

4

6

8

10

12

14

16

18

20

ρv = 0049

ρv = 0070 ρv = 0098

Mom

ent (

kNm

)

Normal (kN) (e)




81 DURABILITY







(EN 1996-1-1 2005 433)















REFERENCES









prestressed masonry


2005-018120



018120








buildingsrdquo












Zeland Wellingston





Italian)


New Jersey



















or








































password
















1 INTRODUCTION



















































(MN Italy)



(PR Italy)












































Precast RC shed



















312)









detail























masonry system























insulation










25cm ie 425 mmsup2m
























obtained

(a)

(b)























given































412 Wind loading






the turbulent wind









(43)


(44)











































(46a)

(46b)

(46c)

(46d)













1998-1-1]






(47)



(48a)

(48b)

(48c)

(48d)


spectra








(49a)

(49b)

(49c)

(49d)























(410a)

(410b)







favourable 090 000 100 000 100 000




of actions

(411)





ψEi = φ ψ2i (412)









(413)



















































beams








422 Wind loading





























satisfied







of the floor area












analysis y


rx ge ls (414b)






















enlargement




Figure 22d)


































51 INTRODUCTION


























vertical edges



tef = ρt t (51)








hef = ρn h (52)






if hl le 35

(53a)

if hl gt 35

(53b)


if hl le 115

(54a)

if hl gt 115

(54b)















0

2

4

6

8

10

12

14

16

18

50 54 58 62 66 70 74 78 82 86 90 94 98 102

106

110

114

118

122

126

130

134

138

142

146

150

154

158

162

166

170 ht

λ

λ2 (e le 025 t)λ2 (e gt 025 t)




ratio)


00

01

02

03

04

05

06

07

08

09

10

053

065

080

095

110

125

140

155

170

185

200

215

230

245

260

275

290

305

320

335

350

365

380

395

410

425

440

455

470

485

500 hl

ρ






0

1

2

3

4

5

6

7

8

9

10

50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600

l (cm)

λ





0

2

4

6

8

10

12

14

16

18

20

50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600

l (cm)

λ


















(55)





(G4) Vertical Holes








vh

kvvkhhk AA

fAfAf

++

= (56)











Masonry columns

Masonry panels

Masonry system

l (mm) 630 920 1550

fexp (Nmm2) 559 271 390

fth (eq 56) (Nmm2) - - 388

Error () - - 0005


10

15

20

25

30

35

40

45

50

55

60

500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500 3750 4000 4250

lw (mm)

f (Nmm2)

fexpfdα fd


the wall



































524 Design charts


750 mm1000 mm

1250 mm1500 mm

1750 mm2000 mm

2250 mm2500 mm

2750 mm3000 mm3250 mm3500 mm

4000 mm4250 mm

50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)


3750 mm

500 mm


150 400 mm


50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)





50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)





50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash14 mm

2oslash16 mm


4oslash16 mm




50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash16 mm

2oslash18 mm

2oslash20 mm

4oslash16 mm




50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash18 mm

2oslash20 mm

4oslash16 mm





50200

350500650

800950

11001250

140015501700

185020002150

23002450

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash20 mm

4oslash16 mm




50200

350500650

800950

110012501400

155017001850

20002150

23002450

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash20 mm

4oslash16 mm








0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)





eccentricity






























a reduction of 08


column

column

M

ccckeffd s

lff sdotsdot

=γ

α (57)












0

5

10

15

20

25

30

35

40

00 05 10 15 20 25 30 35 40



0

5

10

15

20

25

30

35

40

00 05 10 15 20 25 30 35 40




stress-strain-curve

0

5

10

15

20

25

30

35

40

00 20 40 60 80 100 120 140 160



0

5

10

15

20

25

30

35

40

00 20 40 60 80 100 120 140 160



stress-strain-curve




equation

( ) ( ) ( )c u sc u s

A A AE









fy yield strength








Hole 5000 3000












































fcmas


fcmas

corr cal fcmas


182 SU-VC-NM

136

163 SU-VC

353

168

mean 162

327 050 283 057

236 SU-SCC 445

216

mean 226

327 069 346 065

247 DU-SCC

438 175

mean 211

286 074 304 069

223 DU-SCC-DR 399

234

mean 229

295 078 272 084

261 DU-SCC-SR 365

257

mean 259

321 081 317 082


0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3






0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3








0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35







0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35






0

5

10

15

20

25

30

35

0 05 1 15 2 25 3 35





0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35











SdRd NN ge (58)













comparison


534 Design charts













the design charts










105 (lt12)










Material properties















544 Design charts

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

Nrd

(kN

)

(et)




00 01 02 03 04 050

500

1000

1500

2000

2500

3000L=160cm

As = 0036 As = 0045 As = 0074 As = 011 As = 017

Nrd

(kN

)

(et)

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

As = 0035 As = 0045 As = 0070 As = 011 As = 018

Nrd

(kN

)

(et)

L=280cm

(a) (b)



00 01 02 03 04 050

500

1000

1500

2000

2500

3000

As = 0022 As = 0034 As = 0045 As = 0070 As = 010

Nrd

(kN

)

(et)

L=400cm

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

3500

As = 0022 As = 0034 As = 0045 As = 0070 As = 010

Nrd

(kN

)

(et)

L=560cm

(a) (b)





61 INTRODUCTION













1 2 3R R R RV V V V= + + (61)



























NZS 4230 (2004) ltfC

ltN

vd 8080tan90

02 sdot⎟⎠

⎞⎜⎝

⎛+

sdotα lt

stfA

fC ydswvd 80)

80( 01 sdot

sdot+ 0

ACI 530 (2005) Nftl

VLM

d 250)7514(0830 +minus slfA ydsw 50 0

















































(62)






















is reliable













0

50

100

150

200

250

0 50 100 150 200 250 300 350 400

NEd (kN)

MRd (kNm)



5-150 400 mm


NTC 1500 mm

EC6 1500 mm

100

150

200

250

300

0 100 200 300 400 500 600

NEd (kN)

VRd (kN)



RNDZ-5-150 400 mm






















624 Design charts


500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm

2250 mm2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm

0

200

400

600

800

1000

1200

1400

1600

1800

2000

00 02 04 06 08 10 12 14σd (Nmm2)

MRd (kNm)




500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm

2250 mm2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 200 400 600 800 1000 1200 1400 1600

NEd (kN)

MRd (kNm)








100

150

200

250

300

350

400

450

500

550

00 02 04 06 08 10 12 14

σd (Nmm2)

VRd (kN)



500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm2250 mm

2500 mm2750 mm

3000 mm3250 mm

3500 mm

3750 mm4000 mm

4250 mm

100

150

200

250

300

350

400

450

500

550

0 200 400 600 800 1000 1200 1400 1600

NEd (kN)

VRd (kN)






0

200

400

600

800

1000

1200

1400

1600

1800

2000

-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400

NRd (kN)



500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm2250 mm

2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm




100

150

200

250

300

350

400

450

500

550

0 250 500 750 1000 1250 1500 1750 2000

MRd (kNm)

VRd (kN)







0

10

20

30

40

50

60

70

-400 -300 -200 -100 0 100 200 300 400 500 600 700 800 900

NRd (kN)

MRd (kNm)




0

50

100

150

200

250

-400 -200 0 200 400 600 800 1000 1200

NRd (kN)

MRd (kNm)




0

50

100

150

200

250

300

350

400

-400 -200 0 200 400 600 800 1000 1200 1400

NRd (kN)

MRd (kNm)




0

100

200

300

400

500

600

-400 -200 0 200 400 600 800 1000 1200 1400 1600

NRd (kN)

MRd (kNm)




0

100

200

300

400

500

600

700

800

900

-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800

NRd (kN)

MRd (kNm)




0

200

400

600

800

1000

1200

-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000

NRd (kN)

MRd (kNm)

2oslash18 mm

2oslash20 mm

4oslash16 mm




0

200

400

600

800

1000

1200

1400

-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

NRd (kN)

MRd (kNm)

2oslash20 mm

4oslash16 mm



0

300

600

900

1200

1500

1800

-600 -300 0 300 600 900 1200 1500 1800 2100 2400

NRd (kN)

MRd (kNm)

2oslash20 mm

4oslash16 mm




1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm


100

110

120

130

140

150

0 10 20 30 40 50 60 70 80 90 100

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


100

110

120

130

140

150

160

170

180

190

200

0 25 50 75 100 125 150 175 200 225 250

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


150

160

170

180

190

200

210

220

230

240

250

50 100 150 200 250 300 350 400 450

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


160

180

200

220

240

260

280

300

150 200 250 300 350 400 450 500 550 600 650

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm



200

220

240

260

280

300

320

340

360

250 300 350 400 450 500 550 600 650 700 750 800 850

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


220

240

260

280

300

320

340

360

380

400

420

350 450 550 650 750 850 950 1050 1150

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


240

260

280

300

320

340

360

380

400

420

440

460

550 650 750 850 950 1050 1150 1250 1350 1450

MRd (kNm)

VRd (kN)

2oslash20 mm

4oslash16 mm

σd = 01 Nmmsup2

σd = 02 Nmmsup2

σd = 03 Nmmsup2


σd = 06 Nmmsup2

σd = 07 Nmmsup2

σd = 08 Nmmsup2

σd ge 09 Nmmsup2


RNDZ-5-150 400 mm


280

300

320

340

360

380

400

420

440

460

480

500

520

650 750 850 950 1050 1150 1250 1350 1450 1550 1650 1750 1850

MRd (kNm)

VRd (kN)

2oslash20 mm

4oslash16 mm

σd = 01 Nmmsup2

σd = 02 Nmmsup2

σd = 03 Nmmsup2


σd = 06 Nmmsup2

σd = 07 Nmmsup2

σd = 08 Nmmsup2

σd ge 09 Nmmsup2


RNDZ-5-150 400 mm
















relevant






significantly







fck Nmm2SCC



















(63)

(64)

(65)

(66)





634 Design charts











Vd (MdNd) [kN]-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250

Md [kNm]

Nd [

kN]

0 10 20

30 40 50

60 70 80

90 Loadings




Vd (MdNd) [kN]-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250

Md [kNm]

Nd [

kN]

0 10 20

30 40 50

60 70 80

90 Loadings




Vd (MdNd) [kN]-3500

-3000

-2500

-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250 300 350 400 450

Md [kNm]

Nd [

kN]

0 20 40

60 80 100

120 140 160

180 Loadings



Vd (MdNd) [kN]-3500

-3000

-2500

-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250 300 350 400 450

Md [kNm]

Nd [

kN]

0 20 40

60 80 100

120 140 160

180 Loadings




Vd (MdNd) [kN]-5000

-4000

-3000

-2000

-1000

0

1000

0 200 400 600 800 1000 1200 1400 1600

Md [kNm]

Nd [

kN]

0 30 60

90 120 150

180 210 240

270 Loadings



Vd (MdNd) [kN]-5000

-4000

-3000

-2000

-1000

0

1000

0 200 400 600 800 1000 1200 1400 1600

Md [kNm]

Nd [

kN]

0 30 60

90 120 150

180 210 240

270 Loadings




Vd (MdNd) [kN]-9000

-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

0 500 1000 1500 2000 2500 3000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings



Vd (MdNd) [kN]-9000

-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings




Vd (MdNd) [kN]-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000 3500 4000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings



Vd (MdNd) [kN]-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000 3500 4000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings





-12000

-10000

-8000

-6000

-4000

-2000

0

2000

0 1000 2000 3000 4000 5000 6000 7000

Md [kNm]

Nd [

kN]

0 70 140

210 280 350

420 490 560

630 Loadings




-12000

-10000

-8000

-6000

-4000

-2000

0

2000

0 1000 2000 3000 4000 5000 6000 7000

Md [kNm]

Nd [

kN]

0 70 140

210 280 350

420 490 560

630 Loadings







































Material properties

fb Nmm2 1000

fm Nmm2 1000

K - 045

α - 070

β - 030

fk Nmm2 450

γM - 150

fd Nmm2 300

fyk0 Nmm2 020

fyk Nmm2 500

γS - 115

fyd Nmm2 43478

E Nmm2 210000

εyd permil 207



















xdx i

sim

minus=

minus εε (67)

sissi E εσ = (68)

summinus=i

sim FFN (69)

xtfF wam 80= (610)



sum ⎟⎠⎞

⎜⎝⎛ minus+⎟

⎠⎞

⎜⎝⎛ minus==

i

wisi

wmfR

bdFx

bFzHM

240

2 (612)



σ400 += vv ff bv ff 0650le (614)










644 Design charts







stress of 2 MPa

-500 0 500 1000 1500 2000 2500 3000 3500 40000

500

1000

1500

2000

2500

3000

3500

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Mom

ent (

kNm

)

Normal (kN) (a)

-500 0 500 1000 1500 2000 2500 3000 3500 40000

100

200

300

400

500

600

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Shea

r (kN

)

Normal (kN) (b)

0 500 1000 1500 2000 2500 3000 35000

100

200

300

400

500

600

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

She

ar (k

N)

Moment (kNm) (c)


(c) V x M





-500 0 500 1000 1500 2000100

150

200

250

300

350

400

450

500

ρh = 0035 ρ

h = 0049

ρh = 0098

Shea

r (kN

)

Normal (kN) (a)

0 100 200 300 400 500 600 700 800 900 1000

150

200

250

300

350

400

450

ρh = 0035 ρh = 0049 ρh = 0098

Shea

r (kN

)

Moment (kNm) (b)






-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000

500

1000

1500

2000

2500

3000

3500

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091

Mom

ent (

kNm

)

Normal (kN) (a)

0 400 800 1200 1600 2000 2400 2800 3200 3600

200

250

300

350

400

450

500

550

600

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091

Shea

r (kN

)

Moment (kNm) (b)




-500 0 500 1000 1500 2000 2500 30000

200

400

600

800

1000

1200

1400

1600

1800

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Mom

ent (

kNm

)

Normal (kN) (a)

-200 0 200 400 600 800 1000 1200 1400 1600 1800150

200

250

300

350

400

450

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Shea

r (kN

)

Moment (kNm) (b)



-500 0 500 1000 1500 20000

100

200

300

400

500

600

700

800

900

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Mom

ent (

kNm

)

Normal (kN) (a)

0 200 400 600 800 1000100

150

200

250

300

350

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Shea

r (kN

)

Moment (kNm) (b)




-300 0 300 600 900 12000

50

100

150

200

250

300

ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086

Mom

ent (

kNm

)

Normal (kN) (a)

-50 0 50 100 150 200 250 300

120

150

180

210

240

ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086

Shea

r (kN

)

Moment (kNm) (b)



-100 0 100 200 300 400 500 6000

10

20

30

40

50

60

70

ρv = 0049 ρv = 0070 ρv = 0098M

omen

t (kN

m)

Normal (kN) (a)

-10 0 10 20 30 40 50 60 7090

100

110

120

130

140

150

ρv = 0049 ρv = 0070 ρv = 0098

Shea

r (kN

)

Moment (kNm) (b)





71 INTRODUCTION






































Material property

CISEDIL













(71)














⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛minus=

Lxvy

2cos1max

π (72)




max2

2

41 v

LEJM

ry

base

π==⎟

⎠⎞


















N kN 50 50 50 M kNm 702 148 85

vmax mm 296 296 296




















724 Design charts


TensionCompression

Limit 2-3

Limit 3-4

Limit 4-5

Limit 5-6

Limit 60

50

100

150

200

250

300

350

-10000 -8000 -6000 -4000 -2000 0 2000 4000

NRd (kN)

MRd (kNm)






0

5

10

15

20

25

30

35

0 5 10 15 20 25 30 35

N (kN)

MRD (kNm)


t = 380 mm λ ge 12 Feb 44k




0

1

2

3

4

5

6

7

0 10 20 30 40 50

N (kN)

LIdeg (kN)

rmC-45m

rmC-5m

rmC-6m

rmC-7m

rmC-8m

t = 380 mm λ gt 12 Feb 44k

















fck Nmm2SCC




γS - 115











(74)

with

(75)


(76)








734 Design charts












0

20

40

60

80

100

120

140

0 2 4 6 8 10 12

as [cmsup2m]

MR

d [kN

mm

]

ABCDEFGHIJKL



0

20

40

60

80

100

120

140

160

0 2 4 6 8 10 12

as [cmsup2m]

MR

d [kN

mm

]

ABCDEFGHIJKL
































642











xεm

εsc

εst






744 Design charts






-500 0 500 1000 1500 2000 2500 3000 3500 40000

20

40

60

80

100

120

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Mom

ent (

kNm

)





-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000

20

40

60

80

100

120

ρv = 0035

ρv = 0049 ρv = 0070 ρv = 0091

Mom

ent (

kNm

)

Normal (kN)(a)

-500 0 500 1000 1500 2000 2500 30000

10

20

30

40

50

60

70

80

90

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Mom

ent (

kNm

)

Normal (kN)(b)

-500 0 500 1000 1500 200005

101520253035404550556065

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Mom

ent (

kNm

)

Normal (kN)(c)

-300 0 300 600 900 12000

5

10

15

20

25

30

35

40

ρv = 0037

ρv = 0049 ρv = 0070 ρv = 0086

Mom

ent (

kNm

)

Normal (kN)(d)


-100 0 100 200 300 400 500 6000

2

4

6

8

10

12

14

16

18

20

ρv = 0049

ρv = 0070 ρv = 0098

Mom

ent (

kNm

)

Normal (kN) (e)




81 DURABILITY







(EN 1996-1-1 2005 433)















REFERENCES









prestressed masonry


2005-018120



018120








buildingsrdquo












Zeland Wellingston





Italian)


New Jersey



















or








































password






1 INTRODUCTION



















































(MN Italy)



(PR Italy)












































Precast RC shed



















312)









detail























masonry system























insulation










25cm ie 425 mmsup2m
























obtained

(a)

(b)























given































412 Wind loading






the turbulent wind









(43)


(44)











































(46a)

(46b)

(46c)

(46d)













1998-1-1]






(47)



(48a)

(48b)

(48c)

(48d)


spectra








(49a)

(49b)

(49c)

(49d)























(410a)

(410b)







favourable 090 000 100 000 100 000




of actions

(411)





ψEi = φ ψ2i (412)









(413)



















































beams








422 Wind loading





























satisfied







of the floor area












analysis y


rx ge ls (414b)






















enlargement




Figure 22d)


































51 INTRODUCTION


























vertical edges



tef = ρt t (51)








hef = ρn h (52)






if hl le 35

(53a)

if hl gt 35

(53b)


if hl le 115

(54a)

if hl gt 115

(54b)















0

2

4

6

8

10

12

14

16

18

50 54 58 62 66 70 74 78 82 86 90 94 98 102

106

110

114

118

122

126

130

134

138

142

146

150

154

158

162

166

170 ht

λ

λ2 (e le 025 t)λ2 (e gt 025 t)




ratio)


00

01

02

03

04

05

06

07

08

09

10

053

065

080

095

110

125

140

155

170

185

200

215

230

245

260

275

290

305

320

335

350

365

380

395

410

425

440

455

470

485

500 hl

ρ






0

1

2

3

4

5

6

7

8

9

10

50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600

l (cm)

λ





0

2

4

6

8

10

12

14

16

18

20

50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600

l (cm)

λ


















(55)





(G4) Vertical Holes








vh

kvvkhhk AA

fAfAf

++

= (56)











Masonry columns

Masonry panels

Masonry system

l (mm) 630 920 1550

fexp (Nmm2) 559 271 390

fth (eq 56) (Nmm2) - - 388

Error () - - 0005


10

15

20

25

30

35

40

45

50

55

60

500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500 3750 4000 4250

lw (mm)

f (Nmm2)

fexpfdα fd


the wall



































524 Design charts


750 mm1000 mm

1250 mm1500 mm

1750 mm2000 mm

2250 mm2500 mm

2750 mm3000 mm3250 mm3500 mm

4000 mm4250 mm

50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)


3750 mm

500 mm


150 400 mm


50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)





50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)





50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash14 mm

2oslash16 mm


4oslash16 mm




50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash16 mm

2oslash18 mm

2oslash20 mm

4oslash16 mm




50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash18 mm

2oslash20 mm

4oslash16 mm





50200

350500650

800950

11001250

140015501700

185020002150

23002450

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash20 mm

4oslash16 mm




50200

350500650

800950

110012501400

155017001850

20002150

23002450

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash20 mm

4oslash16 mm








0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)





eccentricity






























a reduction of 08


column

column

M

ccckeffd s

lff sdotsdot

=γ

α (57)












0

5

10

15

20

25

30

35

40

00 05 10 15 20 25 30 35 40



0

5

10

15

20

25

30

35

40

00 05 10 15 20 25 30 35 40




stress-strain-curve

0

5

10

15

20

25

30

35

40

00 20 40 60 80 100 120 140 160



0

5

10

15

20

25

30

35

40

00 20 40 60 80 100 120 140 160



stress-strain-curve




equation

( ) ( ) ( )c u sc u s

A A AE









fy yield strength








Hole 5000 3000












































fcmas


fcmas

corr cal fcmas


182 SU-VC-NM

136

163 SU-VC

353

168

mean 162

327 050 283 057

236 SU-SCC 445

216

mean 226

327 069 346 065

247 DU-SCC

438 175

mean 211

286 074 304 069

223 DU-SCC-DR 399

234

mean 229

295 078 272 084

261 DU-SCC-SR 365

257

mean 259

321 081 317 082


0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3






0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3








0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35







0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35






0

5

10

15

20

25

30

35

0 05 1 15 2 25 3 35





0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35











SdRd NN ge (58)













comparison


534 Design charts













the design charts










105 (lt12)










Material properties















544 Design charts

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

Nrd

(kN

)

(et)




00 01 02 03 04 050

500

1000

1500

2000

2500

3000L=160cm

As = 0036 As = 0045 As = 0074 As = 011 As = 017

Nrd

(kN

)

(et)

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

As = 0035 As = 0045 As = 0070 As = 011 As = 018

Nrd

(kN

)

(et)

L=280cm

(a) (b)



00 01 02 03 04 050

500

1000

1500

2000

2500

3000

As = 0022 As = 0034 As = 0045 As = 0070 As = 010

Nrd

(kN

)

(et)

L=400cm

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

3500

As = 0022 As = 0034 As = 0045 As = 0070 As = 010

Nrd

(kN

)

(et)

L=560cm

(a) (b)





61 INTRODUCTION













1 2 3R R R RV V V V= + + (61)



























NZS 4230 (2004) ltfC

ltN

vd 8080tan90

02 sdot⎟⎠

⎞⎜⎝

⎛+

sdotα lt

stfA

fC ydswvd 80)

80( 01 sdot

sdot+ 0

ACI 530 (2005) Nftl

VLM

d 250)7514(0830 +minus slfA ydsw 50 0

















































(62)






















is reliable













0

50

100

150

200

250

0 50 100 150 200 250 300 350 400

NEd (kN)

MRd (kNm)



5-150 400 mm


NTC 1500 mm

EC6 1500 mm

100

150

200

250

300

0 100 200 300 400 500 600

NEd (kN)

VRd (kN)



RNDZ-5-150 400 mm






















624 Design charts


500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm

2250 mm2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm

0

200

400

600

800

1000

1200

1400

1600

1800

2000

00 02 04 06 08 10 12 14σd (Nmm2)

MRd (kNm)




500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm

2250 mm2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 200 400 600 800 1000 1200 1400 1600

NEd (kN)

MRd (kNm)








100

150

200

250

300

350

400

450

500

550

00 02 04 06 08 10 12 14

σd (Nmm2)

VRd (kN)



500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm2250 mm

2500 mm2750 mm

3000 mm3250 mm

3500 mm

3750 mm4000 mm

4250 mm

100

150

200

250

300

350

400

450

500

550

0 200 400 600 800 1000 1200 1400 1600

NEd (kN)

VRd (kN)






0

200

400

600

800

1000

1200

1400

1600

1800

2000

-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400

NRd (kN)



500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm2250 mm

2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm




100

150

200

250

300

350

400

450

500

550

0 250 500 750 1000 1250 1500 1750 2000

MRd (kNm)

VRd (kN)







0

10

20

30

40

50

60

70

-400 -300 -200 -100 0 100 200 300 400 500 600 700 800 900

NRd (kN)

MRd (kNm)




0

50

100

150

200

250

-400 -200 0 200 400 600 800 1000 1200

NRd (kN)

MRd (kNm)




0

50

100

150

200

250

300

350

400

-400 -200 0 200 400 600 800 1000 1200 1400

NRd (kN)

MRd (kNm)




0

100

200

300

400

500

600

-400 -200 0 200 400 600 800 1000 1200 1400 1600

NRd (kN)

MRd (kNm)




0

100

200

300

400

500

600

700

800

900

-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800

NRd (kN)

MRd (kNm)




0

200

400

600

800

1000

1200

-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000

NRd (kN)

MRd (kNm)

2oslash18 mm

2oslash20 mm

4oslash16 mm




0

200

400

600

800

1000

1200

1400

-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

NRd (kN)

MRd (kNm)

2oslash20 mm

4oslash16 mm



0

300

600

900

1200

1500

1800

-600 -300 0 300 600 900 1200 1500 1800 2100 2400

NRd (kN)

MRd (kNm)

2oslash20 mm

4oslash16 mm




1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm


100

110

120

130

140

150

0 10 20 30 40 50 60 70 80 90 100

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


100

110

120

130

140

150

160

170

180

190

200

0 25 50 75 100 125 150 175 200 225 250

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


150

160

170

180

190

200

210

220

230

240

250

50 100 150 200 250 300 350 400 450

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


160

180

200

220

240

260

280

300

150 200 250 300 350 400 450 500 550 600 650

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm



200

220

240

260

280

300

320

340

360

250 300 350 400 450 500 550 600 650 700 750 800 850

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


220

240

260

280

300

320

340

360

380

400

420

350 450 550 650 750 850 950 1050 1150

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


240

260

280

300

320

340

360

380

400

420

440

460

550 650 750 850 950 1050 1150 1250 1350 1450

MRd (kNm)

VRd (kN)

2oslash20 mm

4oslash16 mm

σd = 01 Nmmsup2

σd = 02 Nmmsup2

σd = 03 Nmmsup2


σd = 06 Nmmsup2

σd = 07 Nmmsup2

σd = 08 Nmmsup2

σd ge 09 Nmmsup2


RNDZ-5-150 400 mm


280

300

320

340

360

380

400

420

440

460

480

500

520

650 750 850 950 1050 1150 1250 1350 1450 1550 1650 1750 1850

MRd (kNm)

VRd (kN)

2oslash20 mm

4oslash16 mm

σd = 01 Nmmsup2

σd = 02 Nmmsup2

σd = 03 Nmmsup2


σd = 06 Nmmsup2

σd = 07 Nmmsup2

σd = 08 Nmmsup2

σd ge 09 Nmmsup2


RNDZ-5-150 400 mm
















relevant






significantly







fck Nmm2SCC



















(63)

(64)

(65)

(66)





634 Design charts











Vd (MdNd) [kN]-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250

Md [kNm]

Nd [

kN]

0 10 20

30 40 50

60 70 80

90 Loadings




Vd (MdNd) [kN]-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250

Md [kNm]

Nd [

kN]

0 10 20

30 40 50

60 70 80

90 Loadings




Vd (MdNd) [kN]-3500

-3000

-2500

-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250 300 350 400 450

Md [kNm]

Nd [

kN]

0 20 40

60 80 100

120 140 160

180 Loadings



Vd (MdNd) [kN]-3500

-3000

-2500

-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250 300 350 400 450

Md [kNm]

Nd [

kN]

0 20 40

60 80 100

120 140 160

180 Loadings




Vd (MdNd) [kN]-5000

-4000

-3000

-2000

-1000

0

1000

0 200 400 600 800 1000 1200 1400 1600

Md [kNm]

Nd [

kN]

0 30 60

90 120 150

180 210 240

270 Loadings



Vd (MdNd) [kN]-5000

-4000

-3000

-2000

-1000

0

1000

0 200 400 600 800 1000 1200 1400 1600

Md [kNm]

Nd [

kN]

0 30 60

90 120 150

180 210 240

270 Loadings




Vd (MdNd) [kN]-9000

-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

0 500 1000 1500 2000 2500 3000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings



Vd (MdNd) [kN]-9000

-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings




Vd (MdNd) [kN]-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000 3500 4000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings



Vd (MdNd) [kN]-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000 3500 4000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings





-12000

-10000

-8000

-6000

-4000

-2000

0

2000

0 1000 2000 3000 4000 5000 6000 7000

Md [kNm]

Nd [

kN]

0 70 140

210 280 350

420 490 560

630 Loadings




-12000

-10000

-8000

-6000

-4000

-2000

0

2000

0 1000 2000 3000 4000 5000 6000 7000

Md [kNm]

Nd [

kN]

0 70 140

210 280 350

420 490 560

630 Loadings







































Material properties

fb Nmm2 1000

fm Nmm2 1000

K - 045

α - 070

β - 030

fk Nmm2 450

γM - 150

fd Nmm2 300

fyk0 Nmm2 020

fyk Nmm2 500

γS - 115

fyd Nmm2 43478

E Nmm2 210000

εyd permil 207



















xdx i

sim

minus=

minus εε (67)

sissi E εσ = (68)

summinus=i

sim FFN (69)

xtfF wam 80= (610)



sum ⎟⎠⎞

⎜⎝⎛ minus+⎟

⎠⎞

⎜⎝⎛ minus==

i

wisi

wmfR

bdFx

bFzHM

240

2 (612)



σ400 += vv ff bv ff 0650le (614)










644 Design charts







stress of 2 MPa

-500 0 500 1000 1500 2000 2500 3000 3500 40000

500

1000

1500

2000

2500

3000

3500

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Mom

ent (

kNm

)

Normal (kN) (a)

-500 0 500 1000 1500 2000 2500 3000 3500 40000

100

200

300

400

500

600

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Shea

r (kN

)

Normal (kN) (b)

0 500 1000 1500 2000 2500 3000 35000

100

200

300

400

500

600

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

She

ar (k

N)

Moment (kNm) (c)


(c) V x M





-500 0 500 1000 1500 2000100

150

200

250

300

350

400

450

500

ρh = 0035 ρ

h = 0049

ρh = 0098

Shea

r (kN

)

Normal (kN) (a)

0 100 200 300 400 500 600 700 800 900 1000

150

200

250

300

350

400

450

ρh = 0035 ρh = 0049 ρh = 0098

Shea

r (kN

)

Moment (kNm) (b)






-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000

500

1000

1500

2000

2500

3000

3500

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091

Mom

ent (

kNm

)

Normal (kN) (a)

0 400 800 1200 1600 2000 2400 2800 3200 3600

200

250

300

350

400

450

500

550

600

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091

Shea

r (kN

)

Moment (kNm) (b)




-500 0 500 1000 1500 2000 2500 30000

200

400

600

800

1000

1200

1400

1600

1800

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Mom

ent (

kNm

)

Normal (kN) (a)

-200 0 200 400 600 800 1000 1200 1400 1600 1800150

200

250

300

350

400

450

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Shea

r (kN

)

Moment (kNm) (b)



-500 0 500 1000 1500 20000

100

200

300

400

500

600

700

800

900

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Mom

ent (

kNm

)

Normal (kN) (a)

0 200 400 600 800 1000100

150

200

250

300

350

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Shea

r (kN

)

Moment (kNm) (b)




-300 0 300 600 900 12000

50

100

150

200

250

300

ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086

Mom

ent (

kNm

)

Normal (kN) (a)

-50 0 50 100 150 200 250 300

120

150

180

210

240

ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086

Shea

r (kN

)

Moment (kNm) (b)



-100 0 100 200 300 400 500 6000

10

20

30

40

50

60

70

ρv = 0049 ρv = 0070 ρv = 0098M

omen

t (kN

m)

Normal (kN) (a)

-10 0 10 20 30 40 50 60 7090

100

110

120

130

140

150

ρv = 0049 ρv = 0070 ρv = 0098

Shea

r (kN

)

Moment (kNm) (b)





71 INTRODUCTION






































Material property

CISEDIL













(71)














⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛minus=

Lxvy

2cos1max

π (72)




max2

2

41 v

LEJM

ry

base

π==⎟

⎠⎞


















N kN 50 50 50 M kNm 702 148 85

vmax mm 296 296 296




















724 Design charts


TensionCompression

Limit 2-3

Limit 3-4

Limit 4-5

Limit 5-6

Limit 60

50

100

150

200

250

300

350

-10000 -8000 -6000 -4000 -2000 0 2000 4000

NRd (kN)

MRd (kNm)






0

5

10

15

20

25

30

35

0 5 10 15 20 25 30 35

N (kN)

MRD (kNm)


t = 380 mm λ ge 12 Feb 44k




0

1

2

3

4

5

6

7

0 10 20 30 40 50

N (kN)

LIdeg (kN)

rmC-45m

rmC-5m

rmC-6m

rmC-7m

rmC-8m

t = 380 mm λ gt 12 Feb 44k

















fck Nmm2SCC




γS - 115











(74)

with

(75)


(76)








734 Design charts












0

20

40

60

80

100

120

140

0 2 4 6 8 10 12

as [cmsup2m]

MR

d [kN

mm

]

ABCDEFGHIJKL



0

20

40

60

80

100

120

140

160

0 2 4 6 8 10 12

as [cmsup2m]

MR

d [kN

mm

]

ABCDEFGHIJKL
































642











xεm

εsc

εst






744 Design charts






-500 0 500 1000 1500 2000 2500 3000 3500 40000

20

40

60

80

100

120

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Mom

ent (

kNm

)





-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000

20

40

60

80

100

120

ρv = 0035

ρv = 0049 ρv = 0070 ρv = 0091

Mom

ent (

kNm

)

Normal (kN)(a)

-500 0 500 1000 1500 2000 2500 30000

10

20

30

40

50

60

70

80

90

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Mom

ent (

kNm

)

Normal (kN)(b)

-500 0 500 1000 1500 200005

101520253035404550556065

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Mom

ent (

kNm

)

Normal (kN)(c)

-300 0 300 600 900 12000

5

10

15

20

25

30

35

40

ρv = 0037

ρv = 0049 ρv = 0070 ρv = 0086

Mom

ent (

kNm

)

Normal (kN)(d)


-100 0 100 200 300 400 500 6000

2

4

6

8

10

12

14

16

18

20

ρv = 0049

ρv = 0070 ρv = 0098

Mom

ent (

kNm

)

Normal (kN) (e)




81 DURABILITY







(EN 1996-1-1 2005 433)















REFERENCES









prestressed masonry


2005-018120



018120








buildingsrdquo












Zeland Wellingston





Italian)


New Jersey



















or








































password


1 INTRODUCTION



















































(MN Italy)



(PR Italy)












































Precast RC shed



















312)









detail























masonry system























insulation










25cm ie 425 mmsup2m
























obtained

(a)

(b)























given































412 Wind loading






the turbulent wind









(43)


(44)











































(46a)

(46b)

(46c)

(46d)













1998-1-1]






(47)



(48a)

(48b)

(48c)

(48d)


spectra








(49a)

(49b)

(49c)

(49d)























(410a)

(410b)







favourable 090 000 100 000 100 000




of actions

(411)





ψEi = φ ψ2i (412)









(413)



















































beams








422 Wind loading





























satisfied







of the floor area












analysis y


rx ge ls (414b)






















enlargement




Figure 22d)


































51 INTRODUCTION


























vertical edges



tef = ρt t (51)








hef = ρn h (52)






if hl le 35

(53a)

if hl gt 35

(53b)


if hl le 115

(54a)

if hl gt 115

(54b)















0

2

4

6

8

10

12

14

16

18

50 54 58 62 66 70 74 78 82 86 90 94 98 102

106

110

114

118

122

126

130

134

138

142

146

150

154

158

162

166

170 ht

λ

λ2 (e le 025 t)λ2 (e gt 025 t)




ratio)


00

01

02

03

04

05

06

07

08

09

10

053

065

080

095

110

125

140

155

170

185

200

215

230

245

260

275

290

305

320

335

350

365

380

395

410

425

440

455

470

485

500 hl

ρ






0

1

2

3

4

5

6

7

8

9

10

50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600

l (cm)

λ





0

2

4

6

8

10

12

14

16

18

20

50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600

l (cm)

λ


















(55)





(G4) Vertical Holes








vh

kvvkhhk AA

fAfAf

++

= (56)











Masonry columns

Masonry panels

Masonry system

l (mm) 630 920 1550

fexp (Nmm2) 559 271 390

fth (eq 56) (Nmm2) - - 388

Error () - - 0005


10

15

20

25

30

35

40

45

50

55

60

500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500 3750 4000 4250

lw (mm)

f (Nmm2)

fexpfdα fd


the wall



































524 Design charts


750 mm1000 mm

1250 mm1500 mm

1750 mm2000 mm

2250 mm2500 mm

2750 mm3000 mm3250 mm3500 mm

4000 mm4250 mm

50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)


3750 mm

500 mm


150 400 mm


50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)





50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)





50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash14 mm

2oslash16 mm


4oslash16 mm




50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash16 mm

2oslash18 mm

2oslash20 mm

4oslash16 mm




50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash18 mm

2oslash20 mm

4oslash16 mm





50200

350500650

800950

11001250

140015501700

185020002150

23002450

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash20 mm

4oslash16 mm




50200

350500650

800950

110012501400

155017001850

20002150

23002450

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash20 mm

4oslash16 mm








0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)





eccentricity






























a reduction of 08


column

column

M

ccckeffd s

lff sdotsdot

=γ

α (57)












0

5

10

15

20

25

30

35

40

00 05 10 15 20 25 30 35 40



0

5

10

15

20

25

30

35

40

00 05 10 15 20 25 30 35 40




stress-strain-curve

0

5

10

15

20

25

30

35

40

00 20 40 60 80 100 120 140 160



0

5

10

15

20

25

30

35

40

00 20 40 60 80 100 120 140 160



stress-strain-curve




equation

( ) ( ) ( )c u sc u s

A A AE









fy yield strength








Hole 5000 3000












































fcmas


fcmas

corr cal fcmas


182 SU-VC-NM

136

163 SU-VC

353

168

mean 162

327 050 283 057

236 SU-SCC 445

216

mean 226

327 069 346 065

247 DU-SCC

438 175

mean 211

286 074 304 069

223 DU-SCC-DR 399

234

mean 229

295 078 272 084

261 DU-SCC-SR 365

257

mean 259

321 081 317 082


0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3






0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3








0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35







0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35






0

5

10

15

20

25

30

35

0 05 1 15 2 25 3 35





0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35











SdRd NN ge (58)













comparison


534 Design charts













the design charts










105 (lt12)










Material properties















544 Design charts

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

Nrd

(kN

)

(et)




00 01 02 03 04 050

500

1000

1500

2000

2500

3000L=160cm

As = 0036 As = 0045 As = 0074 As = 011 As = 017

Nrd

(kN

)

(et)

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

As = 0035 As = 0045 As = 0070 As = 011 As = 018

Nrd

(kN

)

(et)

L=280cm

(a) (b)



00 01 02 03 04 050

500

1000

1500

2000

2500

3000

As = 0022 As = 0034 As = 0045 As = 0070 As = 010

Nrd

(kN

)

(et)

L=400cm

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

3500

As = 0022 As = 0034 As = 0045 As = 0070 As = 010

Nrd

(kN

)

(et)

L=560cm

(a) (b)





61 INTRODUCTION













1 2 3R R R RV V V V= + + (61)



























NZS 4230 (2004) ltfC

ltN

vd 8080tan90

02 sdot⎟⎠

⎞⎜⎝

⎛+

sdotα lt

stfA

fC ydswvd 80)

80( 01 sdot

sdot+ 0

ACI 530 (2005) Nftl

VLM

d 250)7514(0830 +minus slfA ydsw 50 0

















































(62)






















is reliable













0

50

100

150

200

250

0 50 100 150 200 250 300 350 400

NEd (kN)

MRd (kNm)



5-150 400 mm


NTC 1500 mm

EC6 1500 mm

100

150

200

250

300

0 100 200 300 400 500 600

NEd (kN)

VRd (kN)



RNDZ-5-150 400 mm






















624 Design charts


500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm

2250 mm2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm

0

200

400

600

800

1000

1200

1400

1600

1800

2000

00 02 04 06 08 10 12 14σd (Nmm2)

MRd (kNm)




500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm

2250 mm2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 200 400 600 800 1000 1200 1400 1600

NEd (kN)

MRd (kNm)








100

150

200

250

300

350

400

450

500

550

00 02 04 06 08 10 12 14

σd (Nmm2)

VRd (kN)



500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm2250 mm

2500 mm2750 mm

3000 mm3250 mm

3500 mm

3750 mm4000 mm

4250 mm

100

150

200

250

300

350

400

450

500

550

0 200 400 600 800 1000 1200 1400 1600

NEd (kN)

VRd (kN)






0

200

400

600

800

1000

1200

1400

1600

1800

2000

-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400

NRd (kN)



500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm2250 mm

2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm




100

150

200

250

300

350

400

450

500

550

0 250 500 750 1000 1250 1500 1750 2000

MRd (kNm)

VRd (kN)







0

10

20

30

40

50

60

70

-400 -300 -200 -100 0 100 200 300 400 500 600 700 800 900

NRd (kN)

MRd (kNm)




0

50

100

150

200

250

-400 -200 0 200 400 600 800 1000 1200

NRd (kN)

MRd (kNm)




0

50

100

150

200

250

300

350

400

-400 -200 0 200 400 600 800 1000 1200 1400

NRd (kN)

MRd (kNm)




0

100

200

300

400

500

600

-400 -200 0 200 400 600 800 1000 1200 1400 1600

NRd (kN)

MRd (kNm)




0

100

200

300

400

500

600

700

800

900

-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800

NRd (kN)

MRd (kNm)




0

200

400

600

800

1000

1200

-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000

NRd (kN)

MRd (kNm)

2oslash18 mm

2oslash20 mm

4oslash16 mm




0

200

400

600

800

1000

1200

1400

-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

NRd (kN)

MRd (kNm)

2oslash20 mm

4oslash16 mm



0

300

600

900

1200

1500

1800

-600 -300 0 300 600 900 1200 1500 1800 2100 2400

NRd (kN)

MRd (kNm)

2oslash20 mm

4oslash16 mm




1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm


100

110

120

130

140

150

0 10 20 30 40 50 60 70 80 90 100

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


100

110

120

130

140

150

160

170

180

190

200

0 25 50 75 100 125 150 175 200 225 250

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


150

160

170

180

190

200

210

220

230

240

250

50 100 150 200 250 300 350 400 450

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


160

180

200

220

240

260

280

300

150 200 250 300 350 400 450 500 550 600 650

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm



200

220

240

260

280

300

320

340

360

250 300 350 400 450 500 550 600 650 700 750 800 850

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


220

240

260

280

300

320

340

360

380

400

420

350 450 550 650 750 850 950 1050 1150

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


240

260

280

300

320

340

360

380

400

420

440

460

550 650 750 850 950 1050 1150 1250 1350 1450

MRd (kNm)

VRd (kN)

2oslash20 mm

4oslash16 mm

σd = 01 Nmmsup2

σd = 02 Nmmsup2

σd = 03 Nmmsup2


σd = 06 Nmmsup2

σd = 07 Nmmsup2

σd = 08 Nmmsup2

σd ge 09 Nmmsup2


RNDZ-5-150 400 mm


280

300

320

340

360

380

400

420

440

460

480

500

520

650 750 850 950 1050 1150 1250 1350 1450 1550 1650 1750 1850

MRd (kNm)

VRd (kN)

2oslash20 mm

4oslash16 mm

σd = 01 Nmmsup2

σd = 02 Nmmsup2

σd = 03 Nmmsup2


σd = 06 Nmmsup2

σd = 07 Nmmsup2

σd = 08 Nmmsup2

σd ge 09 Nmmsup2


RNDZ-5-150 400 mm
















relevant






significantly







fck Nmm2SCC



















(63)

(64)

(65)

(66)





634 Design charts











Vd (MdNd) [kN]-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250

Md [kNm]

Nd [

kN]

0 10 20

30 40 50

60 70 80

90 Loadings




Vd (MdNd) [kN]-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250

Md [kNm]

Nd [

kN]

0 10 20

30 40 50

60 70 80

90 Loadings




Vd (MdNd) [kN]-3500

-3000

-2500

-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250 300 350 400 450

Md [kNm]

Nd [

kN]

0 20 40

60 80 100

120 140 160

180 Loadings



Vd (MdNd) [kN]-3500

-3000

-2500

-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250 300 350 400 450

Md [kNm]

Nd [

kN]

0 20 40

60 80 100

120 140 160

180 Loadings




Vd (MdNd) [kN]-5000

-4000

-3000

-2000

-1000

0

1000

0 200 400 600 800 1000 1200 1400 1600

Md [kNm]

Nd [

kN]

0 30 60

90 120 150

180 210 240

270 Loadings



Vd (MdNd) [kN]-5000

-4000

-3000

-2000

-1000

0

1000

0 200 400 600 800 1000 1200 1400 1600

Md [kNm]

Nd [

kN]

0 30 60

90 120 150

180 210 240

270 Loadings




Vd (MdNd) [kN]-9000

-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

0 500 1000 1500 2000 2500 3000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings



Vd (MdNd) [kN]-9000

-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings




Vd (MdNd) [kN]-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000 3500 4000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings



Vd (MdNd) [kN]-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000 3500 4000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings





-12000

-10000

-8000

-6000

-4000

-2000

0

2000

0 1000 2000 3000 4000 5000 6000 7000

Md [kNm]

Nd [

kN]

0 70 140

210 280 350

420 490 560

630 Loadings




-12000

-10000

-8000

-6000

-4000

-2000

0

2000

0 1000 2000 3000 4000 5000 6000 7000

Md [kNm]

Nd [

kN]

0 70 140

210 280 350

420 490 560

630 Loadings







































Material properties

fb Nmm2 1000

fm Nmm2 1000

K - 045

α - 070

β - 030

fk Nmm2 450

γM - 150

fd Nmm2 300

fyk0 Nmm2 020

fyk Nmm2 500

γS - 115

fyd Nmm2 43478

E Nmm2 210000

εyd permil 207



















xdx i

sim

minus=

minus εε (67)

sissi E εσ = (68)

summinus=i

sim FFN (69)

xtfF wam 80= (610)



sum ⎟⎠⎞

⎜⎝⎛ minus+⎟

⎠⎞

⎜⎝⎛ minus==

i

wisi

wmfR

bdFx

bFzHM

240

2 (612)



σ400 += vv ff bv ff 0650le (614)










644 Design charts







stress of 2 MPa

-500 0 500 1000 1500 2000 2500 3000 3500 40000

500

1000

1500

2000

2500

3000

3500

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Mom

ent (

kNm

)

Normal (kN) (a)

-500 0 500 1000 1500 2000 2500 3000 3500 40000

100

200

300

400

500

600

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Shea

r (kN

)

Normal (kN) (b)

0 500 1000 1500 2000 2500 3000 35000

100

200

300

400

500

600

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

She

ar (k

N)

Moment (kNm) (c)


(c) V x M





-500 0 500 1000 1500 2000100

150

200

250

300

350

400

450

500

ρh = 0035 ρ

h = 0049

ρh = 0098

Shea

r (kN

)

Normal (kN) (a)

0 100 200 300 400 500 600 700 800 900 1000

150

200

250

300

350

400

450

ρh = 0035 ρh = 0049 ρh = 0098

Shea

r (kN

)

Moment (kNm) (b)






-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000

500

1000

1500

2000

2500

3000

3500

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091

Mom

ent (

kNm

)

Normal (kN) (a)

0 400 800 1200 1600 2000 2400 2800 3200 3600

200

250

300

350

400

450

500

550

600

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091

Shea

r (kN

)

Moment (kNm) (b)




-500 0 500 1000 1500 2000 2500 30000

200

400

600

800

1000

1200

1400

1600

1800

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Mom

ent (

kNm

)

Normal (kN) (a)

-200 0 200 400 600 800 1000 1200 1400 1600 1800150

200

250

300

350

400

450

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Shea

r (kN

)

Moment (kNm) (b)



-500 0 500 1000 1500 20000

100

200

300

400

500

600

700

800

900

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Mom

ent (

kNm

)

Normal (kN) (a)

0 200 400 600 800 1000100

150

200

250

300

350

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Shea

r (kN

)

Moment (kNm) (b)




-300 0 300 600 900 12000

50

100

150

200

250

300

ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086

Mom

ent (

kNm

)

Normal (kN) (a)

-50 0 50 100 150 200 250 300

120

150

180

210

240

ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086

Shea

r (kN

)

Moment (kNm) (b)



-100 0 100 200 300 400 500 6000

10

20

30

40

50

60

70

ρv = 0049 ρv = 0070 ρv = 0098M

omen

t (kN

m)

Normal (kN) (a)

-10 0 10 20 30 40 50 60 7090

100

110

120

130

140

150

ρv = 0049 ρv = 0070 ρv = 0098

Shea

r (kN

)

Moment (kNm) (b)





71 INTRODUCTION






































Material property

CISEDIL













(71)














⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛minus=

Lxvy

2cos1max

π (72)




max2

2

41 v

LEJM

ry

base

π==⎟

⎠⎞


















N kN 50 50 50 M kNm 702 148 85

vmax mm 296 296 296




















724 Design charts


TensionCompression

Limit 2-3

Limit 3-4

Limit 4-5

Limit 5-6

Limit 60

50

100

150

200

250

300

350

-10000 -8000 -6000 -4000 -2000 0 2000 4000

NRd (kN)

MRd (kNm)






0

5

10

15

20

25

30

35

0 5 10 15 20 25 30 35

N (kN)

MRD (kNm)


t = 380 mm λ ge 12 Feb 44k




0

1

2

3

4

5

6

7

0 10 20 30 40 50

N (kN)

LIdeg (kN)

rmC-45m

rmC-5m

rmC-6m

rmC-7m

rmC-8m

t = 380 mm λ gt 12 Feb 44k

















fck Nmm2SCC




γS - 115











(74)

with

(75)


(76)








734 Design charts












0

20

40

60

80

100

120

140

0 2 4 6 8 10 12

as [cmsup2m]

MR

d [kN

mm

]

ABCDEFGHIJKL



0

20

40

60

80

100

120

140

160

0 2 4 6 8 10 12

as [cmsup2m]

MR

d [kN

mm

]

ABCDEFGHIJKL
































642











xεm

εsc

εst






744 Design charts






-500 0 500 1000 1500 2000 2500 3000 3500 40000

20

40

60

80

100

120

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Mom

ent (

kNm

)





-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000

20

40

60

80

100

120

ρv = 0035

ρv = 0049 ρv = 0070 ρv = 0091

Mom

ent (

kNm

)

Normal (kN)(a)

-500 0 500 1000 1500 2000 2500 30000

10

20

30

40

50

60

70

80

90

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Mom

ent (

kNm

)

Normal (kN)(b)

-500 0 500 1000 1500 200005

101520253035404550556065

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Mom

ent (

kNm

)

Normal (kN)(c)

-300 0 300 600 900 12000

5

10

15

20

25

30

35

40

ρv = 0037

ρv = 0049 ρv = 0070 ρv = 0086

Mom

ent (

kNm

)

Normal (kN)(d)


-100 0 100 200 300 400 500 6000

2

4

6

8

10

12

14

16

18

20

ρv = 0049

ρv = 0070 ρv = 0098

Mom

ent (

kNm

)

Normal (kN) (e)




81 DURABILITY







(EN 1996-1-1 2005 433)















REFERENCES









prestressed masonry


2005-018120



018120








buildingsrdquo












Zeland Wellingston





Italian)


New Jersey



















or








































password

















(MN Italy)



(PR Italy)












































Precast RC shed



















312)









detail























masonry system























insulation










25cm ie 425 mmsup2m
























obtained

(a)

(b)























given































412 Wind loading






the turbulent wind









(43)


(44)











































(46a)

(46b)

(46c)

(46d)













1998-1-1]






(47)



(48a)

(48b)

(48c)

(48d)


spectra








(49a)

(49b)

(49c)

(49d)























(410a)

(410b)







favourable 090 000 100 000 100 000




of actions

(411)





ψEi = φ ψ2i (412)









(413)



















































beams








422 Wind loading





























satisfied







of the floor area












analysis y


rx ge ls (414b)






















enlargement




Figure 22d)


































51 INTRODUCTION


























vertical edges



tef = ρt t (51)








hef = ρn h (52)






if hl le 35

(53a)

if hl gt 35

(53b)


if hl le 115

(54a)

if hl gt 115

(54b)















0

2

4

6

8

10

12

14

16

18

50 54 58 62 66 70 74 78 82 86 90 94 98 102

106

110

114

118

122

126

130

134

138

142

146

150

154

158

162

166

170 ht

λ

λ2 (e le 025 t)λ2 (e gt 025 t)




ratio)


00

01

02

03

04

05

06

07

08

09

10

053

065

080

095

110

125

140

155

170

185

200

215

230

245

260

275

290

305

320

335

350

365

380

395

410

425

440

455

470

485

500 hl

ρ






0

1

2

3

4

5

6

7

8

9

10

50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600

l (cm)

λ





0

2

4

6

8

10

12

14

16

18

20

50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600

l (cm)

λ


















(55)





(G4) Vertical Holes








vh

kvvkhhk AA

fAfAf

++

= (56)











Masonry columns

Masonry panels

Masonry system

l (mm) 630 920 1550

fexp (Nmm2) 559 271 390

fth (eq 56) (Nmm2) - - 388

Error () - - 0005


10

15

20

25

30

35

40

45

50

55

60

500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500 3750 4000 4250

lw (mm)

f (Nmm2)

fexpfdα fd


the wall



































524 Design charts


750 mm1000 mm

1250 mm1500 mm

1750 mm2000 mm

2250 mm2500 mm

2750 mm3000 mm3250 mm3500 mm

4000 mm4250 mm

50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)


3750 mm

500 mm


150 400 mm


50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)





50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)





50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash14 mm

2oslash16 mm


4oslash16 mm




50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash16 mm

2oslash18 mm

2oslash20 mm

4oslash16 mm




50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash18 mm

2oslash20 mm

4oslash16 mm





50200

350500650

800950

11001250

140015501700

185020002150

23002450

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash20 mm

4oslash16 mm




50200

350500650

800950

110012501400

155017001850

20002150

23002450

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash20 mm

4oslash16 mm








0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)





eccentricity






























a reduction of 08


column

column

M

ccckeffd s

lff sdotsdot

=γ

α (57)












0

5

10

15

20

25

30

35

40

00 05 10 15 20 25 30 35 40



0

5

10

15

20

25

30

35

40

00 05 10 15 20 25 30 35 40




stress-strain-curve

0

5

10

15

20

25

30

35

40

00 20 40 60 80 100 120 140 160



0

5

10

15

20

25

30

35

40

00 20 40 60 80 100 120 140 160



stress-strain-curve




equation

( ) ( ) ( )c u sc u s

A A AE









fy yield strength








Hole 5000 3000












































fcmas


fcmas

corr cal fcmas


182 SU-VC-NM

136

163 SU-VC

353

168

mean 162

327 050 283 057

236 SU-SCC 445

216

mean 226

327 069 346 065

247 DU-SCC

438 175

mean 211

286 074 304 069

223 DU-SCC-DR 399

234

mean 229

295 078 272 084

261 DU-SCC-SR 365

257

mean 259

321 081 317 082


0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3






0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3








0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35







0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35






0

5

10

15

20

25

30

35

0 05 1 15 2 25 3 35





0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35











SdRd NN ge (58)













comparison


534 Design charts













the design charts










105 (lt12)










Material properties















544 Design charts

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

Nrd

(kN

)

(et)




00 01 02 03 04 050

500

1000

1500

2000

2500

3000L=160cm

As = 0036 As = 0045 As = 0074 As = 011 As = 017

Nrd

(kN

)

(et)

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

As = 0035 As = 0045 As = 0070 As = 011 As = 018

Nrd

(kN

)

(et)

L=280cm

(a) (b)



00 01 02 03 04 050

500

1000

1500

2000

2500

3000

As = 0022 As = 0034 As = 0045 As = 0070 As = 010

Nrd

(kN

)

(et)

L=400cm

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

3500

As = 0022 As = 0034 As = 0045 As = 0070 As = 010

Nrd

(kN

)

(et)

L=560cm

(a) (b)





61 INTRODUCTION













1 2 3R R R RV V V V= + + (61)



























NZS 4230 (2004) ltfC

ltN

vd 8080tan90

02 sdot⎟⎠

⎞⎜⎝

⎛+

sdotα lt

stfA

fC ydswvd 80)

80( 01 sdot

sdot+ 0

ACI 530 (2005) Nftl

VLM

d 250)7514(0830 +minus slfA ydsw 50 0

















































(62)






















is reliable













0

50

100

150

200

250

0 50 100 150 200 250 300 350 400

NEd (kN)

MRd (kNm)



5-150 400 mm


NTC 1500 mm

EC6 1500 mm

100

150

200

250

300

0 100 200 300 400 500 600

NEd (kN)

VRd (kN)



RNDZ-5-150 400 mm






















624 Design charts


500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm

2250 mm2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm

0

200

400

600

800

1000

1200

1400

1600

1800

2000

00 02 04 06 08 10 12 14σd (Nmm2)

MRd (kNm)




500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm

2250 mm2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 200 400 600 800 1000 1200 1400 1600

NEd (kN)

MRd (kNm)








100

150

200

250

300

350

400

450

500

550

00 02 04 06 08 10 12 14

σd (Nmm2)

VRd (kN)



500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm2250 mm

2500 mm2750 mm

3000 mm3250 mm

3500 mm

3750 mm4000 mm

4250 mm

100

150

200

250

300

350

400

450

500

550

0 200 400 600 800 1000 1200 1400 1600

NEd (kN)

VRd (kN)






0

200

400

600

800

1000

1200

1400

1600

1800

2000

-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400

NRd (kN)



500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm2250 mm

2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm




100

150

200

250

300

350

400

450

500

550

0 250 500 750 1000 1250 1500 1750 2000

MRd (kNm)

VRd (kN)







0

10

20

30

40

50

60

70

-400 -300 -200 -100 0 100 200 300 400 500 600 700 800 900

NRd (kN)

MRd (kNm)




0

50

100

150

200

250

-400 -200 0 200 400 600 800 1000 1200

NRd (kN)

MRd (kNm)




0

50

100

150

200

250

300

350

400

-400 -200 0 200 400 600 800 1000 1200 1400

NRd (kN)

MRd (kNm)




0

100

200

300

400

500

600

-400 -200 0 200 400 600 800 1000 1200 1400 1600

NRd (kN)

MRd (kNm)




0

100

200

300

400

500

600

700

800

900

-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800

NRd (kN)

MRd (kNm)




0

200

400

600

800

1000

1200

-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000

NRd (kN)

MRd (kNm)

2oslash18 mm

2oslash20 mm

4oslash16 mm




0

200

400

600

800

1000

1200

1400

-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

NRd (kN)

MRd (kNm)

2oslash20 mm

4oslash16 mm



0

300

600

900

1200

1500

1800

-600 -300 0 300 600 900 1200 1500 1800 2100 2400

NRd (kN)

MRd (kNm)

2oslash20 mm

4oslash16 mm




1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm


100

110

120

130

140

150

0 10 20 30 40 50 60 70 80 90 100

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


100

110

120

130

140

150

160

170

180

190

200

0 25 50 75 100 125 150 175 200 225 250

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


150

160

170

180

190

200

210

220

230

240

250

50 100 150 200 250 300 350 400 450

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


160

180

200

220

240

260

280

300

150 200 250 300 350 400 450 500 550 600 650

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm



200

220

240

260

280

300

320

340

360

250 300 350 400 450 500 550 600 650 700 750 800 850

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


220

240

260

280

300

320

340

360

380

400

420

350 450 550 650 750 850 950 1050 1150

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


240

260

280

300

320

340

360

380

400

420

440

460

550 650 750 850 950 1050 1150 1250 1350 1450

MRd (kNm)

VRd (kN)

2oslash20 mm

4oslash16 mm

σd = 01 Nmmsup2

σd = 02 Nmmsup2

σd = 03 Nmmsup2


σd = 06 Nmmsup2

σd = 07 Nmmsup2

σd = 08 Nmmsup2

σd ge 09 Nmmsup2


RNDZ-5-150 400 mm


280

300

320

340

360

380

400

420

440

460

480

500

520

650 750 850 950 1050 1150 1250 1350 1450 1550 1650 1750 1850

MRd (kNm)

VRd (kN)

2oslash20 mm

4oslash16 mm

σd = 01 Nmmsup2

σd = 02 Nmmsup2

σd = 03 Nmmsup2


σd = 06 Nmmsup2

σd = 07 Nmmsup2

σd = 08 Nmmsup2

σd ge 09 Nmmsup2


RNDZ-5-150 400 mm
















relevant






significantly







fck Nmm2SCC



















(63)

(64)

(65)

(66)





634 Design charts











Vd (MdNd) [kN]-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250

Md [kNm]

Nd [

kN]

0 10 20

30 40 50

60 70 80

90 Loadings




Vd (MdNd) [kN]-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250

Md [kNm]

Nd [

kN]

0 10 20

30 40 50

60 70 80

90 Loadings




Vd (MdNd) [kN]-3500

-3000

-2500

-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250 300 350 400 450

Md [kNm]

Nd [

kN]

0 20 40

60 80 100

120 140 160

180 Loadings



Vd (MdNd) [kN]-3500

-3000

-2500

-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250 300 350 400 450

Md [kNm]

Nd [

kN]

0 20 40

60 80 100

120 140 160

180 Loadings




Vd (MdNd) [kN]-5000

-4000

-3000

-2000

-1000

0

1000

0 200 400 600 800 1000 1200 1400 1600

Md [kNm]

Nd [

kN]

0 30 60

90 120 150

180 210 240

270 Loadings



Vd (MdNd) [kN]-5000

-4000

-3000

-2000

-1000

0

1000

0 200 400 600 800 1000 1200 1400 1600

Md [kNm]

Nd [

kN]

0 30 60

90 120 150

180 210 240

270 Loadings




Vd (MdNd) [kN]-9000

-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

0 500 1000 1500 2000 2500 3000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings



Vd (MdNd) [kN]-9000

-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings




Vd (MdNd) [kN]-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000 3500 4000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings



Vd (MdNd) [kN]-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000 3500 4000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings





-12000

-10000

-8000

-6000

-4000

-2000

0

2000

0 1000 2000 3000 4000 5000 6000 7000

Md [kNm]

Nd [

kN]

0 70 140

210 280 350

420 490 560

630 Loadings




-12000

-10000

-8000

-6000

-4000

-2000

0

2000

0 1000 2000 3000 4000 5000 6000 7000

Md [kNm]

Nd [

kN]

0 70 140

210 280 350

420 490 560

630 Loadings







































Material properties

fb Nmm2 1000

fm Nmm2 1000

K - 045

α - 070

β - 030

fk Nmm2 450

γM - 150

fd Nmm2 300

fyk0 Nmm2 020

fyk Nmm2 500

γS - 115

fyd Nmm2 43478

E Nmm2 210000

εyd permil 207



















xdx i

sim

minus=

minus εε (67)

sissi E εσ = (68)

summinus=i

sim FFN (69)

xtfF wam 80= (610)



sum ⎟⎠⎞

⎜⎝⎛ minus+⎟

⎠⎞

⎜⎝⎛ minus==

i

wisi

wmfR

bdFx

bFzHM

240

2 (612)



σ400 += vv ff bv ff 0650le (614)










644 Design charts







stress of 2 MPa

-500 0 500 1000 1500 2000 2500 3000 3500 40000

500

1000

1500

2000

2500

3000

3500

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Mom

ent (

kNm

)

Normal (kN) (a)

-500 0 500 1000 1500 2000 2500 3000 3500 40000

100

200

300

400

500

600

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Shea

r (kN

)

Normal (kN) (b)

0 500 1000 1500 2000 2500 3000 35000

100

200

300

400

500

600

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

She

ar (k

N)

Moment (kNm) (c)


(c) V x M





-500 0 500 1000 1500 2000100

150

200

250

300

350

400

450

500

ρh = 0035 ρ

h = 0049

ρh = 0098

Shea

r (kN

)

Normal (kN) (a)

0 100 200 300 400 500 600 700 800 900 1000

150

200

250

300

350

400

450

ρh = 0035 ρh = 0049 ρh = 0098

Shea

r (kN

)

Moment (kNm) (b)






-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000

500

1000

1500

2000

2500

3000

3500

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091

Mom

ent (

kNm

)

Normal (kN) (a)

0 400 800 1200 1600 2000 2400 2800 3200 3600

200

250

300

350

400

450

500

550

600

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091

Shea

r (kN

)

Moment (kNm) (b)




-500 0 500 1000 1500 2000 2500 30000

200

400

600

800

1000

1200

1400

1600

1800

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Mom

ent (

kNm

)

Normal (kN) (a)

-200 0 200 400 600 800 1000 1200 1400 1600 1800150

200

250

300

350

400

450

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Shea

r (kN

)

Moment (kNm) (b)



-500 0 500 1000 1500 20000

100

200

300

400

500

600

700

800

900

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Mom

ent (

kNm

)

Normal (kN) (a)

0 200 400 600 800 1000100

150

200

250

300

350

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Shea

r (kN

)

Moment (kNm) (b)




-300 0 300 600 900 12000

50

100

150

200

250

300

ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086

Mom

ent (

kNm

)

Normal (kN) (a)

-50 0 50 100 150 200 250 300

120

150

180

210

240

ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086

Shea

r (kN

)

Moment (kNm) (b)



-100 0 100 200 300 400 500 6000

10

20

30

40

50

60

70

ρv = 0049 ρv = 0070 ρv = 0098M

omen

t (kN

m)

Normal (kN) (a)

-10 0 10 20 30 40 50 60 7090

100

110

120

130

140

150

ρv = 0049 ρv = 0070 ρv = 0098

Shea

r (kN

)

Moment (kNm) (b)





71 INTRODUCTION






































Material property

CISEDIL













(71)














⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛minus=

Lxvy

2cos1max

π (72)




max2

2

41 v

LEJM

ry

base

π==⎟

⎠⎞


















N kN 50 50 50 M kNm 702 148 85

vmax mm 296 296 296




















724 Design charts


TensionCompression

Limit 2-3

Limit 3-4

Limit 4-5

Limit 5-6

Limit 60

50

100

150

200

250

300

350

-10000 -8000 -6000 -4000 -2000 0 2000 4000

NRd (kN)

MRd (kNm)






0

5

10

15

20

25

30

35

0 5 10 15 20 25 30 35

N (kN)

MRD (kNm)


t = 380 mm λ ge 12 Feb 44k




0

1

2

3

4

5

6

7

0 10 20 30 40 50

N (kN)

LIdeg (kN)

rmC-45m

rmC-5m

rmC-6m

rmC-7m

rmC-8m

t = 380 mm λ gt 12 Feb 44k

















fck Nmm2SCC




γS - 115











(74)

with

(75)


(76)








734 Design charts












0

20

40

60

80

100

120

140

0 2 4 6 8 10 12

as [cmsup2m]

MR

d [kN

mm

]

ABCDEFGHIJKL



0

20

40

60

80

100

120

140

160

0 2 4 6 8 10 12

as [cmsup2m]

MR

d [kN

mm

]

ABCDEFGHIJKL
































642











xεm

εsc

εst






744 Design charts






-500 0 500 1000 1500 2000 2500 3000 3500 40000

20

40

60

80

100

120

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Mom

ent (

kNm

)





-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000

20

40

60

80

100

120

ρv = 0035

ρv = 0049 ρv = 0070 ρv = 0091

Mom

ent (

kNm

)

Normal (kN)(a)

-500 0 500 1000 1500 2000 2500 30000

10

20

30

40

50

60

70

80

90

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Mom

ent (

kNm

)

Normal (kN)(b)

-500 0 500 1000 1500 200005

101520253035404550556065

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Mom

ent (

kNm

)

Normal (kN)(c)

-300 0 300 600 900 12000

5

10

15

20

25

30

35

40

ρv = 0037

ρv = 0049 ρv = 0070 ρv = 0086

Mom

ent (

kNm

)

Normal (kN)(d)


-100 0 100 200 300 400 500 6000

2

4

6

8

10

12

14

16

18

20

ρv = 0049

ρv = 0070 ρv = 0098

Mom

ent (

kNm

)

Normal (kN) (e)




81 DURABILITY







(EN 1996-1-1 2005 433)















REFERENCES









prestressed masonry


2005-018120



018120








buildingsrdquo












Zeland Wellingston





Italian)


New Jersey



















or








































password










































Precast RC shed



















312)









detail























masonry system























insulation










25cm ie 425 mmsup2m
























obtained

(a)

(b)























given































412 Wind loading






the turbulent wind









(43)


(44)











































(46a)

(46b)

(46c)

(46d)













1998-1-1]






(47)



(48a)

(48b)

(48c)

(48d)


spectra








(49a)

(49b)

(49c)

(49d)























(410a)

(410b)







favourable 090 000 100 000 100 000




of actions

(411)





ψEi = φ ψ2i (412)









(413)



















































beams








422 Wind loading





























satisfied







of the floor area












analysis y


rx ge ls (414b)






















enlargement




Figure 22d)


































51 INTRODUCTION


























vertical edges



tef = ρt t (51)








hef = ρn h (52)






if hl le 35

(53a)

if hl gt 35

(53b)


if hl le 115

(54a)

if hl gt 115

(54b)















0

2

4

6

8

10

12

14

16

18

50 54 58 62 66 70 74 78 82 86 90 94 98 102

106

110

114

118

122

126

130

134

138

142

146

150

154

158

162

166

170 ht

λ

λ2 (e le 025 t)λ2 (e gt 025 t)




ratio)


00

01

02

03

04

05

06

07

08

09

10

053

065

080

095

110

125

140

155

170

185

200

215

230

245

260

275

290

305

320

335

350

365

380

395

410

425

440

455

470

485

500 hl

ρ






0

1

2

3

4

5

6

7

8

9

10

50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600

l (cm)

λ





0

2

4

6

8

10

12

14

16

18

20

50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600

l (cm)

λ


















(55)





(G4) Vertical Holes








vh

kvvkhhk AA

fAfAf

++

= (56)











Masonry columns

Masonry panels

Masonry system

l (mm) 630 920 1550

fexp (Nmm2) 559 271 390

fth (eq 56) (Nmm2) - - 388

Error () - - 0005


10

15

20

25

30

35

40

45

50

55

60

500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500 3750 4000 4250

lw (mm)

f (Nmm2)

fexpfdα fd


the wall



































524 Design charts


750 mm1000 mm

1250 mm1500 mm

1750 mm2000 mm

2250 mm2500 mm

2750 mm3000 mm3250 mm3500 mm

4000 mm4250 mm

50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)


3750 mm

500 mm


150 400 mm


50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)





50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)





50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash14 mm

2oslash16 mm


4oslash16 mm




50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash16 mm

2oslash18 mm

2oslash20 mm

4oslash16 mm




50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash18 mm

2oslash20 mm

4oslash16 mm





50200

350500650

800950

11001250

140015501700

185020002150

23002450

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash20 mm

4oslash16 mm




50200

350500650

800950

110012501400

155017001850

20002150

23002450

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash20 mm

4oslash16 mm








0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)





eccentricity






























a reduction of 08


column

column

M

ccckeffd s

lff sdotsdot

=γ

α (57)












0

5

10

15

20

25

30

35

40

00 05 10 15 20 25 30 35 40



0

5

10

15

20

25

30

35

40

00 05 10 15 20 25 30 35 40




stress-strain-curve

0

5

10

15

20

25

30

35

40

00 20 40 60 80 100 120 140 160



0

5

10

15

20

25

30

35

40

00 20 40 60 80 100 120 140 160



stress-strain-curve




equation

( ) ( ) ( )c u sc u s

A A AE









fy yield strength








Hole 5000 3000












































fcmas


fcmas

corr cal fcmas


182 SU-VC-NM

136

163 SU-VC

353

168

mean 162

327 050 283 057

236 SU-SCC 445

216

mean 226

327 069 346 065

247 DU-SCC

438 175

mean 211

286 074 304 069

223 DU-SCC-DR 399

234

mean 229

295 078 272 084

261 DU-SCC-SR 365

257

mean 259

321 081 317 082


0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3






0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3








0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35







0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35






0

5

10

15

20

25

30

35

0 05 1 15 2 25 3 35





0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35











SdRd NN ge (58)













comparison


534 Design charts













the design charts










105 (lt12)










Material properties















544 Design charts

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

Nrd

(kN

)

(et)




00 01 02 03 04 050

500

1000

1500

2000

2500

3000L=160cm

As = 0036 As = 0045 As = 0074 As = 011 As = 017

Nrd

(kN

)

(et)

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

As = 0035 As = 0045 As = 0070 As = 011 As = 018

Nrd

(kN

)

(et)

L=280cm

(a) (b)



00 01 02 03 04 050

500

1000

1500

2000

2500

3000

As = 0022 As = 0034 As = 0045 As = 0070 As = 010

Nrd

(kN

)

(et)

L=400cm

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

3500

As = 0022 As = 0034 As = 0045 As = 0070 As = 010

Nrd

(kN

)

(et)

L=560cm

(a) (b)





61 INTRODUCTION













1 2 3R R R RV V V V= + + (61)



























NZS 4230 (2004) ltfC

ltN

vd 8080tan90

02 sdot⎟⎠

⎞⎜⎝

⎛+

sdotα lt

stfA

fC ydswvd 80)

80( 01 sdot

sdot+ 0

ACI 530 (2005) Nftl

VLM

d 250)7514(0830 +minus slfA ydsw 50 0

















































(62)






















is reliable













0

50

100

150

200

250

0 50 100 150 200 250 300 350 400

NEd (kN)

MRd (kNm)



5-150 400 mm


NTC 1500 mm

EC6 1500 mm

100

150

200

250

300

0 100 200 300 400 500 600

NEd (kN)

VRd (kN)



RNDZ-5-150 400 mm






















624 Design charts


500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm

2250 mm2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm

0

200

400

600

800

1000

1200

1400

1600

1800

2000

00 02 04 06 08 10 12 14σd (Nmm2)

MRd (kNm)




500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm

2250 mm2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 200 400 600 800 1000 1200 1400 1600

NEd (kN)

MRd (kNm)








100

150

200

250

300

350

400

450

500

550

00 02 04 06 08 10 12 14

σd (Nmm2)

VRd (kN)



500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm2250 mm

2500 mm2750 mm

3000 mm3250 mm

3500 mm

3750 mm4000 mm

4250 mm

100

150

200

250

300

350

400

450

500

550

0 200 400 600 800 1000 1200 1400 1600

NEd (kN)

VRd (kN)






0

200

400

600

800

1000

1200

1400

1600

1800

2000

-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400

NRd (kN)



500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm2250 mm

2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm




100

150

200

250

300

350

400

450

500

550

0 250 500 750 1000 1250 1500 1750 2000

MRd (kNm)

VRd (kN)







0

10

20

30

40

50

60

70

-400 -300 -200 -100 0 100 200 300 400 500 600 700 800 900

NRd (kN)

MRd (kNm)




0

50

100

150

200

250

-400 -200 0 200 400 600 800 1000 1200

NRd (kN)

MRd (kNm)




0

50

100

150

200

250

300

350

400

-400 -200 0 200 400 600 800 1000 1200 1400

NRd (kN)

MRd (kNm)




0

100

200

300

400

500

600

-400 -200 0 200 400 600 800 1000 1200 1400 1600

NRd (kN)

MRd (kNm)




0

100

200

300

400

500

600

700

800

900

-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800

NRd (kN)

MRd (kNm)




0

200

400

600

800

1000

1200

-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000

NRd (kN)

MRd (kNm)

2oslash18 mm

2oslash20 mm

4oslash16 mm




0

200

400

600

800

1000

1200

1400

-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

NRd (kN)

MRd (kNm)

2oslash20 mm

4oslash16 mm



0

300

600

900

1200

1500

1800

-600 -300 0 300 600 900 1200 1500 1800 2100 2400

NRd (kN)

MRd (kNm)

2oslash20 mm

4oslash16 mm




1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm


100

110

120

130

140

150

0 10 20 30 40 50 60 70 80 90 100

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


100

110

120

130

140

150

160

170

180

190

200

0 25 50 75 100 125 150 175 200 225 250

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


150

160

170

180

190

200

210

220

230

240

250

50 100 150 200 250 300 350 400 450

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


160

180

200

220

240

260

280

300

150 200 250 300 350 400 450 500 550 600 650

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm



200

220

240

260

280

300

320

340

360

250 300 350 400 450 500 550 600 650 700 750 800 850

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


220

240

260

280

300

320

340

360

380

400

420

350 450 550 650 750 850 950 1050 1150

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


240

260

280

300

320

340

360

380

400

420

440

460

550 650 750 850 950 1050 1150 1250 1350 1450

MRd (kNm)

VRd (kN)

2oslash20 mm

4oslash16 mm

σd = 01 Nmmsup2

σd = 02 Nmmsup2

σd = 03 Nmmsup2


σd = 06 Nmmsup2

σd = 07 Nmmsup2

σd = 08 Nmmsup2

σd ge 09 Nmmsup2


RNDZ-5-150 400 mm


280

300

320

340

360

380

400

420

440

460

480

500

520

650 750 850 950 1050 1150 1250 1350 1450 1550 1650 1750 1850

MRd (kNm)

VRd (kN)

2oslash20 mm

4oslash16 mm

σd = 01 Nmmsup2

σd = 02 Nmmsup2

σd = 03 Nmmsup2


σd = 06 Nmmsup2

σd = 07 Nmmsup2

σd = 08 Nmmsup2

σd ge 09 Nmmsup2


RNDZ-5-150 400 mm
















relevant






significantly







fck Nmm2SCC



















(63)

(64)

(65)

(66)





634 Design charts











Vd (MdNd) [kN]-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250

Md [kNm]

Nd [

kN]

0 10 20

30 40 50

60 70 80

90 Loadings




Vd (MdNd) [kN]-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250

Md [kNm]

Nd [

kN]

0 10 20

30 40 50

60 70 80

90 Loadings




Vd (MdNd) [kN]-3500

-3000

-2500

-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250 300 350 400 450

Md [kNm]

Nd [

kN]

0 20 40

60 80 100

120 140 160

180 Loadings



Vd (MdNd) [kN]-3500

-3000

-2500

-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250 300 350 400 450

Md [kNm]

Nd [

kN]

0 20 40

60 80 100

120 140 160

180 Loadings




Vd (MdNd) [kN]-5000

-4000

-3000

-2000

-1000

0

1000

0 200 400 600 800 1000 1200 1400 1600

Md [kNm]

Nd [

kN]

0 30 60

90 120 150

180 210 240

270 Loadings



Vd (MdNd) [kN]-5000

-4000

-3000

-2000

-1000

0

1000

0 200 400 600 800 1000 1200 1400 1600

Md [kNm]

Nd [

kN]

0 30 60

90 120 150

180 210 240

270 Loadings




Vd (MdNd) [kN]-9000

-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

0 500 1000 1500 2000 2500 3000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings



Vd (MdNd) [kN]-9000

-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings




Vd (MdNd) [kN]-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000 3500 4000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings



Vd (MdNd) [kN]-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000 3500 4000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings





-12000

-10000

-8000

-6000

-4000

-2000

0

2000

0 1000 2000 3000 4000 5000 6000 7000

Md [kNm]

Nd [

kN]

0 70 140

210 280 350

420 490 560

630 Loadings




-12000

-10000

-8000

-6000

-4000

-2000

0

2000

0 1000 2000 3000 4000 5000 6000 7000

Md [kNm]

Nd [

kN]

0 70 140

210 280 350

420 490 560

630 Loadings







































Material properties

fb Nmm2 1000

fm Nmm2 1000

K - 045

α - 070

β - 030

fk Nmm2 450

γM - 150

fd Nmm2 300

fyk0 Nmm2 020

fyk Nmm2 500

γS - 115

fyd Nmm2 43478

E Nmm2 210000

εyd permil 207



















xdx i

sim

minus=

minus εε (67)

sissi E εσ = (68)

summinus=i

sim FFN (69)

xtfF wam 80= (610)



sum ⎟⎠⎞

⎜⎝⎛ minus+⎟

⎠⎞

⎜⎝⎛ minus==

i

wisi

wmfR

bdFx

bFzHM

240

2 (612)



σ400 += vv ff bv ff 0650le (614)










644 Design charts







stress of 2 MPa

-500 0 500 1000 1500 2000 2500 3000 3500 40000

500

1000

1500

2000

2500

3000

3500

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Mom

ent (

kNm

)

Normal (kN) (a)

-500 0 500 1000 1500 2000 2500 3000 3500 40000

100

200

300

400

500

600

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Shea

r (kN

)

Normal (kN) (b)

0 500 1000 1500 2000 2500 3000 35000

100

200

300

400

500

600

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

She

ar (k

N)

Moment (kNm) (c)


(c) V x M





-500 0 500 1000 1500 2000100

150

200

250

300

350

400

450

500

ρh = 0035 ρ

h = 0049

ρh = 0098

Shea

r (kN

)

Normal (kN) (a)

0 100 200 300 400 500 600 700 800 900 1000

150

200

250

300

350

400

450

ρh = 0035 ρh = 0049 ρh = 0098

Shea

r (kN

)

Moment (kNm) (b)






-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000

500

1000

1500

2000

2500

3000

3500

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091

Mom

ent (

kNm

)

Normal (kN) (a)

0 400 800 1200 1600 2000 2400 2800 3200 3600

200

250

300

350

400

450

500

550

600

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091

Shea

r (kN

)

Moment (kNm) (b)




-500 0 500 1000 1500 2000 2500 30000

200

400

600

800

1000

1200

1400

1600

1800

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Mom

ent (

kNm

)

Normal (kN) (a)

-200 0 200 400 600 800 1000 1200 1400 1600 1800150

200

250

300

350

400

450

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Shea

r (kN

)

Moment (kNm) (b)



-500 0 500 1000 1500 20000

100

200

300

400

500

600

700

800

900

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Mom

ent (

kNm

)

Normal (kN) (a)

0 200 400 600 800 1000100

150

200

250

300

350

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Shea

r (kN

)

Moment (kNm) (b)




-300 0 300 600 900 12000

50

100

150

200

250

300

ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086

Mom

ent (

kNm

)

Normal (kN) (a)

-50 0 50 100 150 200 250 300

120

150

180

210

240

ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086

Shea

r (kN

)

Moment (kNm) (b)



-100 0 100 200 300 400 500 6000

10

20

30

40

50

60

70

ρv = 0049 ρv = 0070 ρv = 0098M

omen

t (kN

m)

Normal (kN) (a)

-10 0 10 20 30 40 50 60 7090

100

110

120

130

140

150

ρv = 0049 ρv = 0070 ρv = 0098

Shea

r (kN

)

Moment (kNm) (b)





71 INTRODUCTION






































Material property

CISEDIL













(71)














⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛minus=

Lxvy

2cos1max

π (72)




max2

2

41 v

LEJM

ry

base

π==⎟

⎠⎞


















N kN 50 50 50 M kNm 702 148 85

vmax mm 296 296 296




















724 Design charts


TensionCompression

Limit 2-3

Limit 3-4

Limit 4-5

Limit 5-6

Limit 60

50

100

150

200

250

300

350

-10000 -8000 -6000 -4000 -2000 0 2000 4000

NRd (kN)

MRd (kNm)






0

5

10

15

20

25

30

35

0 5 10 15 20 25 30 35

N (kN)

MRD (kNm)


t = 380 mm λ ge 12 Feb 44k




0

1

2

3

4

5

6

7

0 10 20 30 40 50

N (kN)

LIdeg (kN)

rmC-45m

rmC-5m

rmC-6m

rmC-7m

rmC-8m

t = 380 mm λ gt 12 Feb 44k

















fck Nmm2SCC




γS - 115











(74)

with

(75)


(76)








734 Design charts












0

20

40

60

80

100

120

140

0 2 4 6 8 10 12

as [cmsup2m]

MR

d [kN

mm

]

ABCDEFGHIJKL



0

20

40

60

80

100

120

140

160

0 2 4 6 8 10 12

as [cmsup2m]

MR

d [kN

mm

]

ABCDEFGHIJKL
































642











xεm

εsc

εst






744 Design charts






-500 0 500 1000 1500 2000 2500 3000 3500 40000

20

40

60

80

100

120

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Mom

ent (

kNm

)





-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000

20

40

60

80

100

120

ρv = 0035

ρv = 0049 ρv = 0070 ρv = 0091

Mom

ent (

kNm

)

Normal (kN)(a)

-500 0 500 1000 1500 2000 2500 30000

10

20

30

40

50

60

70

80

90

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Mom

ent (

kNm

)

Normal (kN)(b)

-500 0 500 1000 1500 200005

101520253035404550556065

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Mom

ent (

kNm

)

Normal (kN)(c)

-300 0 300 600 900 12000

5

10

15

20

25

30

35

40

ρv = 0037

ρv = 0049 ρv = 0070 ρv = 0086

Mom

ent (

kNm

)

Normal (kN)(d)


-100 0 100 200 300 400 500 6000

2

4

6

8

10

12

14

16

18

20

ρv = 0049

ρv = 0070 ρv = 0098

Mom

ent (

kNm

)

Normal (kN) (e)




81 DURABILITY







(EN 1996-1-1 2005 433)















REFERENCES









prestressed masonry


2005-018120



018120








buildingsrdquo












Zeland Wellingston





Italian)


New Jersey



















or








































password





Precast RC shed



















312)









detail























masonry system























insulation










25cm ie 425 mmsup2m
























obtained

(a)

(b)























given































412 Wind loading






the turbulent wind









(43)


(44)











































(46a)

(46b)

(46c)

(46d)













1998-1-1]






(47)



(48a)

(48b)

(48c)

(48d)


spectra








(49a)

(49b)

(49c)

(49d)























(410a)

(410b)







favourable 090 000 100 000 100 000




of actions

(411)





ψEi = φ ψ2i (412)









(413)



















































beams








422 Wind loading





























satisfied







of the floor area












analysis y


rx ge ls (414b)






















enlargement




Figure 22d)


































51 INTRODUCTION


























vertical edges



tef = ρt t (51)








hef = ρn h (52)






if hl le 35

(53a)

if hl gt 35

(53b)


if hl le 115

(54a)

if hl gt 115

(54b)















0

2

4

6

8

10

12

14

16

18

50 54 58 62 66 70 74 78 82 86 90 94 98 102

106

110

114

118

122

126

130

134

138

142

146

150

154

158

162

166

170 ht

λ

λ2 (e le 025 t)λ2 (e gt 025 t)




ratio)


00

01

02

03

04

05

06

07

08

09

10

053

065

080

095

110

125

140

155

170

185

200

215

230

245

260

275

290

305

320

335

350

365

380

395

410

425

440

455

470

485

500 hl

ρ






0

1

2

3

4

5

6

7

8

9

10

50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600

l (cm)

λ





0

2

4

6

8

10

12

14

16

18

20

50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600

l (cm)

λ


















(55)





(G4) Vertical Holes








vh

kvvkhhk AA

fAfAf

++

= (56)











Masonry columns

Masonry panels

Masonry system

l (mm) 630 920 1550

fexp (Nmm2) 559 271 390

fth (eq 56) (Nmm2) - - 388

Error () - - 0005


10

15

20

25

30

35

40

45

50

55

60

500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500 3750 4000 4250

lw (mm)

f (Nmm2)

fexpfdα fd


the wall



































524 Design charts


750 mm1000 mm

1250 mm1500 mm

1750 mm2000 mm

2250 mm2500 mm

2750 mm3000 mm3250 mm3500 mm

4000 mm4250 mm

50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)


3750 mm

500 mm


150 400 mm


50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)





50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)





50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash14 mm

2oslash16 mm


4oslash16 mm




50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash16 mm

2oslash18 mm

2oslash20 mm

4oslash16 mm




50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash18 mm

2oslash20 mm

4oslash16 mm





50200

350500650

800950

11001250

140015501700

185020002150

23002450

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash20 mm

4oslash16 mm




50200

350500650

800950

110012501400

155017001850

20002150

23002450

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash20 mm

4oslash16 mm








0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)





eccentricity






























a reduction of 08


column

column

M

ccckeffd s

lff sdotsdot

=γ

α (57)












0

5

10

15

20

25

30

35

40

00 05 10 15 20 25 30 35 40



0

5

10

15

20

25

30

35

40

00 05 10 15 20 25 30 35 40




stress-strain-curve

0

5

10

15

20

25

30

35

40

00 20 40 60 80 100 120 140 160



0

5

10

15

20

25

30

35

40

00 20 40 60 80 100 120 140 160



stress-strain-curve




equation

( ) ( ) ( )c u sc u s

A A AE









fy yield strength








Hole 5000 3000












































fcmas


fcmas

corr cal fcmas


182 SU-VC-NM

136

163 SU-VC

353

168

mean 162

327 050 283 057

236 SU-SCC 445

216

mean 226

327 069 346 065

247 DU-SCC

438 175

mean 211

286 074 304 069

223 DU-SCC-DR 399

234

mean 229

295 078 272 084

261 DU-SCC-SR 365

257

mean 259

321 081 317 082


0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3






0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3








0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35







0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35






0

5

10

15

20

25

30

35

0 05 1 15 2 25 3 35





0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35











SdRd NN ge (58)













comparison


534 Design charts













the design charts










105 (lt12)










Material properties















544 Design charts

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

Nrd

(kN

)

(et)




00 01 02 03 04 050

500

1000

1500

2000

2500

3000L=160cm

As = 0036 As = 0045 As = 0074 As = 011 As = 017

Nrd

(kN

)

(et)

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

As = 0035 As = 0045 As = 0070 As = 011 As = 018

Nrd

(kN

)

(et)

L=280cm

(a) (b)



00 01 02 03 04 050

500

1000

1500

2000

2500

3000

As = 0022 As = 0034 As = 0045 As = 0070 As = 010

Nrd

(kN

)

(et)

L=400cm

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

3500

As = 0022 As = 0034 As = 0045 As = 0070 As = 010

Nrd

(kN

)

(et)

L=560cm

(a) (b)





61 INTRODUCTION













1 2 3R R R RV V V V= + + (61)



























NZS 4230 (2004) ltfC

ltN

vd 8080tan90

02 sdot⎟⎠

⎞⎜⎝

⎛+

sdotα lt

stfA

fC ydswvd 80)

80( 01 sdot

sdot+ 0

ACI 530 (2005) Nftl

VLM

d 250)7514(0830 +minus slfA ydsw 50 0

















































(62)






















is reliable













0

50

100

150

200

250

0 50 100 150 200 250 300 350 400

NEd (kN)

MRd (kNm)



5-150 400 mm


NTC 1500 mm

EC6 1500 mm

100

150

200

250

300

0 100 200 300 400 500 600

NEd (kN)

VRd (kN)



RNDZ-5-150 400 mm






















624 Design charts


500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm

2250 mm2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm

0

200

400

600

800

1000

1200

1400

1600

1800

2000

00 02 04 06 08 10 12 14σd (Nmm2)

MRd (kNm)




500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm

2250 mm2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 200 400 600 800 1000 1200 1400 1600

NEd (kN)

MRd (kNm)








100

150

200

250

300

350

400

450

500

550

00 02 04 06 08 10 12 14

σd (Nmm2)

VRd (kN)



500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm2250 mm

2500 mm2750 mm

3000 mm3250 mm

3500 mm

3750 mm4000 mm

4250 mm

100

150

200

250

300

350

400

450

500

550

0 200 400 600 800 1000 1200 1400 1600

NEd (kN)

VRd (kN)






0

200

400

600

800

1000

1200

1400

1600

1800

2000

-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400

NRd (kN)



500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm2250 mm

2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm




100

150

200

250

300

350

400

450

500

550

0 250 500 750 1000 1250 1500 1750 2000

MRd (kNm)

VRd (kN)







0

10

20

30

40

50

60

70

-400 -300 -200 -100 0 100 200 300 400 500 600 700 800 900

NRd (kN)

MRd (kNm)




0

50

100

150

200

250

-400 -200 0 200 400 600 800 1000 1200

NRd (kN)

MRd (kNm)




0

50

100

150

200

250

300

350

400

-400 -200 0 200 400 600 800 1000 1200 1400

NRd (kN)

MRd (kNm)




0

100

200

300

400

500

600

-400 -200 0 200 400 600 800 1000 1200 1400 1600

NRd (kN)

MRd (kNm)




0

100

200

300

400

500

600

700

800

900

-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800

NRd (kN)

MRd (kNm)




0

200

400

600

800

1000

1200

-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000

NRd (kN)

MRd (kNm)

2oslash18 mm

2oslash20 mm

4oslash16 mm




0

200

400

600

800

1000

1200

1400

-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

NRd (kN)

MRd (kNm)

2oslash20 mm

4oslash16 mm



0

300

600

900

1200

1500

1800

-600 -300 0 300 600 900 1200 1500 1800 2100 2400

NRd (kN)

MRd (kNm)

2oslash20 mm

4oslash16 mm




1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm


100

110

120

130

140

150

0 10 20 30 40 50 60 70 80 90 100

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


100

110

120

130

140

150

160

170

180

190

200

0 25 50 75 100 125 150 175 200 225 250

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


150

160

170

180

190

200

210

220

230

240

250

50 100 150 200 250 300 350 400 450

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


160

180

200

220

240

260

280

300

150 200 250 300 350 400 450 500 550 600 650

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm



200

220

240

260

280

300

320

340

360

250 300 350 400 450 500 550 600 650 700 750 800 850

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


220

240

260

280

300

320

340

360

380

400

420

350 450 550 650 750 850 950 1050 1150

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


240

260

280

300

320

340

360

380

400

420

440

460

550 650 750 850 950 1050 1150 1250 1350 1450

MRd (kNm)

VRd (kN)

2oslash20 mm

4oslash16 mm

σd = 01 Nmmsup2

σd = 02 Nmmsup2

σd = 03 Nmmsup2


σd = 06 Nmmsup2

σd = 07 Nmmsup2

σd = 08 Nmmsup2

σd ge 09 Nmmsup2


RNDZ-5-150 400 mm


280

300

320

340

360

380

400

420

440

460

480

500

520

650 750 850 950 1050 1150 1250 1350 1450 1550 1650 1750 1850

MRd (kNm)

VRd (kN)

2oslash20 mm

4oslash16 mm

σd = 01 Nmmsup2

σd = 02 Nmmsup2

σd = 03 Nmmsup2


σd = 06 Nmmsup2

σd = 07 Nmmsup2

σd = 08 Nmmsup2

σd ge 09 Nmmsup2


RNDZ-5-150 400 mm
















relevant






significantly







fck Nmm2SCC



















(63)

(64)

(65)

(66)





634 Design charts











Vd (MdNd) [kN]-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250

Md [kNm]

Nd [

kN]

0 10 20

30 40 50

60 70 80

90 Loadings




Vd (MdNd) [kN]-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250

Md [kNm]

Nd [

kN]

0 10 20

30 40 50

60 70 80

90 Loadings




Vd (MdNd) [kN]-3500

-3000

-2500

-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250 300 350 400 450

Md [kNm]

Nd [

kN]

0 20 40

60 80 100

120 140 160

180 Loadings



Vd (MdNd) [kN]-3500

-3000

-2500

-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250 300 350 400 450

Md [kNm]

Nd [

kN]

0 20 40

60 80 100

120 140 160

180 Loadings




Vd (MdNd) [kN]-5000

-4000

-3000

-2000

-1000

0

1000

0 200 400 600 800 1000 1200 1400 1600

Md [kNm]

Nd [

kN]

0 30 60

90 120 150

180 210 240

270 Loadings



Vd (MdNd) [kN]-5000

-4000

-3000

-2000

-1000

0

1000

0 200 400 600 800 1000 1200 1400 1600

Md [kNm]

Nd [

kN]

0 30 60

90 120 150

180 210 240

270 Loadings




Vd (MdNd) [kN]-9000

-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

0 500 1000 1500 2000 2500 3000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings



Vd (MdNd) [kN]-9000

-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings




Vd (MdNd) [kN]-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000 3500 4000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings



Vd (MdNd) [kN]-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000 3500 4000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings





-12000

-10000

-8000

-6000

-4000

-2000

0

2000

0 1000 2000 3000 4000 5000 6000 7000

Md [kNm]

Nd [

kN]

0 70 140

210 280 350

420 490 560

630 Loadings




-12000

-10000

-8000

-6000

-4000

-2000

0

2000

0 1000 2000 3000 4000 5000 6000 7000

Md [kNm]

Nd [

kN]

0 70 140

210 280 350

420 490 560

630 Loadings







































Material properties

fb Nmm2 1000

fm Nmm2 1000

K - 045

α - 070

β - 030

fk Nmm2 450

γM - 150

fd Nmm2 300

fyk0 Nmm2 020

fyk Nmm2 500

γS - 115

fyd Nmm2 43478

E Nmm2 210000

εyd permil 207



















xdx i

sim

minus=

minus εε (67)

sissi E εσ = (68)

summinus=i

sim FFN (69)

xtfF wam 80= (610)



sum ⎟⎠⎞

⎜⎝⎛ minus+⎟

⎠⎞

⎜⎝⎛ minus==

i

wisi

wmfR

bdFx

bFzHM

240

2 (612)



σ400 += vv ff bv ff 0650le (614)










644 Design charts







stress of 2 MPa

-500 0 500 1000 1500 2000 2500 3000 3500 40000

500

1000

1500

2000

2500

3000

3500

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Mom

ent (

kNm

)

Normal (kN) (a)

-500 0 500 1000 1500 2000 2500 3000 3500 40000

100

200

300

400

500

600

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Shea

r (kN

)

Normal (kN) (b)

0 500 1000 1500 2000 2500 3000 35000

100

200

300

400

500

600

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

She

ar (k

N)

Moment (kNm) (c)


(c) V x M





-500 0 500 1000 1500 2000100

150

200

250

300

350

400

450

500

ρh = 0035 ρ

h = 0049

ρh = 0098

Shea

r (kN

)

Normal (kN) (a)

0 100 200 300 400 500 600 700 800 900 1000

150

200

250

300

350

400

450

ρh = 0035 ρh = 0049 ρh = 0098

Shea

r (kN

)

Moment (kNm) (b)






-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000

500

1000

1500

2000

2500

3000

3500

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091

Mom

ent (

kNm

)

Normal (kN) (a)

0 400 800 1200 1600 2000 2400 2800 3200 3600

200

250

300

350

400

450

500

550

600

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091

Shea

r (kN

)

Moment (kNm) (b)




-500 0 500 1000 1500 2000 2500 30000

200

400

600

800

1000

1200

1400

1600

1800

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Mom

ent (

kNm

)

Normal (kN) (a)

-200 0 200 400 600 800 1000 1200 1400 1600 1800150

200

250

300

350

400

450

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Shea

r (kN

)

Moment (kNm) (b)



-500 0 500 1000 1500 20000

100

200

300

400

500

600

700

800

900

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Mom

ent (

kNm

)

Normal (kN) (a)

0 200 400 600 800 1000100

150

200

250

300

350

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Shea

r (kN

)

Moment (kNm) (b)




-300 0 300 600 900 12000

50

100

150

200

250

300

ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086

Mom

ent (

kNm

)

Normal (kN) (a)

-50 0 50 100 150 200 250 300

120

150

180

210

240

ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086

Shea

r (kN

)

Moment (kNm) (b)



-100 0 100 200 300 400 500 6000

10

20

30

40

50

60

70

ρv = 0049 ρv = 0070 ρv = 0098M

omen

t (kN

m)

Normal (kN) (a)

-10 0 10 20 30 40 50 60 7090

100

110

120

130

140

150

ρv = 0049 ρv = 0070 ρv = 0098

Shea

r (kN

)

Moment (kNm) (b)





71 INTRODUCTION






































Material property

CISEDIL













(71)














⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛minus=

Lxvy

2cos1max

π (72)




max2

2

41 v

LEJM

ry

base

π==⎟

⎠⎞


















N kN 50 50 50 M kNm 702 148 85

vmax mm 296 296 296




















724 Design charts


TensionCompression

Limit 2-3

Limit 3-4

Limit 4-5

Limit 5-6

Limit 60

50

100

150

200

250

300

350

-10000 -8000 -6000 -4000 -2000 0 2000 4000

NRd (kN)

MRd (kNm)






0

5

10

15

20

25

30

35

0 5 10 15 20 25 30 35

N (kN)

MRD (kNm)


t = 380 mm λ ge 12 Feb 44k




0

1

2

3

4

5

6

7

0 10 20 30 40 50

N (kN)

LIdeg (kN)

rmC-45m

rmC-5m

rmC-6m

rmC-7m

rmC-8m

t = 380 mm λ gt 12 Feb 44k

















fck Nmm2SCC




γS - 115











(74)

with

(75)


(76)








734 Design charts












0

20

40

60

80

100

120

140

0 2 4 6 8 10 12

as [cmsup2m]

MR

d [kN

mm

]

ABCDEFGHIJKL



0

20

40

60

80

100

120

140

160

0 2 4 6 8 10 12

as [cmsup2m]

MR

d [kN

mm

]

ABCDEFGHIJKL
































642











xεm

εsc

εst






744 Design charts






-500 0 500 1000 1500 2000 2500 3000 3500 40000

20

40

60

80

100

120

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Mom

ent (

kNm

)





-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000

20

40

60

80

100

120

ρv = 0035

ρv = 0049 ρv = 0070 ρv = 0091

Mom

ent (

kNm

)

Normal (kN)(a)

-500 0 500 1000 1500 2000 2500 30000

10

20

30

40

50

60

70

80

90

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Mom

ent (

kNm

)

Normal (kN)(b)

-500 0 500 1000 1500 200005

101520253035404550556065

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Mom

ent (

kNm

)

Normal (kN)(c)

-300 0 300 600 900 12000

5

10

15

20

25

30

35

40

ρv = 0037

ρv = 0049 ρv = 0070 ρv = 0086

Mom

ent (

kNm

)

Normal (kN)(d)


-100 0 100 200 300 400 500 6000

2

4

6

8

10

12

14

16

18

20

ρv = 0049

ρv = 0070 ρv = 0098

Mom

ent (

kNm

)

Normal (kN) (e)




81 DURABILITY







(EN 1996-1-1 2005 433)















REFERENCES









prestressed masonry


2005-018120



018120








buildingsrdquo












Zeland Wellingston





Italian)


New Jersey



















or








































password














312)









detail























masonry system























insulation










25cm ie 425 mmsup2m
























obtained

(a)

(b)























given































412 Wind loading






the turbulent wind









(43)


(44)











































(46a)

(46b)

(46c)

(46d)













1998-1-1]






(47)



(48a)

(48b)

(48c)

(48d)


spectra








(49a)

(49b)

(49c)

(49d)























(410a)

(410b)







favourable 090 000 100 000 100 000




of actions

(411)





ψEi = φ ψ2i (412)









(413)



















































beams








422 Wind loading





























satisfied







of the floor area












analysis y


rx ge ls (414b)






















enlargement




Figure 22d)


































51 INTRODUCTION


























vertical edges



tef = ρt t (51)








hef = ρn h (52)






if hl le 35

(53a)

if hl gt 35

(53b)


if hl le 115

(54a)

if hl gt 115

(54b)















0

2

4

6

8

10

12

14

16

18

50 54 58 62 66 70 74 78 82 86 90 94 98 102

106

110

114

118

122

126

130

134

138

142

146

150

154

158

162

166

170 ht

λ

λ2 (e le 025 t)λ2 (e gt 025 t)




ratio)


00

01

02

03

04

05

06

07

08

09

10

053

065

080

095

110

125

140

155

170

185

200

215

230

245

260

275

290

305

320

335

350

365

380

395

410

425

440

455

470

485

500 hl

ρ






0

1

2

3

4

5

6

7

8

9

10

50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600

l (cm)

λ





0

2

4

6

8

10

12

14

16

18

20

50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600

l (cm)

λ


















(55)





(G4) Vertical Holes








vh

kvvkhhk AA

fAfAf

++

= (56)











Masonry columns

Masonry panels

Masonry system

l (mm) 630 920 1550

fexp (Nmm2) 559 271 390

fth (eq 56) (Nmm2) - - 388

Error () - - 0005


10

15

20

25

30

35

40

45

50

55

60

500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500 3750 4000 4250

lw (mm)

f (Nmm2)

fexpfdα fd


the wall



































524 Design charts


750 mm1000 mm

1250 mm1500 mm

1750 mm2000 mm

2250 mm2500 mm

2750 mm3000 mm3250 mm3500 mm

4000 mm4250 mm

50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)


3750 mm

500 mm


150 400 mm


50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)





50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)





50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash14 mm

2oslash16 mm


4oslash16 mm




50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash16 mm

2oslash18 mm

2oslash20 mm

4oslash16 mm




50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash18 mm

2oslash20 mm

4oslash16 mm





50200

350500650

800950

11001250

140015501700

185020002150

23002450

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash20 mm

4oslash16 mm




50200

350500650

800950

110012501400

155017001850

20002150

23002450

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash20 mm

4oslash16 mm








0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)





eccentricity






























a reduction of 08


column

column

M

ccckeffd s

lff sdotsdot

=γ

α (57)












0

5

10

15

20

25

30

35

40

00 05 10 15 20 25 30 35 40



0

5

10

15

20

25

30

35

40

00 05 10 15 20 25 30 35 40




stress-strain-curve

0

5

10

15

20

25

30

35

40

00 20 40 60 80 100 120 140 160



0

5

10

15

20

25

30

35

40

00 20 40 60 80 100 120 140 160



stress-strain-curve




equation

( ) ( ) ( )c u sc u s

A A AE









fy yield strength








Hole 5000 3000












































fcmas


fcmas

corr cal fcmas


182 SU-VC-NM

136

163 SU-VC

353

168

mean 162

327 050 283 057

236 SU-SCC 445

216

mean 226

327 069 346 065

247 DU-SCC

438 175

mean 211

286 074 304 069

223 DU-SCC-DR 399

234

mean 229

295 078 272 084

261 DU-SCC-SR 365

257

mean 259

321 081 317 082


0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3






0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3








0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35







0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35






0

5

10

15

20

25

30

35

0 05 1 15 2 25 3 35





0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35











SdRd NN ge (58)













comparison


534 Design charts













the design charts










105 (lt12)










Material properties















544 Design charts

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

Nrd

(kN

)

(et)




00 01 02 03 04 050

500

1000

1500

2000

2500

3000L=160cm

As = 0036 As = 0045 As = 0074 As = 011 As = 017

Nrd

(kN

)

(et)

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

As = 0035 As = 0045 As = 0070 As = 011 As = 018

Nrd

(kN

)

(et)

L=280cm

(a) (b)



00 01 02 03 04 050

500

1000

1500

2000

2500

3000

As = 0022 As = 0034 As = 0045 As = 0070 As = 010

Nrd

(kN

)

(et)

L=400cm

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

3500

As = 0022 As = 0034 As = 0045 As = 0070 As = 010

Nrd

(kN

)

(et)

L=560cm

(a) (b)





61 INTRODUCTION













1 2 3R R R RV V V V= + + (61)



























NZS 4230 (2004) ltfC

ltN

vd 8080tan90

02 sdot⎟⎠

⎞⎜⎝

⎛+

sdotα lt

stfA

fC ydswvd 80)

80( 01 sdot

sdot+ 0

ACI 530 (2005) Nftl

VLM

d 250)7514(0830 +minus slfA ydsw 50 0

















































(62)






















is reliable













0

50

100

150

200

250

0 50 100 150 200 250 300 350 400

NEd (kN)

MRd (kNm)



5-150 400 mm


NTC 1500 mm

EC6 1500 mm

100

150

200

250

300

0 100 200 300 400 500 600

NEd (kN)

VRd (kN)



RNDZ-5-150 400 mm






















624 Design charts


500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm

2250 mm2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm

0

200

400

600

800

1000

1200

1400

1600

1800

2000

00 02 04 06 08 10 12 14σd (Nmm2)

MRd (kNm)




500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm

2250 mm2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 200 400 600 800 1000 1200 1400 1600

NEd (kN)

MRd (kNm)








100

150

200

250

300

350

400

450

500

550

00 02 04 06 08 10 12 14

σd (Nmm2)

VRd (kN)



500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm2250 mm

2500 mm2750 mm

3000 mm3250 mm

3500 mm

3750 mm4000 mm

4250 mm

100

150

200

250

300

350

400

450

500

550

0 200 400 600 800 1000 1200 1400 1600

NEd (kN)

VRd (kN)






0

200

400

600

800

1000

1200

1400

1600

1800

2000

-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400

NRd (kN)



500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm2250 mm

2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm




100

150

200

250

300

350

400

450

500

550

0 250 500 750 1000 1250 1500 1750 2000

MRd (kNm)

VRd (kN)







0

10

20

30

40

50

60

70

-400 -300 -200 -100 0 100 200 300 400 500 600 700 800 900

NRd (kN)

MRd (kNm)




0

50

100

150

200

250

-400 -200 0 200 400 600 800 1000 1200

NRd (kN)

MRd (kNm)




0

50

100

150

200

250

300

350

400

-400 -200 0 200 400 600 800 1000 1200 1400

NRd (kN)

MRd (kNm)




0

100

200

300

400

500

600

-400 -200 0 200 400 600 800 1000 1200 1400 1600

NRd (kN)

MRd (kNm)




0

100

200

300

400

500

600

700

800

900

-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800

NRd (kN)

MRd (kNm)




0

200

400

600

800

1000

1200

-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000

NRd (kN)

MRd (kNm)

2oslash18 mm

2oslash20 mm

4oslash16 mm




0

200

400

600

800

1000

1200

1400

-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

NRd (kN)

MRd (kNm)

2oslash20 mm

4oslash16 mm



0

300

600

900

1200

1500

1800

-600 -300 0 300 600 900 1200 1500 1800 2100 2400

NRd (kN)

MRd (kNm)

2oslash20 mm

4oslash16 mm




1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm


100

110

120

130

140

150

0 10 20 30 40 50 60 70 80 90 100

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


100

110

120

130

140

150

160

170

180

190

200

0 25 50 75 100 125 150 175 200 225 250

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


150

160

170

180

190

200

210

220

230

240

250

50 100 150 200 250 300 350 400 450

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


160

180

200

220

240

260

280

300

150 200 250 300 350 400 450 500 550 600 650

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm



200

220

240

260

280

300

320

340

360

250 300 350 400 450 500 550 600 650 700 750 800 850

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


220

240

260

280

300

320

340

360

380

400

420

350 450 550 650 750 850 950 1050 1150

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


240

260

280

300

320

340

360

380

400

420

440

460

550 650 750 850 950 1050 1150 1250 1350 1450

MRd (kNm)

VRd (kN)

2oslash20 mm

4oslash16 mm

σd = 01 Nmmsup2

σd = 02 Nmmsup2

σd = 03 Nmmsup2


σd = 06 Nmmsup2

σd = 07 Nmmsup2

σd = 08 Nmmsup2

σd ge 09 Nmmsup2


RNDZ-5-150 400 mm


280

300

320

340

360

380

400

420

440

460

480

500

520

650 750 850 950 1050 1150 1250 1350 1450 1550 1650 1750 1850

MRd (kNm)

VRd (kN)

2oslash20 mm

4oslash16 mm

σd = 01 Nmmsup2

σd = 02 Nmmsup2

σd = 03 Nmmsup2


σd = 06 Nmmsup2

σd = 07 Nmmsup2

σd = 08 Nmmsup2

σd ge 09 Nmmsup2


RNDZ-5-150 400 mm
















relevant






significantly







fck Nmm2SCC



















(63)

(64)

(65)

(66)





634 Design charts











Vd (MdNd) [kN]-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250

Md [kNm]

Nd [

kN]

0 10 20

30 40 50

60 70 80

90 Loadings




Vd (MdNd) [kN]-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250

Md [kNm]

Nd [

kN]

0 10 20

30 40 50

60 70 80

90 Loadings




Vd (MdNd) [kN]-3500

-3000

-2500

-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250 300 350 400 450

Md [kNm]

Nd [

kN]

0 20 40

60 80 100

120 140 160

180 Loadings



Vd (MdNd) [kN]-3500

-3000

-2500

-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250 300 350 400 450

Md [kNm]

Nd [

kN]

0 20 40

60 80 100

120 140 160

180 Loadings




Vd (MdNd) [kN]-5000

-4000

-3000

-2000

-1000

0

1000

0 200 400 600 800 1000 1200 1400 1600

Md [kNm]

Nd [

kN]

0 30 60

90 120 150

180 210 240

270 Loadings



Vd (MdNd) [kN]-5000

-4000

-3000

-2000

-1000

0

1000

0 200 400 600 800 1000 1200 1400 1600

Md [kNm]

Nd [

kN]

0 30 60

90 120 150

180 210 240

270 Loadings




Vd (MdNd) [kN]-9000

-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

0 500 1000 1500 2000 2500 3000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings



Vd (MdNd) [kN]-9000

-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings




Vd (MdNd) [kN]-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000 3500 4000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings



Vd (MdNd) [kN]-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000 3500 4000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings





-12000

-10000

-8000

-6000

-4000

-2000

0

2000

0 1000 2000 3000 4000 5000 6000 7000

Md [kNm]

Nd [

kN]

0 70 140

210 280 350

420 490 560

630 Loadings




-12000

-10000

-8000

-6000

-4000

-2000

0

2000

0 1000 2000 3000 4000 5000 6000 7000

Md [kNm]

Nd [

kN]

0 70 140

210 280 350

420 490 560

630 Loadings







































Material properties

fb Nmm2 1000

fm Nmm2 1000

K - 045

α - 070

β - 030

fk Nmm2 450

γM - 150

fd Nmm2 300

fyk0 Nmm2 020

fyk Nmm2 500

γS - 115

fyd Nmm2 43478

E Nmm2 210000

εyd permil 207



















xdx i

sim

minus=

minus εε (67)

sissi E εσ = (68)

summinus=i

sim FFN (69)

xtfF wam 80= (610)



sum ⎟⎠⎞

⎜⎝⎛ minus+⎟

⎠⎞

⎜⎝⎛ minus==

i

wisi

wmfR

bdFx

bFzHM

240

2 (612)



σ400 += vv ff bv ff 0650le (614)










644 Design charts







stress of 2 MPa

-500 0 500 1000 1500 2000 2500 3000 3500 40000

500

1000

1500

2000

2500

3000

3500

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Mom

ent (

kNm

)

Normal (kN) (a)

-500 0 500 1000 1500 2000 2500 3000 3500 40000

100

200

300

400

500

600

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Shea

r (kN

)

Normal (kN) (b)

0 500 1000 1500 2000 2500 3000 35000

100

200

300

400

500

600

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

She

ar (k

N)

Moment (kNm) (c)


(c) V x M





-500 0 500 1000 1500 2000100

150

200

250

300

350

400

450

500

ρh = 0035 ρ

h = 0049

ρh = 0098

Shea

r (kN

)

Normal (kN) (a)

0 100 200 300 400 500 600 700 800 900 1000

150

200

250

300

350

400

450

ρh = 0035 ρh = 0049 ρh = 0098

Shea

r (kN

)

Moment (kNm) (b)






-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000

500

1000

1500

2000

2500

3000

3500

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091

Mom

ent (

kNm

)

Normal (kN) (a)

0 400 800 1200 1600 2000 2400 2800 3200 3600

200

250

300

350

400

450

500

550

600

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091

Shea

r (kN

)

Moment (kNm) (b)




-500 0 500 1000 1500 2000 2500 30000

200

400

600

800

1000

1200

1400

1600

1800

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Mom

ent (

kNm

)

Normal (kN) (a)

-200 0 200 400 600 800 1000 1200 1400 1600 1800150

200

250

300

350

400

450

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Shea

r (kN

)

Moment (kNm) (b)



-500 0 500 1000 1500 20000

100

200

300

400

500

600

700

800

900

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Mom

ent (

kNm

)

Normal (kN) (a)

0 200 400 600 800 1000100

150

200

250

300

350

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Shea

r (kN

)

Moment (kNm) (b)




-300 0 300 600 900 12000

50

100

150

200

250

300

ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086

Mom

ent (

kNm

)

Normal (kN) (a)

-50 0 50 100 150 200 250 300

120

150

180

210

240

ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086

Shea

r (kN

)

Moment (kNm) (b)



-100 0 100 200 300 400 500 6000

10

20

30

40

50

60

70

ρv = 0049 ρv = 0070 ρv = 0098M

omen

t (kN

m)

Normal (kN) (a)

-10 0 10 20 30 40 50 60 7090

100

110

120

130

140

150

ρv = 0049 ρv = 0070 ρv = 0098

Shea

r (kN

)

Moment (kNm) (b)





71 INTRODUCTION






































Material property

CISEDIL













(71)














⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛minus=

Lxvy

2cos1max

π (72)




max2

2

41 v

LEJM

ry

base

π==⎟

⎠⎞


















N kN 50 50 50 M kNm 702 148 85

vmax mm 296 296 296




















724 Design charts


TensionCompression

Limit 2-3

Limit 3-4

Limit 4-5

Limit 5-6

Limit 60

50

100

150

200

250

300

350

-10000 -8000 -6000 -4000 -2000 0 2000 4000

NRd (kN)

MRd (kNm)






0

5

10

15

20

25

30

35

0 5 10 15 20 25 30 35

N (kN)

MRD (kNm)


t = 380 mm λ ge 12 Feb 44k




0

1

2

3

4

5

6

7

0 10 20 30 40 50

N (kN)

LIdeg (kN)

rmC-45m

rmC-5m

rmC-6m

rmC-7m

rmC-8m

t = 380 mm λ gt 12 Feb 44k

















fck Nmm2SCC




γS - 115











(74)

with

(75)


(76)








734 Design charts












0

20

40

60

80

100

120

140

0 2 4 6 8 10 12

as [cmsup2m]

MR

d [kN

mm

]

ABCDEFGHIJKL



0

20

40

60

80

100

120

140

160

0 2 4 6 8 10 12

as [cmsup2m]

MR

d [kN

mm

]

ABCDEFGHIJKL
































642











xεm

εsc

εst






744 Design charts






-500 0 500 1000 1500 2000 2500 3000 3500 40000

20

40

60

80

100

120

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Mom

ent (

kNm

)





-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000

20

40

60

80

100

120

ρv = 0035

ρv = 0049 ρv = 0070 ρv = 0091

Mom

ent (

kNm

)

Normal (kN)(a)

-500 0 500 1000 1500 2000 2500 30000

10

20

30

40

50

60

70

80

90

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Mom

ent (

kNm

)

Normal (kN)(b)

-500 0 500 1000 1500 200005

101520253035404550556065

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Mom

ent (

kNm

)

Normal (kN)(c)

-300 0 300 600 900 12000

5

10

15

20

25

30

35

40

ρv = 0037

ρv = 0049 ρv = 0070 ρv = 0086

Mom

ent (

kNm

)

Normal (kN)(d)


-100 0 100 200 300 400 500 6000

2

4

6

8

10

12

14

16

18

20

ρv = 0049

ρv = 0070 ρv = 0098

Mom

ent (

kNm

)

Normal (kN) (e)




81 DURABILITY







(EN 1996-1-1 2005 433)















REFERENCES









prestressed masonry


2005-018120



018120








buildingsrdquo












Zeland Wellingston





Italian)


New Jersey



















or








































password












312)









detail























masonry system























insulation










25cm ie 425 mmsup2m
























obtained

(a)

(b)























given































412 Wind loading






the turbulent wind









(43)


(44)











































(46a)

(46b)

(46c)

(46d)













1998-1-1]






(47)



(48a)

(48b)

(48c)

(48d)


spectra








(49a)

(49b)

(49c)

(49d)























(410a)

(410b)







favourable 090 000 100 000 100 000




of actions

(411)





ψEi = φ ψ2i (412)









(413)



















































beams








422 Wind loading





























satisfied







of the floor area












analysis y


rx ge ls (414b)






















enlargement




Figure 22d)


































51 INTRODUCTION


























vertical edges



tef = ρt t (51)








hef = ρn h (52)






if hl le 35

(53a)

if hl gt 35

(53b)


if hl le 115

(54a)

if hl gt 115

(54b)















0

2

4

6

8

10

12

14

16

18

50 54 58 62 66 70 74 78 82 86 90 94 98 102

106

110

114

118

122

126

130

134

138

142

146

150

154

158

162

166

170 ht

λ

λ2 (e le 025 t)λ2 (e gt 025 t)




ratio)


00

01

02

03

04

05

06

07

08

09

10

053

065

080

095

110

125

140

155

170

185

200

215

230

245

260

275

290

305

320

335

350

365

380

395

410

425

440

455

470

485

500 hl

ρ






0

1

2

3

4

5

6

7

8

9

10

50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600

l (cm)

λ





0

2

4

6

8

10

12

14

16

18

20

50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600

l (cm)

λ


















(55)





(G4) Vertical Holes








vh

kvvkhhk AA

fAfAf

++

= (56)











Masonry columns

Masonry panels

Masonry system

l (mm) 630 920 1550

fexp (Nmm2) 559 271 390

fth (eq 56) (Nmm2) - - 388

Error () - - 0005


10

15

20

25

30

35

40

45

50

55

60

500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500 3750 4000 4250

lw (mm)

f (Nmm2)

fexpfdα fd


the wall



































524 Design charts


750 mm1000 mm

1250 mm1500 mm

1750 mm2000 mm

2250 mm2500 mm

2750 mm3000 mm3250 mm3500 mm

4000 mm4250 mm

50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)


3750 mm

500 mm


150 400 mm


50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)





50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)





50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash14 mm

2oslash16 mm


4oslash16 mm




50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash16 mm

2oslash18 mm

2oslash20 mm

4oslash16 mm




50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash18 mm

2oslash20 mm

4oslash16 mm





50200

350500650

800950

11001250

140015501700

185020002150

23002450

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash20 mm

4oslash16 mm




50200

350500650

800950

110012501400

155017001850

20002150

23002450

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash20 mm

4oslash16 mm








0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)





eccentricity






























a reduction of 08


column

column

M

ccckeffd s

lff sdotsdot

=γ

α (57)












0

5

10

15

20

25

30

35

40

00 05 10 15 20 25 30 35 40



0

5

10

15

20

25

30

35

40

00 05 10 15 20 25 30 35 40




stress-strain-curve

0

5

10

15

20

25

30

35

40

00 20 40 60 80 100 120 140 160



0

5

10

15

20

25

30

35

40

00 20 40 60 80 100 120 140 160



stress-strain-curve




equation

( ) ( ) ( )c u sc u s

A A AE









fy yield strength








Hole 5000 3000












































fcmas


fcmas

corr cal fcmas


182 SU-VC-NM

136

163 SU-VC

353

168

mean 162

327 050 283 057

236 SU-SCC 445

216

mean 226

327 069 346 065

247 DU-SCC

438 175

mean 211

286 074 304 069

223 DU-SCC-DR 399

234

mean 229

295 078 272 084

261 DU-SCC-SR 365

257

mean 259

321 081 317 082


0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3






0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3








0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35







0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35






0

5

10

15

20

25

30

35

0 05 1 15 2 25 3 35





0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35











SdRd NN ge (58)













comparison


534 Design charts













the design charts










105 (lt12)










Material properties















544 Design charts

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

Nrd

(kN

)

(et)




00 01 02 03 04 050

500

1000

1500

2000

2500

3000L=160cm

As = 0036 As = 0045 As = 0074 As = 011 As = 017

Nrd

(kN

)

(et)

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

As = 0035 As = 0045 As = 0070 As = 011 As = 018

Nrd

(kN

)

(et)

L=280cm

(a) (b)



00 01 02 03 04 050

500

1000

1500

2000

2500

3000

As = 0022 As = 0034 As = 0045 As = 0070 As = 010

Nrd

(kN

)

(et)

L=400cm

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

3500

As = 0022 As = 0034 As = 0045 As = 0070 As = 010

Nrd

(kN

)

(et)

L=560cm

(a) (b)





61 INTRODUCTION













1 2 3R R R RV V V V= + + (61)



























NZS 4230 (2004) ltfC

ltN

vd 8080tan90

02 sdot⎟⎠

⎞⎜⎝

⎛+

sdotα lt

stfA

fC ydswvd 80)

80( 01 sdot

sdot+ 0

ACI 530 (2005) Nftl

VLM

d 250)7514(0830 +minus slfA ydsw 50 0

















































(62)






















is reliable













0

50

100

150

200

250

0 50 100 150 200 250 300 350 400

NEd (kN)

MRd (kNm)



5-150 400 mm


NTC 1500 mm

EC6 1500 mm

100

150

200

250

300

0 100 200 300 400 500 600

NEd (kN)

VRd (kN)



RNDZ-5-150 400 mm






















624 Design charts


500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm

2250 mm2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm

0

200

400

600

800

1000

1200

1400

1600

1800

2000

00 02 04 06 08 10 12 14σd (Nmm2)

MRd (kNm)




500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm

2250 mm2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 200 400 600 800 1000 1200 1400 1600

NEd (kN)

MRd (kNm)








100

150

200

250

300

350

400

450

500

550

00 02 04 06 08 10 12 14

σd (Nmm2)

VRd (kN)



500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm2250 mm

2500 mm2750 mm

3000 mm3250 mm

3500 mm

3750 mm4000 mm

4250 mm

100

150

200

250

300

350

400

450

500

550

0 200 400 600 800 1000 1200 1400 1600

NEd (kN)

VRd (kN)






0

200

400

600

800

1000

1200

1400

1600

1800

2000

-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400

NRd (kN)



500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm2250 mm

2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm




100

150

200

250

300

350

400

450

500

550

0 250 500 750 1000 1250 1500 1750 2000

MRd (kNm)

VRd (kN)







0

10

20

30

40

50

60

70

-400 -300 -200 -100 0 100 200 300 400 500 600 700 800 900

NRd (kN)

MRd (kNm)




0

50

100

150

200

250

-400 -200 0 200 400 600 800 1000 1200

NRd (kN)

MRd (kNm)




0

50

100

150

200

250

300

350

400

-400 -200 0 200 400 600 800 1000 1200 1400

NRd (kN)

MRd (kNm)




0

100

200

300

400

500

600

-400 -200 0 200 400 600 800 1000 1200 1400 1600

NRd (kN)

MRd (kNm)




0

100

200

300

400

500

600

700

800

900

-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800

NRd (kN)

MRd (kNm)




0

200

400

600

800

1000

1200

-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000

NRd (kN)

MRd (kNm)

2oslash18 mm

2oslash20 mm

4oslash16 mm




0

200

400

600

800

1000

1200

1400

-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

NRd (kN)

MRd (kNm)

2oslash20 mm

4oslash16 mm



0

300

600

900

1200

1500

1800

-600 -300 0 300 600 900 1200 1500 1800 2100 2400

NRd (kN)

MRd (kNm)

2oslash20 mm

4oslash16 mm




1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm


100

110

120

130

140

150

0 10 20 30 40 50 60 70 80 90 100

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


100

110

120

130

140

150

160

170

180

190

200

0 25 50 75 100 125 150 175 200 225 250

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


150

160

170

180

190

200

210

220

230

240

250

50 100 150 200 250 300 350 400 450

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


160

180

200

220

240

260

280

300

150 200 250 300 350 400 450 500 550 600 650

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm



200

220

240

260

280

300

320

340

360

250 300 350 400 450 500 550 600 650 700 750 800 850

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


220

240

260

280

300

320

340

360

380

400

420

350 450 550 650 750 850 950 1050 1150

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


240

260

280

300

320

340

360

380

400

420

440

460

550 650 750 850 950 1050 1150 1250 1350 1450

MRd (kNm)

VRd (kN)

2oslash20 mm

4oslash16 mm

σd = 01 Nmmsup2

σd = 02 Nmmsup2

σd = 03 Nmmsup2


σd = 06 Nmmsup2

σd = 07 Nmmsup2

σd = 08 Nmmsup2

σd ge 09 Nmmsup2


RNDZ-5-150 400 mm


280

300

320

340

360

380

400

420

440

460

480

500

520

650 750 850 950 1050 1150 1250 1350 1450 1550 1650 1750 1850

MRd (kNm)

VRd (kN)

2oslash20 mm

4oslash16 mm

σd = 01 Nmmsup2

σd = 02 Nmmsup2

σd = 03 Nmmsup2


σd = 06 Nmmsup2

σd = 07 Nmmsup2

σd = 08 Nmmsup2

σd ge 09 Nmmsup2


RNDZ-5-150 400 mm
















relevant






significantly







fck Nmm2SCC



















(63)

(64)

(65)

(66)





634 Design charts











Vd (MdNd) [kN]-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250

Md [kNm]

Nd [

kN]

0 10 20

30 40 50

60 70 80

90 Loadings




Vd (MdNd) [kN]-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250

Md [kNm]

Nd [

kN]

0 10 20

30 40 50

60 70 80

90 Loadings




Vd (MdNd) [kN]-3500

-3000

-2500

-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250 300 350 400 450

Md [kNm]

Nd [

kN]

0 20 40

60 80 100

120 140 160

180 Loadings



Vd (MdNd) [kN]-3500

-3000

-2500

-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250 300 350 400 450

Md [kNm]

Nd [

kN]

0 20 40

60 80 100

120 140 160

180 Loadings




Vd (MdNd) [kN]-5000

-4000

-3000

-2000

-1000

0

1000

0 200 400 600 800 1000 1200 1400 1600

Md [kNm]

Nd [

kN]

0 30 60

90 120 150

180 210 240

270 Loadings



Vd (MdNd) [kN]-5000

-4000

-3000

-2000

-1000

0

1000

0 200 400 600 800 1000 1200 1400 1600

Md [kNm]

Nd [

kN]

0 30 60

90 120 150

180 210 240

270 Loadings




Vd (MdNd) [kN]-9000

-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

0 500 1000 1500 2000 2500 3000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings



Vd (MdNd) [kN]-9000

-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings




Vd (MdNd) [kN]-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000 3500 4000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings



Vd (MdNd) [kN]-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000 3500 4000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings





-12000

-10000

-8000

-6000

-4000

-2000

0

2000

0 1000 2000 3000 4000 5000 6000 7000

Md [kNm]

Nd [

kN]

0 70 140

210 280 350

420 490 560

630 Loadings




-12000

-10000

-8000

-6000

-4000

-2000

0

2000

0 1000 2000 3000 4000 5000 6000 7000

Md [kNm]

Nd [

kN]

0 70 140

210 280 350

420 490 560

630 Loadings







































Material properties

fb Nmm2 1000

fm Nmm2 1000

K - 045

α - 070

β - 030

fk Nmm2 450

γM - 150

fd Nmm2 300

fyk0 Nmm2 020

fyk Nmm2 500

γS - 115

fyd Nmm2 43478

E Nmm2 210000

εyd permil 207



















xdx i

sim

minus=

minus εε (67)

sissi E εσ = (68)

summinus=i

sim FFN (69)

xtfF wam 80= (610)



sum ⎟⎠⎞

⎜⎝⎛ minus+⎟

⎠⎞

⎜⎝⎛ minus==

i

wisi

wmfR

bdFx

bFzHM

240

2 (612)



σ400 += vv ff bv ff 0650le (614)










644 Design charts







stress of 2 MPa

-500 0 500 1000 1500 2000 2500 3000 3500 40000

500

1000

1500

2000

2500

3000

3500

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Mom

ent (

kNm

)

Normal (kN) (a)

-500 0 500 1000 1500 2000 2500 3000 3500 40000

100

200

300

400

500

600

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Shea

r (kN

)

Normal (kN) (b)

0 500 1000 1500 2000 2500 3000 35000

100

200

300

400

500

600

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

She

ar (k

N)

Moment (kNm) (c)


(c) V x M





-500 0 500 1000 1500 2000100

150

200

250

300

350

400

450

500

ρh = 0035 ρ

h = 0049

ρh = 0098

Shea

r (kN

)

Normal (kN) (a)

0 100 200 300 400 500 600 700 800 900 1000

150

200

250

300

350

400

450

ρh = 0035 ρh = 0049 ρh = 0098

Shea

r (kN

)

Moment (kNm) (b)






-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000

500

1000

1500

2000

2500

3000

3500

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091

Mom

ent (

kNm

)

Normal (kN) (a)

0 400 800 1200 1600 2000 2400 2800 3200 3600

200

250

300

350

400

450

500

550

600

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091

Shea

r (kN

)

Moment (kNm) (b)




-500 0 500 1000 1500 2000 2500 30000

200

400

600

800

1000

1200

1400

1600

1800

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Mom

ent (

kNm

)

Normal (kN) (a)

-200 0 200 400 600 800 1000 1200 1400 1600 1800150

200

250

300

350

400

450

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Shea

r (kN

)

Moment (kNm) (b)



-500 0 500 1000 1500 20000

100

200

300

400

500

600

700

800

900

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Mom

ent (

kNm

)

Normal (kN) (a)

0 200 400 600 800 1000100

150

200

250

300

350

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Shea

r (kN

)

Moment (kNm) (b)




-300 0 300 600 900 12000

50

100

150

200

250

300

ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086

Mom

ent (

kNm

)

Normal (kN) (a)

-50 0 50 100 150 200 250 300

120

150

180

210

240

ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086

Shea

r (kN

)

Moment (kNm) (b)



-100 0 100 200 300 400 500 6000

10

20

30

40

50

60

70

ρv = 0049 ρv = 0070 ρv = 0098M

omen

t (kN

m)

Normal (kN) (a)

-10 0 10 20 30 40 50 60 7090

100

110

120

130

140

150

ρv = 0049 ρv = 0070 ρv = 0098

Shea

r (kN

)

Moment (kNm) (b)





71 INTRODUCTION






































Material property

CISEDIL













(71)














⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛minus=

Lxvy

2cos1max

π (72)




max2

2

41 v

LEJM

ry

base

π==⎟

⎠⎞


















N kN 50 50 50 M kNm 702 148 85

vmax mm 296 296 296




















724 Design charts


TensionCompression

Limit 2-3

Limit 3-4

Limit 4-5

Limit 5-6

Limit 60

50

100

150

200

250

300

350

-10000 -8000 -6000 -4000 -2000 0 2000 4000

NRd (kN)

MRd (kNm)






0

5

10

15

20

25

30

35

0 5 10 15 20 25 30 35

N (kN)

MRD (kNm)


t = 380 mm λ ge 12 Feb 44k




0

1

2

3

4

5

6

7

0 10 20 30 40 50

N (kN)

LIdeg (kN)

rmC-45m

rmC-5m

rmC-6m

rmC-7m

rmC-8m

t = 380 mm λ gt 12 Feb 44k

















fck Nmm2SCC




γS - 115











(74)

with

(75)


(76)








734 Design charts












0

20

40

60

80

100

120

140

0 2 4 6 8 10 12

as [cmsup2m]

MR

d [kN

mm

]

ABCDEFGHIJKL



0

20

40

60

80

100

120

140

160

0 2 4 6 8 10 12

as [cmsup2m]

MR

d [kN

mm

]

ABCDEFGHIJKL
































642











xεm

εsc

εst






744 Design charts






-500 0 500 1000 1500 2000 2500 3000 3500 40000

20

40

60

80

100

120

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Mom

ent (

kNm

)





-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000

20

40

60

80

100

120

ρv = 0035

ρv = 0049 ρv = 0070 ρv = 0091

Mom

ent (

kNm

)

Normal (kN)(a)

-500 0 500 1000 1500 2000 2500 30000

10

20

30

40

50

60

70

80

90

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Mom

ent (

kNm

)

Normal (kN)(b)

-500 0 500 1000 1500 200005

101520253035404550556065

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Mom

ent (

kNm

)

Normal (kN)(c)

-300 0 300 600 900 12000

5

10

15

20

25

30

35

40

ρv = 0037

ρv = 0049 ρv = 0070 ρv = 0086

Mom

ent (

kNm

)

Normal (kN)(d)


-100 0 100 200 300 400 500 6000

2

4

6

8

10

12

14

16

18

20

ρv = 0049

ρv = 0070 ρv = 0098

Mom

ent (

kNm

)

Normal (kN) (e)




81 DURABILITY







(EN 1996-1-1 2005 433)















REFERENCES









prestressed masonry


2005-018120



018120








buildingsrdquo












Zeland Wellingston





Italian)


New Jersey



















or








































password























masonry system























insulation










25cm ie 425 mmsup2m
























obtained

(a)

(b)























given































412 Wind loading






the turbulent wind









(43)


(44)











































(46a)

(46b)

(46c)

(46d)













1998-1-1]






(47)



(48a)

(48b)

(48c)

(48d)


spectra








(49a)

(49b)

(49c)

(49d)























(410a)

(410b)







favourable 090 000 100 000 100 000




of actions

(411)





ψEi = φ ψ2i (412)









(413)



















































beams








422 Wind loading





























satisfied







of the floor area












analysis y


rx ge ls (414b)






















enlargement




Figure 22d)


































51 INTRODUCTION


























vertical edges



tef = ρt t (51)








hef = ρn h (52)






if hl le 35

(53a)

if hl gt 35

(53b)


if hl le 115

(54a)

if hl gt 115

(54b)















0

2

4

6

8

10

12

14

16

18

50 54 58 62 66 70 74 78 82 86 90 94 98 102

106

110

114

118

122

126

130

134

138

142

146

150

154

158

162

166

170 ht

λ

λ2 (e le 025 t)λ2 (e gt 025 t)




ratio)


00

01

02

03

04

05

06

07

08

09

10

053

065

080

095

110

125

140

155

170

185

200

215

230

245

260

275

290

305

320

335

350

365

380

395

410

425

440

455

470

485

500 hl

ρ






0

1

2

3

4

5

6

7

8

9

10

50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600

l (cm)

λ





0

2

4

6

8

10

12

14

16

18

20

50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600

l (cm)

λ


















(55)





(G4) Vertical Holes








vh

kvvkhhk AA

fAfAf

++

= (56)











Masonry columns

Masonry panels

Masonry system

l (mm) 630 920 1550

fexp (Nmm2) 559 271 390

fth (eq 56) (Nmm2) - - 388

Error () - - 0005


10

15

20

25

30

35

40

45

50

55

60

500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500 3750 4000 4250

lw (mm)

f (Nmm2)

fexpfdα fd


the wall



































524 Design charts


750 mm1000 mm

1250 mm1500 mm

1750 mm2000 mm

2250 mm2500 mm

2750 mm3000 mm3250 mm3500 mm

4000 mm4250 mm

50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)


3750 mm

500 mm


150 400 mm


50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)





50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)





50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash14 mm

2oslash16 mm


4oslash16 mm




50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash16 mm

2oslash18 mm

2oslash20 mm

4oslash16 mm




50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash18 mm

2oslash20 mm

4oslash16 mm





50200

350500650

800950

11001250

140015501700

185020002150

23002450

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash20 mm

4oslash16 mm




50200

350500650

800950

110012501400

155017001850

20002150

23002450

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash20 mm

4oslash16 mm








0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)





eccentricity






























a reduction of 08


column

column

M

ccckeffd s

lff sdotsdot

=γ

α (57)












0

5

10

15

20

25

30

35

40

00 05 10 15 20 25 30 35 40



0

5

10

15

20

25

30

35

40

00 05 10 15 20 25 30 35 40




stress-strain-curve

0

5

10

15

20

25

30

35

40

00 20 40 60 80 100 120 140 160



0

5

10

15

20

25

30

35

40

00 20 40 60 80 100 120 140 160



stress-strain-curve




equation

( ) ( ) ( )c u sc u s

A A AE









fy yield strength








Hole 5000 3000












































fcmas


fcmas

corr cal fcmas


182 SU-VC-NM

136

163 SU-VC

353

168

mean 162

327 050 283 057

236 SU-SCC 445

216

mean 226

327 069 346 065

247 DU-SCC

438 175

mean 211

286 074 304 069

223 DU-SCC-DR 399

234

mean 229

295 078 272 084

261 DU-SCC-SR 365

257

mean 259

321 081 317 082


0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3






0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3








0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35







0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35






0

5

10

15

20

25

30

35

0 05 1 15 2 25 3 35





0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35











SdRd NN ge (58)













comparison


534 Design charts













the design charts










105 (lt12)










Material properties















544 Design charts

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

Nrd

(kN

)

(et)




00 01 02 03 04 050

500

1000

1500

2000

2500

3000L=160cm

As = 0036 As = 0045 As = 0074 As = 011 As = 017

Nrd

(kN

)

(et)

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

As = 0035 As = 0045 As = 0070 As = 011 As = 018

Nrd

(kN

)

(et)

L=280cm

(a) (b)



00 01 02 03 04 050

500

1000

1500

2000

2500

3000

As = 0022 As = 0034 As = 0045 As = 0070 As = 010

Nrd

(kN

)

(et)

L=400cm

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

3500

As = 0022 As = 0034 As = 0045 As = 0070 As = 010

Nrd

(kN

)

(et)

L=560cm

(a) (b)





61 INTRODUCTION













1 2 3R R R RV V V V= + + (61)



























NZS 4230 (2004) ltfC

ltN

vd 8080tan90

02 sdot⎟⎠

⎞⎜⎝

⎛+

sdotα lt

stfA

fC ydswvd 80)

80( 01 sdot

sdot+ 0

ACI 530 (2005) Nftl

VLM

d 250)7514(0830 +minus slfA ydsw 50 0

















































(62)






















is reliable













0

50

100

150

200

250

0 50 100 150 200 250 300 350 400

NEd (kN)

MRd (kNm)



5-150 400 mm


NTC 1500 mm

EC6 1500 mm

100

150

200

250

300

0 100 200 300 400 500 600

NEd (kN)

VRd (kN)



RNDZ-5-150 400 mm






















624 Design charts


500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm

2250 mm2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm

0

200

400

600

800

1000

1200

1400

1600

1800

2000

00 02 04 06 08 10 12 14σd (Nmm2)

MRd (kNm)




500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm

2250 mm2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 200 400 600 800 1000 1200 1400 1600

NEd (kN)

MRd (kNm)








100

150

200

250

300

350

400

450

500

550

00 02 04 06 08 10 12 14

σd (Nmm2)

VRd (kN)



500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm2250 mm

2500 mm2750 mm

3000 mm3250 mm

3500 mm

3750 mm4000 mm

4250 mm

100

150

200

250

300

350

400

450

500

550

0 200 400 600 800 1000 1200 1400 1600

NEd (kN)

VRd (kN)






0

200

400

600

800

1000

1200

1400

1600

1800

2000

-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400

NRd (kN)



500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm2250 mm

2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm




100

150

200

250

300

350

400

450

500

550

0 250 500 750 1000 1250 1500 1750 2000

MRd (kNm)

VRd (kN)







0

10

20

30

40

50

60

70

-400 -300 -200 -100 0 100 200 300 400 500 600 700 800 900

NRd (kN)

MRd (kNm)




0

50

100

150

200

250

-400 -200 0 200 400 600 800 1000 1200

NRd (kN)

MRd (kNm)




0

50

100

150

200

250

300

350

400

-400 -200 0 200 400 600 800 1000 1200 1400

NRd (kN)

MRd (kNm)




0

100

200

300

400

500

600

-400 -200 0 200 400 600 800 1000 1200 1400 1600

NRd (kN)

MRd (kNm)




0

100

200

300

400

500

600

700

800

900

-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800

NRd (kN)

MRd (kNm)




0

200

400

600

800

1000

1200

-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000

NRd (kN)

MRd (kNm)

2oslash18 mm

2oslash20 mm

4oslash16 mm




0

200

400

600

800

1000

1200

1400

-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

NRd (kN)

MRd (kNm)

2oslash20 mm

4oslash16 mm



0

300

600

900

1200

1500

1800

-600 -300 0 300 600 900 1200 1500 1800 2100 2400

NRd (kN)

MRd (kNm)

2oslash20 mm

4oslash16 mm




1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm


100

110

120

130

140

150

0 10 20 30 40 50 60 70 80 90 100

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


100

110

120

130

140

150

160

170

180

190

200

0 25 50 75 100 125 150 175 200 225 250

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


150

160

170

180

190

200

210

220

230

240

250

50 100 150 200 250 300 350 400 450

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


160

180

200

220

240

260

280

300

150 200 250 300 350 400 450 500 550 600 650

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm



200

220

240

260

280

300

320

340

360

250 300 350 400 450 500 550 600 650 700 750 800 850

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


220

240

260

280

300

320

340

360

380

400

420

350 450 550 650 750 850 950 1050 1150

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


240

260

280

300

320

340

360

380

400

420

440

460

550 650 750 850 950 1050 1150 1250 1350 1450

MRd (kNm)

VRd (kN)

2oslash20 mm

4oslash16 mm

σd = 01 Nmmsup2

σd = 02 Nmmsup2

σd = 03 Nmmsup2


σd = 06 Nmmsup2

σd = 07 Nmmsup2

σd = 08 Nmmsup2

σd ge 09 Nmmsup2


RNDZ-5-150 400 mm


280

300

320

340

360

380

400

420

440

460

480

500

520

650 750 850 950 1050 1150 1250 1350 1450 1550 1650 1750 1850

MRd (kNm)

VRd (kN)

2oslash20 mm

4oslash16 mm

σd = 01 Nmmsup2

σd = 02 Nmmsup2

σd = 03 Nmmsup2


σd = 06 Nmmsup2

σd = 07 Nmmsup2

σd = 08 Nmmsup2

σd ge 09 Nmmsup2


RNDZ-5-150 400 mm
















relevant






significantly







fck Nmm2SCC



















(63)

(64)

(65)

(66)





634 Design charts











Vd (MdNd) [kN]-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250

Md [kNm]

Nd [

kN]

0 10 20

30 40 50

60 70 80

90 Loadings




Vd (MdNd) [kN]-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250

Md [kNm]

Nd [

kN]

0 10 20

30 40 50

60 70 80

90 Loadings




Vd (MdNd) [kN]-3500

-3000

-2500

-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250 300 350 400 450

Md [kNm]

Nd [

kN]

0 20 40

60 80 100

120 140 160

180 Loadings



Vd (MdNd) [kN]-3500

-3000

-2500

-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250 300 350 400 450

Md [kNm]

Nd [

kN]

0 20 40

60 80 100

120 140 160

180 Loadings




Vd (MdNd) [kN]-5000

-4000

-3000

-2000

-1000

0

1000

0 200 400 600 800 1000 1200 1400 1600

Md [kNm]

Nd [

kN]

0 30 60

90 120 150

180 210 240

270 Loadings



Vd (MdNd) [kN]-5000

-4000

-3000

-2000

-1000

0

1000

0 200 400 600 800 1000 1200 1400 1600

Md [kNm]

Nd [

kN]

0 30 60

90 120 150

180 210 240

270 Loadings




Vd (MdNd) [kN]-9000

-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

0 500 1000 1500 2000 2500 3000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings



Vd (MdNd) [kN]-9000

-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings




Vd (MdNd) [kN]-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000 3500 4000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings



Vd (MdNd) [kN]-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000 3500 4000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings





-12000

-10000

-8000

-6000

-4000

-2000

0

2000

0 1000 2000 3000 4000 5000 6000 7000

Md [kNm]

Nd [

kN]

0 70 140

210 280 350

420 490 560

630 Loadings




-12000

-10000

-8000

-6000

-4000

-2000

0

2000

0 1000 2000 3000 4000 5000 6000 7000

Md [kNm]

Nd [

kN]

0 70 140

210 280 350

420 490 560

630 Loadings







































Material properties

fb Nmm2 1000

fm Nmm2 1000

K - 045

α - 070

β - 030

fk Nmm2 450

γM - 150

fd Nmm2 300

fyk0 Nmm2 020

fyk Nmm2 500

γS - 115

fyd Nmm2 43478

E Nmm2 210000

εyd permil 207



















xdx i

sim

minus=

minus εε (67)

sissi E εσ = (68)

summinus=i

sim FFN (69)

xtfF wam 80= (610)



sum ⎟⎠⎞

⎜⎝⎛ minus+⎟

⎠⎞

⎜⎝⎛ minus==

i

wisi

wmfR

bdFx

bFzHM

240

2 (612)



σ400 += vv ff bv ff 0650le (614)










644 Design charts







stress of 2 MPa

-500 0 500 1000 1500 2000 2500 3000 3500 40000

500

1000

1500

2000

2500

3000

3500

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Mom

ent (

kNm

)

Normal (kN) (a)

-500 0 500 1000 1500 2000 2500 3000 3500 40000

100

200

300

400

500

600

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Shea

r (kN

)

Normal (kN) (b)

0 500 1000 1500 2000 2500 3000 35000

100

200

300

400

500

600

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

She

ar (k

N)

Moment (kNm) (c)


(c) V x M





-500 0 500 1000 1500 2000100

150

200

250

300

350

400

450

500

ρh = 0035 ρ

h = 0049

ρh = 0098

Shea

r (kN

)

Normal (kN) (a)

0 100 200 300 400 500 600 700 800 900 1000

150

200

250

300

350

400

450

ρh = 0035 ρh = 0049 ρh = 0098

Shea

r (kN

)

Moment (kNm) (b)






-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000

500

1000

1500

2000

2500

3000

3500

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091

Mom

ent (

kNm

)

Normal (kN) (a)

0 400 800 1200 1600 2000 2400 2800 3200 3600

200

250

300

350

400

450

500

550

600

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091

Shea

r (kN

)

Moment (kNm) (b)




-500 0 500 1000 1500 2000 2500 30000

200

400

600

800

1000

1200

1400

1600

1800

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Mom

ent (

kNm

)

Normal (kN) (a)

-200 0 200 400 600 800 1000 1200 1400 1600 1800150

200

250

300

350

400

450

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Shea

r (kN

)

Moment (kNm) (b)



-500 0 500 1000 1500 20000

100

200

300

400

500

600

700

800

900

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Mom

ent (

kNm

)

Normal (kN) (a)

0 200 400 600 800 1000100

150

200

250

300

350

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Shea

r (kN

)

Moment (kNm) (b)




-300 0 300 600 900 12000

50

100

150

200

250

300

ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086

Mom

ent (

kNm

)

Normal (kN) (a)

-50 0 50 100 150 200 250 300

120

150

180

210

240

ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086

Shea

r (kN

)

Moment (kNm) (b)



-100 0 100 200 300 400 500 6000

10

20

30

40

50

60

70

ρv = 0049 ρv = 0070 ρv = 0098M

omen

t (kN

m)

Normal (kN) (a)

-10 0 10 20 30 40 50 60 7090

100

110

120

130

140

150

ρv = 0049 ρv = 0070 ρv = 0098

Shea

r (kN

)

Moment (kNm) (b)





71 INTRODUCTION






































Material property

CISEDIL













(71)














⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛minus=

Lxvy

2cos1max

π (72)




max2

2

41 v

LEJM

ry

base

π==⎟

⎠⎞


















N kN 50 50 50 M kNm 702 148 85

vmax mm 296 296 296




















724 Design charts


TensionCompression

Limit 2-3

Limit 3-4

Limit 4-5

Limit 5-6

Limit 60

50

100

150

200

250

300

350

-10000 -8000 -6000 -4000 -2000 0 2000 4000

NRd (kN)

MRd (kNm)






0

5

10

15

20

25

30

35

0 5 10 15 20 25 30 35

N (kN)

MRD (kNm)


t = 380 mm λ ge 12 Feb 44k




0

1

2

3

4

5

6

7

0 10 20 30 40 50

N (kN)

LIdeg (kN)

rmC-45m

rmC-5m

rmC-6m

rmC-7m

rmC-8m

t = 380 mm λ gt 12 Feb 44k

















fck Nmm2SCC




γS - 115











(74)

with

(75)


(76)








734 Design charts












0

20

40

60

80

100

120

140

0 2 4 6 8 10 12

as [cmsup2m]

MR

d [kN

mm

]

ABCDEFGHIJKL



0

20

40

60

80

100

120

140

160

0 2 4 6 8 10 12

as [cmsup2m]

MR

d [kN

mm

]

ABCDEFGHIJKL
































642











xεm

εsc

εst






744 Design charts






-500 0 500 1000 1500 2000 2500 3000 3500 40000

20

40

60

80

100

120

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Mom

ent (

kNm

)





-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000

20

40

60

80

100

120

ρv = 0035

ρv = 0049 ρv = 0070 ρv = 0091

Mom

ent (

kNm

)

Normal (kN)(a)

-500 0 500 1000 1500 2000 2500 30000

10

20

30

40

50

60

70

80

90

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Mom

ent (

kNm

)

Normal (kN)(b)

-500 0 500 1000 1500 200005

101520253035404550556065

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Mom

ent (

kNm

)

Normal (kN)(c)

-300 0 300 600 900 12000

5

10

15

20

25

30

35

40

ρv = 0037

ρv = 0049 ρv = 0070 ρv = 0086

Mom

ent (

kNm

)

Normal (kN)(d)


-100 0 100 200 300 400 500 6000

2

4

6

8

10

12

14

16

18

20

ρv = 0049

ρv = 0070 ρv = 0098

Mom

ent (

kNm

)

Normal (kN) (e)




81 DURABILITY







(EN 1996-1-1 2005 433)















REFERENCES









prestressed masonry


2005-018120



018120








buildingsrdquo












Zeland Wellingston





Italian)


New Jersey



















or








































password






















insulation










25cm ie 425 mmsup2m
























obtained

(a)

(b)























given































412 Wind loading






the turbulent wind









(43)


(44)











































(46a)

(46b)

(46c)

(46d)













1998-1-1]






(47)



(48a)

(48b)

(48c)

(48d)


spectra








(49a)

(49b)

(49c)

(49d)























(410a)

(410b)







favourable 090 000 100 000 100 000




of actions

(411)





ψEi = φ ψ2i (412)









(413)



















































beams








422 Wind loading





























satisfied







of the floor area












analysis y


rx ge ls (414b)






















enlargement




Figure 22d)


































51 INTRODUCTION


























vertical edges



tef = ρt t (51)








hef = ρn h (52)






if hl le 35

(53a)

if hl gt 35

(53b)


if hl le 115

(54a)

if hl gt 115

(54b)















0

2

4

6

8

10

12

14

16

18

50 54 58 62 66 70 74 78 82 86 90 94 98 102

106

110

114

118

122

126

130

134

138

142

146

150

154

158

162

166

170 ht

λ

λ2 (e le 025 t)λ2 (e gt 025 t)




ratio)


00

01

02

03

04

05

06

07

08

09

10

053

065

080

095

110

125

140

155

170

185

200

215

230

245

260

275

290

305

320

335

350

365

380

395

410

425

440

455

470

485

500 hl

ρ






0

1

2

3

4

5

6

7

8

9

10

50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600

l (cm)

λ





0

2

4

6

8

10

12

14

16

18

20

50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600

l (cm)

λ


















(55)





(G4) Vertical Holes








vh

kvvkhhk AA

fAfAf

++

= (56)











Masonry columns

Masonry panels

Masonry system

l (mm) 630 920 1550

fexp (Nmm2) 559 271 390

fth (eq 56) (Nmm2) - - 388

Error () - - 0005


10

15

20

25

30

35

40

45

50

55

60

500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500 3750 4000 4250

lw (mm)

f (Nmm2)

fexpfdα fd


the wall



































524 Design charts


750 mm1000 mm

1250 mm1500 mm

1750 mm2000 mm

2250 mm2500 mm

2750 mm3000 mm3250 mm3500 mm

4000 mm4250 mm

50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)


3750 mm

500 mm


150 400 mm


50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)





50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)





50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash14 mm

2oslash16 mm


4oslash16 mm




50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash16 mm

2oslash18 mm

2oslash20 mm

4oslash16 mm




50

200

350

500

650

800

950

1100

1250

1400

1550

1700

1850

2000

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash18 mm

2oslash20 mm

4oslash16 mm





50200

350500650

800950

11001250

140015501700

185020002150

23002450

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash20 mm

4oslash16 mm




50200

350500650

800950

110012501400

155017001850

20002150

23002450

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)

2oslash20 mm

4oslash16 mm








0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

000 005 010 015 020 025 030 035 040 045 050

et (-)

NRd (kN)





eccentricity






























a reduction of 08


column

column

M

ccckeffd s

lff sdotsdot

=γ

α (57)












0

5

10

15

20

25

30

35

40

00 05 10 15 20 25 30 35 40



0

5

10

15

20

25

30

35

40

00 05 10 15 20 25 30 35 40




stress-strain-curve

0

5

10

15

20

25

30

35

40

00 20 40 60 80 100 120 140 160



0

5

10

15

20

25

30

35

40

00 20 40 60 80 100 120 140 160



stress-strain-curve




equation

( ) ( ) ( )c u sc u s

A A AE









fy yield strength








Hole 5000 3000












































fcmas


fcmas

corr cal fcmas


182 SU-VC-NM

136

163 SU-VC

353

168

mean 162

327 050 283 057

236 SU-SCC 445

216

mean 226

327 069 346 065

247 DU-SCC

438 175

mean 211

286 074 304 069

223 DU-SCC-DR 399

234

mean 229

295 078 272 084

261 DU-SCC-SR 365

257

mean 259

321 081 317 082


0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3






0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3








0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35







0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35






0

5

10

15

20

25

30

35

0 05 1 15 2 25 3 35





0

5

10

15

20

25

30

35

40

0 05 1 15 2 25 3 35











SdRd NN ge (58)













comparison


534 Design charts













the design charts










105 (lt12)










Material properties















544 Design charts

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

Nrd

(kN

)

(et)




00 01 02 03 04 050

500

1000

1500

2000

2500

3000L=160cm

As = 0036 As = 0045 As = 0074 As = 011 As = 017

Nrd

(kN

)

(et)

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

As = 0035 As = 0045 As = 0070 As = 011 As = 018

Nrd

(kN

)

(et)

L=280cm

(a) (b)



00 01 02 03 04 050

500

1000

1500

2000

2500

3000

As = 0022 As = 0034 As = 0045 As = 0070 As = 010

Nrd

(kN

)

(et)

L=400cm

00 01 02 03 04 050

500

1000

1500

2000

2500

3000

3500

As = 0022 As = 0034 As = 0045 As = 0070 As = 010

Nrd

(kN

)

(et)

L=560cm

(a) (b)





61 INTRODUCTION













1 2 3R R R RV V V V= + + (61)



























NZS 4230 (2004) ltfC

ltN

vd 8080tan90

02 sdot⎟⎠

⎞⎜⎝

⎛+

sdotα lt

stfA

fC ydswvd 80)

80( 01 sdot

sdot+ 0

ACI 530 (2005) Nftl

VLM

d 250)7514(0830 +minus slfA ydsw 50 0

















































(62)






















is reliable













0

50

100

150

200

250

0 50 100 150 200 250 300 350 400

NEd (kN)

MRd (kNm)



5-150 400 mm


NTC 1500 mm

EC6 1500 mm

100

150

200

250

300

0 100 200 300 400 500 600

NEd (kN)

VRd (kN)



RNDZ-5-150 400 mm






















624 Design charts


500 mm750 mm1000 mm1250 mm1500 mm1750 mm2000 mm

2250 mm2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm

0

200

400

600

800

1000

1200

1400

1600

1800

2000

00 02 04 06 08 10 12 14σd (Nmm2)

MRd (kNm)




500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm

2250 mm2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 200 400 600 800 1000 1200 1400 1600

NEd (kN)

MRd (kNm)








100

150

200

250

300

350

400

450

500

550

00 02 04 06 08 10 12 14

σd (Nmm2)

VRd (kN)



500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm2250 mm

2500 mm2750 mm

3000 mm3250 mm

3500 mm

3750 mm4000 mm

4250 mm

100

150

200

250

300

350

400

450

500

550

0 200 400 600 800 1000 1200 1400 1600

NEd (kN)

VRd (kN)






0

200

400

600

800

1000

1200

1400

1600

1800

2000

-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400

NRd (kN)



500 mm750 mm

1000 mm1250 mm

1500 mm1750 mm

2000 mm2250 mm

2500 mm

2750 mm

3000 mm

3250 mm

3500 mm

3750 mm

4000 mm

4250 mm




100

150

200

250

300

350

400

450

500

550

0 250 500 750 1000 1250 1500 1750 2000

MRd (kNm)

VRd (kN)







0

10

20

30

40

50

60

70

-400 -300 -200 -100 0 100 200 300 400 500 600 700 800 900

NRd (kN)

MRd (kNm)




0

50

100

150

200

250

-400 -200 0 200 400 600 800 1000 1200

NRd (kN)

MRd (kNm)




0

50

100

150

200

250

300

350

400

-400 -200 0 200 400 600 800 1000 1200 1400

NRd (kN)

MRd (kNm)




0

100

200

300

400

500

600

-400 -200 0 200 400 600 800 1000 1200 1400 1600

NRd (kN)

MRd (kNm)




0

100

200

300

400

500

600

700

800

900

-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800

NRd (kN)

MRd (kNm)




0

200

400

600

800

1000

1200

-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000

NRd (kN)

MRd (kNm)

2oslash18 mm

2oslash20 mm

4oslash16 mm




0

200

400

600

800

1000

1200

1400

-600 -400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

NRd (kN)

MRd (kNm)

2oslash20 mm

4oslash16 mm



0

300

600

900

1200

1500

1800

-600 -300 0 300 600 900 1200 1500 1800 2100 2400

NRd (kN)

MRd (kNm)

2oslash20 mm

4oslash16 mm




1500 mm 2000 mm 2500 mm 3000 mm 3500 mm 4000 mm


100

110

120

130

140

150

0 10 20 30 40 50 60 70 80 90 100

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


100

110

120

130

140

150

160

170

180

190

200

0 25 50 75 100 125 150 175 200 225 250

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


150

160

170

180

190

200

210

220

230

240

250

50 100 150 200 250 300 350 400 450

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


160

180

200

220

240

260

280

300

150 200 250 300 350 400 450 500 550 600 650

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm



200

220

240

260

280

300

320

340

360

250 300 350 400 450 500 550 600 650 700 750 800 850

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


220

240

260

280

300

320

340

360

380

400

420

350 450 550 650 750 850 950 1050 1150

MRd (kNm)

VRd (kN)



RNDZ-5-150 400 mm


240

260

280

300

320

340

360

380

400

420

440

460

550 650 750 850 950 1050 1150 1250 1350 1450

MRd (kNm)

VRd (kN)

2oslash20 mm

4oslash16 mm

σd = 01 Nmmsup2

σd = 02 Nmmsup2

σd = 03 Nmmsup2


σd = 06 Nmmsup2

σd = 07 Nmmsup2

σd = 08 Nmmsup2

σd ge 09 Nmmsup2


RNDZ-5-150 400 mm


280

300

320

340

360

380

400

420

440

460

480

500

520

650 750 850 950 1050 1150 1250 1350 1450 1550 1650 1750 1850

MRd (kNm)

VRd (kN)

2oslash20 mm

4oslash16 mm

σd = 01 Nmmsup2

σd = 02 Nmmsup2

σd = 03 Nmmsup2


σd = 06 Nmmsup2

σd = 07 Nmmsup2

σd = 08 Nmmsup2

σd ge 09 Nmmsup2


RNDZ-5-150 400 mm
















relevant






significantly







fck Nmm2SCC



















(63)

(64)

(65)

(66)





634 Design charts











Vd (MdNd) [kN]-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250

Md [kNm]

Nd [

kN]

0 10 20

30 40 50

60 70 80

90 Loadings




Vd (MdNd) [kN]-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250

Md [kNm]

Nd [

kN]

0 10 20

30 40 50

60 70 80

90 Loadings




Vd (MdNd) [kN]-3500

-3000

-2500

-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250 300 350 400 450

Md [kNm]

Nd [

kN]

0 20 40

60 80 100

120 140 160

180 Loadings



Vd (MdNd) [kN]-3500

-3000

-2500

-2000

-1500

-1000

-500

0

500

0 50 100 150 200 250 300 350 400 450

Md [kNm]

Nd [

kN]

0 20 40

60 80 100

120 140 160

180 Loadings




Vd (MdNd) [kN]-5000

-4000

-3000

-2000

-1000

0

1000

0 200 400 600 800 1000 1200 1400 1600

Md [kNm]

Nd [

kN]

0 30 60

90 120 150

180 210 240

270 Loadings



Vd (MdNd) [kN]-5000

-4000

-3000

-2000

-1000

0

1000

0 200 400 600 800 1000 1200 1400 1600

Md [kNm]

Nd [

kN]

0 30 60

90 120 150

180 210 240

270 Loadings




Vd (MdNd) [kN]-9000

-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

0 500 1000 1500 2000 2500 3000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings



Vd (MdNd) [kN]-9000

-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings




Vd (MdNd) [kN]-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000 3500 4000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings



Vd (MdNd) [kN]-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000 3500 4000

Md [kNm]

Nd [

kN]

0 40 80

120 160 200

240 280 320

360 Loadings





-12000

-10000

-8000

-6000

-4000

-2000

0

2000

0 1000 2000 3000 4000 5000 6000 7000

Md [kNm]

Nd [

kN]

0 70 140

210 280 350

420 490 560

630 Loadings




-12000

-10000

-8000

-6000

-4000

-2000

0

2000

0 1000 2000 3000 4000 5000 6000 7000

Md [kNm]

Nd [

kN]

0 70 140

210 280 350

420 490 560

630 Loadings







































Material properties

fb Nmm2 1000

fm Nmm2 1000

K - 045

α - 070

β - 030

fk Nmm2 450

γM - 150

fd Nmm2 300

fyk0 Nmm2 020

fyk Nmm2 500

γS - 115

fyd Nmm2 43478

E Nmm2 210000

εyd permil 207



















xdx i

sim

minus=

minus εε (67)

sissi E εσ = (68)

summinus=i

sim FFN (69)

xtfF wam 80= (610)



sum ⎟⎠⎞

⎜⎝⎛ minus+⎟

⎠⎞

⎜⎝⎛ minus==

i

wisi

wmfR

bdFx

bFzHM

240

2 (612)



σ400 += vv ff bv ff 0650le (614)










644 Design charts







stress of 2 MPa

-500 0 500 1000 1500 2000 2500 3000 3500 40000

500

1000

1500

2000

2500

3000

3500

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Mom

ent (

kNm

)

Normal (kN) (a)

-500 0 500 1000 1500 2000 2500 3000 3500 40000

100

200

300

400

500

600

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Shea

r (kN

)

Normal (kN) (b)

0 500 1000 1500 2000 2500 3000 35000

100

200

300

400

500

600

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

She

ar (k

N)

Moment (kNm) (c)


(c) V x M





-500 0 500 1000 1500 2000100

150

200

250

300

350

400

450

500

ρh = 0035 ρ

h = 0049

ρh = 0098

Shea

r (kN

)

Normal (kN) (a)

0 100 200 300 400 500 600 700 800 900 1000

150

200

250

300

350

400

450

ρh = 0035 ρh = 0049 ρh = 0098

Shea

r (kN

)

Moment (kNm) (b)






-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000

500

1000

1500

2000

2500

3000

3500

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091

Mom

ent (

kNm

)

Normal (kN) (a)

0 400 800 1200 1600 2000 2400 2800 3200 3600

200

250

300

350

400

450

500

550

600

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0091

Shea

r (kN

)

Moment (kNm) (b)




-500 0 500 1000 1500 2000 2500 30000

200

400

600

800

1000

1200

1400

1600

1800

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Mom

ent (

kNm

)

Normal (kN) (a)

-200 0 200 400 600 800 1000 1200 1400 1600 1800150

200

250

300

350

400

450

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Shea

r (kN

)

Moment (kNm) (b)



-500 0 500 1000 1500 20000

100

200

300

400

500

600

700

800

900

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Mom

ent (

kNm

)

Normal (kN) (a)

0 200 400 600 800 1000100

150

200

250

300

350

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Shea

r (kN

)

Moment (kNm) (b)




-300 0 300 600 900 12000

50

100

150

200

250

300

ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086

Mom

ent (

kNm

)

Normal (kN) (a)

-50 0 50 100 150 200 250 300

120

150

180

210

240

ρv = 0037 ρv = 0049 ρv = 0070 ρv = 0086

Shea

r (kN

)

Moment (kNm) (b)



-100 0 100 200 300 400 500 6000

10

20

30

40

50

60

70

ρv = 0049 ρv = 0070 ρv = 0098M

omen

t (kN

m)

Normal (kN) (a)

-10 0 10 20 30 40 50 60 7090

100

110

120

130

140

150

ρv = 0049 ρv = 0070 ρv = 0098

Shea

r (kN

)

Moment (kNm) (b)





71 INTRODUCTION






































Material property

CISEDIL













(71)














⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛minus=

Lxvy

2cos1max

π (72)




max2

2

41 v

LEJM

ry

base

π==⎟

⎠⎞


















N kN 50 50 50 M kNm 702 148 85

vmax mm 296 296 296




















724 Design charts


TensionCompression

Limit 2-3

Limit 3-4

Limit 4-5

Limit 5-6

Limit 60

50

100

150

200

250

300

350

-10000 -8000 -6000 -4000 -2000 0 2000 4000

NRd (kN)

MRd (kNm)






0

5

10

15

20

25

30

35

0 5 10 15 20 25 30 35

N (kN)

MRD (kNm)


t = 380 mm λ ge 12 Feb 44k




0

1

2

3

4

5

6

7

0 10 20 30 40 50

N (kN)

LIdeg (kN)

rmC-45m

rmC-5m

rmC-6m

rmC-7m

rmC-8m

t = 380 mm λ gt 12 Feb 44k

















fck Nmm2SCC




γS - 115











(74)

with

(75)


(76)








734 Design charts












0

20

40

60

80

100

120

140

0 2 4 6 8 10 12

as [cmsup2m]

MR

d [kN

mm

]

ABCDEFGHIJKL



0

20

40

60

80

100

120

140

160

0 2 4 6 8 10 12

as [cmsup2m]

MR

d [kN

mm

]

ABCDEFGHIJKL
































642











xεm

εsc

εst






744 Design charts






-500 0 500 1000 1500 2000 2500 3000 3500 40000

20

40

60

80

100

120

hL = 050 hL = 070 hL = 100 hL = 175 hL = 350

Mom

ent (

kNm

)





-1000 -500 0 500 1000 1500 2000 2500 3000 3500 40000

20

40

60

80

100

120

ρv = 0035

ρv = 0049 ρv = 0070 ρv = 0091

Mom

ent (

kNm

)

Normal (kN)(a)

-500 0 500 1000 1500 2000 2500 30000

10

20

30

40

50

60

70

80

90

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0088

Mom

ent (

kNm

)

Normal (kN)(b)

-500 0 500 1000 1500 200005

101520253035404550556065

ρv = 0035 ρv = 0049 ρv = 0070 ρv = 0084 ρv = 0091

Mom

ent (

kNm

)

Normal (kN)(c)

-300 0 300 600 900 12000

5

10

15

20

25

30

35

40

ρv = 0037

ρv = 0049 ρv = 0070 ρv = 0086

Mom

ent (

kNm

)

Normal (kN)(d)


-100 0 100 200 300 400 500 6000

2

4

6

8

10

12

14

16

18

20

ρv = 0049

ρv = 0070 ρv = 0098

Mom

ent (

kNm

)

Normal (kN) (e)




81 DURABILITY







(EN 1996-1-1 2005 433)















REFERENCES









prestressed masonry


2005-018120



018120








buildingsrdquo












Zeland Wellingston





Italian)


New Jersey



















or








































password

Documents

Deliverable 6.2 Guidelines on the design for end-usersdiswall.dic.unipd.it/Results/D6.2_FINAL.pdf · forces are generally the governing actions, where earthquake forces are high