Unreinforced masonry Shear loading · Design of masonry structures Unreinforced masonry Shear loading Prof. Dr.-Ing. Wolfram Jäger Dresden University of Technology Dr.-Ing. Sebastian

Dissemination of information for training – Brussels, 2-3 April 2009 slide 1 out of 23

EUROCODE 6Background and applications

EUROCODE 6Design of masonry structures

Unreinforced masonry Shear loading

Prof. Dr.-Ing. Wolfram JägerDresden University of Technology

Dr.-Ing. Sebastian OrtleppJaeger Consulting Engineers Ltd., Office for Structural Design

Dipl.-Ing. Carola HauschildJaeger Consulting Engineers Ltd., Office for Structural Design


EUROCODE 6Background and applications Unreinforced masonry – shear loading

Types of actions for verification against shear

In plane Out of plane

• wind action perpendicular to the wall

• pressure of earth.

• transmission of wind loads

• stiffening forces



Bracing of buildingsThe layout of the walls in the ground plan of the building should be foreseen in such a way that the sufficient bracing of a building should be guaranteed.

The principles of bracing are:• concrete ceiling or ring beam• more than 3 walls• the axes should not intersect in one point



Bracing of buildings

• favourable

• unfavourable

• instable

M0

high excentricity

M0

M0M0



Verification format EN 1996-1-1

filled head joints

unfilled head joints

shell bedded masonry

⎩⎨⎧ ⋅

≤⋅+=vlt

bdvkvk f

fff

065,04,00 σ

⎩⎨⎧ ⋅

≤⋅+⋅=vlt

bdvkvk f

fff

045,04,05,0 0 σ

⎩⎨⎧ ⋅

≤⋅+⋅=vlt

bdvkvk f

ff

tgf

045,04,00 σ

cvdRd ltfV ⋅⋅=

NDP - 1

NDP - 2



Verification format

Variables:fvk0: initial shear strength without loadσd: compressive stress, perpendicular with shear loadfb: normalized compressive strength of masonryfvlt: limit of shear strengthg: overall with of mortar stripst: thickness of the wall



Verification format EN 1996-3Simplified calculation methods

with: cv = 3 filled head joints cv = 1,5 unfilled head joints eEd: excentricity of load t: thickness of the wallfvd0= fvk0/γMNEd: vertical loadl: length of the wallfvdu: ultimate shear strength (0,065 fb or fvlt/γM)

vduEdM

EdvdoEdvRd ftelN

ftelcV ⋅⋅⎥⎦⎤

⎢⎣⎡ −≤⋅+⋅⋅⎥⎦

⎤⎢⎣⎡ −⋅=

234,0

2 γ



Verification modelBackground – theory

Failure due toa) gaping of bed joint b) friction of bed jointc) tensile failure of the unitsd) crushing

σDd

a

σDd

b

σDd

d

σDd

τ

tensile strength

cdba

initial shear strength Shear strength



Verification modelBackground – theory

result:friction failure

equilibrium of forces at a masonry unit

theory of principle stresses

tensile failure (anisotrophy)

σ

Δx

τ

τΔy

Δσσ Δσσ

a

bDd

Qb

( ) yx4x

2x22 Δ⋅Δ⋅τ=

Δ⋅

Δ⋅σΔ⋅

( )22

DdDdvb 3,2

42f τ⋅+

σ±

σ=

Ddvk0vk ff σ⋅μ+=bt

Ddbtvk f

1f45,0f σ+=



Comparison to theory

AAC Brick with vertical holes



Procedure in plane shear loadingA) Actions• wind action• bracing forces• normal stresses/forces and

compressed area– Bending action due to in plane lateral

forces– Determination of the compressed area– Bending due to deflection of the ceilings

B) Resistance• Determination of shear strength and

shear resistanceC) Verification• Design action ≤ Design resistance

y

x

NEk

z

HEk

NRF

NEF

f

y

x

NEk

z

NRF

NEF

NRK

f

RdEd V V ≤



Procedure out of plane shear loadingA) Actions• Determination of wind action• Determination of normal stresses/forces

and compressed area– Bending action due to out of plane lateral

forces– Determination of the compressed area

B) Resistance• Determination of shear strength and

shear resistanceC) Verification• Design action ≤ Design resistance

RdEd V V ≤



Working exampleBuildingBrick with vertical holes

longitudinal section A-A



Working exampleBuilding

first floor plan

Beams



Pos. W2 interior wallGeometryt = 0,24ml = 2,24ml1 = 3,60m

Material parametersclay bricks, group 2

fb = 15 N/mm²mortar M 2,5,

fm = 2,5 N/mm²

g = 5,5 kN/m²; q = 1,5 kN/m²Ag= 56,6 kN; Ap= 16,9 kN

zone of beam load

beam

Verification of shear loading acc. EN 1996-1-1



Vertical loadsbeam

Ag=56,6 kN; Aq=16,9 kNangle of load distribution 60°

line force from dead load of the wall gwall=4,67 kN/m²

line supporting force from dead load of the ceilingg = 5,5 kN/m²; q = 1,5 kN/m²

verification of bending in plane: see 3_am_6_Jäger.pdf on the stickdetermination of input data for shear check from bending in

planelc = l = 2,24 m (linear stress distribution)min N = 22,96 kN



Load case combinations

LFK 1

1,35g+1,5q

LFK 2

1,35g

LFK 3 LFK 4 LFK 5

LFK 6

1,35g+1,5q 1,35g

1,35g+1,5q 1,35g+1,5q

1,0 g

1,35g+1,5q

1,35g

1,35g 1,35g

LFK LFK 8 LFK 9

1,0g+1,5q 1,35 g+1,5q

1,0g+1,5q

1,0g

1,0g 1,5H,w

1,35 N +1,5Ng q 1,35 N +1,5Ng q 1,35 Ng 1,35 Ng 1,35 Ng

1,0 Ng 1,0 Ng 1,0 Ng 1,35 N +1,5Ng q

1,35 g+1,5q

1,5H,w 1,5H,w 1,5H,w

1,0g



Verification to shear loading Design value of the shear resistance (load case 1)

with

(filled head joints)

M

cvkRd

ltfV

γ⋅⋅

=

dvkovk 4,0ff σ⋅+=

²m/MN20,0fvko = unit group 2, mortar M2,5 from table NA

m/MN427,024,224,0

23,0ltNminvorh 2

cd =

⋅=

⋅=σ

²m/MN371,0427,04,020,0fvk =⋅+=

²m/MN975,015065,0f065,0 b =⋅=⋅<

γM =1,7 from NA (see table 1 DIN EN 1996-1-1)



Verification to shear loadingDesign value of the shear resistance

(unfilled head joints)

(shell bedded joints)(g/t = 0,5)

(filled head joints)

(unfilled/shell bedded)

kN3,1177,1

24,224,0371,0VRd =⋅⋅

=

RdEd V)kN7,85(kN17,31 kN61,29 V =<=

²m/MN271,0427,04,020,05,0fvk =⋅+⋅=

²m/MN675,015045,0f045,0 b =⋅=⋅<

²m/MN271,0427,04,020,05,0fvk =⋅+⋅=

²m/MN675,015045,0f045,0 b =⋅=⋅<

kN7,857,1

24,224,0271,0VRd =⋅⋅

=



Verification to shear loading simplified method Requirements• stores above ground level ≤ 3; • the walls are fixed either through the ceiling or through appropriate

constructions, such as ring beams; • load depth of the ceiling and the roof on the wall is at least 2 / 3 of wall

thickness, but not less than 85 mm; • floor height ≤ 3.0 m; • the smallest dimensions in the building floor plan is at least 1 / 3 of

building height; • the characteristic values of the variable loads on the ceiling and the roof

≤ 5.0 kN / m²; • span of the ceiling ≤ 6.0 m;

EN 1996-3



Verification to shear loading - simplified method Design value of the shear resistance

cv = 3 (filled head joints)

vduEdM

EdvdoEdvRd fte

2l3

N4,0fte

2lcV ⋅⋅⎥⎦

⎤⎢⎣⎡ −≤

γ⋅+⋅⋅⎥⎦

⎤⎢⎣⎡ −⋅=

7,1371,024,0376,0

224,23

7,1229,04,0

7,12,024,0376,0

224,23VRd

⋅⋅⎥⎦⎤

⎢⎣⎡ −≤

⋅+⋅⋅⎥⎦⎤

⎢⎣⎡ −⋅=

kN117kN180VRd ≤=

RdEd VkN171 kN61,29 V =<=

m376,0585,229031,77

NMe

Ed

EdEd ===



Verification to shear loading - simplified methodDesign value of the shear resistancecv = 1,5 (unfilled head joints)

7,1371,024,0376,0

224,25,1

7,1229,04,0

7,12,024,0376,0

224,25,1VRd

⋅⋅⎥⎦⎤

⎢⎣⎡ −≤

⋅+⋅⋅⎥⎦⎤

⎢⎣⎡ −⋅=

kN5,58kN90VRd ≤=

RdEd VkN8,55 kN61,29 V =<=



Applikation of fvlt

tensile failure of the unit

fbt: tensile strength of the unitfbt = 0,025 · fb hollow blocks;fbt = 0,033 · fb vertically perforated bricks and units with grip hole;fbt = 0,040 · fb full blocks without grip hole;

simplified(filled head joints)(unfilled head joints)

bt

Ddbtvklt f

ff σ+= 145,0

bvklt f065,0f =

bvklt f045,0f =


EUROCODE 6Background and applications Hint to ESECMaSE-Project

Reason: 1,5⋅H/1.0⋅N = 1,5⋅eprevious

Aim: description of the shearfailure closer to reality to usethe reserves

Done:a) Matrial tests/test methodsb) Static/cyclic shear testsc) Pseudodynamic testsd) Shaking tabel testse) Theoretical analysesf) Engineering modelg) Recommandations for the practice

Test on shaking table in Athens (CS)

Collapse analyses

ESECMaSEEnhanced Safety and Efficient Construction of Masonry Structures in Europe


EUROCODE 6Background and applications

for AAC:Tensile

failure of the unit

Friction

Gaping

Bending

Proposal from WP 4

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⋅

−⋅⋅

=flt

NNVv

bending

2

21λ

⎟⎟⎠

⎞⎜⎜⎝

⎛+

⋅=

hhNlV

b

bgaping

112

NV friction ⋅= μ

Hint to ESECMaSE-Project

( ) ( ) ⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−⎟

⎟⎠

⎞⎜⎜⎝

⎛++⋅⋅⋅⋅=

− 1111

,

2*2*,

calbt

dcalbtunit f

FFtlfc

V σ

( ) ( )⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−⎟

⎟⎠

⎞⎜⎜⎝

⎛++⋅⋅⋅⋅⋅=

− 114

121

,

2*2*

,,calbt

dcalbtAACunit f

FFtlfc

V σ

btfF 85.02.1* +=

Eng.-Model: From stress level to force level

ESECMaSEEnhanced Safety and Efficient Construction of Masonry Structures in Europe


EUROCODE 6Background and applications Anauncement of 8th IMC Dresden 2010







Documents

Unreinforced masonry Shear loading · Design of masonry structures Unreinforced masonry Shear loading Prof. Dr.-Ing. Wolfram Jäger Dresden University of Technology Dr.-Ing. Sebastian