Structural Design of an Office Building with Large Spans in

a Seismic Zone

Projecto de um Edifício de Escritórios com Grandes vãos em Zona

Sísmica

Luís Filipe Dias de Almeida

Extended Abstract

Outubro de 2014

1

Structural Design of an Office Building

with Large Spans in a Seismic Zone

Luís Filipe Dias de Almeida

IST, Technical University of Lisbon,

Portugal

Keywords: Structural Design; Large Spans;

Pre-design; Prestressed Slabs; Seismic

Analysis; Eurocodes

1. Introduction

This thesis main goal is to examine the effect

of adopting a superior modeling in an office

building structural design, and verify its

economic efficiency facing inferior structural

modeling. To do so it is presented a quality

structural design, applying the knowledge

acquired throughout the MSc in Civil

Engineering.

The design started with the analysis of the

architectural design, in which the structural

design was based. Then, after the definition of

all the materials, it was possible to pre-design,

with basic calculations, all the structural

elements to ensure that a good solution was

achieved, without major changes in the

design.

The entire analysis of the structure was

performed taking into account the current

Eurocodes to ensure the demands of

functionality and durability (Serviceability

Limit States - SLS) and the stability and safety

of the structure (Ultimate Limit States - ULS).

2. Actions, Materials and Constraints

The architectural design, with the type office

and parking floors plans, presented the

precise location of the columns, spanned to a

maximum of 15 meters, ensuring the necessity

to use prestress despite of its use.

Figure 1: Architectural type floors design

The structural materials were chosen taking

into account the strong seismic action, the

massive axial loads on vertical elements and

the necessity to prestress the slabs.

Concrete C35/45

C25/30

Reinforcement steel bars A500NR

Prestress Strands Y1860 S7

Table 1: Structural Materials

All the actions were quantified according to

the guidelines from the Eurocodes [1] and the

Portuguese Legislation, as well as the

combinations of actions that were relevant to

ensure that the structure can bear out all the

2

actions with a certain degree of reliability. The

zones where it was though the loading did not

represent the reality, such as the slab that

communicates directly to the exterior and the

WC zones, the loads were increased.

3. Structural Pre-Design

Due to the large spans perceived in the

analysis of each floor, it was noticeable the

need to use prestress and, from all the kinds

of slabs, it was chosen the one that best

suited this situation, the waffle slab. It allows

a more rationalized construction achieved by

the increase of efficiency of materials without

adding extra weight. The areas adjacent to

vertical elements are flat, in order to resist to

negative bending moments and punching, as

well as the prestressed slab-bands between

columns.

The thickness was pre-designed based on

span/thickness limit ratios to ensure good

behavior to the SLS. Having chosen the slab’s

cross section, it was possible to calculate the

exact loads at each zone, taking into account

the volume of concrete per square meter of a

manufacturer’s table. At the end were

estimated the reduced bending moment

values by the equivalent frame analysis (Figure

2), as well as the necessary rebar percentage,

and verify they are within the limits of good

structural design. Since the limits refers to

lower quality concretes (C25/30 or less), it was

estimated the equivalent reduced bending

moment referring to a C25/30 concrete. It was

concluded that, as this values exceeded the

established limits, it would cause excessive

deformation of the slabs and consequent bad

behavior in service, suggesting the use of

prestress.

Figure 2: Equivalent frame analysis

The pre-design of vertical elements is of high

importance since they are the elements that

most resist to the seismic action and the axial

stresses from the entire structure.

Therefore, all the vertical structural elements

were classified as primary and secondary

seismic members, according to the

consideration, or not, as part of the seismic

action resistance. From this classification, the

minimum cross section area Ac was calculated

through:

for secondary seismic columns [2];

for primary seismic columns [3];

for primary seismic walls [3];

3

in which Nsd is the axial load on the element,

calculated using each influence area and the

respective deliberation of the distributed load

between the flat and waffle slab areas,

thereby ensuring sufficient ductility of this

elements.

Figure 3: Influence areas of vertical elements

Since the wall’s influence area is of the same

order of magnitude of the columns, a

thickness of 0,2m was more than enough to

ensure the recommendation of the EC8 [3].

Due to constructive issues this value was

increased to 0,25m.

The earth retaining walls were pre-designed

with a thickness of 0,3m, knowing that the

shear resistance is the unfavorable condition

and the shear and bending moment values

were estimated based on a simply supported

beam, loaded with the relevant combination

of actions.

Figure 4: Simply supported beam model

Note that the compression present in this

element contributes to the increase of shear

resistance value, even without specific

reinforcement.

Finally, with the estimated values of the axial

load at the lowest height, it was possible to

calculate the minimum area of each isolated

foundation Amin through:

(1)

with being the maximum admissible soil

tension (400kPa).

Figure 5: Foundation plant

The exiguous number of vertical columns

resulted at large dimensions of the

foundations in plan, followed with the vertical

dimension estimated through:

(2)

where A and a are respectively the dimensions

of the foundation and the column in the same

direction. The dimensions were fixed in order

to ensure that the cantilever dimensions at

each direction are close, resulting in a regular

reinforcement steel grid at the base, and the

height H (2) ensures a rigid behavior and a

reasonable quantity of reinforcement

In the end was done the pre-design of the

stair slabs using again simply supported beam

models.

4

4. Structural Modelling

Using the three dimensional finite elements

program SAP2000, it was possible to create a

three dimensional model of the entire

structure, essentially important to its dynamic

analysis. This allows saving a lot of time

required if done manually by other means.

The structural modelling is an iterative process

to find the solution that best suits the case

and meets all the requirements. For that

reason, an element effort can be controlled by

lowering its stiffness, knowing that it is

redistributed to the remaining elements,

thereby guaranteeing the global equilibrium

of the entire structure.

At first, all necessary materials were defined

with their mechanical and physical properties.

Note that it was created two distinct materials

necessary to properly model the core walls

and the prestress.

The dimensions adopted in the shell elements

(slabs) had to be compatible with the waffles

dimensions to represent precisely the waffle

and flat slab areas, defined with 0,8x0,8m2.

Upon the waffle slab properties definition, it

had to be figured the bending and membrane

thickness. The membrane thickness, in which

the program defines the self-weight, was

calculated as mentioned before. The bending

thickness was calculated through (3):

√

⁄

(3)

where I corresponds to the inertia of the

section of the manufacturer’s table.

All the other structural elements as columns,

walls and beams were modelled as bar finite

elements, with its respective cross section

areas, positioned at their center of gravity.

Figure 6: Finite bar element (top) and wall core (bottom)

The stair slabs weren’t directly applied in the

model. Instead, it was applied, at each end,

the respective loads according to the relevant

combination of actions.

At this time it was possible to verify the

truthfulness of the model by comparing the

values with the ones obtained upon the pre-

design of the structure, whereby the deviation

values were within reasonable ranges.

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5. Prestress

Due to the large spans and taking into account

the obtained pre-design values, special

attention was given in the analysis of the

slabs.

The tracing of the prestress cables should be

the most simple and efficient as possible, like

linear and parabolic 2nd degree sections,

taking advantage of the maximum eccentricity

in the higher bending moment zones.

Figure 7: Maximum prestress eccentricity

Knowing the prestress trace it is possible to

calculate the equivalent and anchorage loads

and apply them into the finite element model.

Figure 8: Prestress anchorage loads [4]

The prestress suffers immediate and time

dependent losses, during the stressing process

and through time, respectively. Since these

effects are very difficult to account

individually, the total losses were estimated

by two decreases of 10% and 15% to the initial

load Po that corresponds to 75% of the

breaking load Pu.

Since a slab-band is in the middle between a

slab and a beam, it was decided to limit the

compressive stress to a maximum of 4MPa.

To verify the Serviceability Limit State of

deflection it needed to be established the

maximum long-term deflection limit according

to the use of the floor and convert this value

to an equivalent instantaneous value [5]

through (for prestressed elements):

(4)

with ac and ae the deformation at long-term

and instantaneous or elastic, respectively.

δ long-term δ long-term(mm) δ elastic(mm)

Parking floor L/250 60 17,1

Office floor L/500 30 8,6

Table 2: Allowable deformations

The quantification of the prestress resulted in

an iterative process until the allowable

deformation was not reached at any point of

the slab.

At the exception of the office floor slabs, all

the prestress is present in flat slab-bands. At

this instead, due to the lack of continuity of

the slab and the increase of loads in the WC

zones, was necessary to adopt monostrands in

the ribs to handle the deformation at the

critical point.

Figure 9: Office type floor (1 to 3) deformation without

and with prestress, respectively top and bottom figure

6

Figure 10: Parking type floor(-3to-1)deformation without and with prestress, respectively top and bottom figure

Floor δe,max without prestress

(mm) δe,max with prestress

(mm)

-3 to -1 23,9 12,6 -0 47,0 17,0 0 41,7 8,5

1 to 3 43,3 8,6 4 43,3 8,6

Table 3: Maximum elastic deformation obtained, at each

floor, without and with prestress

At first it was calculated the required prestress

amount using 4 strand flat cables, but the

great density of cables in the slab-bands as

well as the large number of anchorages

prevented the use of them. So the final

design incorporated 7 strand cables which,

despite the decrease of eccentricity, involved

a smaller number of cables and anchorages,

decreasing the cost of this process.

In some cases the width of the slab-bands had

to be increased to verify the limit compressive

stress as well as the minimum width to keep

the necessary prestressed cables and, at the 0

floor, it had to be increased its thickness.

6. Seismic Analysis

The seismic analysis in Portugal is unavoidable

due to the great seismic action that it faces

and designing an economic and safe structure

is a civil engineer’s main goal. This analysis

was performed according to all EC8

recommendations in which no-collapse and

damage limitation requirements were

satisfied.

The seismic action was represented by an

elastic response spectrum, equal in both plan

directions, in which the vibration period

corresponds to a single degree of freedom

system.

Figure 11: Elastic response spectrum [3]

To avoid a non-linear analysis of the structure,

the energy-dissipation capacity was taken into

account by performing an elastic analysis

based in the reduced elastic response

spectrum decreased by a behavior factor q

depending on the ductility classification of the

structure, i.e., its energy-dissipation capacity.

The cracking and consequent loss of stiffness

of the primary vertical elements was also

7

taking into account by the decrease of its

bending and shear stiffness to a half of its

original.

In order to estimate a reasonable behavior

factor value and perform the analysis of the

structure it had to be characterized the

structural regularity in elevation and in plan.

Due to the existence of one only rigid wall

core near the center of the structure, it

suspected the structure to be torsionally

flexible, which was confirmed upon the

necessary calculations. Knowing that this

classification matched a low behavior factor

value, it was sought an alternate solution to

avoid this classification, creating a model

without stiff vertical elements (structural wall)

to resemble to the original model in terms of

cost/security. Note that to satisfy the damage

limitation requirements in the model, it had to

be increased iteratively the cross section of

the primary vertical elements.

Model "with shear walls"

Model "without shear walls"

q0 kw q u/ q0 kw q

2,0 1,0 2,0 1,3 3,9 1,0 3,9

Table 4: Behavior factor for both structural models

The spatial model analysis confirmed the

previous classification of the models, in which

evidences the first vibration mode associated

to a torsionally behavior due to the lack of

torsional rigidity face the high lateral rigidity

(Model “with shear walls”) and the two first

modes associated to pure translation behavior

due to the non-existence of these elements

(Model “without shear walls”) . In both

models, the first three vibration modes

characterize the behavior of 90% of the

effectively oscillatory mass, since almost 75%

of the mass of the entire structure is in the

basements.

Model “with shear walls”

Mode Períod Frequency Translation X Translaton Y Rotation Z

(s) (Hz) (%) ∑ (%) (%) ∑ (%) (%) ∑ (%)

1 1,23 0,81 0,04 0,04 0,00 0,00 0,06 0,06

2 0,94 1,06 0,09 0,12 0,13 0,13 0,07 0,12

3 0,92 1,09 0,11 0,23 0,10 0,23 0,05 0,18

4 0,44 2,26 0,01 0,24 0,00 0,23 0,01 0,19

5 0,32 3,11 0,02 0,26 0,00 0,24 0,00 0,19

6 0,32 3,14 0,01 0,28 0,00 0,24 0,00 0,19

7 0,32 3,14 0,00 0,28 0,00 0,24 0,00 0,19

8 0,30 3,32 0,00 0,28 0,00 0,24 0,00 0,19

9 0,30 3,32 0,00 0,28 0,00 0,24 0,00 0,19

10 0,29 3,47 0,00 0,28 0,00 0,24 0,00 0,19

Table 5: Modal analysis (Model “with shear walls”)

Model “without shear walls”

Mode Períod Frequency Translation X Translaton Y Rotation Z

(s) (Hz) (%) ∑ (%) (%) ∑ (%) (%) ∑ (%)

1 1,40 0,71 0,00 0,00 0,21 0,21 0,11 0,11

2 1,37 0,73 0,20 0,20 0,00 0,21 0,00 0,11

3 1,23 0,82 0,01 0,21 0,00 0,21 0,05 0,16

4 0,46 2,15 0,00 0,21 0,04 0,25 0,02 0,18

5 0,46 2,18 0,03 0,24 0,00 0,25 0,00 0,19

6 0,40 2,47 0,00 0,24 0,00 0,25 0,01 0,19

7 0,32 3,16 0,00 0,24 0,00 0,25 0,00 0,19

8 0,31 3,20 0,00 0,24 0,00 0,25 0,00 0,19

9 0,31 3,20 0,00 0,24 0,00 0,25 0,00 0,19

10 0,30 3,39 0,00 0,24 0,00 0,25 0,00 0,19

Table 6: Modal analysis (Model “without shear walls”)

At this time, knowing the soil parameters and

the seismic zone, it was possible to define the

design spectra for both seismic actions types.

Type I Type II

Seismic Zone 1,3 2,3

agR (m/s2) 1,5 1,7

ag 1,5 1,7

Solo C

Smáx 1,6 1,6

TB (s) 0,1 0,1

TC (s) 0,6 0,3

TD (s) 2,0 2,0

S 1,50 1,46

Table 7: Seismic parameters

8

0

4,4

8,8

13,2

17,6

22

0 0,05 0,1 0,15 0,2

H (m)

ds (m)

Total Drift

Figure 12: Horizontal design spectra

Due to the vertical modes of the slabs at low

frequencies, it was considered important to

include the vertical seismic action, defined too

by its spectra.

Figure 13: Vertical design spectra

The accidental torsional and second order

effects were taken into account in the analysis

to ensure that several factors of great

unpredictability enter the calculation. As

expected, in the model “with shear walls”, due

to the non-regularity in plan, the accidental

torsional effects were superior while in the

model “without shear walls”, due to the lower

lateral rigidity, the second order effects hat to

be taken into account by increasing the

seismic action depending on the interstorey

drift sensitivity coefficient θ.

At last the damage limitation requirement was

verified through [3]:

(5)

with the reduction factor that takes into

account the lower return period of the seismic

action for the damage limitation requirement.

Figure 14: Interstorey and total drift

At this time, with some calculations, it was

possible to determinate the different in cost

of both models’ vertical elements. Finally it

was chosen the Model “with shear walls” as

the most efficient structure in terms of

cost/safety.

7. Design

The serviceability limit state performed before

had to be enhanced with a crack control to

make sure that cracking is limited, in order

that it does not affect the proper functioning

and the durability of the structure.

Concerning the ultimate limit state design, all

the design was based on the Eurocodes 2 and

8 recommendations. The reinforcement bars

0

2

4

6

8

0 1 2 3

Se(m/s2)

T (s)

0

1

2

3

4

5

0 1 2 3

Sve (m2/s)

0

4,4

8,8

13,2

17,6

22

0,00 0,02 0,04 0,06

H (m)

dr (m)

Interstorey Drift

9

detailing ensured sufficient resistance and

ductility to all structural elements.

The beams were calculated by the capacity

design ensuring shear overstrenght to ensure

ductile instead of brittle rupture.

The slabs design was based on the nodal

stresses from SAP2000 which were

homogenized to avoid spike stresses. Since all

the slabs were prestressed the effective

reinforcement tension was calculated

removing the compression portion and, if the

case, exploited the variation of tension in the

prestress cables (just for adherent cables). To

avoid punching and progressive collapse of

the structure, shear and post-punching

reinforcement were conceived.

Figure 15: Punching failure mechanism and post-

punching reinforcement [6]

The primary columns were also calculated by

the capacity design and it was ensured the

necessary confinement according to EC8 and

the secondary columns according to EC2.

The core walls reinforcement were calculated

based on the design envelopes. Since these

elements are subject to cyclic compression

and tension stresses in a quake situation, the

confinement reinforcement calculation was of

major importance to ensure sufficient ductility

and make sure that spalling of concrete and

buckling of reinforcement does not occur.

Figure 16: Seismic design envelopes [3]

The main drawback of waffle slabs in the fire

safety and that why it were checked all

requirements for 60 min fire resistance listed

in EC2 [2].

8. Constructive Planning and

Measurement Map

At this stage it was possible to present a brief

construction planning and a budget for the

entire structure, as well as the cost per square

meter, and compare this value to the usual

values of construction.

Since a project to this structure has already

been designed in 2004, with a structural

modelling of 7,5x7,5m2, it was possible to

resemble with the actual one. To perform a

fair assessment between both, it was used the

actual unit prices of materials and the values

reached were 91€/m2 and 112€/m2

respectively for the original and actual

designs.

10

0

500000

1000000

1500000

2000000

Modelling 15x15m2 Modelling 7,5x7,5m2

€ Material costs

Total

Concrete

Steel

Prestress

Shuttering

Earthmoving

Figure 17: Material cost for both modellings

This corresponds to an overall cost difference

of approximately 20% and, though reinforcing

the idea that the increase of structural

modelling involves the increase of its cost, it is

a very encouraging result since it was possible

to obtain a good solution that verifies all the

requirements, even with a large structural

modification.

9. Conclusions

This thesis main goal was achieved and it is

presented a structural design for a challenging

structure. Several alternate solutions were

studied with different materials and structural

solutions, and it was chosen the one the best

suited the situation besides the cost which, in

these days, is an important factor. It must be

taken into account that in a “real case project”

the architectural solution would probably be

modified in order to obtain a less expensive

structure, as it can be compared with the

solution with smaller spans.

Nowadays we have in our reach powerful

tools to analyze even the most complex

structures, but it’s of good practice to

corroborate with some simple pre-design

calculations. This allows reaching a good

solution without major structural changes.

These three dimensional finite element

programs proved to be of great help in the

dynamic analysis of the structure and allowed

to save great amounts of time.

A civil engineers’ goal is not to present the

solution, but a good solution that verifies all

the requirements of stability, durability e

functionality during its lifetime at the lowest

cost.

10. References

[1] CEN. N 1991. Eurocode 1 – Actions on

structures, 2008.

[2] CEN. EN 1992. Eurocode 2 – Design of

concrete structures, 2008.

[3] CEN. EN 1998. Eurocode 8 – Design of

structures for earthquake resistance, 2008.

[4] Marchão, Carla e Appleton, Júlio.

Estruturas de Betão II – Folhas de Apoio às

Aulas. Módulo 1 - Pré-Esforço. IST, 2011.

[5] Appleton, Júlio. Estruturas de Betão I -

Folhas de Apoio às Aulas. Módulo 3 –

Verificação do Comportamento em Serviço

(Estados Limites de Utilização - SLS), 2010.

[6] Marchão, Carla e Appleton, Júlio.

Estruturas de Betão II - Folhas de Apoio às

Aulas. Módulo 2 - Lajes de Betão Armado.

Lisboa : Instituto Superior Técnico, 2011.