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Structural Design of a Building Extended Abstract Miguel Ramos Benfica de Melo March 2015

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Page 1: Structural Design of a Building - ULisboa Abstract...Structural Design of a Building Extended Abstract 1 - Introduction This thesis presents the development of a building’s structural

Structural Design of a Building

Extended Abstract

Miguel Ramos Benfica de Melo

March 2015

Page 2: Structural Design of a Building - ULisboa Abstract...Structural Design of a Building Extended Abstract 1 - Introduction This thesis presents the development of a building’s structural
Page 3: Structural Design of a Building - ULisboa Abstract...Structural Design of a Building Extended Abstract 1 - Introduction This thesis presents the development of a building’s structural

1

Structural Design of a Building

Extended Abstract

1 - Introduction

This thesis presents the development of a

building’s structural design. The scope of this

work is to create a structural solution that

ensures the safety of the building when facing

regulatory actions.

The study object is destined to be a warehouse

and a parking lot, in the area of Lisbon. It is

characterized by a considerable area with an

implantation area of approximately 15500 m2

and a total construction area of approximately

64000 m2. It has in its major extent 180 m and

120 m in the perpendicular direction. It features

two underground floors and two others above

ground floor, with a reduction of plan area of

approximately 38% from the ground floor to the

upper floors. The underground floors are

surrounded by an earth retaining wall. The two

underground floors are destined for parking lot

(𝐴 = 2 ∙ 15435 = 30870 𝑚2) and the next two

floors for warehouse (𝐴 = 15435 + 8857 =

24292 𝑚2). The roof (𝐴 = 8857 𝑚2) was

considered not accessible except for normal

maintenance and repair.

Figure 1: Building’s geometry

The goal of this work was to understand the

applicability of the theoretical knowledge

platform gained over the Instituto Superior

Técnico’s Structural Engineering course to the

practical activity of structural design.

Therefore, the different phases of a building’s

structural design, from its initial conception to

the final design, will be presented in this paper,

giving more emphasis in the determination of

the slab solution.

2 - Actions and combination of

actions

Structural analysis must consider the influence

of all actions that might produce significant

stress or strain to the structure’s safety.

Permanent and variable actions in the

structure were considered.

Regarding the permanent actions, apart from

the self-weight of structural elements, imposed

loads of 2,0 kN/m2 for the traffic and storage

areas and 2,5 kN/m2 for the coverage were

considered.

Regarding the variable actions, according to

the regulations, for traffic areas (Category F),

the imposed loads to be used are 4 kN/m2. For

areas of storage (Category E1) and for roofs

(Category H), an imposed load of 10 kN/m2

and 0,44 kN/m2 were used, respectively.

For the seismic action (SA), considering the

study case with an importance class of II and a

ground type B, and that Lisbon is situated in a

seismic zone of 1.3 and 2.3 respectively for

type 1 and 2 response spectra, the values that

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2

define the response spectrum used in the

analysis are presented in the following table:

Table 1: Seismic parameters for Lisbon (EC8-1) with ground type B

Parameters SA

Type

SA

Type

𝑆𝑚𝑎𝑥 1,35 1,35

𝑇𝐵 (s) 0,1 0,1

𝑇𝐶 (s) 0,6 0,25

𝑇𝐷 (s) 2,0 2,0

𝑎𝑔𝑅 (ms-2

) 1,5 1,7

𝑎𝑔 (ms-2

) 1,5 1,7

𝑆 1,292 1,268

Regarding the temperature action, according to

the EC-1, Lisbon is situated in the B thermal

zone, which gives different values of

temperatures depending on the exposure of

the elements and the time of the year. The

uniform temperature represents the difference

between the temperature of the element due to

climate effects and the initial temperature of

the element. Respectively for the traffic area,

storage area, roof and for the earth retaining

wall, the uniform temperature values used in

this work are -2°C, -6°C, -6°C and -2°C, which

are relative to the winter season. The summer

season’s values were not used so the effect of

negative uniform temperature could be

combined with the effect of shrinkage of

concrete.

Safety verification criteria to Ultimate Limit

State (ULS) and Serviceability Limit State

(SLS) were adopted in the structure analysis

and design, according to the European

structures regulation, the Eurocodes, namely

Eurocodes 0, 1, 2 and 8 (EC0, EC1 and EC8,

respectively).

In accordance with the recommendations in

the Eurocodes, different combinations of

actions were considered for the analysis of

ULS and SLS. For ULS two combinations were

adopted, the fundamental combination

(𝐸𝑑 = 𝛾𝐺,𝑗 ∙ 𝐺𝑘,𝑗𝑗>1 " + "𝛾𝑄,1 ∙ 𝑄𝑘,1" +

" 𝛾𝑄,𝑖 ∙ 𝛹0,𝑖 ∙ 𝑄𝑘,𝑖𝑖>1 ) and the combination of

actions for seismic design situations (𝐸𝑑 =

𝐺𝑘,𝑗𝑗>1 " + "𝐴𝐸𝑑" + " 𝛹2,𝑖 ∙ 𝑄𝑘,𝑖𝑖>1 ).

Concerning the SLS, the quasi-permanent

combination was used (𝐸𝑑 = 𝐺𝑘,𝑗𝑗>1 " +

" 𝛹2,𝑖 ∙ 𝑄𝑘,𝑖𝑖>1 ).

For the seismic action, the directional

combination used a combination of 100%

response to one direction with 30% to the

perpendicular direction.

3 - Materials and ground

resistance

The materials adopted were C25/30 for

concrete and A500 NR SD for ordinary rebar.

Considering exposure classes of XC4, rebar

cover was considered to be 35 mm for slabs

and 40 mm for the rest of the structural

elements. Also, for this class of exposure, the

regulations limit the crack’s maximum opening

to 𝑤𝑚𝑎𝑥 = 0,3 𝑚𝑚.

According to the available data, the terrain’s

design admitted stress was considered to be

𝜎𝑎𝑑𝑚 = 300 𝑘𝑁 𝑚2 . Therefore the terrain’s

stress resistance is given by 𝜎𝑅𝑑 = 1,5 ∙ 𝜎𝑎𝑑𝑚 =

450 𝑘𝑁/𝑚2.

4 - Determination of the slab

solution

For this case of study, a grid of columns was

adopted of 8,10 m by 8,10 m. The first step of

this project was to define a slab solution that

combines construction speed and economical

prices. Therefore, four types of slabs were

studied: light weighted waffle slab with

recoverable molds, beam-supported slab, flat

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slab with constant thickness and flat slab with

drop panels. The analysis for the determination

of the slab solution has been made for each

type of floor usage of the building, namely, for

the parking area, for the storage area and for

the roof slab.

For each type of slab, a parametrical analysis

has been made to calculate costs of materials

(concrete and steel rebar) and formwork

system, by changing its geometrical

parameters. In the following table are

presented the costs of materials used in this

analysis.

Table 2: Material costs

Material Costs

Concrete €/m3 100

Rebar (ϕ8) €/ton 850

Rebar (ϕ10) €/ton 820

Rebar (ϕ12) €/ton 800

Rebar (ϕ16) €/ton 795

Rebar (ϕ20) €/ton 795

Rebar (ϕ25) €/ton 805

Should be noted that this analysis was only

made for the fundamental combination of

action. Therefore, there were not considered

the effects of the seismic action which have a

considerable importance in slab’s stresses.

Also, the effect of uniform temperature and

concrete shrinkage were not considered

because they depend of the structural solution

that was chosen, and these analysis only

consider an interior slab panel.

For the case of the light weighted waffle slab,

800 mm by 800 mm recoverable molds were

used, with heights of 200 mm (M200), 300 mm

(M300) and 400 mm (M400). A 90 mm thick

topping slab was considered for all waffle slabs

that were analysed. Between columns, a band

beam was used, with the same depth as the

ribs. On top of columns, a head column was

used, also with the same depth as the ribs.

Regarding the narrow ribs spanning in both

directions, widths of 165 mm, 190 mm and 210

mm were used, respectively for molds of 200

mm, 300 mm and 400 mm.

Figure 2: Light weighted waffle slab plan

Figure 3: Light weighted waffle slab geometry

A finite element model of an internal slab panel

was created for each mold dimension and for

each floor occupation (parking floor, storage

floor and roof floor), which makes a total of 9

models. Stresses, rebar quantities, costs of

materials and formwork systems were

calculated to determine the less expensive

type of mold for each type of slab use, so it

could be compared with the others slab

solutions. In the following table are presented

the less expensive waffle slab dimensions for

each floor occupation and their respective

costs, without and with formwork system costs.

Table 3: Dimensions and respective costs of waffle slabs for each floor occupation

Floor Mold

Costs (€/m2)

w/o

formwork

w/

formwork

Parking M300 50,04 72,85

Storage M400 64,69 87,50

Roof M200 42,99 65,80

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For the case of the beam-supported slab, a

parametric analysis was made to calculate

stresses and rebar required for different

combinations of slab thickness (𝑒), beam depth

(ℎ) and beam width (𝑏). As a simplification, first

was determined the less expensive slab

thickness in terms of costs of materials

(concrete and rebar). Then, the combination of

beam depth and width with less material costs

was determined. In this analysis, slab

thicknesses of 0,20 m (ℎ = 𝐿 41 ) to 0,30 m

(ℎ = 𝐿 27 ) were analysed, with increments of

1 cm between each thickness, making a total

of 11 possibilities. Regarding the beams,

widths went from 0,25 m to 0,50 m with

increments of 5 cm between each width. For

each width, beam depths of 0,40 m (ℎ = 𝐿 20 )

to 0,80 m (ℎ = 𝐿 10 ) were analysed, with

increments of 5 cm between each depth, which

made a total of 54 combinations of different

depth and width beams. In the following table

are presented the less expensive dimensions

and respective costs of beam-supported slabs

for each floor occupation, without and with

formwork system costs.

Table 4: Dimensions and respective costs of beam-supported slabs for each floor occupation

Floor

Slab geometry Costs (€/m2)

𝒆

(m)

𝒃

(m)

𝒉

(m)

w/o

formwork

w/

formwork

Parking 0,20 0,25 0,70 34,18 57,07

Storage 0,23 0,30 0,80 40,94 64,78

Roof 0,20 0,25 0,60 31,65 53,33

For the case of the flat slab with constant

thickness and for the one with drops, a similar

analysis was made. For both, an equivalent

frame analysis was used to determine stresses

in the slab.

For the flat slab with constant thickness,

thicknesses of 0,20 m (ℎ = 𝐿 40,5 ) to 0,35 m

(ℎ = 𝐿 23 ) were analysed, with increments of

1 cm between each thickness, which makes a

total of 16 possibilities. Regarding the slab with

drop panels, the minimal slab thickness used

(ℎ1) was 0,19 m and the maximal was 0,28 m.

Thicknesses with increments of 1 cm have

been analysed between those limits. For the

drop thickness (ℎ2), values of 0,30 m, 0,35 m

and 0,45 m were analysed. For the plan

dimensions of the drop (𝑎), widths of 2,0 m to

3,6 m were analysed, with increments of 10 cm

between each width. As result, 510 possible

combinations of different geometries were

analysed for the slab with drop panels.

For both flat slabs, the costs of materials were

calculated ensuring that the vertical

displacement at mid-span would be less than

𝐿′ 250 , with 𝐿′ = 2 ∙ 8,102 = 11,46 𝑚, for the

quasi-permanent combination of actions. The

geometries that wouldn’t respect that last

criteria, would not be accepted. The elastic

vertical displacement was multiplied by 5 to

take in account the effect of cracking and

creep.

The following table presents the less

expensive dimensions and respective costs of

flat slabs with constant thickness for each floor

occupation, without and with formwork system

costs.

Table 5: Dimensions and respective costs of flat slabs for each floor occupation

Floor Thickness

(m)

Costs (€/m2)

w/o

formwork

w/

formwork

Parking 0,25 57,94 74,29

Storage 0,32 76,27 92,62

Roof 0,22 46,61 62,96

The following table shows the less expensive

dimensions and respective costs of flat slabs

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5

with panel drops for each floor occupation,

without and with formwork system costs.

Table 6: Dimensions and respective costs of flat slabs with panel drops for each floor occupation

Floor

Slab geometry Costs (€/m2)

𝒂

(m)

𝒉𝟏

(m)

𝒉𝟐

(m)

w/o

formwork

w/

formwork

Parking 2,80 0,19 0,40 42,00 58,94

Storage 3,40 0,22 0,40 54,98 71,94

Roof 3,00 0,19 0,40 36,27 53,25

Figure 4 – Flat slab with panel drops geometry

Taking in account the areas of each floor, the

costs of each slab solution per m2

of

construction area are presented in the next

figure, for the all structure, without and with

formwork system costs. Regarding the -2

floor’s slab, a 0,20 m thick slab was used,

which does not participate in the costs

presented below.

Taking in account only the costs of materials

and formwork system, the beam-supported

slab is the less expensive slab solution.

However it is a solution which requires a longer

construction time than the other slab solutions.

It is also a solution that interferes considerably

with the building’s equipment. For those

reasons, the flat slab with drop panels, the

second less expensive slab solution, has been

chosen for the design of the structure.

Should be noted that in the roof floor, the flat

slab with drops has bigger dimensions than the

parking floor’s slab, even though it has smaller

loads. In the parametric analysis resulted less

expensive rebar distribution in the roof slab

than for the parking floor, that combined with

bigger geometric dimensions, results in lower

total costs.

However, this parametric analysis has only

been made for the fundamental combination of

actions and for an interior slab panel.

Considering that in the overall structural

analysis, all the actions will be considered, and

with that, required rebar sections will change,

adopting bigger dimensions for the roof slab

than for the parking slab is not reasonable

anymore. For that reason, same dimensions

than the parking flat slab have been adopted

for the roof flat slab.

Figure 5: Slab solution’s costs

5 - Structural solution

Having determined the slab’s solution, the

resolution of the rest of the structure is as

follows. It consists in choosing the size and

56

,08

37

,10

65

,04

47

,45

78

,89

60

,24

81

,39

64

,40

0,00

20,00

40,00

60,00

80,00

100,00

Costs (€/m2)

Without formwork system costs

With formwork system costs

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arrangement of the different structural

elements that guarantees the safety of the

building, its comfort and proper functioning.

Due to the size in plan of the building, imposed

deformations caused by uniform temperature

and shrinkage of concrete cause high stresses

in vertical elements. For that reason, an

expansion joint was used in the building.

However, expansion joints are inconvenient for

the building’s maintenance, due to water

infiltrations, and to functional quality in the

interior of the building. It has also its limitations

to fire resistance, so elevated lengths of

expansion joints were avoided.

Due to uniform temperature and shrinkage of

concrete, the farther vertical elements of the

building, in the inferior floors, suffer higher

deformations. To reduce those deformations

and also to avoid elevated lengths of

expansion joints, partial expansion joints were

used, as shown in the following figure. It

consists in using expansion joints in the inferior

floors, and with that, avoiding having those

systems in the roof floors, reducing water

infiltration problems due to precipitation. In this

case study, partial expansion joints were used

in all floors except in the roof floor.

Figure 6: Example of structure with partial expansion joints

Due to the fact that flat slabs have a poor

seismic behaviour, structural walls have been

added to the structure. Because of flat slabs

poor behaviour to seismic activity, regulation

recommends to use slabs and the interior

columns as secondary seismic members. To

consider those elements as secondary seismic

members, their lateral rigidity has to be less

than 15% of the total lateral rigidity of the

primary seismic elements.

The orientation of the structural walls in the

structure had to be taken in account. To assure

resistance to the structure, without restricting

imposed deformations due to uniform

temperature and shrinkage of concrete, walls

have been placed with their major axis of

inertia perpendicular to the edge of the nearest

floor’s edge.

To add more resistance to the seismic actions,

in the contour of the superior floors, a beam

has been added. The beam’s pre-design was

based on the condition that the value for “beam

height/span” must be around 𝐿 10 . To control

the beam’s stresses and with the estimated

beam’s height obtained, the normalized

moment, 𝜇, given by 𝜇 = 𝑀𝑆𝑑 𝑏 ∙ 𝑑2 ∙ 𝑓𝑐𝑑 ,

have been limited to 0,25, according to the

influence areas of the beams.

For column’s pre-design, according to their

influence area and for the fundamental

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7

combination of actions, the area required for

each column has been obtained by limiting its

axial stresses as indicated in the following

expression, with 𝜈 = 1,0 for columns with low

ductility requirements (secondary seismic

elements) and 𝜈 = 0,8 for columns with high

ductility requirements (primary seismic

elements).

𝐴𝑐 ≥ 𝑁 𝜈 ∙ 𝑓𝑐𝑑 1

To pre-design stand-alone foundations, it was

insured that the terrain was able to withstand

the transmitted stresses. Calculating the axial

force at the base of the columns, for the

fundamental combination of actions, according

to their influence area, the minimum area of

the foundations (𝐴 ∙ 𝐵) have been determined

according to 𝐴 ∙ 𝐵 ≥ 𝑁𝐸𝑑 𝜎𝑅𝑑 .

Moments in the stand-alone foundations would

be absorbed by tie beams that would link every

element, so the standalone foundations could

be designed for axial force only.

Regarding the earth retaining wall, two

thicknesses have been adopted, one for each

underground floor, in such way that its

resistance to shear actions would withstand

the earth loads on it.

6 - Structure model

Since structural design is currently based on

the application of automatic data processing

tools, the three-dimensional finite elements

program SAP2000, has been used to model

the building’s structure. Columns and beams

were simulated as finite bar elements with two

nodes, one at each end, with six freedom

degrees each. Slabs and the earth retaining

wall were simulated with finite shell elements

with 3 and 4 nodes, also with six freedom

degrees each.

The effect of shrinkage of concrete was

simulated with an equivalent uniform

temperature to the structural elements, 𝛥𝑇𝑒𝑞,

according to the following expression.

𝛥𝑇𝑒𝑞 =𝜀𝑐𝑠𝛼

2

To take in account the effects of imposed

deformations (uniform temperature and

shrinkage of concrete), the concrete’s elastic

modulus, 𝐸𝑐,28, can be adjusted as indicated in

the following expression, where 𝜑 = 2,5, and

𝜒 = 0,8 for the shrinkage effect and 𝜒 = 0,4 for

the uniform temperature effect.

𝐸𝑐,𝑎𝑗 =𝐸𝑐,28

1 + 𝜒 ∙ 𝜑

3

To model this effect without affecting the

concrete’s elastic modulus in the material

properties of the program, the actions of

uniform temperature and shrinkage (𝛥𝑇𝑒𝑞) have

been affected with coefficients of 0,50 and 0,33

respectively.

The rigidity of structural elements has a major

influence in the response of the structure.

Beyond influencing the deformation of the

structural elements, it also affects the

structure’s vibration frequency, and with that,

the value of the seismic action.

To take in account the effect of concrete’s

cracking, structural elements flexural rigidity

have been affected with a coefficient of 50%,

as indicated in the EC8-1 for linear analysis.

For the interior columns of the slab, considered

as secondary seismic elements, a more

precise method has been adopted because of

their higher sensitivity to seismic actions. An

effective rigidity, 𝐸𝐼𝑒𝑓𝑓, indicated in the

following expression, have been adopted for

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8

these elements, with 𝜈 = 1,20 and 𝜙𝑦 =

2,1 ∙ 𝜀𝑠𝑦 𝑑 , according to the regulations.

𝐸𝐼𝑒𝑓𝑓 =𝜈 ∙𝑀𝑅𝑑

𝜙𝑦 4

To simulate this effective rigidity, in the

columns section properties, the moment of

inertia factors took values of 𝐸𝐼𝑒𝑓𝑓 𝐸𝐼0 , with 𝐼0

being the non-cracked column’s moment of

inertia.

7 - Seismic analysis and design

calculation

The frequencies and mass participation factors

(Ux, Uy and Rz) for the first three vibration

modes (shown below) are listed in the

following tables.

Table 7: Mass participation factors - translatory movement in the x direction (first three vibration

modes)

Mode Per. (s)

Freq. (Hz)

Translatory mov. x

Ux ∑Ux

1 0,539 1,855 0,478 0,478

2 0,481 2,080 0,041 0,518

3 0,376 2,657 0,006 0,524

Table 8: Mass participation factors - translatory movement in the y direction (first three vibration

modes)

Mode Per. (s)

Freq. (Hz)

Translatory mov. y

Uy ∑Uy

1 0,539 1,855 0,051 0,051

2 0,481 2,080 0,528 0,579

3 0,376 2,657 0,003 0,582

Table 9: Mass participation factors – rotation about the vertical axis (z) (first three vibration

modes)

Mode Per. (s)

Freq. (Hz)

Rotation about z

Rz ∑Rz

1 0,539 1,855 0,013 0,013

2 0,481 2,080 0,508 0,521

3 0,376 2,657 0,044 0,565

There should be considered a sufficient

number of modes that mobilize at least 90% of

the total mass of the building for the vibrations

modes. In this analysis, 12 modes were

considered, which resulted in a total mass

participation factor of 53% in the x direction,

58% in the y direction and 57% around the

vertical axis (z). Due to the fact that there are

two floors underground, the mass of the

building that actually participate in this analysis

is concentrated above the ground level, which

corresponds approximately to 22,56% of the

total mass. 90% of that percentage (20,30%)

result in the desired participation factor, which

is less than the values that were obtained.

Figure 7: 1st vibration mode – x direction

Figure 8: 2nd vibration mode – y direction

Figure 9: 3rd vibration mode – z rotation

According to the regulations, the behaviour

factor takes the value of 𝑞 = 2,029. Therefore

the spectral acceleration takes the value of

𝑆𝑑 𝑇 = 2,388 𝑚𝑠−2 for the type 1 seismic

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action and 𝑆𝑑 𝑇 = 1,232 𝑚𝑠−2 for the type 2

seismic action. Due to its higher value, only the

type 1 seismic action has been considered in

this work.

Regarding the seismic structural elements,

primary and secondary elements were

considered in this work. Two models were

developed to design both kinds of elements.

The first (model 1) corresponds to the general

structure with no participation to the lateral

rigidity of the secondary seismic elements and

with a behaviour factor of 𝑞 = 2,029, and the

second model (model 2) considers the full

participation of all elements with a behaviour

factor of 𝑞 = 1,5 (that corresponds to the

minimum of 𝑞 value according to the

regulations). For the design of primary seismic

elements, the lateral rigidity of secondary

elements was taken as null (model 1). For the

design of secondary seismic elements,

stresses from model 2 were multiplied by

𝑑𝑒1 𝑑𝑒2 to take in account the increase of

stresses due to the increase of lateral

displacement of the model 1 (𝑑𝑒1) relatively to

lateral displacements of model 2 (𝑑𝑒2).

Secondary seismic elements were designed in

elastic phase and in ductility to compare both

situations in terms of rebar sections required.

For the elastic phase design, forces were

calculated from model 2 as indicated before,

affected by 𝑑𝑒1 𝑑𝑒2 and with 𝑞 = 1,5. For

ductile design, model 1 was used, with

𝑞 = 2,029. In the second situation the

secondary elements had to be detailed with the

recommendations of ductile elements, in order

to meet the same requirements concerning

ductility of primary seismic elements, as

indicated in the EC8-1.

The design and verification of safety of the

structural elements started from the results of

the three-dimensional finite elements program

SAP2000, for ULS.

For columns, compound bending has been

verified using the following simplified

expression presented in the regulations.

𝑀𝐸𝑑,𝑥

𝑀𝑅𝑑,𝑥

𝛼

+ 𝑀𝐸𝑑,𝑦

𝑀𝑅𝑑,𝑦

𝛼

≤ 1,0 6

The values of 𝛼 can be determined with the

following table.

Table 10: Recommended values for 𝜶

𝑵𝑬𝒅 𝑵𝑹𝒅 ≤ 0,1 0,7 1,0

𝜶 1,0 1,5 2,0

In the previous expression, resistant moments

in each direction were calculated considering

only the interaction between the axial force and

bending moment in that direction, not

considering the perpendicular moment.

Regarding the rest of the elements, the ULS

have been verified to guarantee the safety of

the structure.

The crack’s maximum opening has been

verified to be less than the limit of 𝑤𝑚𝑎𝑥 =

0,3 𝑚𝑚 in all structural elements.

Deformation in slabs have also been evaluated

to guarantee that the displacement in the

middle of the slab would be less than 𝐿 250 for

long term deformations and less than 𝐿 500

for the deformation that occurs after the

construction, for a diagonal span of 𝐿 =

8,12 + 8,12 = 11,46 𝑚. Cracking effect in

concrete, negative rebar and creep have been

considered to calculate long term

deformations.

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Horizontal displacements due to seismic action

have also been verified to be less than the

limits set by the EC8-1 and to guarantee a

minimal spacing in the expansion joints of the

structure.

Once established a structural solution with a

three-dimensional static and dynamic analysis

realized, and considering safety criteria listed,

as well as calculation hypotheses to verify, the

building’s structural elements are designed.

The results of this design are presented in the

main document, such as reinforced concrete

drawings and global structure drawings.

8 - Final considerations

Should be noted that the beam-supported slab

has a better seismic behaviour than the flat

slab used in this work.

Should also be noted that the parametric

analysis made to determine the slabs

dimensions only considered vertical loads for

the fundamental combination of actions.

However, seismic actions have a considerable

influence in the design of those elements, so

the choice of this analysis in this situation

should be taken with caution.

Worth mentioning that the costs of materials

used in this work vary from country to country

and depends of the market situation. The

contractors’ technical capacities can also

influence the final costs of structural elements.

Should be noted that the use of partial

expansion joints the way they were installed in

this structure has its disadvantages. By using

expansion joints in every floor except in the

roof’s floor, bring high stresses to the

connecting elements in that area due to the

seismic actions. Nevertheless it is a good

option to reduce stresses in the inferior part of

vertical elements away from the centre of the

building.

This work has permitted to deepen the

knowledge acquired along the course of

Structural Engineering, and has also given the

opportunity to approach the experience to the

real life of a project engineer.

Key-words: structural design, seismic design,

mushroom slab or flat slab with drop panel, flat

slab, waffle slab, beam-supported slab,

punching shear, primary and secondary

seismic member.

9 - Bibliography

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