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U N I V E R S I T Y O F P A T R A S

DEPARTMENT OF CIVIL ENGINEERING

Report Series in Structural and Earthquake Engineering

APPLICATION OF EN-EUROCODE 8 PART 1

FOR THE SEISMIC DESIGN OF

MULTISTOREY CONCRETE BUILDINGS

MICHAEL N. FARDIS, GEORGIOS TSIONIS

Report No. SEE 2011-01

January 2011

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i

APPLICATION OF EN-EUROCODE 8 PART 1

FOR THE SEISMIC DESIGN OF

MULTISTOREY CONCRETE BUILDINGS

by

MICHAEL N. FARDIS and GEORGIOS TSIONIS

University of Patras

The report has been prepared with the

financial support of the European Commission

under FP7 projectA.C.E.S.

Any opinions, findings, and conclusions or recommendations

expressed in this material are those of the author(s)

and do not necessarily reflect those of the European Commission.

Report No. SEE 2011-01

Department of Civil Engineering, University of PatrasJanuary 2011

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iii

Abstract

The report illustrates the application of EN-Eurocodes 2 and 8 for the analysis and design

of a multi-storey concrete building for earthquake resistance. Although fairly regular, the

building has a realistic geometry, not an idealised one. It has six storeys above ground

and two basement floors, extending in one direction beyond the plan of the

superstructure. The basement is surrounded by a continuous perimeter wall, serving as a

deep foundation beam for the outer vertical elements of the building. In one of the two

main horizontal directions the structural system comprises four large walls two at the

perimeter, two interior rendering it a wall system. In the other direction the frames are

complemented by a single interior wall with a U-section, giving a wall-equivalent dual

system. The design peak ground acceleration on rock is 0.25g (moderate seismicity).

The analysis is carried out with computer code ETABS, using the modal response

spectrum method for the seismic action. Key feature of the model are the deep prismatic

elements representing the basement perimeter wall as a foundation beam on closely

spaced elastic supports (Winkler springs). The stiffness of the fictitious vertical members

intervening between these springs and the axis of the deep beam are chosen to reflect

the horizontal stiffness of the perimeter walls.

After giving an overview of (a) the process for detailed seismic design of concrete

buildings, as this is dictated by the interdependencies of design phases according to EN-

Eurocode 8 (mainly owing to capacity design) and (b) of the design and detailing rules in

EN-Eurocode 8 for beams, columns and ductile walls of the three Ductility Classes (DC)

in EN-Eurocode 8 (DC Low, Medium or High), the detailed design of all elements isillustrated, from the roof to the foundation soil. The detailed design is done

automatically, through computational modules having as built-in the dimensioning and

detailing rules of Eurocodes 2 and 8. The modules are activated in a prescribed

sequence, such that all outcomes which are necessary as input to subsequent design

phases of the same or other elements or types of elements are archived for future use.

Examples of such information include: (a) the moment resistances at the end sections of

beams for the capacity design of the columns they frame into; (b) the moment

resistances at the ends of beams and columns for the capacity design in shear of these

elements and of the ones they frame into; (c) the cracked stiffness of beams that restrain

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columns against buckling; (d) the capacity design magnification factors at the base of

columns or walls for the design of their footings, etc. The design is on purpose

minimalistic: the reinforcement is tailored to the demands of the analysis and of EN-

Eurocodes 2 and 8, to avoid overstrengths and margins that are not absolutely needed

and would have reflected the choice of the designer rather than the Eurocodes intention.It is believed that this is the first published illustration of a complete design of a

realistic multi-storey concrete building according to EN-Eurocodes 2 and 8. As such, it is

certainly open to criticism. This is more so as, unlike in analysis, there is no unique

solution in design.

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Table of Contents

Abstract ............................................................................................................................................ iii

1 Introduction .............................................................................................................................. 1

1.1 Scope of the report ................................................................................................................ 1

1.2 Description of the building ................................................................................................... 1

2 Actions ..................................................................................................................................... 72.1 Combination of actions for the seismic design situation ...................................................... 7

2.2 Vertical actions ..................................................................................................................... 7

2.3 Seismic action ....................................................................................................................... 7

2.4 Accidental eccentricity ......................................................................................................... 9

2.5 Storey forces for the lateral force method of analysis ........................................................ 10

3 Modelling ............................................................................................................................... 13

3.1 General ................................................................................................................................ 13

3.2 Effective flange width of beams ......................................................................................... 14

3.3 Modelling of perimeter foundation walls ........................................................................... 15

3.4 Modelling of vertical actions .............................................................................................. 16

3.5 Modelling of the foundation and the soil ............................................................................ 17

4 Analysis .................................................................................................................................. 19

4.1 General ................................................................................................................................ 19

4.2 Modal periods, shapes and participation factors................................................................. 19

4.3 Seismic moments, shears and axial forces .......................................................................... 20

4.4 Action effects of gravity loads ............................................................................................ 22

5 Verifications and detailed design ........................................................................................... 51

5.1 Damage limitation .............................................................................................................. 51

5.2 Second-order effects ........................................................................................................... 51

5.3 ULS and SLS verifications and detailing ........................................................................... 53

5.3.1 General ............................................................................................................................ 535.3.2 Overview of the detailed design procedure ..................................................................... 53

5.3.3 Additional information for the design of beams in bending ........................................... 59

5.3.4 Additional information for the design of columns .......................................................... 59

5.3.5 Additional information for the design of beams in shear ................................................ 60

5.3.6 Additional information for the design of walls ............................................................... 61

5.3.7 Additional information for the design of foundation beams ........................................... 62

5.3.8 Additional information for the design of footings ........................................................... 62

6 Design of beams in bending ................................................................................................... 69

6.1 Frame A .............................................................................................................................. 69

6.2 Frame B .............................................................................................................................. 82

6.3 Frame C .............................................................................................................................. 906.4 Frame 1 ............................................................................................................................. 107

6.5 Frame 2 ............................................................................................................................. 113

6.6 Frame 3 ............................................................................................................................. 122

7 Design of columns ............................................................................................................... 139

7.1 Column C1 ........................................................................................................................ 139

7.2 Column C2 ........................................................................................................................ 142

7.3 Column C3 ........................................................................................................................ 145

7.4 Column C7 ........................................................................................................................ 149

7.5 Column C8 ........................................................................................................................ 153

7.6 Column C11 ...................................................................................................................... 158

7.7 Column C12 ...................................................................................................................... 1617.8 Column C13 ...................................................................................................................... 166

8 Design of beams in shear ..................................................................................................... 173

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8.1 Frame A ............................................................................................................................ 173

8.2 Frame B ............................................................................................................................ 179

8.3 Frame C ............................................................................................................................ 182

8.4 Frame 1 ............................................................................................................................. 190

8.5 Frame 2 ............................................................................................................................. 193

8.6 Frame 3 ............................................................................................................................. 197

9 Design of walls .................................................................................................................... 2039.1 Wall W1 ............................................................................................................................ 203

9.2 Wall W3 ............................................................................................................................ 207

9.3 Wall W5 ............................................................................................................................ 210

10 Design of basement perimeter walls as deep foundation beams ...................................... 217

10.1 Frame A ............................................................................................................................ 217

10.2 Frame 1 ............................................................................................................................. 220

10.3 Frame D ............................................................................................................................ 221

11 Design of foundation elements ......................................................................................... 225

11.1 Footing F7 ......................................................................................................................... 225

11.2 Footing F12 ....................................................................................................................... 226

11.3 Footing F13 ....................................................................................................................... 22711.4 Common footing of columns C8, C9 and walls W3, W4, W5 ......................................... 228

11.5 Strip footing of frame A ................................................................................................... 229

11.6 Strip footing of frame D ................................................................................................... 235

11.7 Strip footing of frame 1 .................................................................................................... 241

REFERENCES............................................................................................................................... 247

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1 Introduction

1.1 Scope of the report

The report illustrates the application of EN-Eurocodes 2 and 8 for the analysis and design of a

multi-storey concrete building for earthquake resistance. Altough fairly regular, the building has a

realistic geometry, not an idealised one.

After giving an overview of the process for detailed seismic design of concrete buildings and

of the design and detailing rules in EN-Eurocode 8 for beams, columns and ductile walls of the

three Ductility Classes in EN-Eurocode 8, the detailed design of all elements is illustrated, from

the roof to the foundation soil. The detailed design is done automatically, through computational

modules having as built-in the dimensioning and detailing rules of Eurocodes 2 and 8. The

modules are activated in a prescribed sequence, such that all outomes which are necessary as input

for subsequent design phases of the same or other elements or types of elements are archived for

future use.

The design is on purpose minimalistic: the reinforcement is tailored to the demands of the

analysis and of EN-Eurocodes 2 and 8, to avoid overstrengths and margins that are not absolutely

needed and would have reflected the choice of the designer rather than the Eurocodes intention.

It is believed that this is the first published illustration of a complete design of a realistic

multi-storey concrete building according to EN-Eurocodes 2 and 8. As such, it is certainly open to

criticism. This is more so as, unlike in analysis, there is no unique solution in design.

Where not explicitly stated, clauses refer to Part 1 of Eurocode 8 [1].

1.2 Description of the building

The examined structure is an eight-storey residential building, including two basements. A typical

section and floor plan above the basement are shown respectively in Figures 1.1 and 1.2. The

horizontal axis X is parallel to the long direction of the plan; axis Y is parallel to the short

direction. The height of the ground storey is 4.0 m, while the height of all other storeys and the

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two basements is 3.0 m.

Structural elements are arranged on a 67 m grid. The perimeter columns have a rectangular

cross-section with dimensions 0.300.60 m at the corners and 0.300.70 m elsewhere. The

internal columns have a square cross-section with dimensions 0.500.50 m. All beams have width

bw = 0.30 m and depth hb = 0.50 m. The slabs are 0.18 m thick. Two rectangular walls, W1 and

W2, with dimensions 0.304.00 m are placed at the middle of the external frames in direction Y.

At the centre of the plan, two rectangular walls, W3 and W4, with dimensions 0.254.00 m

accommodate the staircase; a U-shaped wall, W5, with external dimensions 1.803.60 m and

thickness 0.25 m forms the elevator shaft.

In the two basements the building has an additional bay in direction Y, as shown in Figures

1.2 and 1.3. The cross-section dimensions of columns and beams as well as the slab thickness are

the same as for the upper storeys. A 0.30 m-thick wall runs all along the perimeter of the

basement.

The plan of the foundation is shown in Figure 1.4. Single footings with dimensions

2.02.00.7 (widthdepthheight in meters) are used for the interior columns. A common footing

with dimensions 7.09.00.8 is used for columns C8 and C9 and walls W3, W4 and W5. A strip

footing with width 1.0 m and height 0.30 m is used for the perimeter walls. Instead of a system of

two-way tie-beams, horizontal connection of the footings and the foundation strip of the basement

perimeter walls is provided by a foundation slab cast right below the top of the footings and the

perimeter foundation strip (see clause 5.4.1.2 para. (2), (3) and (7) of EN 1998-5:2004). This slab

serves also as floor of the lower basement and helps create a rigid-box foundation system together

with the perimeter walls and the slab at the roof of the upper basement.

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A

B

D

1 2 3 4 5 6

C

SLAB

Fig. 1.1 Typical floor plan above the basement

ABD C

SCHEMATIC SECTION

Fig. 1.2 Section in the Y direction

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A

B

D

1 2 3 4 5 6

C

SLAB

Fig. 1.3 Plan of the basement

A

B

D

1 2 3 4 5 6

C

FOUNDATION

Fig. 1.4 Plan of the foundation

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The geometry originates from the example building prepared for the Lisbon workshop

Eurocode 8: Seismic design of buildings, organised by the European Commission (February

2011), but a wide range of modifications were introduced, in the geometry and the modelling.

Differences in the geometry include:

Beams are now 0.3 m wide, to better accommodate the longitudinal reinforcement at

supports, in view of the large concrete cover of the reinforcement;

The corner columns have a 0.300.60 m section, to meet the rule in clause 5.4.1.2.1(2) of

Eurocode 8 for an eccentricity between the axis of a beam and the supporting column not

more than 25% of the parallel column dimension.

For the analysis and design of the building the following specifications apply:

the structure is an ordinary building belonging to Importance Class II, according to the

classification in clause 4.2.5(4);

the building is designed for reference peak ground acceleration agR = 0.25 g and for

medium ductility (DCM);

the vertical component of the seismic action is ignored;

the dead load for partitions and finishings (additional to the self-weight) is 2 kN/m2; the

live load is also 2 kN/m2;

concrete C25/30 and steel S500 of Class C are used;

exposure class is XC3 giving a nominal concrete cover of 35 mm;

the soil is clay with design value of undrained shear strength cud = 300 kPa (reduced by

10% to cud = 270 kPa for the seismic design situation), design value of friction angle d =

20o

and design value of drained cohesion cd = 50 kPa; it corresponds to Ground type B for

the purposes of the definition of the seismic action at the top of the ground.

the masonry infills are ignored as far as the seismic response and design ar concerned.

Section 4.2.3 of Eurocode 8 [4] prescribes detailed criteria for structural regularity in plan and

in elevation. The classification of a building as regular or irregular affects the type of structural

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model and analysis allowed and also the value of the behaviour factor. The verifications regarding

regularity in plan (namely the approximate symmetry about two orthogonal axes, the compactness

of the shape of the plan, the magnitude of the eccentricities between the centres of mass and

stiffness, and the relative magnitude of the radius of gyration and of the torsional radii at each

floor) are all met. The same applies for the criteria for regularity in elevation regarding the

variation of the mass, stiffness and plan dimensions from storey to storey. It is worth pointing out

in this connection that the large difference in stiffness and in plan dimensions between the two

rigid basements and the six floors above ground does not count for the characterisation of the

building as regular or not in elevation: regularity in elevation is a pre-requisite for the applicability

of the lateral force analysis procedure of clause 4.3.3.2 of EN 1998-1:2004; that clause makes

several references (e.g., para. 4.3.3.2.2(3) and 4.3.3.2.3(3)) to buildings with a rigid basement as

being within its scope. So, the building is characterised as regular both in plan and in elevation.

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2 Actions

2.1 Combination of actions for the seismic design situation

According to clause 6.4.3.4(2) of EN 1990 [1], the combination of actions Gk,j +AEd + 2,i

Qk,i applies in the seismic design situation, where G corresponds to the self-weight of the structure

and any additional dead load,AEd denotes the seismic action, Q stands for the live loads and 2,i is

the partial factor for the quasi-permanent value of variable action i. The recommended value 2 =

0.3 for residential/office areas is used, as in Table A1.1 of EN 1990 [1].

2.2 Vertical actions

Vertical actions consist of permanent, G, and variable, Q, loads. Permanent loads comprise the

self-weight of the structure and additional 2 kN/m2

to account for finishings, partitions, etc. The

self-weight is calculated on the basis of the geometry and the concrete density, = 25 kN/m3

for

normal concrete including normal percentage of reinforcing steel according to Table A.1 of

Eurocode 1 [2]. Regarding variable loads, the value recommended in clause 6.3.1.2(1) of

Eurocode 1, is used: for Category A (i.e. domestic/residential use in clause 6.3.1.1(1) of Eurocode

1), the variable load on floors is qk= 2 kN/m2.

2.3 Seismic action

The seismic action is described by the elastic response spectrum of Type 1 and for Ground type B,

as in clauses 3.2.2.2(1) and 3.2.2.2(2) of Eurocode 8 [4]. The recommended values S= 1.2, TB =

0.15 sec, TC = 0.5 sec and TD = 2.0 sec are used. The reference peak ground acceleration is gR =

0.25 g and the design peak ground acceleration is g = IgR = 1.00.25g = 0.25g, where, from

clause 4.2.5(5), the importance factor is I= 1.0 for Importance Class II.

The analysis is performed based on the design response spectrum, for which the value of the

behaviour factor q has to be calculated depending on the structural system and Ductility Class

according to clause 5.2.2.2. In clause 5.1.2(1), structural systems are classified on the basis of the

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percentage of total shear force taken by the walls for the seismic design situation Vbase,wall /Vbase,tot.

The base shears were calculated from the analysis according to the lateral force method (see

section 2.5 of this report); the analysis results give:

- Vbase,wall /Vbase,tot= 63.7% in direction X and

- Vbase,wall /Vbase,tot= 91.4% in direction Y.

Then, the building is classified as wall-equivalent dual system in direction X and as wall system in

direction Y. According to clause 5.2.2.2(2), the corresponding basic values of the behaviour factor

are:

- qox = 3.0u/1 = 3.01.2 = 3.6 (for wall-equivalent dual systems clause 5.2.2.2(5) gives a

default value ofu/1 = 1.2), and

- qoy = 3.0.

In clause 5.2.2.2(1), the value of the behaviour factor to be used in the analysis is q = qo kw,

where kw reflects the prevailing failure mode in structural systems with walls and, according to

clause 5.2.2.2(11), is calculated as kw = (1 + o) / 3 1.0 for wall and wall-equivalent systems.

The prevailing aspect ratio of the walls is given in clause 5.2.2.2(12) as o =hwi /lwi, where hwi

and lwi are respectively the height and the length of wall i.

- In direction X only wall W1 is considered and it is ox = 25.0/3.60 = 6.9 and kwx =

(1+oX)/3 = (1+6.9)/3 = 2.6,

- In direction Y all walls are considered and it is oy= 625.0/[2(4.0+4.0+1.8)] = 7.7 and

kwy = (1+oY)/3 = (1+7.7)/3 = 2.9; then ox=oy= 1.0.

Finally, the behaviour factors are calculated as:

- qx = qox kwx = 3.61.0 = 3.6

- qy = qoy kwy = 3.01.0 = 3.0

The elastic and the design response spectra in the two directions are shown in Figure 2.1.

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0.0

0.2

0.4

0.6

0.8

0 1 2 3 4

Spectralaccele

ration(

g)

Period (sec)

Se(T)

Sd,x(T)

Sd,y(T)

Fig. 2.1 Elastic and design response spectra for 5% damping

2.4 Accidental eccentricity

In order to account for uncertainties in the location of masses and in the spatial variation of the

seismic motion and according to clause 4.3.3.3.3(1), accidental torsional effects are determined as

the effects resulting from the application of static torsional momentsMai= eai Fi about the vertical

axis of each storey i, where eai is the accidental eccentricity of storey mass i and Fi is the

horizontal force acting on storey i. The horizontal forces Fi are the storey forces used for the

lateral force method analysis (see section 2.5) and the accidental eccentricity is defined in clause

4.3.2(1) as eai = 0.05 Li, where Li is the floor dimension perpendicular to the direction of the

seismic action. Torsional moments in the two directions are combined according to the SRSS rule,

MSRSS= (Mx2

+My2)0.5

. The detailed calculations are shown in Table 2.1.

Table 2.1: Calculation of torsional moments for accidental torsional effects

Storey Fx (kN) Fy (kN) ex (m) ey (m) Mx (kNm) My (kNm) MSRSS (kNm)

roof 622 933 0.715 1.515 444.75 1413.56 1482

5 548 822 0.715 1.515 392.05 1246.06 1306

4 446 668 0.715 1.515 318.54 1012.43 1061

3 343 514 0.715 1.515 245.03 778.79 816

2 240 360 0.715 1.515 171.52 545.15 571

1 141 212 0.715 1.515 101.04 321.14 337

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2.5 Storey forces for the lateral force method of analysis

Following clause 4.3.3.2.2(1), the seismic base shear force is Fb = m Sd(T1), where Sd(T1) is the

ordinate of the design spectrum at the fundamental period of vibration, T1, of the building in the

direction considered, m is the total mass of the building above the top of the basement and is a

correction factor taken as = 0.85 ifT1 < 2 TC and the building has more than two storeys, or =

1.0 otherwise. The fundamental periods in the two main directions are taken from the modal

analysis (see chapter 4) as:

- T1x = 0.85 sec and

- T1y = 0.68 sec.

For TCT1TD, the ordinate of the design spectrum is Sd(T1) = gS2.5 (Tc/T1)/q. In particular

- in direction X it is Sd(T1x) = 0.25 g1.22.50.50/0.85/3.6 = 0.12 g and

- in direction Y it is Sd(T1y) = 0.25g1.22.50.50/0.68/3.0 = 0.18 g.

The total mass of the building is calculated by taking into account the masses associated with

all gravity loads appearing in the combination of actions Gk,j "+" E,i Qk,im whereE,i = 2,i is

the combination coefficient for variable action i. The recommended values of clause 4.2.4(2) are

used, = 1 for the roof and = 0.5 for the remaining storeys.

Using the values calculated above, the total base shear in the two main horizontal directions is

Fbx = m Sd(T1x) = 0.85229390.12 = 2340 kN and

Fby = m Sd(T1y) = 0.85229390.18 = 3510 kN.

Assuming that the fundamental mode shape is approximated by horizontal displacements

increasing linearly along the height, as in clause 4.3.3.2.3(3), the horizontal forces Fi are taken as

Fi = Fbzimi /zjmj, wherezi andzj are the heights of the masses mi and mj above the top of the

rigid basement. The detailed calculation of the storey forces used for the static calculation of the

effects of the accidental eccentricities is given in Table 2.2.

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Table 2.2: Calculation of storey forces for the lateral force method of analysis

Storey zi mi (kN) zimi Fi/Fb Fx (kN) Fy (kN)

roof 19 3661 69553 0.27 622 933

5 16 3832 61311 0.23 548 822

4 13 3832 49816 0.19 446 668

3 10 3832 38320 0.15 343 514

2 7 3832 26824 0.10 240 360

1 4 3950 15802 0.06 141 212

total 22939 261625 1 2340 3510

The storey forces Fx and Fy were multiplied by the associated accidental eccentricities ex and

ey (equal to 5% of the storey dimension at right angles to the direction of the force); the resulting

torques, Fxex and Fyey, were combined according to the SRSS rule into single torques per floor,

[(Fxex)2+(Fyey)

2], which were then statically applied to the model. The outcome of the analysis

reflects the combined effect of the accidental eccentricities of the two horizontal components of

the seismic action, to be superimposed to the combined effect of the two translationa components.

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3 Modelling

3.1 General

According to clause 4.2.3.1(3) and because the structure is regular in plan, a simplified planar

structural model may be used. However, a three-dimensional model of the building was created

using the structural analysis software ETABS [5] and following the requirements of section 4.3.1

of Eurocode 8 [4]. In particular:

all structural members were modelled as linear elements;

the elastic flexural and shear stiffness of elements was taken equal to half the

corresponding stiffness of the uncracked element;

in order to account for the contribution of joint regions to the deformability of the building,

the length of the beam elements inside the joints was taken as rigid this was not done for

columns so as not to overestimate the global stiffness;

floors were considered to act as rigid diaphragms; the masses and the moments of inertia of

each floor were lumped at its centre of gravity;

the masses were calculated from the gravity loads corresponding to the combination of

actions Gk,j "+" E,i Qk,im.

As pointed out in Section 1.2, the building geometry originates from that of the example

building prepared for the Lisbon workshop Eurocode 8: Seismic design of buildings, organised

by the European Commission (February 2011). Besides the modifications in the geometry, there

are important differences in the modelling as well:

Rigid are considered all ends of beams framing into either columns or walls, and not only

into the strong direction of walls.

The compliance of the foundation soil is explicitly included and the foundation elements

are not considered fixed to the ground; this allows computing the action effects in the

perimeter walls of the basement (which are unknown, if these walls are fixed to the ground

all-along their length) and realistically estimating the soil reactions under footings

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including those shared by more than one vertical element.

A different effective slab width is considered for each beam span, as highlighted in the

following section.

3.2 Effective flange width of beams

The effective width of the beam flanges was calculated according to clauses 5.3.2.1(2) and

5.3.2.1(3) of Eurocode 2 [3]. Different expressions are provided for the supports and the span, but

for structural analysis it is allowed to use for the whole beam the values for the span section. The

effective flange width for a T or L beam is beff= beff,i + bwb, where beff,i = 0.2 bi + 0.1lo 0.2lo

and beff,ibi, the sum extends to the two sides of the beam, bw is the width of the beam, bi is half

the distance of adjacent beams, lo = 0.7l2 for the span section and l2 is the beam span. For the

beams of the example building the value 0.2lo is governing; so, for the beams along the X-axis it is

beff,i = 0.20.76.0 0.85 m and for those along the Y-axis it is beff,i = 0.20.77.0 1.0 m. The

cross-sections of the beams used in the structural model are shown in Figure 3.1.

Fig. 3.1 Effective width of beams for the structural analysis

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The slab reinforcement within the effective flange width beff is taken into account for the

calculation of the bending resistance of the beams. For this purpose alone, and following clause

5.4.3.1.1(3), the effective width of beams framing into columns is taken equal to the width bc of

the column increased by 2hf or 4hf on each side of the beam for beams framing respectively into

exterior or interior columns, where hf is the slab thickness. These values are used only in the

design phase and not for the analysis model.

3.3 Modelling of perimeter foundation walls

The internal forces (moments and shears) in the perimeter foundation wall cannot be estimated, if

fixity to the ground is assumed there. To circumvent this problem, vertical springs have been

introduced at the underside of all foundation elements, with a value of the subgrade reaction

modulus of 250/b (kN/m), a value consistent with the soil parameters and as a common average

value for static and seismic loading conditions. Besides, a common footing has been provided

under the two internal walls in the Y direction (W3, W4), the U-shaped one (W5) and two nearby

columns (C8, C9).

The perimeter wall is modelled as a prismatic member with cross-sectional depth and

thickness those of the basement wall and top and bottom flanges about consistent with the

effective width of the top slab of the basement and the strip footing of the perimeter wall. The

vertical members running through the depth of the basement should represent the horizontal

stiffness of the perimeter wall. The main problem with concentrating that stiffness to a few

vertical members right underneath the vertical members of the superstructure, is a big jump in the

moment diagram of the horizontal beam modelling the perimeter basement wall as a deep

foundation beam. So, a fairly large number of fictitious vertical members running through the

depth,H= 6.3 m, of the basement wall should be introduced.

The centroidal axis of the horizontal beam modelling the perimeter basement wall as a deep

foundation beam is placed at Level 0 (ground level). This was found to be the best way to avoid

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erroneous analysis results for the bending moments at the base of the vertical members framing

into this deep horizontal member (notably for the two exterior walls W1 and W2 in the Y-

direction). Nodes are introduced every 1.0 m along it. Each node is connected to a soil node

underneath (at Level -2) via a fictitious vertical member running through the depth H of the

basement. The cross-section of that member is such that the horizontal stiffness of the basement

wall is reproduced. The vertical soil springs, placed every 1 m, have a stiffness of 2501 = 250

kN/m.

3.4 Modelling of vertical actions

The self-weight of the slab and beams was treated as uniform surface load on the floor. The

uniform surface loads due to G and Q were distributed as uniform loads along the beams and as

concentrated loads on walls W3, W4 and W5 according to the tributary areas schematically shown

in Figure 3.2.

A

B

D

1 2 3 4 5 6

C

Fig. 3.2 Tributary areas for vertical actions

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The self-weight of vertical elements was calculated internally by the analysis software and

included in the permanent actions.

The permanent and variable loads on the floor at Level 0 were applied as concentrated loads

on the vertical elements that are positioned at the intersection of the perimeter with the main frame

axes (A to D and 1 to 6 in Figure 3.2). The loads due to G and Q on the floor at Level -1 were

applied as distributed loads on the beam elements used to model the perimeter basement walls.

The self-weight of the perimeter walls was also applied as distributed load on these elements.

3.5 Modelling of the foundation and the soil

In order to account for the compliance of the soil, spring elements were introduced at the nodes of

Level -2. Uniaxial springs in the vertical direction and rotational springs in the two horizontal

directions were placed at the nodes of the individual column footings. The stiffness of the vertical

and rotational springs was calculated as kv = 500 MN/m and k = 625 MNm/rad, assuming a

saturated clay. Only vertical deformation springs with kv = 250 MN/m were placed at the nodes of

the strip footings below the perimeter walls.

As mentioned previously, a common footing was used for walls W3, W4 and W5 together

with columns C8 and C9. The nodes at the base of these elements were connected to the node at

the centre of the footing through fairly rigid linear elements. Springs were placed at the node at the

centre of the footing. There stiffness was calculated to be: kv = 2250 MN/m in the vertical

direction and kx=31000 Mm/rad, ky = 22000 Mm/rad for rotation along the two horizontal

directions.

All nodes of the foundation were taken at the horizontal level of the underside of the strip

footing of the perimeter walls (the small difference with the elevation of the underside of the

interior footings was ignored). All foundation nodes were fixed against translation in both

horizontal directions and for rotation about the vertical.

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4 Analysis

4.1 General

As the building is regular in elevation, clause 4.2.3.1(3) allows performing the analysis for the

calculation of the seismic action effects with the lateral force method. A modal response spectrum

analysis was carried out instead.

4.2 Modal periods, shapes and participation factors

The first three mode shapes of the building are schematically shown in Figure 4.1. The first mode

with T1 = 0.86 sec is translational along the X-axis, the second with T2 = 0.69 sec is translational

along the Y-axis and the third with T3 = 0.49 sec is torsional.

T1 = 0.86 sec T2 = 0.69 sec

T3 = 0.49 sec

Fig. 4.1 The first three modes of the building

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Table 4.1: Modal analysis: periods and participating masses

Mode Period(sec) mx (%) my (%)

1 0.86 53.3 0.0

2 0.68 0.0 53.5

3 0.49 0.1 0.0

4 0.22 11.4 0.0

5 0.16 0.0 21.1

6 0.12 0.3 0.0

7 0.10 6.2 0.0

8 0.08 0.0 17.8

9 0.07 15.9 0.0

10 0.06 3.8 0.0

total: 91.1 92.3

The periods and corresponding effective modal masses for the first vibration modes are listed

in Table 4.1, where it is shown that ten modes are necessary to satisfy the requirements of clause

4.3.3.3.1(3) regarding the number of modes of vibration to take into account in the analysis.

Nevertheless, all 24 modes were taken into account in the analysis.

Following clause 4.3.3.3.2(1), vibration modes may be considered independent of each other

if their periods Ti and Tj, with Ti Tj, satisfy the condition Tj 0.9 Ti. This condition is not

satisfied for a few higher modes not shown in Figure 4.1 and for this reason, the Complete

Quadratic Combination of modal responses was adopted.

4.3 Seismic moments, shears and axial forces

A different design response spectrum was specified in the two main horizontal directions, as given

in Figure 2.1. A single modal response spectrum analysis was performed for the two horizontal

components of the seismic action, and - following clause 4.3.3.5.1(2b) - the maximum value of

each action effect due to the two simultaneous horizontal components was obtained as the square

root of the sum of the squared values of the action effect due to each component.

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The action effects resulting from the modal response spectrum analysis are plotted in the

following. In particular, Figures 4.2 to 4.8 show the in-plane seismic shear forces and bending

moments for the frames. The in-plane seismic shears and moments for wall W3 are given in

Figure 4.9, while Figures 4.10 and 4.11 show the shear forces and bending moments of wall W5

parallel to axes X and Y respectively. Finally, Figures 4.12 to 4.17 present the seismic axial forces

for the frames.

Because of symmetry of the building in plan, results are plotted only for frames A, B and C

along the X-axis, frames 1, 2 and 3 along the Y-axis and for wall W3.

Frame A in Figure 4.2 and Frame 1 in Figure 4.6 include the 6.3 m-deep foundation beam

modelling perimeter walls of the basement, while Frame D in Figure 4.5 comprises just that

foundation beam (it is the counterpart of the foundation beam of Frame A across the plan, but

without the frame of the superstructure). The centroidal axis of the foundation beam is at Level 0

(ground level, 3rd

level from the bottom); the moments and shears of these beams are depicted at

that level; moments and shears below that level are fictitious: they belong to the 6.3 m-tall vertical

members introduced at 1 m centres to connect the centroidal axis of the foundation beam to the

soil nodes at Level -2. The seismic moments and shears along the foundation beam of Frame A (in

Figure 4.2) are partly due to the seismic action component orthogonal to Frame A (i.e., in the Y-

direction); a major part of the overturning moment due to that component is transferred to the

ground by that foundation beam through bearing pressures distributed fairly uniformly along its

length. The seismic moments and shears along the foundation beam of Frame D (in Figure 4.5) are

almost exclusively due to the overturning moment of the seismic action component in the Y-

direction. By contrast, the seismic moments and shears along the foundation beam of Frame 1 (in

Figure 4.5) are almost fully due to the in-plane seismic action component (in the X-direction) and

are controlled by the transfer of the large moment of wall W1 to the ground through that

foundation beam.

Witness in Figures 4.3, 4.4 and 4.7, 4.8, the very small magnitude of seismic moments and

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shears in the beams and columns of the two basement floors, as in those floors the full seismic

action is transferred downwards by the large in-plane stiffness of the perimeter walls. Witness also

in Figures 4.2 to 4.4 the approximately constant magnitude of seismic moments and shears in the

various storeys of the same column or in the same bay of the various floors and their increase from

the ground level to the roof in Figures 4.6 to 4.9 (as the building is a wall system in that direction).

It is also interesting to note that the maximum seismic moments and shears in the beams and

columns of the same frame occur in general at roof level and the smallest ones at the ground floor.

This presages a similar trend for the beam flexural reinforcement.

Witness also in Figures 4.9 to 4.11 the very large seismic shears that walls W3 and W5

develop within the two basement storeys, especially in the upper one. As suggested by the reversal

of the trends in the bending moment digrams of these walls at Level 0 (i.e., at the top of the

basement), these shears have the opposite sense and sign relative to the wall shears in the

superstructure. They reflect the horizontal forces exerted on the wall by the horizontal diaphragms

at the top of the basement and at the level of foundation and vice-versa that create the couple

which fixes these walls to the box-type foundation of the building.

Note that the outcomes of modal analysis and the SRSS combination of the effects of the two

horizontal components of the seismic action produce only the absolute values of peak seismic

action effects. Therefore, the results in Figures 4.2 to 4.17 represent envelopes, to be

superimposed to the absolute values of the corresponding results of the static analyses for the

torsional effect of the accidental eccentricites (not shown here, for the sake of brevity). The sum of

these absolute values is superimposed then, with plus and minus sign, to the effects of the quasi-

permanent gravity actions which are considered concurrent with the seismic and included in the

seismic design situation. These latter gravity action effects are illustrated next.

4.4 Action effects of gravity loads

Separate static analyses were performed for the calculation of the action effects due to the

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permanent, G, and variable, Q, vertical actions. There results were combined according to Eqs.

(6.10a), (6.10b) of EN 1990:2002 for the persistent and transient design situation and into the

quasi-permanent combination G + 0.3 Q which is considered to act concurrently with the design

seismic ction in the seismic design situation.

The analysis results for the quasi-permanent combination G + 0.3 Q are depicted in Figures

4.18 to 4.35. They do have signs and are superimposed with these signs to the seismic action

effect envelopes in Figures 4.2 to 4.17 (as well as the results of the static analyses for the torsional

effect of the accidental eccentricites) with plus and minus signs.

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Fig. 4.2 In-plane seismic shear forces (top) and bending moments (bottom) of frame A

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Fig. 4.3 In-plane seismic shear forces (top) and bending moments (bottom) of frame B

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Fig. 4.4 In-plane seismic shear forces (top) and bending moments (bottom) of frame C

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Fig. 4.5 In-plane seismic shear forces (top) and bending moments (bottom) of frame D

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Fig. 4.6 In-plane seismic shear forces (top) & bending moments (bottom) in frame 1 and Wall W1

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Fig. 4.7 In-plane seismic shear forces (top) and bending moments (bottom) of frame 2

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Fig. 4.8 In-plane seismic shear forces (top) and bending moments (bottom) of frame 3

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Fig. 4.9 In-plane seismic shear forces (top) and bending moments (bottom) of wall W3

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Fig. 4.10 Seismic shear forces (top) and bending moments (bottom) of wall W5 in X-plane

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Fig. 4.11 Seismic shear forces (top) and bending moments (bottom) of wall W5 in Y-plane

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Fig. 4.12 Seismic axial forces in frame A

Fig. 4.13 Seismic axial forces in frame B

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Fig. 4.14 Seismic axial forces in frame C

Fig. 4.15 Seismic axial forces in frame 1

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Fig. 4.16 Seismic axial forces in frame 2

Fig. 4.17 Seismic axial forces of frame 3

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Fig. 4.18 In-plane shear forces (top) and bending moments (bottom) of frame A for G + 0.3 Q

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Fig. 4.19 In-plane shear forces (top) and bending moments (bottom) of frame B for G + 0.3 Q

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Fig. 4.20 In-plane shear forces (top) and bending moments (bottom) of frame C for G + 0.3 Q

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Fig. 4.21 Shear forces (top) and bending moments (bottom) of frame D for G + 0.3 Q

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Fig. 4.22 In-plane shear forces (top) and bending moments (bottom) of frame 1 for G + 0.3 Q

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Fig. 4.23 In-plane shear forces (top) and bending moments (bottom) of frame 2 for G + 0.3 Q

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Fig. 4.24 In-plane shear forces (top) and bending moments (bottom) of frame 3 for G + 0.3 Q

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Fig. 4.25 In-plane shear forces (top) and bending moments (bottom) of wall W3 for G + 0.3 Q

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Fig. 4.26 Shear forces (top) and bending moments (bottom) of wall W5 in X-axis for G + 0.3 Q

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Fig. 4.27 Shear forces (top) and bending moments (bottom) of wall W5 in Y-axis for G + 0.3 Q

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Fig. 4.28 Axial forces of frame A for G + 0.3 Q

Fig. 4.29 Axial forces of frame B for G + 0.3 Q

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Fig. 4.30 Axial forces of frame C for G + 0.3 Q

Fig. 4.31 Axial forces of frame 1 for G + 0.3 Q

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Fig. 4.32 Axial forces of frame 2 for G + 0.3 Q

Fig. 4.33 Axial forces of frame 3 for G + 0.3 Q

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Fig. 4.34 Axial forces of wall W3 for G + 0.3 Q

Fig. 4.35 Axial forces of wall W5 for G + 0.3 Q

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5 Verifications and detailed design

5.1 Damage limitation

According to clause 4.4.3.2(1) and in order to satisfy the damage limitation requirement, the

interstorey drift ratio, r/h, should be limited to certain values depending on the nature on non-

structural elements:

-0.005 for buildings with brittle non-structural elements attached to the structure;

-0.075 for buildings with ductile non-structural elements and

- 0.01 for buildings without non-structural elements or with non-structural elements that do

not interfere with the structural deformations.

For the drift verifications r is the design interstorey drift, h is the storey height and is a

reduction factor which takes into account the lower return period of the seismic action associated

with the damage limitation requirement; according to clause 4.4.3.2(2) has the recommended

value = 0.5 for Importance Class II.

Following clause 4.3.4(1), the storey displacements, ds = qd de, used for the calculation of the

design interstorey drift are those obtained from the elastic analysis, de, multiplied by the

displacement behaviour factor, qd, which is taken equal to q. The detailed calculation of

interstorey drift ratioaccording to this procedure is given in Table 5.1. The displacements at the

storey centre of mass were considered. The height-wise distribution of drift ratio shown in Figure

5.1, shows that the strictest requirement for buildings with brittle non-structural elements is met.

5.2 Second-order effects

According to clause 4.4.2.2(2), second-order effects may be neglected if the interstorey drift

sensitivity index, , is less than 0.10 in all storeys. This index is calculated as = Ntotdr/(Vtoth),

where Ntot is the total gravity load considered in the seismic design situation, dr is the design

interstorey drift, Vtot is the total seismic storey shear and h is the storey height. In the detailed

calculations shown in Table 5.2, Ntot is defined based on the storey masses mi in Table 2.1, dr is

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taken from Table 5.1 and Vtot is taken from the results of the modal response spectrum analysis. In

all storeys it is verified that x 0.10 and y 0.10. Therefore second-order effects are neglected.

-10

-5

0

5

10

15

20

0.0 0.1 0.2 0.3 0.4

Height(m)

Drift ratio (%)

direction X

direction Y

Fig. 5.1 Interstorey drift ratio for the damage limitation verification

Table 5.1: Calculation of interstorey drift ratio

Storey deX(m) deY(m) dsX(m) dsY(m) rX/h (%) rY/h (%)

Roof 0.031 0.031 0.110 0.098 0.258 0.277

5 0.026 0.026 0.095 0.082 0.294 0.288

4 0.021 0.020 0.077 0.064 0.306 0.293

3 0.016 0.015 0.059 0.047 0.324 0.272

2 0.011 0.010 0.039 0.030 0.300 0.235

1 0.006 0.005 0.021 0.016 0.243 0.152

0 0.001 0.001 0.002 0.004 0.012 0.032

-1 0.000 0.001 0.001 0.002 0.018 0.037

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Table 5.2: Calculation of interstorey drift sensitivity coefficient

Storey Ptot (m) VtotX(m) VtotY(m) dsX(m) dsY(m) h (m) X Y

Roof 3661 822 1238 0.0077 0.0083 3.0 0.011 0.008

5 7493 1309 1999 0.0088 0.0086 3.0 0.017 0.011

4 11325 1701 2532 0.0092 0.0088 3.0 0.020 0.013

3 15157 1995 2988 0.0097 0.0082 3.0 0.025 0.014

2 18989 2258 3367 0.0090 0.0070 3.0 0.025 0.013

1 22939 2455 3668 0.0097 0.0061 4.0 0.023 0.010

0 30172 2722 4042 0.0004 0.0010 3.0 0.001 0.002

-1 36225 3002 4311 0.0005 0.0011 3.0 0.002 0.003

5.3 ULS and SLS verifications and detailing

5.3.1General

Clause 4.4.2.1(1) prescribes the conditions regarding resistance, ductility, equilibrium and

foundation stability that should be met at the ultimate limit state. To satisfy the resistance

condition, it is verified that for all structural elements and all critical regionsEdRd, whereEd is

the design value of the action effect due to the seismic design situation andRd is the corresponding

design resistance of the element. In the resistance calculations, clause 5.2.4(2) recommends the

use of the partial factors for material properties applicable for the persistent and transient design

situations. According to clause 2.4.2.4(1) of Eurocode 2 [3], their recommended values are c =

1.5 for concrete and s = 1.15 for reinforcing steel.

5.3.2Overview of the detailed design procedure

Especially in frames, capacity design introduces strong interdependence between various phases

of a buildings detailed seismic design for ductility, within or between members:

dimensioning a column in flexure depends on the amount and layout of the longitudinal

reinforcement of the beams it is connected to in any horizontal direction;

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dimensioning of a column or a beam in shear depends on the amount and detailing of its own

longitudinal reinforcement, as well as of those framing into them at either end;

verification of the foundation soil and design of foundation elements (especially of individual

footings and their tie-beams) depends on the amount and layout of the longitudinal

reinforcement of the vertical elements they support, etc.

dimensioning any storey of a shear wall in shear depends on the amount and detailing of

vertical reinforcement at the base of the bottom storey; etc.

The detailed design operations should follow a certain sequence, so that information necessary

at a step is already available. More important, if detailed design takes place within an integrated

computational environment (as is not only common, but also essential nowadays), this information

should be appropriately transferred between the various modules of the system.

Flow Charts 5.1 and 5.2 depict the interdependence of the various components of a detailed

design process and suggests. A sequence is suggested there (with roman numerals) for their

execution, with specific reference to equations, sections or tables in this or previous chapters. Step

IVa in Flow Chart 5.1 may be carried out before IVb or vice-versa; while Steps V to VII can be

executed at any sequence after II and III, even before IVa and IVb. The same applies to Step IV in

Flow Chart 5.2, with respect to II and III there.

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Flow Chart 5.1: Steps and interdependencies in dimensioning and detailing frame members in

DC M or DC H

JOINTS BEAMS COLUMNSFlexure -

Longitudinalreinforcement

Shear Transversereinforcement

COLUMNFOOTING

V

Dimension

confining

reinforcement

in critical

regions.

Detail

stirrups

(Table 5.4)

I

Maximum beam

bar diameter for

bond in joints

(see Table 5.3):

DCH: VI

Capacity-design shear

force in joint. Joint size

check in shear.

Horizontal hoops in

joint. Column

intermediate barsthrough joint

IIDimension, detail

(Table 5.3) and curtail

beam longitudinal bars

IVa

Capacity-design shear force

(Table 5.3). Check beam

cross-section size and

dimension stirrups.

DCH only: Inclined

reinforcement (Table 5.3).

III

Dimension and detail (Table

5.4) vertical bars. Satisfy

capacity-design check,

unless column exempted

from it (Table 5.4).

IVb

Capacity-design

shear force (Table

5.4). Check column

section size.

Dimension column

stirrups.

VII

Magnification factor on

footings seismic action effects

DCM: VI

Joint hoops as in

column critical regions

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Flow Chart 5.2: Steps and interdependencies in dimensioning and detailing slender ductile walls

of DC M or DC H

INDIVIDUAL WALL OTHER WALLS

Flexure

Vertical &confining

reinforcement

Shear Horizontal(and webvertical)

reinforcement

WALLFOOTING

The procedure for the design of the complete example building follows the steps below:

1. The beams are fully designed for:

- the ULS in bending under the persistent and transient design situation and the

seismic design situation (whichever governs at each beam section) and

- the SLS of stress limitation in concrete and steel and crack width limitation under

the characteristic and the quasi-permanent combination of actions, whichever

applies.

The maximum beam bar diameter that can pass through or terminate at beam-column

joints is detemined at each one of them; the shear stresses that develop in the joint core

due to the beam bars passing or terminating there is calculated as well. The beam design

is carried out for one multi-storey plane frame at a time, possibly with different number

of bays in different storeys. Foundation beams are designed in bending in the same way

and with the same computational module, but specifying them as one-storey elements

II

Design shear force, with V-envelope for dual

systems. Check wall thickness (with

reduction to 40% in DC H). Dimensionhorizontal web reinforcement: and detail it

(Table 5.5). Detail vertical web

reinforcement (Table 5.5)

I

Dimension and detail vertical bars at the edges and theweb of the section, starting from the base and proceeding

to the top according to the M-envelope, including

boundary elements and their confinement within critical

region (Table 5.5)

III

Dimension vertical

and inclined bars at

construction joints forsliding shear (Table

5.5, last two rows)

IV

Magnification factor on footings seismic action effects

Ia

Seismic moments andshears redistributed

from walls with

tensile seismic axial

force to others with

compressive

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and not as the beams at the lowest level of a multistorey plane frame. Archived are:

- the design values of beam moment resistances around joints, to be used in Step 2

for the capacity design of columns and Step 3 for the capacity design of beams in

shear;

- the beam longitudinal bar diameters, for use in Step 3 to determine the maximum

stirrup spacing to prevent buckling of these bars;

- the cracked stiffness of beams around joints, taking into account their reinforcement

and concrete cracking, for use in Step 2 to calculate the effective buckling length of

the columns connected to these beams.

2. The columns are fully designed in bending and in shear, after checking that their cross-

section meets Eurocode 2s slenderness limits for negligible second-order effects in

braced or unbraced conditions whichever applies - under the persistent and transient

design situation. This step is carried out for one multi-storey column at a time (from the

roof to the foundation), using the moment resistance of the beams framing into the

columns joints, as calculated and archived in Step 1. Archived are:

- the design values of column moment resistances around joints under the maximum

and the minimum axial loads encountered in the seismic design situation according

to the analysis, for use in Step 3 for the capacity design of beams in shear;

- the capacity design magnification factors at the connection of the column to the

foundation, for use in Step 5 for the capacity design of the ground and the

foundation elements; they are calculated separately and archived for the different

directions and sense of action of the design earthquake, which produce 8

combinations of signs of the columns seismic biaxial moments and axial force.

3. The beams and their transverse reinforcement are fully designed in shear (per multi-

storey frame, possibly with different number of spans in every storey), using for the

capacity design the moment resistances of columns and beams calculated and archived in

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Steps 1 and 2 and for the maximum stirrup spacing the beam longitudinal bar diameters

from Step 1. As in Step 1, the beams shear design is carried out for one multi-storey

plane frame at a time, possibly with different number of bays in different storeys.

Foundation beams are designed in shear in the same way and with the same

computational module, but specifying them as one-storey elements and not as the beams

at the lowest level of a multistorey plane frame.

4. The walls are fully designed in bending and shear. The step is carried out for one multi-

storey wall at a time (from the roof to the foundation). As for columns in Step 2, archived

are:

- the capacity design magnification factors at the connection of the wall to the

foundation (separately for the 8 combinations of signs of the walls seismic biaxial

moments and axial force), for use in Step 5 for the capacity design of the ground

and the foundation elements.

5. The bearing capacity of the ground is calculated under each footing for biaxial

eccentricity of the vertical load and bidirectional horizontal forces (bidirectional

inclination of the vertical load) and checked aganst the soil pressure at the underside of

the footing. Seismic reaction forces and moments at the node connecting the footing to

the ground are amplified by the corresponding capacity design magnification factor at the

connection of the vertical element to the footing (a different value for the different

directions and sense of action of the design earthquake). The footing itself and its

reinforcement are then dimensioned in shear, in doubly-eccentric punching shear and in

flexure for all directions and sense of action of the design earthquake, as well as for the

persistent and transient design situation (Eqs. (6.10a), (6.10b) in EN 1990:2002). This

step is carried out separately for each individual footing.

6. The strip footings of the foundation beams are then designed, in a one-way version of the

design of individual footings in Step 5. The step is carried out for the full length of the

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strip footings of each foundation beam, that may encompass quite a few intermediate

nodes and vertical soil springs.

5.3.3Additional information for the design of beams in bending

According to clause 5.4.2.1(1), the design values of bending moments are obtained from the

analysis of the structure for the seismic design situation. The bending resistance is calculated in

accordance with Eurocode 2 [3], as prescribed in 5.4.3.1.1(1), taking into account the detailing

requirements in section 5.4.3.1.2. Following 5.8.1(5), the beams within the rigid-box basement

(including those at the basement roof) are expected to remain elastic under the seismic design

situation and are designed for Low Ductility Class (DC L).

An overview of the design and detailing requirements applied to the design of the beams, not

only for the DCs applied in the present example, but also for DC H (High), is given in Table 5.3.

5.3.4Additional information for the design of columns

According to clause 5.4.2.1(1), the design values of bending moments and axial forces are

obtained from the analysis of the structure for the seismic design situation. Capacity design

requirements for columns in bending at beam/column joints do not apply in the present example,

as the building is classified as wall and wall-equivalent structural system.

According to clause 5.4.2.3(1), the design values of shear forces are determined in accordance

with the capacity design rule, on the basis of the equilibrium of the column under end moments

that correspond to the formation of plastic hinges at the ends of the beams connected to the joints

into which the column end frames, or at the ends of the columns (wherever they form first). In

5.4.2.3(1) the end moments are defined as Mi,d = RdMRc,i min (1, MRc /MRb), where Rd is a

factor accounting for overstrength due to steel strain hardening and confinement of the concrete of

the compression zone of the section,MRc,iis the design value of the column moment of resistance

at end i, MRc and MRb are the sum of the design values of the moments of resistance of the

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columns and the sum of the design values of the moments of resistance of the beams framing into

the joint, respectively (Rd= 1.1 for DC M and Rd= 1.3 for DC H).

The bending and shear resistance are calculated in accordance with Eurocode 2 [3], as

prescribed in clause 5.4.3.2.1(1), using the value of the axial force from the analysis in the seismic

design situation and taking into account the detailing requirements in section 5.4.3.2.2.

Following clause 5.8.1(5), the columns within the rigid-box basement are expected to remain

elastic under the seismic design situation and are designed for Low Ductility Class.

An overview of the design and detailing requirements applied to the design of columns, not

only for the DCs applied in the present example, but also for DC H, is given in Table 5.4.

5.3.5Additional information for the design of beams in shear

According to clause 5.4.2.2(1), the design values of shear forces are determined in accordance

with the capacity design rule, on the basis of the equilibrium of the beam under the transverse load

acting on it in the seismic design situation and end moments that correspond to the formation of

plastic hinges at the ends of the beam or at the columns connected to the joints into which the

beam end frames (wherever they form first). In 5.4.2.2(2) the end moments are defined as Mi,d =

RdMRb,i min (1, MRc /MRb), where Rd is a factor accounting for overstrength due to steel strain

hardening and confinement of the concrete of the compression zone of the section and is equal to

Rd = 1.0 for DCM or Rd = 1.2 for DCH, MRb,i is the design value of the beam moment of

resistance at end i, MRc and MRb are the sum of the design values of the moments of resistance

of the columns and the sum of the design values of the moments of resistance of the beams

framing into the joint, respectively.

The bending and shear resistance are calculated in accordance with Eurocode 2 [3], as

prescribed in clause 5.4.3.1.1(1), taking into account the detailing requirements in section

5.4.3.1.2.

Following 5.8.1(5), the beams within the rigid-box basement (including those at the basement

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roof) are expected to remain elastic in the seismic design situation and are designed for DC Low.

5.3.6Additional information for the design of walls

To account for uncertainties regarding the moment distribution along the height of slender walls,

i.e. walls with height to length ratio hw/ lw > 2.0, clause 5.4.2.4(5) specifies that the design

bending moment diagram along the height of the wall is given by an envelope of the bending

moment diagram from the analysis, vertically displaced by hcr. The height of the critical region

above the top of the rigid-box foundation is defined in 5.4.3.4.2(1) as hcr = max [lw, hw / 6]. The

critical height must be less than 2lw and also, for buildings with up to six storeys, less than the

clear storey height, hs. A linear envelope is allowed, as the structure does not exhibit discontinuity

in mass, stiffness or resistance along its height.

According to 5.8.1(5), shear walls in box-type basements are designed for development of a

plastic hinge at the base of the roof slab and the critical region extends below the basement roof

level up to a depth ofhcr.

To account for the possible increase in shear forces after yielding at the base, clause 5.4.2.4(7)

specifies that the design shear forces are taken as being 50% higher than the shear forces obtained

from the analysis. Moreover and according to 5.8.1(5), the walls within the basement are

dimensioned in shear assuming that they develop their flexural overstrength RdMRd at the

basement roof level and zero moment at the foundation level.

The bending and shear resistance are calculated in accordance with Eurocode 2 [3], as

prescribed in clause 5.4.3.4.1(1), taking into account the detailing requirements in section

5.4.3.4.2.

An overview of the design and detailing requirements applied to the design of the walls for

DC L (Low), M (Medium) and H (High), is given in Table 5.5.

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5.3.7Additional information for the design of foundation beams

The perimeter walls of the basement are treated as deep beams, i.e. beams with span-to-depth ratio

less than 3 according to the definition of clause 5.3.1(3) of Eurocode 2 [3]. The design values of

bending moments and shear forces are obtained from the analysis for the seismic design situation,

multiplied by the capacity design factor Rd = 1.4 specified in clause 4.4.2.6(4), (5) and (8) for

foundation elements serving more than one vertical element (in the present case, all vertical

elements on the side of the perimeter in question). Owing to the applicaton of this capacity design

factor aCD = 1.4, the bending and shear resistance are calculated in accordance with Eurocode 2,

taking into account the detailing requirements for deep beams in section 9.7 of Eurocode 2.

5.3.8Additional information for the design of footings

The design action effects for the foundation elements are derived on the basis of capacity design.

According to clause 4.4.2.6(4), action effects are calculated asEFd =EF,G + RdEF,E, whereEF,G

is the action effect due to the combination Gk,j + 2,i Qk,i, Rd is an overstrength factor equal

to 1.2 for q > 3 and EF,E is the action effect from the analysis for the design seismic action.

According to 4.4.2.6(5), for columns q is the ratio of the design bending resistance, MRd, to

the design bending moment,MEd, for the seismic design situation, both taken at the cross-section

above the footing. For the common footing of C8, C9, W3, W4 and W5 and for the strip

foundations, clause 4.4.2.6(8) allows the use of the values = 1 and Rd = 1.4 instead of more

detailed calculations.

Clause 5.8.1(1) requires the design of the foundation elements to follow the relevant rules of

Eurocode 8 Part 5. As capacity design requirements are met, according to 5.8.1(2), no energy

dissipation is expected in the foundation elements for the seismic design situation and therefore

the rules for Low Ductility Class apply.

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Table 5.3: EC8 rules for detailing and dimensioning of primary beams (secondary beams as in

DCL)

DC H DCM DCL

critical region length 1.5hw hw

Longitudinal bars (L):

min, tension side 0.5fctm/fyk 0.26fctm/fyk, 0.13%(0)

max, critical regions(1) +0.0018fcd/(sy,dfyd)(1) 0.04As,min, top & bottom 214 (308mm2) -As,min, top-span As,top-supports/4 -

As,min, critical regions bottom 0.5As,top(2)

-

As,min, supports bottom As,bottom-span/4(0)

dbL/hc - bar crossing interior joint(3)

yd

ctmd

f

f

)'

75.01(

)8.01(25.6

max

+

+

yd

ctmd

f

f

)'

5.01(

)8.01(5.7

max

+

+

-

dbL/hc - bar anchored at exterior joint(3)

yd

ctmd

f

f)8.01(25.6 +

yd

ctmd

f

f )8.01(5.7 + -

Transverse bars (w):(i) outside critical regions

spacing sw 0.75dw 0.08(fck(MPa)/fyk(MPa)

(0)

(ii) in critical regions:

dbw 6mm

spacing sw6dbL,

4

wh , 24dbw, 175mm 8dbL,4wh , 24dbw, 225mm -

Shear design:

VEd, seismic(4)

qgo

cl

Rb Vl

M2,

2.1+

(4) qgo

cl

Rb Vl

M2, +

(4)from analysis for

design seismic

action plus gravity

VRd,max seismic (5) As in EC2: VRd,max=0.3(1-fck(MPa)/250)bwozfcdsin2(5), 1cot2.5

VRd,s, outside critical regions(5)

As in EC2: VRd,s=bwzwfywdcot(5)

, 1cot2.5

VRd,s, critical regions(5)

VRd,s=bwzwfywd(=45o) As in EC2: VRd,s=bwzwfywdcot, 1cot2.5

IfVEmin/VEmax(6)

1:As=0.5VEmax/fydsin

& stirrups for 0.5VEmax

-

(0) NDP (Nationally Determined Parameter) according to Eurocode 2. The Table gives the value

recommended in Eurocode 2.

(1) is the value of the curvature ductility factor that corresponds to the basic value, qo, of the

behaviour factor used in the design as: =2qo-1 ifTTC or =1+2(qo-1)TC/TifTMRc, MRb isreplaced in the calculation of the design shear force, VEd, by MRb(MRc/MRb)

(5) z is the internal lever arm, taken equal to 0.9d or to the distance between the tension and the

compression reinforcement, d-d1.

(6) VEmax, VE,minare the algebraically maximum and minimum values of VEd resulting from the sign;VEmaxis the absolutely largest of the two values, and is taken positive in the calculation of; thesign of VEmin is determined according to whether it is the same as that of VEmax or not.

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Table 5.4: EC8 rules for detailing and dimensioning of primary columns (secondary ones as DCL)

DCH DCM DCL

Cross-section sides, hc, bc0.25m;

hv/10 if=P/Vh>0.1(1) -

critical region length(1) 1.5hc, 1.5bc, 0.6m, lc/5

hc, bc, 0.45m, lc/6 hc, bc

Longitudinal bars (L):

1% 0.1Nd/Acfyd, 0.2%(0)

4% 4%(0)

8mm

3 2

Spacing between restrained bars 150mm 200mm -Distance of unrestrained bar from

nearest restrained150mm

Transverse bars (w):

Outside critical regions:

6mm, dbL/4

20dbL

, hc, b

c, 400mm

12dbL, 0.6hc, 0.6bc,

240mm12dbL, 0.6hc, 0.6bc, 240mm

Within critical regions:(2)

6mm, 0.4(fyd/fywd)1/2

dbL 6mm, dbL/4

6dbL, bo/3, 125mm 8dbL, bo/2, 175mm -

0.08 -

30*dsy,dbc/bo-0.035 -

In critical region at column base:

0.12 0.08 -

30dsy,dbc/bo-0.035 -Capacity design check at beam-column

oints: (10)

1.3MRbMRcNo moment in transverse direction of column -

Verification forMx-My-N: Truly biaxial, or uniaxial with (Mz/0.7, N), (My/0.7, N)

Axial load ratiod=NEd/Acfcd 0.55 0.65 -Shear design:

cl

endsRc

l

M3.1 (11)

cl

endsRc

l

M1.1 (11)

from analysis for

design seismic action

plus gravity

As in EC2: VRd,max=0.3(1-fck(MPa)/250)bwozfcdsin2, 1cot2.5As in EC2: VRd,s=bwzwfywdcot+NEd(h-x)/lcl

(13), 1cot2 .5

(0) Note (0) of Table 5.3 applies.(1) hv is the distance of the inflection point to the column end further away, for bending within a plane

parallel to the side of interest; lc is the column clear length.(2) For DCM: f a value of q not greater than 2 is used for the design, the transverse reinforcement in

critical regions of columns with axial load ratio d not greater than 0.2 may just follow the rulesapplying to DCL columns.

(3) For DCH: In the two lower storeys of the building, the requirements on dbw, sw apply over adistance from the end section not less than 1.5 times the critical region length.

(4) Index c denotes the full concrete section and index o the confined core to the centreline of theperimeter hoop; bois the smaller side of this core.

(5) wd is the ratio of the volume of confining hoops to that of the confined core to the centreline of theperimeter hoop, times fyd/fcd.

(6) is the confinement effectiveness factor, computed as = sn; where: s = (1-s/2bo)(1-s/2ho)for hoops and s = (1-s/2bo) for spirals; n = 1 for circular hoops and n=1-{bo/((nh-1)ho)+ho/((nb-1)bo)}/3 for rectangular hoops with nb legs parallel to the side of the core with length bo and nh legsparallel to the one with length ho.

(7) For DCH: at column ends protected from plastic hinging through the capacity design check at

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beam-column joints, *is the value of the curvature ductility factor that corresponds to 2/3 of the

basic value, qo, of the behaviour factor used in the design (see Eqs. (5.2)); at the ends of columnswhere plastic hinging is not prevented because of the exemptions listed in Note (10) below,

*is

taken equal to defined in Note (1) of Table 5.3 (see also Note (9) below); sy,d= fyd/s.(8) Note (1) of Table 5.3 applies.(9) For DCH: The requirement applies also in the critical regions at the ends of columns where plastic

hinging is not prevented, because of the exemptions in Note (10) below.

(10) The capacity design check does not need to be fulfilled at beam-column joints: (a) of the top floor,(b) of the ground storey in two-storey buildings with axial load ratio d not greater than 0.3 in allcolumns, (c) if shear walls resist at least 50% of the base shear parallel to the plane of the frame(wall buildings or wall-equivalent dual buildings), and (d) in one-out-of-four columns of planeframes with columns of similar size.

(11) At a member end where the moment capacities around the joint satisfy: MRb

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Table 5.5: EC8 rules for the detailing and dimensioning of ductile walls

DCH DCM DCL

Web thickness, bwo max(150mm, hstorey/20) -

critical region length, hcr

max(lw, Hw/6)

(1)

min(2lw, hstorey) if wall 6 storeysmin(2lw, 2hstorey) if wall > 6 storeys

-

Boundary elements:a) in critical region:

- length lc from edge 0.15lw, 1.5bw, length over which c> 0.0035 -- thickness bw over lc 0.2m; hst/15 if lcmax(2bw, lw/5), hst/10 if lc>max(2bw, lw/5) -- vertical reinforcement:

0.5% 0.2%(0)

4%(0)

- confining hoops (w)(2)

:

6mm, 0.4(fyd/fywd)1/2

dbL 6mm, in the part of the

section where L>2%:as over the rest of the

wall (case b, below)

6dbL, bo/3, 125mm 8dbL, bo/2, 175mm

0.12 0.08

30(d+)sy,dbw/bo-0.035

b) over the rest of the wall

height:

In parts of the section where c>0.2%: v,min = 0.5%; elsewhere 0.2%In parts of the section where L>2%:- distance of unrestrained bar in compression zone from nearest restrained bar

150mm;- hoops with dbw max(6mm, dbL/4) & spacing sw min(12dbL, 0.6bwo,

240mm)(0)

up to a distance of 4bw above or below floor beams or slabs, or swmin(20dbL, bwo, 400mm)

(0)beyond that distance

Web:

- vertical bars (v):

Wherever in the section c>0.2%: 0.5%; elsewhere 0.2% 0.2%(0)

4%8mm -

bwo/8 -

min(25dbv, 250mm) min(3bwo, 400mm)

- horizontal bars:

0.2% max(0.1%, 0.25v)(0)

8mm -

bwo/8 -

min(25dbh, 250mm) 400mm

axial load ratiod=NEd/Acfcd

0.35 0.4 -

Design moments MEd:If Hw/lw2, design moments from linear envelope ofmaximum moments MEd from analysis for the seismic

design situation, shifted up by the tension shift al

from analysis for

design seismic action

& gravity

Shear design:

Design shear force VEd =

shear force VEd from the

analysis for the design

seismic action, times factor

:

if Hw/lw2(5)

:

=1.2MRdo/MEdoqif Hw/lw>2

(5), (6):

( )( )

qTS

TSq

M

M

e

Ce

Edo

Rdo

+

=

2

1

2

1.02.1

=1.5 =1.0

Design shear force in walls

of dual systems with

Hw/lw>2, for z between Hw/3

and Hw:(7)

+

=

3

5.15.1)0(

4

175.0)( wEd

wEd

wEd

HV

H

zV

H

zzV

from analysis fordesign seismic action

& gravity

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VRd,max outside critical

regionAs in EC2: VRd,max=0.3(1-fck(MPa)/250)bwo(0.8lw)fcdsin2, with 1cot2.5

VRd,max in critical region 40% of EC2 value As in EC2

VRd,s in critical region; web

reinforcement ratios: h, (i) ifs=MEd/VEdlw2 :

=v,min, h from VRd,s:VRd,s=bwo(0.8lw)hfywd

As in EC2: VRd,s=bwo(0.8lw)hfywdcot,

1cot2.5(ii) ifs

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6 Design of beams in bending

6.1 Frame A

*-----------------------------------------------------------------------------*

* STOREY: 6 * BEAMS: 1 2 3 4 5

*-----------------------------------------------------------------------------*

* Concrete: C25 - Long. Reinforcement: S500 - Stirrups: S500 - Cover: 35(mm) *

*-----------------------------------------------------------------------------*

GEOMETRY - BENDING MOMENTS MEd - LONGITUDINAL REINFORCEMENT

+-----------------------------------------------------------------------------+

|Beam: 1|Length l: 5.50m|X-section InvL | Depth h: 0.50m| Width bw: 0.30m |

|-----------+-----------------------------------------------------------------|

| |Top flange thickness (m): 0.18 (L end) 0.18 (centre) 0.18 (R end)|

|-----------+-----------------------------------------------------------------|

| Location |Effect. | max MEd | Required | Beam bars | Provided |Flexural|

| |fl width| |steel area |Contin Addit |steel area|capacity|

|-----------+--(m)---+--(kNm)---+---(mm2)---+-------------+--(mm2)---+-(kNm)--|

|L end top | 0.30 | 61.2 | 471. | 214 -- | 435. | 80.9 |

|L end bot. | 0.48 | 31.3 | 344. | 214 -- | 462. | 87.2 |

|midspan | 1.32 | 35.2 | 344. | 214 114| 462. | 88.8 |

|R end top | 0.30 | 90.0 | 524. | 214 -- | 488. | 90.2 ||R end bot. | 0.66 | 33.6 | 344. | 214 -- | 462. | 87.9 |

|Note: Top reinforcements include 250mm2/m of EC8s eff. slab width in tension |

|Note:1. Addit. bot. midsp