structural design of g+5 building (final year project for bsc in civil engineering)

MEKELLE UNIVERSITY

FACULTY OF SCIENCE AND TECHNOLOGY

DEPARTMENT OF CIVIL ENGINEERING

In Partial Fulfillment of B.Sc. Degree in Civil

Engineering

Structural Design of A G+4 Commercial Building with Solid &

Pre-cast Slab and Cost Comparison Prepared by:- Keralem Adane

Osman Giragn Samuel Tesfaye

Tewodros Kassa

Tigistu Fisseha

Advisor:- Kibrealem Mebratu June 2008

Senior project, structural design & cost comparison June 2008

Mekelle University, Department of Civil Engineering Page 1

Table of content Acknowledgment…………………………………………………………..3 Introduction…………………………………………………………….…..4 Specification………………………………………………………………..5 1. Roof design...............................................................................................6

1.1. Wind load analysis………………………………………………...6

1.2. Analysis of lattice purlin………………………………………… 14

1.3. Design of truss……………………………………………………15

1.4. Design of lattice purloin………………………………………… 21

1.5. Slab roof design………………………………………………… 23

1.6. Weld design……………………………………………………… 25

2. Design of slab…………………………………………………………...26 2.1 Solid slab design…………………………………………………. 26 2.1.1 Depth determination……………………………………… 26 2.1.2 Loading…………………………………………………… 28 2.1.3 Analysis…………………………………………………… 29 2.1.4 Reinforcement design……………………………………… 38 2.2 Pre-cast slab design……………………………………………….39

2.2.1 Loading…………………………………………………… 40 2.2.2 Analysis and design……………………………………… 41

3. Design of stair………………………………………………………… 48 4. Frame analysis………………………………………………………… 55

4.1 Vertical load analysis…………………………………………… 55. 4.1.1 Solid slab………………………………………………… 55 4.1.2 Pre-cast slab……………………………………………… 59 4.2 Lateral load analysis…………………………………………… 62. 4.2.1 Earth quake analysis……………………………………… 62 4.2.2 Wind load analysis……………………………………… 64 4.3 Distribution of storey shear…………………………………… 67 4.4 Load combination……………………………………………… 83 5.Design of beam and column…………………………………………… 85 5.1 Beam design……………………………………………………85

5.1.1 Solid slab beams…………………………………………86 5.1.2 Pre-cast beams………………………………………… 93 5.1.3 Design of beams for shear and torsion………………… 99

5.2 Column design…………………………………………………104 5.2.1 Design procedure………………………………………. 104 5.2.2 Design of isolated columns…………………………… 111 5.2.3 Reinforcement design………………………………… 120 5.2.3.1 Solid slab column……………………………… 120 5.2.3.2 Pre-cast slab column…………………………… 121 6. Foundation design…………………………………………………… 124



6.1 Footing design……………………………………………… 125 6.2 Mat foundation design…………………………………………128 7. Cost estimation…………………………………………………………135 Conclusion and recommendation…………………………………… 138 References…………………………………………………………… 139



Acknowledgment We would like to express our sincere gratitude to our advisor Ato Kibrealem Mebratu for giving us critical advices throughout the project work. We would also like to thank our friend Fasil Meles for his material support. At last but not the least, we would like to thank to our parents for giving their countless material & moral support.



Introduction

Now a day’s it is being practical to choose types of structural members for different criteria’s especially economy after assuring safety.

So in this particular project we have determined the cost variation for solid and pre-cast floor system. To do this we have passed many steps.

This paper is prepared in partial fulfillment for the B.Sc. degree in civil engineering. The project is a structural design of a G+4 commercial building with solid and pre-cast slab systems with cost estimation & comparison for each staff. The building is located in Mekelle city. The structural design consists of the design of roof truss, Slabs, Staircase, Beams, Columns and foundation. The cost estimation comprises of cost for slabs, beams, columns and footings with their respective formwork.

As can be seen from the architectural drawing, the floor arrangement is typical for all floors except some modification on the cantilever parts.

For the solid type we first determine depth for deflection and made analysis for dead and live load as EBCS recommends. During the design of beams, columns and footings we have grouped them in reference to the stress they are bearing i.e. each group is taking relatively similar stress.

Limit state design method has been adopted for the whole components. Ethiopian building code of standard EBCS 1, EBCS 2, EBCS 7 and EBCS 8, are referred for the design of the building.

The roof truss, ribs and frame are analyzed using SAP 2000 V 9 for different combination of loads. And a combination with a critical effect is taken for sizing members and determination of rebar.

Working drawings for beams, columns, footings stair case and floor slabs are prepared. And finally Bill of Quantity for Concrete work, Rebar and Footing are prepared.

Generally in this project we have shown the basic steps for analysis and design of frame structures and we believe we have done a fabulous work which is almost accurate and we deserve a big hug.



Specification

Purpose – commercial building Approach- Limit state design method Material – Concrete – 25, class – I works Steel S – 300 deformed bars RHS for roof truss and purlin EGA- 300 for roof cover is used. Partial safety factors – concrete γc=1.5 Steel γs=1.15 Unit weight of concrete γc=24KN/m3 Supporting ground condition = sandy gravel with bearing capacity of 560KPa Design Data and Materials Concrete fck = 0.8*25MPa =20MPa fctk= 0.21*fck 2/3 =1.547MPa fcd= 0.85*fck =11.33MPa γc fctd= fctk=1.032MPa γc Steel fyk= 300MPa fcd= 260.87MPa Design loads Fd= γf*Fk Where Fk = characteristics loads γf = partial safety factor for loads = 1.3 for dead loads = 1.6 for live loads Seismic condition Mekelle – Zone 4



1. Roof Design Roof layout

1.1 Wind load Analysis The roof is categorized according to EBCS-1,1995 table 2.1.3 under category-H :- roof not accessible except normal maintenance, repair, painting and minor repairs. From table 2.1.4 the roof will be sloping roof with category-H qk=0.25KN/m

2 Qk=1.0KN

Characteristics wind load

Wind pressure (EBCS-1, 1995 Art. 3.5) I. External wind pressure

Wind pressure acting on external surface of the structure will be obtained from We =qref.Ce(ze) (Cpe)

Where qref =reference wind pressure = ρ/2 Vref

2 …………… (Art. 3.7.1) ρ= air density (from site with altitude above sea level) > 2000m (Mekelle)

ρ=0.94 Kg/m3

Vref = reference wind velocity

Vref = Cdir .Ctem .Calt .Vref o

= 1*1*1*22m/s

qref = ρ/2 Vref2 =0.5* 0.94Kg/m3*222 =227.48N/m2

Ce=pressure coefficient that accounts the effect of terrain roughness, topography and height above the ground on the mean wind speed is defined as



Ce(z) =

+

)(*)(

*71*)(*)(2

ZCZC

KZCZC

tr

Ttr

Where KT = terrain factor - For urban area in which at least 15% of the surface is covered with buildings by their

average height is 15m. KT = 0.24 Cr(ze)= roughness coefficient = KT.ln.(z/z0) for Z min≤ Z Cr(ze)=Cr(Z min) for Z<Z min Z0 is the roughness length ( from table 3.2 Art. 3.8.3) Z min is the minimum height Z min=16m , Z0 =1m ( from table 3.2 Art. 3.8.3) Z= the height of the building at roof level Z=16.91m

Cr(Ze)=KT*ln

o

e

Z

Z = 0.24*ln(16.91/1)

Cr(Ze = 0.679 Ct(ze)= is the topography coefficient (Art. 3.8.4) and is unity or 1 for not topography unaffected zone Ce(ze)= 0.6792 *12*[ 1+(7* 0.24/(.679 *1))]= 1.602 Cpe is the external pressure coefficient derived from appendix .A of EBCS-1, 1995 (Art. A.2.5 for duo pitch roofs)

- the roof should be divided in to zones as shown below

Case -1 when wind direction 00

I

J

H

F G F

6.8

0.8m

26m

6.5m

13m

6.5m

2.6m

0.8m

2.6m

Wind θ=00



Reference height Ze=h=16.91m e=b=26m Area F=16.9m2 H= 20.8m2 J=67.6m2 G= 33.8m2 I=20.8m2 For duo pitch roof the external pressure coefficient is given on table A.4 EBCS 1, 1995 Wind ward side ( upwind face )

Pitch angle =150 Lee ward side α= 150 Since for A ≥ 10m2 Cpe= Cpe10 (EBCS 1, 1995 Art. A.2.1)

Case-2 when wind direction θ = 900

e/4=1.7m 1.7m 1.7m Θ=900 e/4 =1.7m

Pitch angle

Zone for wind ward direction θ=00 F G H I J

Cpe,10 Cpe,10 Cpe,10 Cpe,10

Cpe,10

15o -0.9 -0.8 -0.3 -0.4 -1.0

0.2 0.2

0.2

_

_

F

H

I

G

G

H

I

F



e/10=0.68m 2.72m 3.4m b=6.8m e= min b=6.8m e=6.8m 2h=33.82m Area: F = 1.156 m2 G = 1.156m2

H = 9.248 m2 I = 11.56 m2

External pressure coefficient

Pitch angle

Zone for wind direction θ = 900

F G H I

Cpe,10 Cpe,1 Cpe,10 Cpe,1 Cpe,10 Cpe,10

150 -1.3 -2.0 -1.3 -2.0 -0.6 -0.5

We = qref Ce(z) cpe = 227.48*1.602 Cpe = 0.3644Cpe KN/m2 = 0.3644 cpe K2/m 2 Cpe = Cpe 1 , a <1 m

2 Cpe = Cpe1 + ( Cpe10 – Cpe1) log

A10 for 1m

2 < A <10m2 Cpe = Cpe10 ; a<10 m

2

The calculation for the external pressure for each zones are calculated below Case1 θ=0

0

Zone F = 0.3644*-0.9= - 0.328KN/m2 = 0.3644*0.2 = 0.073 KN/m2 Zone G = 0.3644*- 0.8 = -0.292 KN/m2 =0.3644*0.2 = 0.073 KN/m2 Zone H =0.3644*-0.3 = -0.109 KN/m2 = 0.3644*0.2 = 0.073 KN/m2 Zone J = 0.3644*-1.0 = -0.3644 KN/m2



Zone I = 0.3644 *-o.4 = -0.146 KN/m2

Case 2 θ=90

0

Cpe for F Cpe = Cpe 1 + (Cpe10 – Cpe1) log

A10

= -2+ (-1.3+2) log1.156 = -1.96

For G = -1.96 For H=-0.62 Zone F = 0.3644*-1.96 = -0.714 KN/m2 Zone G = 0.3644*-1.96 = -0.714KN/m2 Zone H = 0.3644*-0.62 = -0.226 KN/m2 Zone I = 0.3644 *-0.5 = -0.184 KN/m2 II. Internal wind pressure

Wi = qref Ce(zi) Cpi Where Cpi is the internal pressure coefficient obtained from appendix of EBCS 1-1995 (Art 1.2.9) -For closed buildings with internal partitions and opening windows the extreme values Cpi = 0.8 or Cpi = -0.5 - therefore the critical wind load on the roof

Wi =0.3644 *0.8 = 0.292 K*/m2 or

Wi =0.3644 *-0.5 = -0.182 K*/m2 Critical wind load Critical external wind pressure occurs On zone For G of case-2 =-0.714K*/m2

(-ve pressure)

On zone F,H or G of case-1=0.073K*/m2 (+ve pressure)

Net -ve wind pressure = -0.714-0.292 =-1.006 K*/m2

Net +ve wind pressure = 0.073+0.182 = 0.255K*/m2



Cpe calculation for the flat roof

The roof is divided as shown below

e/4=0.675 m wind 1.35m e/4 =0.675m e/10=0.27m 1.08m 5.3m b=2.7m

e=min{b=2.7, 2h=2(19)=38 } e=2.7

Areas F=.675*.27=.182m2 G=1.35*.27=.364m2 H=1.08*2.7=2.916 I=2.7*5.3=14.31m2 External pressure coefficients F G H I Sharp eves

Cpe10 Cpe1 Cpe10 Cpe1 Cpe10 Cpe1 Cpe10 -1.8 -2.5 -1.2 -2 -0.7 -1.2 ±0.2

Cr(z) roughness coefficient Cr(z)=Kt ln(z/z0) for zmin < Z Zo is the roughness length z0=1m (EBCS-1,1995 table 3.2 Art 3.8.3 ) Zmin is the minimum height =16m Z= the height of the building at roof level

F

H

I

G F



Z=19m Cr(z)=Kt ln(z/z0) =0.24*ln(19/1)=0.707 Ct(z) is topography coefficient (Art 3.8.4) Ct(z)=1 for not topography affected zone Ce(Ze)=0.707

2*12 *(1+(7*0.24)/(0.707*1)) =1.688 We = qref Ce(z) cpe =227.48N/m2 (1.688)Cpe =384Cpe N/m2

The calculation for the external pressure for each zones are calculated below Zone F = Cpe1= -2.5 Zone G = Cpe1=-2

Zone H = Cpe = Cpe1 + ( Cpe10 – Cpe1) logA10 for 1m

2 < A <10m2

= -1.432 Zone F = 0.384*-2.5 = -0.86 KN/m2

Zone G = 0.384*-o.2 = -0.768 KN/m2 Zone H = 0.384*-1.432 = -0.55 KN/m2 Zone I = 0.384*-o.2 = -0.768 KN/m2

Internal wind pressure

Wi= 0.384*0.8=0.3072 Wi= 0.384*-0.5=0.192

Critical wind load

Occurs on zone F=-0.96KN/m2 Occurs on zone I=0.077 KN/m2 Net -ve wind pressure =-0.96 – 0.3072=-1.267 K*/m2 Net +ve wind pressure =0.077 + 0.192= 0.269 K*/m2

Point load calculation and determination of purloin spacing

By looking into the wind pressures and referring “MA*UAL OF COLD FORMED

WELDED STRUCTURAL A*D FUR*ITURE STEEL TUBI*G “(from kaliti steel industry) we have selected EGA-300 with thickness of 0.4mm. The possible loads on purloin -wind load - Self weight of EGA-300 - distributed imposed load Using EGA-300 of thickness 0.4mm from the previous table weight =3.14Kg/m or 0.0314 KN/m To determine per area load the weight is divided by width of the sheet =(0.0314KN/m)/0.823 DL=0.0382KN/m2 (dead load)



40mm ST-20 Ø8 deformed bars

The LL=0.25KN/m2

Case-1 wind load (+ve pressure)

WL=0.255KN/m2 * cos15=0.246 KN/m2

Load combination Pd=1.3DL + 1.6LL + WL Pd=1.3(0.0382) + 1.6(0.25) + 0.246 =0.696 KN/m

2

So from table taking this load and thickness of EGA the purloin spacing is found to be = 1.75 m

Case-2 Wind load (-ve) (suction)

Pd=1.3(0.0382) + 1.6(0.25) – 1.006 cos 15 = -0.522 KN/m2 From table for this loading purloin spacing will be 2m Use purloin spacing of 1.75m.

Total design load on purloin (lattice girder purloin) To get the total design load three cases are considered and compiled.

Case-1 Dead Load + Live Load (concentrated)

205mm

Assuming a ST-30 from table which is having a weight =0.0203 Pd = 0.038cos15 *1.25+ 1KNcos15 *1 = 0.045KN/m + 0.966KN We have only considered for design the vertical perpendicular load to the EGA sheet. We neglect the effect of the load which is parallel since its effect is counter balance by its weight and the wind pressure.

Case -2 Dead Load + Live Load (distributed)

Pd=0.038cos15 + 0.25*1m*cos15 = 0.036KN/m + 0.24KN/m

Case -3 Dead Load + Wind Load

11@410m



Pd (+ve) =0.036KN/m + 0.255KN/m2 *1m

=0.036KN/m + 0.255KN/m

Pd (-ve) = 0.036KN/m – 1.006KN/m2 *1m

= 0.036KN/m – 1.006KN/m

Reaction determination

For case -1 0.966KN 0.0375KN/m 1.75m R R R=0.0394KN and 1KN at center 2R=.0788KN

For case- 2 R=0.249 2R=0.498 For case- 3 R(+ve) = 0.218 2R = 0.436 R(-ve) = -0.665 2R = -1.33 We have used factor of safety 1- for live load 0.8 – for wind load

1.25 – for dead load, according to EBCS 1, 2, 3, 1995

1.2 Analysis of lattice purloin

The analysis is done for each case and we include the effect of self weight when we do SAP analysis by defining the sections. And also we apply the distributed load on the purloin which is calculated as reaction from the EGA sheet. To apply this to the nodes we concentrate the distributed load to the center and divide it to the no of nodes, but the concentrated 1KN load is applied at the middle of the purloin as the code requires.



Load Combination where:- COMB 1 = 1(DL) + 1.3(DLp) + LLc DLr= dead load of roof COMB 2 = 1(DL + LLD) + 1.3DLP DLP = dead load of purloin COMB 3 = 1(DLr + WL

+) + 1.3DLP LLc = live load concentrated COMB 4 = 1(DLr + WL

-) + 1.3DLP WL+= wind load +ve

WL- = wind load -ve SAP result(max result) COMB 1 Top = -7.67 Diag = -1.27 Bott = 8.16 COMB 2 Top =-8.14 Diag = -1.9 Bott = 8.25 COMB 3 Top = -7.31 Diag tension = 1.79 Diag compression = -1.7 Bott = 7.4

Critical loads Top = -8.14 Diag tesion = 1.99 Diag compress = -1.9 Bott = 8.25



1.3 Design of truss The load on truss comprises of reaction from the purloins and the dead load of the truss itself.

Determination of reactions of purloin

Case -1 wind load

i. positive wind

Reaction from purloin R= 0.89 KN Rx= 0.23KN Ry= 0.86KN 2Rx= 0.46KN 2Ry= 1.72KN ii. *egative (suction) wind

Reaction from purloin R= -3.51 KN Rx= -0.91KN Ry= -3.39 KN 2Rx= -1.82KN 2Ry= -6.78KN

Case-2 Live load (distributed)

R= 1.09 KN 2R= 2.18KN

Case -3 Dead load

*EGA sheet R= .167KN 2R= 0.334KN * Purloin R=0.15KN 2R= 0.3 KN Total dead load = 0.334 + 0.3 = 0.634KN

Load combinations

COMB -1, 1.25DL + 0.8 WL+ COMB – 2, 1.25DL + LL COMB – 3, 1.25DL + WL-



Analysis result COMB -1 upper chord max. comp.=10.96 KN Max. tens. = 6.42 KN Diagonal max. comp.= 3.04 KN Max. tens. =12.46 KN Bottom chord max. comp = 10.42KN Max. tens. = 11.11KN

COMB -2 upper chord max. comp. = 10.22 KN Max. tens. = 7.3 KN Diagonal max. comp. = 3.38 KN Max. tens. = 11.27 KN Bottom chord max. comp = 11.09KN Max. Tens. = 10.63KN

COMB -3 upper chord max. comp. = 11.66 KN Max. tens. = 22.78KN Diagonal max. comp.= 25.43 KN Max. tens. = 5.19 KN Bottom chord max. comp = 22.63KN

Maximum tension upper chord = 22.78 K* Diagonal = 12.46K*

Bottom chord = 20.09K*

Post = 13.88K*

Maximum compression upper chord = 22.78 K*

Diagonal = 25.43K*

Bottom chord = 20.09K*

Post = 6.99K*

DESIG* OF TRUSS MEMBERS

Material: - Fe 430 Fy= 275 MPA Fu= 430 MPA

Diagonal steel member design Design actions Nsd =12.46 KN



Ncd = 25.43 KN Design is made for the longer member of the diagonal member i.e

1.13 1.13 1.13 tan 150 = y/2.26m y= 0.61m tan α = 0.61/1.13 α = 28.360 α y l = √1.13 + .61 = 1.28 m design is done for compression action and checked for tension actions

section selection

Nbrd = χβAfy γM1 where βA=1 For class 1-3 χ is reduction factor for the relevant buckling mode Assuming the reduction factor to be χ = 0.4 25.43= 0.4*1*A*275*103 /1.1 A= 2.543cm2 So lets use ST-30 with t = 3mm

SECTIO*AL PROPERTIES

H= 30mm b= 30mm 30mm t = 3mm A= 3.01 cm2 Ix=Iz=3.5 cm

4 Wplx = wplz=2.34cm3 30mm rx = rz=1.08 cm check class of the x-section

d/t ≤ 90 E2 24/3 = 8 ≤ 90*0.922= 76.17

So the section is at least class 3 ⇒ βA =1



Determination of λ λ1= 86.4 λx= λz= l/r =1.28/0.0108 = 118.52 λ-x= λ-z= (118.52/86.4) * 11/2 =1.372 using curve c, x=0.354 check for Nb,Rd

*b,Rd= 26.64K* ≥ *sd= 25.43K* ⇒⇒⇒⇒OK!

Check for tension Our design tension force Nsd=12.46KN since our connection is welding Aeff=Agross Resistance capacity

Npl,Rd=Afy/ γM0=3.01*10-4m2*275*106N/m2/1.1=75.25KN

Nu,Rd=0.9Aefffy/ γM2=0.9*3.01*10-4m2*275*106N/m2/1.25=59.59KN

*sd=25.43K*< *u,Rd=59.59K* ⇒⇒⇒⇒ OK!

Therefore the section is capable to carry both tension and compression forces

Post steel member design

Design actions Nsd =13.88 KN Ncd = 6.99 KN

Check for tension

for rolled section first we calculate the gross area

Nu,Rd=0.9Aefffy/ γM2 ⇒ Aeff= Nu,Rd γM1/0.9fu=13.88*103*1.25/0.9*275

=70mm2 since our connection is welding Aeff=Agross Let’s assume a square section ST-25 with the following sectional properties A=0.93 cm

2

Ix=0.88cm4

25mm S=0.71cm3

r=0.97cm

w=0.97Kg

25mm t=1mm In the absence of any information check for slenderness ratio

λ≤ 180 ⇒ le/r ≤ 180

⇒ r≥910mm/180 =5.056mm =.5056 cm

⇒ rmin=0.5056

For rmin≥0.5056 take nominal size of 25 * 25 ry=0.97 A= 0.93 cm2



⇒ 0.93cm2 > 0.7cm2

Therefore no need to check for Npl,Rd and Nu,Rd

Check for compression

Nsd=6.99KN l= 0.91m taking the above trial section

d/t≤90E 23/1≤90*0.92 ⇒ 23≤82.8 OK! Therefore the class is at least class-3 and has no problem of local buckling thus βA=1 Determine λ-

λ1= 86.4 λx= λz= l/r =910/97 =9.381 λ-x= λ-z= (9.381/86.4) * 11/2 =0.109 for cold formed RHS we use curve C and the value of the reduction factor x=2.784 calculate the design buckling resistance

Nbrd = χβAfy = 2.784*1*93*275/1.1 = 64.73KN>>6.99KN γM1

Compression design Member design for upper and lower chords

Nsd=22.78KN use Fe430 fy=275 Determination of buckling length L=1.17m Selection of trial section by assuming trial value of reduction factor x=0.8 Nbrd = χβAfy 22.78=0.8*1*A*275/1.1 A=113.9mm

2 γM1 Trial section use ST-30 with cross sectional properties t=2mm I=2.72cm4 30mm r=1.13cm 30mm

Class of x-section d/t ≤ 90 E2 24.5/2 = 12.25 ≤ 90*0.922= 76.17

Therefore the class is at least class-3 and has no problem of local buckling thus βA=1 Determine λ-

λ1= 86.4 λx= λz= l/r =1.17*10

2/1.13 =103.54



λ-x= λ-z= (103.54/86.4) * 11/2 =1.2 for cold formed RHS we use curve C and the value of the reduction factor x=0.4338 calculate the design buckling resistance

Nbrd = χβAfy = 0.4338*1*214*275/1.1 = 23.21KN >22.78 OK! γM1

1.4 Design of members for the lattice purlion

CHECK FOR TE*SIO* Nu,Rd=0.9Aefffy/ γM2 =0.9*214*275*/1.25 =42.37K* >22.78K* OK ! Therefore use ST-30 with thickness 2mm for lower and upper chords

Top members Nsd=8.14KN use Fe430 fy=275

Determination of buckling length L=0.41m Selection of trial section by assuming trial value of reduction factor x=0.45 Nbrd = χβAfy 8.14=0.45*1*A*275/1.1 A=72.36mm

2 γM1 Trial section use ST-20 with thickness t=1mm A=0.73cm2 I=0.73 cm4 20mm r=0.77cm t=1.2mm

20mm Class of x-section

d/t ≤ 90 E2 17/1.2 = 14.17 ≤ 90*0.922= 76.17

Therefore the class is at least class-3 and has no problem of local buckling thus βA=1 Determine λ-

λ1= 86.4 λx= λz= l/r =0.41*10

2/0.77 =53.25 λ-x= λ-z= (53.25/86.4) * 11/2 =0.616 for cold formed RHS we use curve C and the value of the reduction factor x=0.7757 calculate the design buckling resistance

Nbrd = χβAfy = 0.7757*1*73*275/1.1 = 14.16K* >8.14K* OK! γM1

Bottom members Nsd=8.25KN(tension) take asection of ST-20 with thickness t=1mm A=0.73 I=0.73



r=0.77 Nu,Rd=0.9Aefffy/ γM2 =0.9*73*275/1.25 =14.45KN>8.25KN OK!

DESIG* ACTIO*S FOR THE DIAGO*AL MEMBERS

Nsd=1.99KN Ncd=1.9KN Material Ø8 ,S-300 fy=260.8 Check is done for both compression and tension actions .

Check for compression resistance

Φ8 deformed bar

� buckling length for pin –pin support l= 289.91mm � class determination :-the class of the section is taken as

class -2⇒βa=1 � determination of slenderness ratio (λ)

λ1=93.9є=93.9*0.92=86.4

λx= λy=l/r,r=√(I/A), A=πD2/4=π*0.82/4=0.503cm2

I=πr4/4=0.02cm4

r= √(0.02/0.503)=0.199≅0.2cm λx= λy=28.91cm/0.2cm=144.55 λ-=[144.55/86.4]* βa1/2=1.673

using curve C , χ =0.2667 � determination of buckling resistance

Nbrd = χβAfy =0.2677*0.503*10

-4m2*260.87*106N/m2 γM1 1.1

Nbrd=3.193KN > Ncd=1.9KN OK !

� Check for tensile capcity ,Nsd=1.99KN Aeff=Agross Npl,rd=Afy =0.503*10

-4m2*260.87*106N/m2 γM1 1.1



=11.93KN >1.99KN OK! Nu,rd= 0.9Aeff*fy = 0.9*0.503*10

-4m2*260.87*106N/m2 γM2 1.25

=9.45 KN > 1.99 KN OK! So the section can carry both tensile and compressive action

1.5 Slab roof Design For the design purpose we take the max positive pressure. The suction pressure can be easily counter balanced by the weight of the slab. Net positive wind pressure = 0.269 KN Changing into equivalent rectangular section using Bare’s equation Equivalent rectangular section c/a= 3.9/5= 0.78 > 0.25 ar =2/3[(2c +a)*a/(a +c)] = 4.79

4.79 br = b-{a*(a – c)} 6*(a + c) br= 2.599≅2.6

2.6

� Depth determination

[From EBCS 2-1995 Art. 5.2.3] for ps

d= [0.4 + 0.6*fyk]le =0.85*2600/24= 108.32 mm 400 βa For pc d= 0.85*1650 =116.87 mm 12 Use for both slabs overall depth, D= d +15 +5= 116.87 + 15 +5=136.87 Use D= 150 mm

� Loading :-

From water tank having a capacity of 5000 lit = 5m3

ps

pc



unit wt of water= 9.81KN/ m3 P= 5*9.81= 49.05 KN Distributed load =49.05 KN =4.08 KN/ m2 12.015 m2 Self weight wt of slab = 0.15* 24KN/ m3=3.6 KN/m2 Live load =0.5KN/ m2 Wind load =0.269 KN/ m2 Pd=1.25DL+ LL + 0.8WL = 1.25*7.68 +0.5 + 0.8*.269

Pd =10.31 KN/ m2

� Design of slab

For ps ly/lx= 1.84 s.c =8 αxf =0.0922 αys= 0.0584 αyf = 0.045 Mi = αi*Pd*lx

2 Mys =0.0584* 10.31*2.7

2= 4.36 KN-m Myf =0.044*10.31*2.7

2 =3.31 KN-m Mxf = 0.0922*10.31*2.7

2 = 6.85 KN-m Moment for cantilever slab ps ,pd=5.21KN/m M= 0.5*wl2= 5.21*1.65^2*0.5 =7.099 KN-m Moment adjustment Reinforcement calculation Moment km ks As 7.091 20.35 3.96 216 Asmin =ρmin*b*d= 0.002*1000*130=260mm

2 Asmin<As ⇒ use all slab minimum reinforcement =260mm

2 S=1000*50.3 = 193.46mm 260 Use Ø8 c/c 190mm � Reinforcement detail

See the reinforcement detail in the auto cad file



Design of roof slab 2 is the same as that of the previous roof slab of spacing Ø8 c/c 190mm

1.3

1.65 3.9

1.6 Weld design For the upper chord

Design actions �Nsd=22.78KN Ncom=22.7KN Arrangement of the weld : section selection to be upper chord �ST-30 with 2mm thickness Fe=430 s 10mm,Ls available =30mm so lets take S=10mm a=0.7075�0.707*10mm=7.07mm lets use fy=270Mpa fu=430Mpa Fw,Rd =fvw,da fvw,d=0.63fy/gmw 0.65fu/gmw where Fw,Rd=design strength of the fillet weld per unit 0f length fvw,d=design shear strength gmw=1.25 fvw,d =0.63*270Mpa/1.25 =136.08Mpa 0.65fu/gmw Fw,Rd= 136.08 N/mm2*7.07mm=962.085N/mm But Nsd/2Fw,Rd =22.78*10^3N/2*962.085N/mm =11.84mm So the available Ls=30mm >the needed Ls=11.84mm So use fillet weld with length Ls=30mm and also use connected plate with Fe-430 and thickness 2mm. and also use this conection for all other joints since their design action is less than this.



2. DESIG* OF SLAB 2.1-SOLID SLAB DESIG*

Sample floor layout

2.1.1 Depth determination

The effective depth requirement for deflection can be calculated by using the following formula (EBCS- 2; 1995 Art 5.2.3) D ≥ (0.4+0.6 fyk) Le 400 βa Where fyk = is the characteristics strength of the reinforcement Le = is the effective span and for two span the shorter span Βa = is the appropriate constant from table 5.1



Fourth floor slab

Panel 1

Ly/Lx = 1 Lx = 5000mm Ly = 5000 mm βa= 45 d ≥ (0.4+0.6*300) 5000 = 94.44mm 400 45 Panel 4

Lx = 5000mm Ly = 5000 mm Ly/Lx = 1 βa= 40 d ≥ (0.4+0.6*300) 5000 = 106.25mm Panel 8 400 40

Ly/Lx = 5/1.65 = 3.03



βa= 12 d ≥ (0.4+0.6*300) 1650 = 116.88mm 400 12

First and second floor

A = ½ ЛD2 = 0.5*Л*3.82 = 5.67m 2

4 4 βa= 12

Equivalent rectangle

d ≥ (0.4+0.6*300) 1530 = 108.37mm 400 12 �Comparing all the above critical panels d ≥ 116.88mm Over all depth D = 116.88 + 10 + 15 = 141.88mm Use D = 150 mm Actual depth d =150 – 10 – 15 = 125mm For first and second floor slabs

2.1.2 Loading Unit weight -pvc – 16 KN/m3 -Cement – 23 KN/m3 -Terrazzo - 23 KN/m3



- Concrete - 24 KN/m3

Dead load -pvc tile = 16 *0.008 = 0.128 KN/m2 -Cement screed = 23 *0.03 = 0.69 KN/m2 -terrazzo tile = 23 *0.02 = 0.46 KN/m2 -slab concrete = 24*0.15 = 3.6 KN/m2 -plaster = 23*0.03 = 0.69 KN/m2 -partition load = 1,2 KN/m2

DL1 = (PVC floor finish) = (0.128 + 0.69 + 3.6 + 0.69 + 1.2) KN/m

2 = 6.31 KN/m2

DL2 = (Terrazzo tile floor finish = (0.46 + 0.69 + 3.6 + 0.69 + 1.2) KN/m2 = 6.64 KN/m2

Live load (from EBCS-1-1995 Table 2.9 and 2.10) Category D1 (Areas in general retail shops) = 5 KN/m

2 For stairs = 3 KN/m2 Balconies = 4 KN/m2

2.1.3 Analysis

Design moment calculation The support and span moment of simply supported (external edges) or fully fixed (contentious edges) are calculated as Mi = αi Pd LX

2 Where; Mi = the design moment per unit width at point of reference Pd = the uniformly distributed load αi = the coefficient given in table A-1 as function of aspect ratio (Ly/Lx) and Support condition Lx = shorter span of the panel Ly = longer span of the panel Fig. Where; s = support f = field (span) x = direction of shorter span y = direction of longer span



Panel 1

Ly/Lx =1 αxs = 0.039 αys = 0.039 αxs = 0.029 αyf = 0.029 DL1 = 6.31 KN/m

2 LL = 5 KN/m2 Pd = ((1.3* DL1) + (1.6*LL)) ((1.3* 6.31) + (1.6*5)) KN/m2 = 16.203 KN/m2 Mi = αi Pd LX

2 Mys = Mxs = 0.039*16.203 KN/m2 *(5m)2 = 15.8 KN.m Myf = Mxf = 0.029*16.203 KN/m2 *(5m)2 = 11.75 KN.m

Panel 2,3 and 4

Ly/Lx =1 αxs = 0.032 αys = 0.032 αxs = 0.024 αyf = 0.024 DL1 = 6.31 KN/m

2 LL = 5 KN/m2 Pd =16.203KN/m2

Mys = Mxs = 0.032*16.203 KN/m2 *(5m)2 = 12.96 KN.m Myf = Mxf = 0.024*16.203 KN/m2 *(5m)2 = 9.72 KN.m



Panel 5

Ly/Lx =1 αxs = αys = 0.039 αxs = αyf = 0.03 Pd =16.203KN/m2

Mys = Mxs = 0.039*16.203 KN/m2 *(5m)2 = 15.8 KN.m Myf = Mxf = 0.03*16.203 KN/m2 *(5m)2 = 12.15 KN.m Panel 6

Equivalent rectangular section Let’s take equivalent rectangular area Fig Ly/Lx = 5/0.905 = 5.52m �one way slab Pd =16.203KN/m2 * 1m = 16.203KN/m Fig Mxs = Pd Lx2 2



= 16.203KN/m * (0,905m)2 = 6.64KN.m 2 Panel 7

Equivalent rectangular section A = ½ ЛD2 = 0.5*Л*3.82 = 5.67m 2

4 4 Equivalent rectangular area Ly*Lx = 5.67m 2

Lx = 5.67m 2 = 1.49m 3.8m Ly/Lx = 3.8/1.49 = 2.55 � one way slab Pd = 16 203 KN/m Fig Mxs = Pd Lx2 = 16.203KN/m* (1.49m)2 = 17.986KN.m 2 2 Panel 8

Equivalent rectangular area using Bales theorem ar =2*((2c + a) * a ) 3 (a + c) br = b – a(a – c) b(a + c) so, ar =2*((2* 1.2m + 1.9m) * 1.9 ) = 1.756 m 3 (1.9m + 1.2m) br = 5 m – 1.9m(1.9m – 1.2m) = 4.57 m 5(1.9m + 1.2 m)



Ly/Lx = 4.57/ 1.756 = 2.6 > 2 � one way slab Pd = 16.203KN/m Mys = Pd Lx2 = 16.203KN/m *(1.756m)2 = 24.81KN.m 2 2 Panel 9

Equivalent rectangle ar =2*((2c + a) * a ) 3 (a + c) br = b – a(a – c) b(a + c) so, ar =2*((2* 0.525m + 1.2m) * 1.2 ) = 1.043 m 3 (1.2m + 0.525m) br = 3.1 m – 1.2m(1.2m – 0.525m) = 2.95 m 3.1(1.2m + 0.525 m) Ly/Lx = 2.95m/ 1.043m = 2.8 > 2 � one way slab Pd = 16.203KN/m Mys = Pd Ly2 = 16.203KN/m *(1.043m)2 = 8.8132KN.m 2 Panel 10

Lx/Ly = 3.4m/ 1.35m = 2.52 > 2 � one way slab Pd = 16.203KN/m Mys = Pd Ly2 = 16.203KN/m *(1.35m)2 = 14.76KN.m 2 2 Panel 11



Equvalent rectangular area Ly/Lx = 3.25m/ 1.4m = 2.62 > 2 � one way slab Pd = 16.203KN/m Mys = Pd Ly2 = 16.203KN/m *(1.4m)2 = 15.88 KN.m 2 2 Panel 12’ 13,14 and 15

Ly/Lx = 5m/ 1.55m = 3.23 > 2 � one way slab Pd2 = 16.632 KN/m

2

Mys = Pd2 Ly2 = 16.632KN/m *(1.55m)2 = 19.98 KN.m

2 2 Panel 17

Pd2 = 16.632 KN/m

2 Mys = Pd2 Ly

2 = 16.632KN/m *(1.55m)2 = 19.98 KN.m 2 2 Panel 18

Ly/Lx = 4.65m/ 1.1m = 4.23 > 2 � one way slab DL2 = 6.31 KN/m

2 LL = 5 KN/m2



Pd = ((1.3* DL1) + (1.6*LL)) ((1.3* 6.31) + (1.6*5)) KN/m2 = 16.203 KN/m2 For one meter strip Pd =16.203KN/m Mys = Pd Lx2 = 16.203KN/m *(1.1m)2 = 2.45 KN.m 8 8 Panel 1 Is cantilever slab with length of 1.03m Pd2 = 16.632 KN/m

2

Mys = Pd Ly2 = 16.632KN/m *(1.03m)2 = 8.82KN.m 2 2

Adjustment of support and span moment Support adjustment

Between 1&4 and 4&5 MR = 15.8 KN.m M = 12.96 KN.m ΛM = 15.8 – 12.96 = 2.84 ΛM = 2.84 *100% = 17.97% < 20% ; Then Md =15.8 +12.86 = 14.38KN/m 2 Between 5&6

MR = 6.64 KN.m ML = 15.8 KN.m Md = 15.8 KN. m ; Since it is cantilever Span moment Panel 1&5 Mxfd = Mxf + Cx ΛM = 11.75 + 0.38*(2.84) =12.83 KN.m Panel 5

Mxfd = Mxf + Cx ΛM = 12.15 + 0.38*(2.84) = 13.58 KN.m



After moment adjustment check depth for flexure, taking the maximum moment Mmax =24.81 KN-m

From material used the design constants fcd=11.33Mpa c1=0.0858 fyd= 260.87Mpa c2=3074 m= 28.78 ρb= 0.8Ecu * fcd ( Ecu + Eyd ) fyd b= 1000mm, Ecu= 0.0035, Eyd= (260.87/(200*10

3) = 0.0013 ρb=0.8*0.0035*11.33*0.75 = ( 0.0035 + 0.0013) *260.87 Check for effective depth

d=79.89< 125 mm OK!!



Reinforcement design

Reinforcement detail

NB: The full reinforcement details are attached with AutoCAD files.

Moment Km Ks As Asmin S calculated S provided

19.98 35.76 4.108 656.62 212.5 119.55 Φ10c/c110

12.83 28.66 4.03 413.64 212.5 189.78 Φ10c/c180

17.986 33.92 4.09 588.50 212.5 133.39 Φ10c/c130

24.81 39.85 4.16 825.68 212.5 95.07 Φ10c/c90

14.38 30.34 4.05 465.91 212.5 168.49 Φ10c/c160

9.72 24.94 4 311.04 212.5 252.38 Φ10c/c250

12.96 28.8 4.04 418.87 212.5 187.41 Φ10c/c180

14.76 30.73 4.06 479.40 212.5 163.74 Φ10c/c160

15.88 31.88 4.07 517.05 212.5 151.82 Φ10c/c150

13.58 29.48 4.05 439.99 212.5 178.41 Φ10c/c170

2.45 12.52 3.87 75.85 212.5 236.71 Φ8c/c220

8.813 23.75 3.982 280.75 212.5 179.16 Φ8c/c170

6.64 20.65 3.961 210.41 212.5 236.71 Φ8c/c220



2.2Pre-cast slab design General Precast beam slab system is a system of slab construction in which reinforced concrete precast beam elements, with their latticed reinforcement bars projected out, are used. During construction, these beam elements will be placed at certain intervals, to accommodate hollow concrete block. These blocks of specified dimensions are placed along these prefabricated beams and across the span of these elements in a similar fashion as in the case of ribbed slab construction. Concrete will be casted over the blocks and the beam elements. The projected reinforcement bars from the beam elements are used as an anchorage for the concrete, in addition to their main purpose, i.e. shear resistance. The beam elements, together with the blocks, act as formwork for the concrete casted. In addition the beam elements will acts as flexural members to carry the loads until the cast in-situ concrete attains its full strength The pre-cast beam span is 5m and it is only one type therefore from the GTZ technical manual- II the section is recommended as follows

And also the cross-sectional dimensions of the HCB is given below 220mm 550mm



Design constants and assumptions Material properties

C-25 fcd = 0.85 fck in compression fctd=fck/gc in tension Therefore fcd=11.33 Mpa fctd=1.0 Mpa steel S-300 fyd=fyk/gs Hollow concrete block (HCB) g=14KN/m2

Design of pre-cast beam element

For starting use Ø10 for top members and Ø8 for diagonal members

2.2.1Loading

A) Initial condition

Dead load – pre-cast beam and Hollow Block Pre-cast beam = 1.3*0.12*0.08*24=0.299KN/m Hollow block = 1.3*0.069*14=1.256 KN/m Live load = 1.6*2*0.625= 2KN/m qd= 0.299+1.256+2= 3.6K*/m

B)Final condition

Dead load –

hf

625mm

60

220mm

280

625mm



Pre-cast beam 1.3*.12*.08*24 = .299 KN/m

Hollow Block 1.3*.069*14 = 1.256 KN/m Cast In situ Concrete 1.3(.625*.06+2(.14*0.06))*24= 1.69KN/m Concrete Floor finishes and partition wall Partition load=0.625*1.2*1.3=0.975 KN/m Plastering = 1.3*23*0.03*0.625=0.561KN/m PVC floor finish = 1.3*16*0.002*0.625=0.104KN/m Terrazzo floor finish=1.3*23*0.02*0.625=0.374KN/m Live load =5*0.625*1.6=5KN/m qd1= 0.299+1.256+1.69+0.975+0.561+0.104+5=9.884K*/m (for PVC floor finish)

qd2= 0.299+1.256+1.69+0.975+0.561+0.374+5=10.154K*/m (for terrazzo floor finish)

2.2.2Analysis and design

Final condition Mmax=wl2/8=10.154*52/8=31.73KNm 10.154K*/m

The minimum depth required for deflection

d≥ (.4+.6*300/400)5000/20=212.5 Actual d=D-Ø/2 –cover = 280-16/2-15=257>212.5 OK!!!

be ≤ bw + le/5=120+5000/5=1120 actual=625 be = 625mm

Determination of neutral axis

ρ= ½ c1-√(c12-4M/(c2bd

2)) ρ= 0.00305 m=fyd/fcd*0.8=260.87/0.8*11.33=28.78



x= ρmd=0.00305*28.78*257=22.56 y=0.8X=0.8*22.56=18.05<60 the section is rectangular with b=be=625 M=31.73 using design table Km=(√(m/b))/d = 27.72 Ks=4.024 As=KsM/d=4.024*31.73/0.257=496.81mm2 Therefore use 2Ø20

Check for shear

Acting shear Vsd=pdl/2=10.173*5/2=25.385KN The shear force VC carried by the concrete in members with out significant axial forces shall be taken as VC = 0.25fctdK1K2bwd Where K1= 1.6-d =1.6-0.257=1.343 K2= (1+50ρ)=1.1` fctd= 1 Mpa Vc=0.25*1*1.343*1.1*120*257=11.41 KN For T-section Vc=1.1*11.41=12.55KN VRD=0.25 *fcd *bw*d=0.25*11.33*120*257=87.354KN Vs=Vsd-Vc=25.385-12.55=12.84KN

S=

Assume spacing =150mm S=2*50.3*260.87*(257-20)(cos72.6+sin72.6)/12.84 S=289.69mm 240mm Assume s=200mm 67.30 β= α=67.380 200mm S=2*50.3*260.87*(257-20)(cos67.38+sin67.38)/12.84 S=372.66mm Let’s use Ø8 c/c 200mm

Check for initial condition

3-dimentional truss model analysis



q=3.6KN/m ∆l=200mm p=q*∆l/2 = 3.6KN/m*0.2m/2=0.36KN p/2 =0.18K*

Location of neutral axis Assume the neutral axis depth x to be above the concrete section (i.e x<180)

Moment about N.A As1*x= As2*(235-X) = 628*(235-x) 78.5x = 147.58-628.x X=208.89mm So the concrete part that carry the compression load is (120*(208.89-200)=1066.8mm2 Force resisted by concrete section is =11.33Mpa*1066.8mm2=12.086KN To get the compressive force acting on steel members we have modeled the pre-cast beam as 3-D truss whose members are pin connected and also we reduced the acting compressive force which is resisted by the concrete section.



SAP result (1) Max. Tension =6.13 KN (2) Max. Compression = 11.91 KN (3) Max. compression =2.72KN Max. Tension = 1.99KN (4) Max. Tension 0.3KN

Capacity check for members According to EBCS-3,1995 N t,rd ≤ A*fy / γM1 γM1 = 1.1

0.9 Aeff fU/ γM2 γM2 = 1.25 Since the Top reinforcement bar is ф10 using Fe430

N t,rd 78.5*260.87/1.1=18.62 KN 0.9*78.5*300/1.25=16.96 KN So take Ntrd = 16.96KN

2

1

3

4



And also the buckling resistance of axial loaded compression members is Nb,rd= Nbrd = χβAfy / γM1 Design axial load Nsd=11.91KN Buckling length l=0.2m

Determination of λ λ1= 89.12 λx= λz= l/r =80 βA=1 λ-x= λ-z= (80/89.12) * 11/2 =0.898 using curve c, x=0.5998 check for Nb,Rd Nb,Rd= 11.16KN is alittle bit less than Nsd=11.91 Since the centroid of the section is below the concrete section the concrete section carrys alittle bit so the total Nsd doesn’t apply on the steel so it’s safe. But for the safety purpose we insert the formwork at the mid span. Case 1 when all the LL at the 1st span and to get the maximum span moment.

2.5m 2.5m Case 2 when all live loads are distributed over the whole span

For case 1 P1=1/2*(3.6*0.2)=0.36 KN P1’=1/2(1.6*0.2)=0.16KN For case 2 P2=0.36KN Case 1 The maximum tension for(2)=1.94KN Compression for (2) =2.37KN Diagonal (3) comp.= 1.25KN Tension= 1.15KN Bott (1) comp.=1.5KN Tens. =0.57KN For case 2 For (2) max. tens. 2.57KN Max.comp. 2.02KN For bott (1) =1.2KN tension



For diagonal comp. (3) =1.02 KN Tens. =0.76KN For bottom horizontal comp.=0.1KN Critical actions from the two cases Tension = 2.57KN Compression = 2.37KN Ntrd = 0.9Aeff*fyd / γM2 = 0.9*78.5*300/1.25 = 16.96 Ntsd=2.57< Ntrd=16.96 KN For compression x=0.5998 Nbrd= χβAfy / γM1=0.5998*78.5*260.87/1.1 Nbrd=11.17 KN Nsd=2.37<11.17KN OK! For diagonal members Maximum tension =1.15 Maximum compression=1.25 Ntrd = 0.9Aeff*fyd / γM2 =0.9*50.3*300/1.25=10.865KN Ntsd=1.15<Ntrd=10.865KN OK!

For compression

Buckling length =0.26 λ1= 89.92 λx= λz= l/r =130 βA=1 λ-x= λ-z= (130/89.92) * 11/2 =1.446

using curve c, x=0.332 Nbrd= χβAfy / γM1=0.332*50.3*260.87/1.1 Nbrd=3.96 KN Nsd=1.25<3.96KN =Ntrd OK! For bottom longitudinal reinforcement the max. Compression and tension are in significant, thus no need of checking. Hence use ф10 fo the top members and ф8 for the diagonal members. 1Ф10 Ф8

2 Ф20



NB: The irregular solid slabs are already designed in the solid slab design part.

Sample pre-cast slab layout and reinforcement detail

*B:- the remaining details are attached with AutoCAD files



3. Design of stair DESIG* OF STAIR 1

No of risers in one flight =9 Risers height =0.17 Length of thread =0.3 tanø = 0.17 =29.50 0.3 1.65m 2.4m 2.15m Depth required for deflection From survisability limt state(EBCS-2 ,1995-Art 5-2-3) d = (0.4+0.6 *fyk)/400 (le/βa ) fyk=300mpa, βa =24 (end span) le=5400 d=0.85*4550/24=161.1 D =161.1 + 15 +8 =184.1 take D =190 for end slab Actual d=167mm Loading (taking 1m strip) Dead load on the stair

� RC slab (inclined) = 0.91*1*24 =5.24KN/m Cos 29.5

� Due to steps per meter width = 0.3*0.17*1*24*1 = 2.04KN/m 2 0.3

� Floor Finishing Terrazzo tile (2cm) = 0.02*23 = 0.46KN/m2 Cement Screed (2 cm) = 0.03*23 = 0.69 KN/m2 Plastering =23*0.03=0.69 KN/m2 On the tread = (0.46+0.69)*1=1.15KN/m On the riser = 1.15*0.17*1*9/2.4 =0.73KN/m Dead load on stair = (5.24+2.04+1.15+0.73+0.69/cos29.5) = 9.95 KN/m Dead load on the landing portion

� Landing Slab = 0.19*1*24 = 4.56KN/m � Plastering = 0.3*1*23 = 0.69KN/m � Cement screed = 0.69*1 = 0.69KN/m � Terrazzo tile =23*0.02*1 = 0.46KN/m

6.4KN/m



Total load on the landing = 6.4KN/m Live Load On stair category A, qt = 3 KN/m2 (EBCS-2,1995 table 2.10) Total live load on stair case = 3 KN/m2 * 1m = 3 KN/m Design Load On stair, DL1 = 1.3*9.95+1.6*3 = 17.735 KN/m

On landing, DL2 = 1.3*6.4+1.6*3 = 13.12 KN/m

Shear Force Diagram

Bending moment Diagram

Reinforcement Design Reinforcements are calculated using design table At support Mdes =17.86KNm Km = √(M/b) = √(17.86/1) = 25.3 d 0.167 Ks =3.994 Hence As = Ks * M = 3.994 * 17.86 = 427.12 mm2 d 0.167 Asmin=0.002*1000*167=334 mm2 Spacing S = as * b = 113 * 1000 = 264.56mm As 427.12



Spacing provided Ф12 c/c 260 Transverse reinforcement As=0.2As=0.2*427.12=85.424 S = as * b = 50.3 * 1000 = 588.8mm As 85.424 Smax 2D =380 350 Use Ф8 c/c 350mm

Span moment m=31.65KN.m

Km= =33.68 Ks=4.087

As=Ks m/d =4.087*31.63/0.167 =774.05 mm2

S= = =145.98

�use ø12 c/c 140 Distribution reinforcement A=0.2As=154.81

S= = =324.91mm

�use ø8 c/c 200

Design of Stair 2 No of risers in one flight =14 Risers height =2.3/14=0.165 Length of thread =0.3 tanø = 0.165 =28.810 0.3 3.9m 2.15 Depth required for deflection d= (0.4+0.6fyk) le/ba fyk=300mpa, ba=24

400 le=6050



d=(0.4+0.6*300)*6050 =214.27mm

400 24

D=214.27+15+8 = 237.27mm Use D=240mm d=240-15-8=217mm Loading (taking 1m strip) Dead load on the stair

� RC slab (inclined) = 0.24*1*24 =6.574KN/m Cos 28.81

� Due to steps per meter width = 0.3*0.165*1*24*1 = 1.98KN/m 2 0.3

� Floor Finishing Terrazzo tile (2cm) = 0.02*23 = 0.46KN/m2 Cement Screed (2 cm) = 0.03*23 = 0.69 KN/m2 Plastering =23*0.03=0.69 KN/m2 On the tread = (0.46+0.69)*1=1.15KN/m On the riser = 1.15*0.165*1*14/3.9 =0.681KN/m Dead load on stair = (6.574+1.98+0.681+1.15+0.69/cos28.81) = 11.17 KN/m Dead load on the landing portion

� Landing Slab = 0.24*1*24 = 5.76KN/m � Plastering = 0.3*1*23 = 0.69KN/m � Cement screed = 0.69*1 = 0.69KN/m � Terrazzo tile =23*0.02*1 = 0.46KN/m

7.6KN/m Total load on the landing = 7.6KN/m Live Load On stair category A, qt = 3 KN/m2 (EBCS-2,1995 table 2.10) Total live load on stair case = 3 KN/m2 * 1m = 3 KN/m Design Load On stair, DL1 = 1.3*11.17+1.6*3 = 19.321 KN/m

On landing, DL2 = 1.3*7.6+1.6*3 = 14.68 KN/m



Shear Force Diagram

Bending moment Diagram

Reinforcement Design Reinforcements are calculated using design table At span Mdes =82.93KNm Km = √(M/b) = √(82.93/1) = 41.97 d 0.217 Ks =4.2094 Hence As = Ks * M = 4.2094 * 82.93 = 1608.69 mm2 d 0.217 Spacing S = as * b = 201 * 1000 = 124.95mm As 1608.69 Spacing provided Ф16 c/c 120 Transverse reinforcement Asmin =0.002*1000*217= 434mm2 Asmin =0.2As=0.2*1608.69=321.738mm2 Asmin=434 mm2 S = as * b = 50.3 * 1000 = 156.34mm As 434 Use Ф8 c/c 150mm Check for shear Vc = 0.25fctdK1 K2bwd d=240.15-8=217mm



Where: K1 = (1+50ρ)=1.37 ≤ 2.0 K2=1.6-d=1.383 ≥ 1.0 (d in meter) Fctd=(0.1(25/1.25)^2/3)/1.5=1.032 Vc=0.25*1.032*1.383*1.37*1000*217 Vc=106.07 KN Vsd=56.67<106.07KN OK!

Staircase for precast and solid slab which is continuous with the slab

2.4m 2.15m No of risers in one flight =9 Risers height =2.3/14=0.17 Length of thread =0.3 tanø = 0.165 =29.810 0.3 Depth required for deflection d= (0.4+0.6fyk) le/ba fyk=300mpa, ba=24

400 le=6050 d=(0.4+0.6*300)*4550 =161.1mm

400 24 D=161.1+15+8=184.1 take D=190mm

Loading on one meter strip from the previous cases On stair =17.35 KN/m On landing = 13.12 KN/ m



Shear force diagram

Bending moment diagram


At the support m=39.63KN.m d=190-15-8=167mm

Km= =37.69 Ks=4.15

As=Ks m/d =4.15*39.63/0.167 =984.82 mm2 >Asmin=334mm2

S= = =114.74

�use ø12 c/c 110mm Since the moment on the span is minimum the design is governed by top reinforcement For span use ø12 c/c 110mm Transverse reinforcement Asmin Use ø8 c/c 350mm



4. FRAME A*ALYSIS 4.1Vertical load analysis

The load on the beam includes self weight, load from the wall on it, transferred load from slab, Live load on the beam. According to EBCS-2, 1995(Art. 3.4) the load transferred to beams supporting a two way slab distribution on a supporting beam is shown in figure 4.5 of EBCS-2, 1995

4.1.1Solid slabs The design loads on beams supporting the solid slabs spanning in two directions right angles supporting uniformly distributed loads may be assessed by using EBCS-2 1995 Art A.3.8

The equn. Is given by the formula, V=βv PdLx βv is a constant that depends on the support condition of the panel and Lx is the shortest span of the panel. The assumed distribution of the load on the supporting beam is shown. Which assures that the load is assumed to be transferred only to 75% of the beam length.

To convert such a distribution to uniformly distributed load through out the span, we compared the fixed end moment equation value with the span moment equation value and we took the maximum. From fixed end moment



Fixed end moment: MF

AB= -MF BA=W*S/24(3L

2-S2) Span moment: MS =0.75L/2*WL/2-0.076WL

2+ (0.75L/2)2*W/2. For the equivalent beam having UDL W| and length L W| Fixed end moment: MF

AB=-MF BA= W

|L2/12

Span moment: MS = W|L2/24

Equating the fixed end moment equation W*S/24(3L2-S2) = W|L2/12 W| = 0.914W Equating the span moment equations: 0.75L/2*WL/2-0.076WL2+ (0.75L/2)2*W/2 = W|L2/24

W| =0.984W Taking weighted moment distribution factor =0.914+0.984/2=0.949 W= 0.949Vs

load transfer to beams 1st and 2nd

βvx βvy

panel type of panel Lx Ly Ly/LX βvxc βvxD βvyc βvyD Pd Lx vxc vxD vyc

1&5 3 5 5 1 0.36 0.24 0.36 16.2 5 27.68 18 27.68 2,3,4 1 5 5 1 0.33 0.24 0.33 16.2 5 25.37 25.37 p6 cantilever 16.2 0.9 14.66 p7 cantilever 16.2 1.5 24.14 p8 cantilever 16.2 1.8 28.45 p9 cantilever 16.2 1 16.9 p10 cantilever 16.2 1.4 21.87 p11 cantilever 16.2 1.4 22.68 p12 cantilever 16.63 1.6 25.78 p13,14,15 cantilever 16.63 1.6 25.78 p16 cantilever 13.12 1.7 20.25 p17 cantilever 16.63 1.6 25.78 p18 cantilever 16.2 1.1 17.82



Vertical load on the frames

AXIS-3

AXIS-4



AXIS-A



4.1.2 Pre-cast slab

The total loads on beams include slab load, wall loads and reactions from cantilevers. The load distribution from slab to beam is a serious of concentrated loads

AXIS-A



AXIS-E



AXIS-3



4.2 Lateral Load Analysis The lateral loads to be considered are:

a) earthquake analysis and b) wind load analysis

The analysis for both will be done and the critical load condition will be considered for the design.

4.2.1 Earthquake Analysis Determination of base shear According to EBCS-8, 1995 static method of analysis is used The seismic base shear force Fb for each main direction is determined by the equation. Fb = Sd (T) WT

Where Sd(T) = ordinate of the design spectrum at period T and is given by: = α β γ The parameter α is the ratio of the design bed rock acceleration to acceleration of gravity, g, and given by: α = αoI α0 = the bed rock acceleration ratio for the site and depends on the seismic zone as given in table 1.1 of EBCS-8, 1995. For zone 4, building location in mekelle, αo=0.10 I = the importance factor of the building i.e. 1.4 for important buildings such as hospital and 1.2 for buildings whose seismic resistance is of importance in view of the consequences associated with a collapse e.g. schools, assembly halls, cultural institutions etc. (Table 2.4, EBCS-1995) use I = 1.2 The parameter β is the design response factor for the site and is given by: β = 1.2 S ≤ 2.5 T1

2/3 S = site coefficient for soil characteristics, table 1.2 = 1.0 for subsoil class A.(includes rocks, stiff deposits of sand, gravel or over consolidated clay T1 = the fundamental period of vibration of the structure (in sec) for translational motion in the direction of motion. For buildings with heights up to 80m, the value of T1 may be approximated using: T1= C1 H

¾ H=height of the building= 19.3m C1=0.075 for moment resisting concrete frames T1 = 0.075* 19.3

¾ =0.691 sec



β = 1.2 *1.2 =1.84 ≤ 2.5 ok! 0.691

2/3

The parameter, γ, is the behavior factor to account energy dissipation capacity given by: γ = γokDkRkW ≤ 0.7 γo= basic type of the behavior factor, dependent on structural type (table 3.2) for frame system , γo=0.20 kD= factor reflecting ductility class ,use kD =2.0 for DC “L”

kR= factor reflecting the structural regularity in elevation use kR =1.0

kW= factor reflecting the prevailing failure mode in Structural system with walls. =1.0 for frame and frame equivalent dual systems. γ =0.2*2.0*1.0*1.0=0.4 ≤ 0.7 ok! Sd(T) = α β γ = 0.12*1.84*0.4= 0.0883 WT = seismic dead load, obtained as the total permanent load =11360.26 The base shear will be Fb =0.0883*11360.26 = 1003.11 KN

Distribution of base shear over height of a building The base shear force shall be distributed over the height of a structure, concentrated at each floor level,

∑=

−=

n

j

jj

iitbi

hW

hWFFF

0

)(

Where n = number of stories Fi = the concentrated lateral force acting at floor i Ft = the concentrated extra force at the top of the building accounting whiplash effect for slender building, which is given by: Ft =0.07*T1*Fb (EBCS- 8,1995 Art. 2.3.3.2.3) =0.07*0.691*1002KN =48.47KN Wi, Wj =that portion of total weight W located at or assigned to level i or j, respectively. hi, hj = height above the base to level i or j, respectively.



4.2.2 Wind Load Analysis

According to EBCS, 1995, the wind pressure acting on external surface, We & internal surface, Wi are: We=qref Ce(Zi)Cpe WI=qref Ce(Zi)Cpi

� Reference wind pressure, qref

qref = 1/2*ρ*Vref 2

Where Vref =CDIRCTEMPCALT Vref,O =1.0*1.0*1.0*22 m/s = 22 m/s ρ=air density = 0.94Kg/m3 Hence, qref =0.5*0.94*22

2 =227.48N/m2 � Exposure coefficient

To get the critical wind load we calculate the wind acting on the longest side of the building. Long side elevation of the building

level hi wihi Fi(K*)

Ground floor 1.50 1546.76 13.29

first floor 5.30 12276.74 105.45

second floor 8.35 19082.77 163.90

third floor 11.40 26566.53 228.18

fourth floor 14.45 35161.19 302.00

roof 17.50 12704.15 109.12

head room 20.55 3677.63 31.59

∑ 111015.8



4.3m

16m

27.75m

Ce(Z)=Cr(z)2Ct(z)2{ 1+7Kt/ Cr(z)Ct(z)} Where Z is reference height write wind load analysis

� Reference height Cross wind width, b=28m h<b, hence the building is considered as one part.

Terrain category: category 4, urban areas in which at least 15% of the surface is covered with buildings and their average height exceeds 15m. (table 3.1, EBCS-1995) KT=0.24 Zo=1m Zmin=16m

� Roughness coefficient, Cr(z)

KTln(Z/ Zo) ; Z ≥ Zmin Cr(z) = Cr(Zmin) ; Z < Zmin Case-1

Where Ze =16m= Zmin =16m Cr(16) = Cr(16) = 0.24*ln16=0.67 Case-2

Where Ze=20.3m



Cr(20.3) = 0.24*ln20.3=0.723

� Topography coefficient Ct = 1, assuming that it is topography unaffected.

The exposure coefficient will be; Case-1 Ce(16)=Cr(16)2Ct(16)2{ 1+7Kt/ Cr(16)Ct(16)} = 0.672*1*{1+7*0.24/(0.67*1) } = 1.575 Case-2

Ce(20.3)=1.74 � External pressure coefficient, Cpe

Wall zonation: emin= b= 27.75 e=27.75, d <e 2h=32 The zonation is according to EBCS-1

Determination of external pressures and internal pressure Face

Cpe10 upper @ 20.3m

lower @ 16m

Net external internal upper lower D 0.8 0.32 0.29 0.52 E -0.3 -0.12 -0.11 -0.44

D -0.5 -0.2 -0.18 0.47 E 0.8 0.32 0.29 -0.4

We neglect the effect of wind on adjacent faces due to its possession of high moment of inertia.

zone A B D E d/h=0.425 Cpe10 Cpe10 Cpe10 Cpe10 ≤1 -1 -0.8 0.8 -0.3 ≥4 -1 -0.8 0.6 -0.3



By looking in to the earth quake and wind pressures the earth quake pressure governs and design is done for the earth quake forces.

4.3 Distribution of Storey Shear The horizontal forces at each level, Fi, determined in the above manner are distributed to lateral load resistive structural elements in proportion to their rigidities assuming rigid floor diaphragms.

a) Determination of center of mass Center of mass is a point on a floor level where the whole mass and its inertial effects can be replaced using lumped equivalent mass.

Xm = ∑WiXi ; Ym = ∑WiYi ∑ Wi ∑ Wi

Xm Ym = the coordinate of the point of application of Fi when the seismic action is parallel to the Y- directin and X – direction respectively.

GROUND FLOOR

BLDNG PART TOTAL WT TOTAL MOMENT

WX WY

wall 659.27 9487.16 2830.32

beam 209.09 2890.80 638.25 column 162.82 2362.87 761.16 TOTAL 1031.17 14740.83 4229.73 Xm,Ym 14.30 4.10



FIRST FLOOR BLDNG PART TOTAL WT TOTAL MOMENT WX WY wall 709.69 9876.74 2798.11 beam 294.42 3934.78 1001.36 column 218.40 3244.09 1045.84 slab 734.59 8986.83 2005.45 inclined slab 56.52 1198.14 415.39 landing 19.44 464.62 117.13 pvc finishing 33.19 407.79 170.40 screed finishing 250.13 3090.75 677.47 Total 2316.37 31203.74 8231.15 Xm,Ym 13.47 3.55

SECOND FLOOR BLDNG PART TOTAL WT TOTAL MOMENT WX WY wall 709.69 9876.74 2798.11 beam 294.42 3934.78 1001.36 column 187.39 2719.53 876.06 slab 734.59 8986.83 2005.45 inclined slab 56.52 1198.14 415.39 landing 19.44 464.62 117.13 pvc finishing 33.19 407.79 170.40 screed finishing 250.13 3090.75 677.47 Total 2285.36 30679.17 8061.37

Xm,Ym 13.42 3.53



THIRD FLOOR BLDNG PART TOTAL WT TOTAL MOMENT Wx Wy wall 732.78 9664.66 2992.85 beam 294.42 3934.78 1001.36 column 187.39 2719.53 876.06 slab 744.23 8981.63 2053.64 inclined slab 56.52 1198.14 415.39 landing 19.44 464.62 117.13 pvc finishing 40.31 422.13 157.06 screed finishing 255.30 3139.18 695.70 Total 2330.40 30524.65 8309.19 Xm,Ym 13.10 3.57 FOURTH FLOOR BLDNG PART TOTAL WT TOTAL MOMENT Wx Wy wall 845.74 10937.92 3060.36 beam 294.42 3934.78 1001.36 column 187.39 2719.53 876.06 slab 745.32 9053.85 2084.45 inclined slab 56.52 1198.14 415.39 landing 19.44 464.62 117.13 pvc finishing 40.04 414.53 156.94 screed finishing 244.43 2839.08 690.89 Total 2433.30 31562.45 8402.57 Xm,Ym 12.97 3.45

ROOF LEVEL BLDNG PART TOTAL WT TOTAL MOMENT Wx Wy wall 237.21 4578.80 1170.83 beam 212.25 3017.76 713.01 column 117.12 1904.78 520.01 slab 39.37 793.86 297.03 inclined slab 56.52 1198.14 415.39



landing 19.44 464.62 117.13 TRUSS+EGA+CHIPWOOD 44.05 577.53 149.76 Total 725.95 12535.49 3383.17 Xm,Ym 17.27 4.66

HEAD ROOM LEVEL BLDNG PART TOTAL WT TOTAL MOMENT

Wx Wy beam 52.92 1138.04 330.90

column 23.42 518.84 148.74 slab 64.64 1379.37 407.03

inclined slab 28.26 599.07 207.70 landing 9.72 232.31 58.56 Total 178.96 3867.64 1152.92

Xm,Ym 21.61 6.44

Determination of center of stiffness Center of stiffness is a point where the stiffness or strength of the floor is concentrated. Xs = ∑ DiyXi ; Ys = ∑ DixYi ∑ Diy ∑ Dix Where Xi, Yi = coordinates of the shear center of the frame element Dix, Diy = lateral stiffness of a particular element along X and Y axes, respectively. The rigidity, D of a column has a relation with:

- stiffness of the column itself - stiffness of upper and lower beams - heights of upper and lower columns - upper and lower shear forces - location of storey

D = a Kc Kc = column stiffness a = factor depending on boundary conditions Computation of ‘a’ If K represents the total sum of stiffness ratios of beams above and below the column divided by 2Kc, the approximate formula to obtain ‘a’ for general cases is: a = K / (2+K)



k1 k2

k3 k4

Kc

k =0.5*k1+k2+k3+k4

Kc

k2

k4

Kc

k =0.5*k2+k4

Kc

k = I/ L

The above expressions of ‘a’ for cases of fixed column base is a = (0.5+K) and K = ∑Ktop (2+k) Kc

and for pin supported columns

Calculation of shear center

LEVEL Axis Dy Xi DyXi Axis Dx Yi DxYi GROUND A 0.000894 0 0 4 0.00299 0 0 B 0.000894 5 0.00447 3 0.003182 5 0.01590825 C 0.000894 10 0.00894 2 0.001377 7.7 0.01060269 D 0.000894 15 0.01341 1 0.001198 9 0.01078116 E 0.002393 20 0.04785 ∑ 0.008746 0.0372921

F 0.000576 23.54 0.01356 Ys 4.26372227 G 0.000103 24.02 0.00247 H 0.000913 25 0.02281 ∑ 0.00756 0.11352 xS 15.0157 FIRST Axis Dy Xi DyXi Axis Dx Yi DxYi

A 0.00038 0 0 4 0.012172 0 0 B 0.00038 5 0.0019 3 0.012976 5 0.06488222



C 0.00038 10 0.0038 2 0.004799 7.7 0.03695594 D 0.00038 15 0.00571 1 0.004908 9 0.0441748 E 0.009963 20 0.19925 ∑ 0.034857 0.14601295 F 0.002886 23.54 0.06794 Ys 4.18896113 G 0.003373 24.02 0.08101

H 0.002142 25 0.05355 ∑ 0.019885 0.41317 Xs 20.7777

1ST-4th Axis Dy Xi DyXi Axis Dx Yi DxYi A 0.00038 0 0 4 0.001574 0 0 B 0.00038 5 0.0019 3 0.001678 5 0.00838865

C 0.00038 10 0.0038 2 0.00062 7.7 0.0047703 D 0.00038 15 0.00569 1 0.000634 9 0.00570805 E 0.001437 20 0.02875 ∑ 0.004505 0.018867 F 0.000369 23.54 0.00869 Ys 4.18777854 G 0.000429 24.02 0.0103 H 0.000442 25 0.01105

∑ 0.004196 0.07018 Xs 16.7262 ROOF Axis Dy Xi DyXi Axis Dx Yi DxYi A 0.00028 0 0 4 0.001212 0 0 B 0.00028 5 0.0014 3 0.001293 5 0.00646251 C 0.00028 10 0.0028 2 0.000484 7.7 0.00372346

D 0.00028 15 0.0042 1 0.000491 9 0.00441705 E 0.001185 20 0.0237 ∑ 0.003479 0.01460303 F 0.000305 23.54 0.00718 Ys 4.19713009 G 0.000368 24.02 0.00885 H 0.000334 25 0.00836 ∑ 0.003312 0.05648

Xs 17.0533 H.ROOM Axis Dy Xi DyXi Axis Dx Yi DxYi E 0.000268 20 0.00535 3 0.000206 5 0.00103186 G 0.000116 24.02 0.0028 2 0.00024 7.7 0.00184569 H 0.000116 25 0.00291 0.000446 0.00287755 ∑ 0.0005 0.01106 ∑ Ys 6.45086338

Xs 22.0981



Direct shear force distribution

For a given storey shear Qix = Dix * Q, Qix = Diy * Q ∑ Dix ∑ Diy

Axes in x-dxn

FLOOR GROUND FIRST SECOND THIRD

FORCE 13.29 105.78 164.42 228.27

AXIS D-VALUE Qi

D-VALUE Qi

D-VALUE Qi

D-VALUE Qi

4 0.003 4.543171 0.012 36.9382 0.002 57.44 0.001574 79.74

3 0.0032 4.83463 0.013 39.3783 0.002 61.23 0.001678 85.007 2 0.0014 2.092359 0.005 14.5645 6E-04 22.61 0.00062 31.39 1 0.0012 1.820261 0.005 14.8947 6E-04 23.15 0.000634 32.135

0.0087 0.035 0.005 0.004505

FOURTH ROOF HEADROOM FLOOR

302.12 109.16 31.60 FORCE

D-VALUE Qi D-VALUE Qi D-VALUE Qi AXIS

0.00157377 105.5368 0.001212 38.03917 4 0.00167773 112.508 0.001293 40.55121 0.000206372 14.61945 3 0.00061952 41.54477 0.000484 15.17151 0.0002397 16.98038 2 0.00063423 42.53109 0.000491 15.39791 1 0.00450525 0.003479 0.000446072

Axes in y-dxn FLOOR GROUND FIRST SECOND THIRD FORCE 13.29042136 105.7757269 164.4221758 228.2715446

D-

VALUE Qi D-

VALUE Qi D-

VALUE Qi D-

VALUE Qi A 0.0009 1.57154 4E-04 2.02353 0.00038 14.87 0.00038 20.65 B 0.0009 1.57154 4E-04 2.02353 0.00038 14.87 0.00038 20.65 C 0.0009 1.57154 4E-04 2.02353 0.00038 14.87 0.00038 20.65

D 0.0009 1.57154 4E-04 2.02353 0.00038 14.87 0.00038 20.65 E 0.0024 4.206323 0.01 52.9951 0.00144 56.32 0.001437 78.197 F 0.0006 1.012809 0.003 15.3529 0.00037 14.47 0.000369 20.084 G 0.0001 0.180896 0.003 17.9401 0.00043 16.81 0.000429 23.338 H 0.0009 1.604234 0.002 11.3935 0.00044 17.33 0.000442 24.053 0.0076 0.02 0.0042 0.004196



FOURTH ROOF HEADROOM FLOOR 302.1207209 109.1597995 31.59983145 FORCE

D-VALUE Qi D-

VALUE Qi D-VALUE Qi AXIS

0.00037955 27.33061 0.00028 9.22275 4 0.00037955 27.33061 0.00028 9.22275 3 0.00037955 27.33061 0.00028 9.22275 2 0.00037955 27.33061 0.00028 9.22275 1 0.00143729 103.4949 0.001185 39.05695 0.00026757 16.89932 0 0.00036915 26.58108 0.000305 10.05581 0

0.00042895 30.88771 0.000368 12.13888 0.000116378 7.350258 0 0.0004421 31.8346 0.000334 11.01716 0.000116378 7.350258 0.00419571 0.003312 0.000500326

Calculation of eccentricities

Eccentricity is the difference between the center of mass and center of stiffness of the floor. Actual eccentricities ex = Xm – Xs ey = Ys – Ym Accidental eccentricities For various sources of eccentricities in locating the masses and spatial variation of seismic motion, an additional accidental eccentricity, eli is considered in addition to the actual eccentricity. It is given by: eli = ± 0.05 li Where eli is the floor dimension perpendicular to the direction of seismic action. Design eccentricities

ed,x = ex + elx and ed,y = ey + ely



eccentrities ground first second third fourth roof head room

actual ex 0.72 7.22 3.21 3.63 3.76 -0.21 0.49 ey 0.16 0.62 0.64 0.62 0.73 -0.46 0.01

accidental ex ±1.25 ±1.25 ±1.25 ±1.25 ±1.25 ±1.25 ±0.25 ey ±0.45 ±0.45 ±0.45 ±0.45 ±0.45 ±0.45 ±0.135

DESIGN ECCENTRICITIES

LEVEL ground first second third fourth roof head room

edx1 1.97 8.47 4.46 4.88 5.01 1.04 1.74 edx2 -0.53 5.97 1.96 2.38 2.51 -1.46 -0.76 edy1 0.61 1.07 1.09 1.07 1.18 -0.01 0.46 edy2 -0.29 0.17 0.19 0.17 0.28 -0.91 -0.44

Calculation of shear correction factor

When the shear center and mass center do not coincide, torsion will be developed due to the lateral forces. This is also somehow amplified by the inherent existence of accidental eccentricities. As a result the direct shear forces obtained above need to be corrected to take this effect. The shear correction factors are calculated using αix = 1+(Dix)edy *yi Jr αiy = 1+(Diy)edx *xi Jr Jr = Jx + Jy where Jx =∑ (Dix yi

2) Jy =∑ (Diy xi

2) xi = Xi – Xs yi =Ys – Yi



Ground floor

DIR

AXIS

Ys-Yi

Xs-Xi DX DY

DX(Ys-Yi)2

DY(Xi-Xs)2 αx1 αx2 αy1 αy2

αx,max

αy,max

X

4 4.26 0.003

0.0544

1.013

0.994 1.013

3

-0.74

0.0032

0.0017

0.998

1.001 1.001

2

-3.44

0.0014

0.0163

0.995

1.002 1.002

1

-4.74

0.0012

0.0269

0.994

1.003 1.003

Y

A 15.01

6 9E-04 0.2

1.0431

0.988 1.043

B 10.01

6 9E-04 0.09

1.0288

0.992 1.029

C 5.015

7 9E-04 0.02

1.0144

0.996 1.014

D 0.015

7 9E-04 0 1 1 1

E -

4.984 0.002 0.06

0.9617 1.01 1.01

F -

8.524 6E-04 0.04

0.9842

1.004 1.004

G -

9.004 1E-04 0.01 0.997

1.001 1.001

H -

9.984 9E-04 0.09

0.9707

1.008 1.008

0.099

2 0.51 Jx Jy



First floor

X

4 4.19

0.0122

0.2136

1.067

1.011

1.067

3

-0.81 0.013

0.0085

0.986

0.998

0.998

2

-3.51

0.0048

0.0592

0.978

0.996

0.996

1

-4.81

0.0049

0.1136

0.969

0.995

0.995

Y

A 20.77

8 4E-04

0.16

1.0824

1.058

1.082

B 15.77

8 4E-04

0.09

1.0625

1.044

1.063

C 10.77

8 4E-04

0.04

1.0427 1.03

1.043

D 5.777

7 4E-04

0.01

1.0229

1.016

1.023

E 0.777

7 0.01 0.01

1.0807

1.057

1.081

F -2.762 0.003

0.02

0.9169

0.941

0.941

G -3.242 0.003

0.04

0.8861 0.92 0.92

H -4.222 0.002

0.04

0.9058

0.934

0.934

0.394

9 0.42

Jx Jy

Second floor

X

4 4.19 0.0016 0.0276 1.023 1.004 1.023

3 -

0.81 0.0017 0.0011 0.995 0.999 0.999

2 -

3.51 0.0006 0.0076 0.992 0.999 0.999

1 -

4.81 0.0006 0.0147 0.989 0.998 0.998

Y A 16.726 4E-04 0.11 1.0904 1.04 1.09 B 11.726 4E-04 0.05 1.0633 1.028 1.063



C 6.7262 4E-04 0.02 1.0363 1.016 1.036 D 1.7262 4E-04 0 1.0093 1.004 1.009 E -3.274 0.001 0.02 0.933 0.971 0.971 F -6.814 4E-04 0.02 0.9642 0.984 0.984 G -7.294 4E-04 0.02 0.9555 0.98 0.98 H -8.274 4E-04 0.03 0.9479 0.977 0.977

0.051 0.26 Jx Jy

Third floor

X

4.00 4.19 0.00 0.03 1.02 1.00 1.02

3.00 -0.81 0.00 0.00 1.00 1.00 1.00

2.00 -3.51 0.00 0.01 0.99 1.00 1.00

1.00 -4.81 0.00 0.01 0.99 1.00 1.00

Y

A 16.73 0.00 0.11 1.10 1.05 1.10

B 11.73 0.00 0.05 1.07 1.03 1.07

C 6.73 0.00 0.02 1.04 1.02 1.04

D 1.73 0.00 0.00 1.01 1.00 1.01

E -3.27 0.00 0.02 0.93 0.96 0.96

F -6.81 0.00 0.02 0.96 0.98 0.98

G -7.29 0.00 0.02 0.95 0.98 0.98

H -8.27 0.00 0.03 0.94 0.97 0.97

0.05 0.26

Jx Jy



Fourth floor

X

4.00 4.26 0.00 0.03 1.03 1.01 1.03

3.00 -0.81 0.00 0.00 0.99 1.00 1.00

2.00 -3.51 0.00 0.01 0.99 1.00 1.00

1.00 -4.81 0.00 0.01 0.99 1.00 1.00

Y

A 16.73 0.00 0.11 1.10 1.05 1.10

B 11.73 0.00 0.05 1.07 1.04 1.07

C 6.73 0.00 0.02 1.04 1.02 1.04

D 1.73 0.00 0.00 1.01 1.01 1.01

E -3.27 0.00 0.02 0.93 0.96 0.96

F -6.81 0.00 0.02 0.96 0.98 0.98

G -7.29 0.00 0.02 0.95 0.98 0.98

H -8.27 0.00 0.03 0.94 0.97 0.97

0.05 0.26

Jx Jy

Roof

X

4 4.2 0.0012 0.0214 1 0.981 1 3 -0.8 0.0013 0.0008 1 1.004 1.004 2 -3.5 0.0005 0.0059 1 1.006 1.006 1 -4.8 0.0005 0.0113 1 1.009 1.009

Y

A 17.053 3E-04 0.08 1.0207 0.971 1.021 B 12.053 3E-04 0.04 1.0146 0.979 1.015 C 7.0533 3E-04 0.01 1.0086 0.988 1.009 D 2.0533 3E-04 0 1.0025 0.996 1.002 E -2.947 0.001 0.01 0.9848 1.021 1.021 F -6.487 3E-04 0.01 0.9914 1.012 1.012 G -6.967 4E-04 0.02 0.9889 1.016 1.016 H -7.947 3E-04 0.02 0.9885 1.016 1.016

0.0394 0.2 Jx Jy



Head room

X

3 1.45

0.0002 0.0004

1.04

0.961 1.04

2

-1.25

0.0002 0.0004

0.96

1.039

1.039

Y

E 2.098

1 3E-04 0 1.287

0.874

1.287

G -1.922 1E-04 0

0.8856 1.05 1.05

H -2.902 1E-04 0

0.8273

1.076

1.076

0.0008 0 Jx Jy

Corrected shear forces for torsion

Corrected shear forces are given by = αmax * Q LEVEL GROUND FIRST SECOND THIRD

Axis αmax*Qi αmax αmax*Qi

αmax

αmax*Qi αmax

αmax*Qi

4 4.60 1.07 39.42 1.02 58.76 1.02 81.54 3 4.84 1.00 39.29 1.00 61.18 1.00 84.94 2 2.10 1.00 14.51 1.00 22.58 1.00 31.35 1 1.83 1.00 14.82 1.00 23.10 1.00 32.08

A 1.64 1.08 2.19 1.09 16.22 1.10 22.69 B 1.62 1.06 2.15 1.06 15.82 1.07 22.08 C 1.59 1.04 2.11 1.04 15.41 1.04 21.47 D 1.57 1.02 2.07 1.01 15.01 1.01 20.86 E 4.25 1.08 57.27 0.97 54.67 0.96 75.40 F 1.02 0.94 14.45 0.98 14.24 0.98 19.70 G 0.18 0.92 16.50 0.98 16.48 0.98 22.78 H 1.62 0.93 10.64 0.98 16.93 0.97 23.39



FOURTH ROOF HEAD ROOM LEVEL αmax

αmax*Qi Qi

αmax

αmax*Qi Qi

αmax

αmax*Qi Axis

1.03 108.20 1.00 38.03 4 1.00 112.37 1.00 40.71 1.04 15.21 3 1.00 41.46 1.01 15.27 1.04 17.64 2 1.00 42.41 1.01 15.54 1 1.10 30.09 1.02 9.41 A 1.07 29.27 1.01 9.36 B 1.04 28.44 1.01 9.30 C 1.01 27.62 1.00 9.25 D 0.96 99.61 1.02 39.89 1.29 21.75 E 0.98 26.05 1.01 10.18 F 0.98 30.12 1.02 12.33 1.05 7.72 G 0.97 30.91 1.02 11.20 1.08 7.91 H



Earth quake loading on frames

AXIS-A



AXIS-E



AXIS-3

4.4 Load combination

The final critical design bending moments, shear forces and axial forces will be obtained from whichever the following five combinations of loading that produces the critical effect. Case 1. Consider vertical load only Case 2. Consider 75% of vertical load with earthquake effect from positive X– direction Case 3. Consider 75% of vertical load with earthquake effect from negative X– direction Case 4. Consider 75% of vertical load with earthquake effect from positive Y– direction Case 5. Consider 75% of vertical load with earthquake effect from negative Y– direction The frame is analyzed using sap2000 version 9



NB:- The same procedure is performed for the pre-cast slab system.



5. DESIG* OF BEAMS A*D COLUM*S

5.1 Beam design

Beams are flexural members which are used to transfer the loads from slab to columns. Basically beams should be designed for flexure (moment). Furthermore it is essential to check and design the beam sections for torsion and shear. Beams may be designed for flexural moment depending on the magnitude of the moment and the X- sectional dimensions. on the other hand the beam can be singly reinforced, doubly reinforced T or Г section.

Style of beam reinforcement

� Singly reinforced cross section

The moment capacity of a given singly reinforced beam is given by M=ρbd2fyd (1-0.4ρm) ρ is taken to be 0.75 ρb to re assure ductility of the material. Afterward for the given sectional dimensions and material data, the total area of reinforcement required for the applied moment M is given by As=ρbd Where:

ρ =1/2(c1 + )/4( 22

21 bdCMC −

M=moment m=fyd/ (0.8fcd) d=effective depth

� Doubly reinforced cross section

Incase when the dimension of the section is limited, the concrete may be subjected to higher compression stress. Thus additional steel bars are placed in the compression zone of the section. Hence the design moment, Md is obtained by Md = M1+M2 Where; M1=the moment resisted by concrete and partial steel As M2= The moment resisted by steel in compression, As’, and the left over steel As2 M1 can be computed via in the manner of singly reinforced section M1=0.8ρbd

2 fcd*m(1-0.4ρm), ρ is stated above. As1= ρbd but since M2=M-M1=As’fs’(d-dc’)=As2fyd(d-dc’) At yielding the compression steel both area of steel becomes equal As’=As2= (M-M1)/ ( fyd(d-dc

’) = (M-M1)/( fs’(d-dc’)…….i.e. fyd = fs

’

fs’=(x-dc’)Es*Єc/x ,x= ρmb



Longitudinal reinforcement design

In this specific project we have used design tables for the calculation of reinforcement area as per the provision of EBCS 2, 1995.

5.1.1 Solid slab beams

AXIS-A moment LOCATION b d Km KS AS1 Ф(As1 )

22.42 TTBeam 0.25 0.307 30.85 4.06 296.499 2Ф12 12.4 TTBeam 0.25 0.307 22.94 3.98 Asmin 2Ф12 44.97 TTBeam 0.25 0.307 43.69 4.252 622.8418 4Ф12+1Ф16 173.14 1st &2nd 0.25 0.446 59.01 2410.72 4Ф24+3Ф16 102.74 1st &2nd 0.25 0.446 45.45 4.296 989.6212 5Ф16 174.08 1st &2nd 0.25 0.455 58.00 2410.72 4Ф24+3Ф16 128.5 3rd&4th 0.25 0.446 50.83 4.425 1274.916 4Ф20 71.05 3rd&4th 0.25 0.455 37.05 4.12 643.3538 3Ф16+2Ф20 14.31 3rd&4th 0.25 0.455 16.63 3.963 124.6385 2Ф12 141.28 3rd&4th 0.25 0.455 52.25 4.47 1387.96 4Ф20+1Ф14 96.44 Gbeam 0.25 0.355 55.33 1285.81 4Ф20 102.44 Gbeam 0.25 0.355 57.02 1275.096 4Ф20 66.6 Gbeam 0.25 0.355 45.98 4.306 807.8299 4Ф16



AXIS-B moment LOCATION b d Km KS As1 Ф(As1 )

17.17 TTBeam 0.25 0.307 26.99 4.015 224.5523 2Ф12 5.16 TTBeam 0.25 0.307 14.80 min 153.5 2Ф12

19.68 TTBeam 0.25 0.307 28.90 4.039 258.917 2Ф14 179.28 1st &2nd 0.25 0.445 60.18 4.27 1720.282 4Ф24 140.87 1st &2nd 0.25 0.445 53.34 4.3 1361.216 3Ф24 205.44 1st &2nd 0.25 0.445 64.42 2707.4 6Ф24 157.05 3rd&4th 0.25 0.445 56.32 4.52 1595.204 3Ф24&1Ф20 90.16 3rd&4th 0.25 0.445 42.68 4.22 855.0004 2Ф20 +2Ф12

158.5 3rd&4th 0.25 0.445 56.58 1595.204 3Ф24&1Ф20 100.71 Gbeam 0.25 0.357 56.22 4.52 1275.096 4Ф20 102.03 Gbeam 0.25 0.357 56.59 1275.096 4Ф20 69.23 Gbeam 0.25 0.357 46.61 4.32 837.7412 2Ф20 +2Ф12

AXIS -C

moment LOCATION b d Km KS AS1 Ф(As1 ) 22.15 TTBeam 0.25 0.307 30.66 3.994 288.1664 3Ф12 9.89 TTBeam 0.25 0.307 20.49 3.97 127.8935 2Ф12 16.01 TTBeam 0.25 0.307 26.07 4 208.5993 2Ф12

177.98 1st&2nd 0.25 0.446 59.82 2416.4 5Ф24+1Ф16 114.32 1st&2nd 0.25 0.446 47.95 4.36 1117.568 4Ф20 35.44 1st&2nd 0.25 0.455 26.17 4.01 312.3393 2Ф16 182.2 1st&2nd 0.25 0.455 59.33 2241 4Ф24+3Ф16 166.48 3rd&4th 0.25 0.446 57.86 1941.5 3Ф24+3Ф16 95.32 3rd&4th 0.25 0.446 43.78 4.26 910.4556 2Ф20+2Ф14

150.1 3rd&4th 0.25 0.455 53.85 4.53 1494.402 2Ф24+3Ф16 115.1 Gbeam 0.25 0.355 60.44 1550 3Ф24+1Ф20 111.28 Gbeam 0.25 0.355 59.43 1550 3Ф24+1Ф20 61.8 Gbeam 0.25 0.355 44.29 4.19 729.4141 4Ф16

AXIS-D

moment LOCATION b d Km KS AS1 Ф(As1 ) 24.86 TTBeam 0.25 0.307 32.48 4.07 329.5772 3Ф14 12.74 TTBeam 0.25 0.307 23.25 3.98 165.1635 2Ф12 14.44 TTBeam 0.25 0.307 24.76 3.988 187.5789 2Ф12 166.42 4th&3rd 0.25 0.446 57.85 1941.5 3Ф24+3Ф16

96.08 4th&3rd 0.25 0.446 43.96 4.26 917.7148 2Ф20+2Ф14 157.49 4th&3rd 0.25 0.455 55.16 1595.204 3Ф24&1Ф20 165.87 1st&2nd 0.25 0.446 57.75 1941.5 3Ф24+3Ф16 105.43 1st&2nd 0.25 0.446 46.04 4.31 1018.841 4Ф20



80.93 1st&2nd 0.25 0.455 39.54 4.16 739.9314 2Ф16+2Ф20 145.5 1st&2nd 0.25 0.455 53.02 4.51 1442.209 4Ф20+1Ф16 103.85 Gbeam 0.25 0.355 57.41 1398.54 3Ф24 99.45 Gbeam 0.25 0.355 56.18 1398.54 3Ф24 74.01 Gbeam 0.25 0.355 48.47 4.37 911.0527 2Ф14+2Ф20

AXIS-E

moment LOCATION b d Km KS AS1 Ф(As1 ) 32.22 HEAD ROOM 0.25 0.307 36.98 4.12 432.3987 3Ф14

6.42 HEAD ROOM 0.25 0.307 16.51 Asmin 2Ф12 31.25 TTBeam 0.25 0.307 36.42 4.11 418.3632 4Ф12 21.98 TTBeam 0.25 0.307 30.54 4.06 290.6801 2Ф14 13.42 TTBeam 0.25 0.307 23.87 Asmin 2Ф12 10.41 TTBeam 0.25 0.307 21.02 Asmin 2Ф12 12.46 TTBeam 0.25 0.307 23.00 3.97 161.1277 2Ф12

3.9 TTBeam 0.25 0.307 12.87 Asmin 2Ф12 157.15 4th&3rd 0.25 0.446 56.22 1744.84 4Ф24 112.47 4th&3rd 0.25 0.446 47.56 4.349 1096.709 2Ф24+1Ф16 121.7 4th&3rd 0.25 0.446 49.47 4.396 1199.536 2Ф24+2Ф14 47.81 4th&3rd 0.25 0.455 30.39 4.04 424.5108 3Ф14 130.59 4th&3rd 0.25 0.455 50.23 4.415 1267.154 2Ф24+2Ф16

81.82 4th&3rd 0.25 0.455 39.76 4.166 749.1475 2Ф20+1Ф12 52.57 4th&3rd 0.25 0.455 31.87 4.054 468.3929 2Ф14+1Ф16 179.08 1st&2nd 0.25 0.446 60.01 1754.68 4Ф24 120.73 1st&2nd 0.25 0.446 49.27 4.392 1188.893 2Ф24+2Ф14 156.16 1st&2nd 0.25 0.446 56.04 1744.84 4Ф24 101.81 1st&2nd 0.25 0.446 45.25 4.29 979.2935 2Ф20+2Ф16

146.86 1st&2nd 0.25 0.446 54.34 1442.209 4Ф20+1Ф16 149.72 1st&2nd 0.25 0.446 54.87 1717.45 4Ф24 150.8 1st&2nd 0.25 0.446 55.07 1717.45 4Ф24 100.84 Gbeam 0.25 0.335 59.95 4.275 1286.839 3Ф20 59.44 Gbeam 0.25 0.335 46.03 4.09 725.7003 2Ф20 97.73 Gbeam 0.25 0.335 59.02 4.28 1248.61 3Ф20

85.69 Gbeam 0.25 0.335 55.27 4.2 1074.322 3Ф20 119.53 Gbeam 0.25 0.335 65.27 4.386 1564.951 2Ф24+2Ф14 106.97 Gbeam 0.25 0.355 58.27 4.32 1301.719 2Ф20+3Ф14 130.62 Gbeam 0.25 0.355 64.39 4.43 1629.99 3Ф20+1Ф24



AXIS-H moment LOCATION b d Km KS AS1 Ф(As1 )

36.14 TTBeam 0.25 0.307 39.16 4.159 489.5969 3Ф16 12.3 TTBeam 0.25 0.307 22.85 Asmin 2Ф12

27.97 TTBeam 0.25 0.307 34.45 4.092 372.8119 2Ф16 151.31 4th&3rd 0.25 0.446 55.16 1717.45 4Ф24 117.03 4th&3rd 0.25 0.446 48.51 4.373 1147.471 3Ф20+2Ф12 83.215 4th&3rd 0.25 0.446 40.91 4.18 779.9074 2Ф20+1Ф14 173.14 1st&2nd 0.25 0.446 59.01 2412.33 4Ф24+2Ф20 154.14 1st&2nd 0.25 0.446 55.67 1744.84 4Ф24

96.66 1st&2nd 0.25 0.446 44.09 4.265 924.3383 3Ф20 100 Gbeam 0.25 0.355 56.34 1394.7 3Ф24

86.56 Gbeam 0.25 0.355 52.42 4.481 1092.607 2Ф24+1Ф16 83.43 Gbeam 0.25 0.355 51.46 4.435 1042.287 2Ф20+3Ф14

AXIS-4

moment LOCATION b d Km KS AS1 Ф(As1 ) 186.912 1st&2nd 0.25 0.446 61.31 4.51 2341 4Ф24+3Ф16 184.18 1st&2nd 0.25 0.446 60.86 2341 4Ф24+3Ф16 150.25 1st&2nd 0.25 0.455 53.88 4.53 1495.896 3Ф24+1Ф14

174 1st&2nd 0.25 0.446 59.15 4.51 1759.507 4Ф24 176.859 1st&2nd 0.25 0.455 58.46 4.51 1753.042 4Ф24 180.71 1st&2nd 0.25 0.455 59.09 1754.68 4Ф24 92.19 1st&2nd 0.25 0.455 42.20 4.25 861.1154 2Ф24 81.38 1st&2nd 0.25 0.455 39.65 4.2 751.2 4Ф16 71.86 1st&2nd 0.25 0.455 37.26 4.15 655.4264 3Ф14+1Ф16

85.69 1st&2nd 0.25 0.455 40.69 4.22 794.7512 4Ф16 104.94 1st&2nd 0.25 0.455 45.03 4.31 994.047 5Ф16 155.98 3rd&4th 0.25 0.446 56.01 4.52 1580.784 3Ф24+2Ф14 148.96 3rd&4th 0.25 0.446 54.73 1717.45 4Ф24 132.93 3rd&4th 0.25 0.455 50.68 4.427 1293.365 2Ф24+2Ф16 134.47 3rd&4th 0.25 0.455 50.97 4.44 1312.191 3Ф20+2Ф16

132.34 3rd&4th 0.25 0.455 50.57 4.42 1285.589 4Ф20 137.81 3rd&4th 0.25 0.455 51.60 4.45 1347.812 2Ф24+3Ф14 82.511 3rd&4th 0.25 0.455 39.93 4.21 763.4534 4Ф16 70.31 3rd&4th 0.25 0.455 36.86 4.14 639.7437 1Ф16+3Ф14 48.76 3rd&4th 0.25 0.455 30.69 4.01 429.731 3Ф14 67.357 3rd&4th 0.25 0.455 36.08 4.13 611.3943 2Ф16+2Ф12

73.61 3rd&4th 0.25 0.455 37.71 4.16 673.0057 2Ф12+3Ф14 42.44 TTBeam 0.25 0.307 42.44 4.25 587.5244 3Ф12+2Ф14 37.65 TTBeam 0.25 0.307 39.97 4.19 513.855 3Ф16



33.94 TTBeam 0.25 0.307 37.95 4.15 458.798 3Ф16 25.63 TTBeam 0.25 0.307 32.98 4.13 344.7945 2Ф16 17.05 TTBeam 0.25 0.307 26.90 4.014 222.9274 2Ф12 25.89 TTBeam 0.25 0.307 33.15 4.082 344.2442 2Ф12+1Ф14 17.73 TTBeam 0.25 0.307 27.43 min 2Ф12

13.94 TTBeam 0.25 0.307 24.32 min 2Ф12 9.27 TTBeam 0.25 0.307 19.83 min 2Ф12 8.61 TTBeam 0.25 0.307 19.12 min 2Ф12 5.69 TTBeam 0.25 0.307 15.54 min 2Ф12 97.3 Gbeam 0.25 0.357 55.26 4.598 1253.18 4Ф20 78.96 Gbeam 0.25 0.357 49.78 4.405 974.2824 2Ф20+2Ф16

81.53 Gbeam 0.25 0.357 50.58 4.425 1010.561 2Ф20+2Ф16 83.34 Gbeam 0.25 0.357 51.14 4.43 1034.163 2Ф20+2Ф16 81.92 Gbeam 0.25 0.357 50.71 4.425 1015.395 2Ф20+2Ф16 22.74 Gbeam 0.25 0.357 26.72 4 254.7899 2Ф14 75.44 Gbeam 0.25 0.357 48.66 4.37 923.4532 3Ф20 66.48 Gbeam 0.25 0.357 45.68 4.29 798.8773 4Ф16

68.82 Gbeam 0.25 0.357 46.47 4.33 834.7076 2Ф20+2Ф12 69.32 Gbeam 0.25 0.357 46.64 4.34 842.7137 2Ф20+2Ф12 73.37 Gbeam 0.25 0.357 47.99 4.34 891.949 2Ф24

AXIS-1 moment LOCATION b d Km KS As1 Ф(As1 )

21.36 TTBeam 0.25 0.307 30.11 3.97 276.2189 2Ф14 11.92 TTBeam 0.25 0.307 22.49 3.96 153.7564 2Ф12 158.02 1st&2nd 0.25 0.455 55.26 4.52 1748 4Ф24 177.72 1st&2nd 0.25 0.455 58.60 1857 5Ф20+2Ф16

164.47 1st&2nd 0.25 0.455 56.37 4.52 1895 5Ф20+2Ф16 117.51 3rd&4th 0.25 0.455 47.65 4.39 1133.778 3Ф20+2Ф12 104.24 3rd&4th 0.25 0.455 44.88 4.282 981.0015 2Ф24+1Ф12

71.82 3rd&4th 0.25 0.455 37.25 4.14 653.4831 3Φ14+2Φ12 122.93 Gbeam 0.25 0.355 62.46 4.63 1817 4Ф24 122.06 Gbeam 0.25 0.355 62.24 1817 4Ф24 95.75 Gbeam 0.25 0.355 55.13 4.57 1232.613 4Ф20


30.11 Head Room 0.25 0.307 35.75 4.11 403.1013 2Ф16 14.5 Head Room 0.25 0.307 24.81 3.97 187.5081 2Ф12 11.27 TTBeam 0.25 0.307 21.87 3.96 145.372 2Ф12 28.93 TTBeam 0.25 0.307 35.04 4.1 386.3616 2Ф16 32.82 TTBeam 0.25 0.307 37.32 4.15 443.658 4Ф12



177.03 1st&2nd 0.25 0.455 58.48 4.7 1857 5Ф20+2Ф16 171.09 1st&2nd 0.25 0.455 57.50 2412.33 4Ф24+2Ф20 121.87 1st&2nd 0.25 0.455 48.53 4.41 1181.202 2Ф24+2Ф14 115.06 3rd&4th 0.25 0.455 47.15 4.38 1107.611 2Ф24+2Ф12 103.82 3rd&4th 0.25 0.455 44.79 4.28 976.5925 2Ф20+2Ф16

57.36 3rd&4th 0.25 0.455 33.29 4.05 510.567 2Ф16+1Ф12 118.84 Gbeam 0.25 0.355 61.42 4.65 1712 3Ф24+2Ф16 116.89 Gbeam 0.25 0.355 60.91 1550 3Ф24+1Ф20 87.01 Gbeam 0.25 0.355 52.55 4.51 1105.395 2Ф24+2Ф12


15.34 Head Room 0.25 0.307 25.52 3.99 199.37 2Ф12 42.74 Head Room 0.25 0.307 42.59 4.23 588.8932 2Ф20 14.28 TTBeam 0.25 0.307 24.62 4.09 190.245 2Ф12

22.64 TTBeam 0.25 0.307 31.00 4.434 326.9894 3Ф12 16.53 TTBeam 0.25 0.307 26.49 4.02 216.4515 2Ф12 17.64 TTBeam 0.25 0.307 27.36 4.03 231.5609 2Ф14 27.43 TTBeam 0.25 0.307 34.12 4.09 365.4355 2Ф16 38.55 TTBeam 0.25 0.307 40.45 4.19 526.1384 2Ф12 +2Ф14 199.64 1st&2nd 0.25 0.446 63.36 4.51 2569 5Ф24+2Ф16

178.245 1st&2nd 0.25 0.446 59.87 4.51 2170 4Ф24+2Ф16 182.77 1st&2nd 0.25 0.446 60.62 2241 4Ф24+3Ф16 182.33 1st&2nd 0.25 0.446 60.55 4.51 2241 4Ф24+3Ф16 148.37 1st&2nd 0.25 0.455 53.54 4.53 1477.178 3Ф24+1Ф14 193.54 1st&2nd 0.25 0.455 61.15 2415.64 4Ф24+2Ф20 117.14 1st&2nd 0.25 0.455 47.57 4.35 1119.91 3Ф20+2Ф12

87.28 1st&2nd 0.25 0.455 41.07 4.2 805.6615 2Ф20+2Ф12 75.44 1st&2nd 0.25 0.455 38.18 4.14 686.4211 3Ф14+2Ф12 94.43 1st&2nd 0.25 0.455 42.71 4.23 877.8877 4Ф16+1Ф12 72.55 1st&2nd 0.25 0.455 37.44 4.15 661.7198 3Ф14+2Ф12 144.86 3rd&4th 0.25 0.446 53.97 4.53 1471.336 2Ф24+2Ф16 154.125 3rd&4th 0.25 0.446 55.67 4.5 1555.073 3Ф24+2Ф12

154.971 3rd&4th 0.25 0.446 55.82 4.51 1567.083 3Ф24+2Ф12 142.89 3rd&4th 0.25 0.446 53.60 4.53 1451.327 4Ф20+1Ф16 145.66 3rd&4th 0.25 0.446 54.12 4.47 1459.866 3Ф24+1Ф12 107.87 3rd&4th 0.25 0.446 46.57 4.28 1035.165 2Ф20+2Ф16 76.46 3rd&4th 0.25 0.455 38.44 4.18 702.4237 2Ф16+2Ф14 77.375 3rd&4th 0.25 0.455 38.67 4.18 710.8297 2Ф16+2Ф14

77.025 3rd&4th 0.25 0.455 38.58 4.18 707.6143 2Ф16+2Ф14 75.474 3rd&4th 0.25 0.455 38.19 4.17 691.7068 2Ф16+2Ф14



48.39 3rd&4th 0.25 0.455 30.58 4.01 426.4701 3Ф14 95.54 Gbeam 0.25 0.355 55.07 4.52 1253 4Ф20 93.45 Gbeam 0.25 0.355 54.46 4.52 1239 4Ф20 92.83 Gbeam 0.25 0.355 54.28 4.52 1230 4Ф20 114.01 Gbeam 0.25 0.355 60.16 1550 3Ф24+1Ф20

94.49 Gbeam 0.25 0.355 54.76 4.52 1252 4Ф20 100.71 Gbeam 0.25 0.355 56.54 4.52 1416 3Ф24+1Ф12 68.65 Gbeam 0.25 0.355 46.68 4.37 845.0718 2Ф20+2Ф12 56.89 Gbeam 0.25 0.355 42.49 4.27 684.2825 3Ф14+2Ф12 57.4 Gbeam 0.25 0.355 42.68 4.27 690.4169 2Ф14+2Ф16 55.78 Gbeam 0.25 0.355 42.08 4.26 669.36 3Ф14+2Ф12

61.71 Gbeam 0.25 0.355 44.26 4.31 749.2115 3Ф16+1Ф14

Inclined beam LOCATION AS Ф(AS) landing beams

Gbeam 1332.63 3Ф20+2Ф16 LOCATION AS Ф(AS) Gbeam 1171.31 3Ф20+2Ф12 G-floor 2179.44 4Ф24+2Ф16 Gbeam 964.61 2Ф20+2Ф16 G-floor 1898.36 3Ф24+3Ф16 Gbeam 1240.9 4Ф20 G-floor 2221.63 4Ф24+3Ф14 Gbeam 924.75 2Ф20+2Ф14 1st&2nd 1560.77 3Ф24+2Ф12 1st&2nd 1645.39 3Ф24+2Ф14 1st&2nd 1357.31 3Ф24

1st&2nd 1194.29 2Ф24+2Ф14 1st&2nd 1728.52 3Ф24+2Ф16 1st&2nd 1201.26 2Ф24+2Ф14 3rd&4th 790.18 4Ф16 1st&2nd 1409.64 4Ф20+1Ф14 3rd&4th 615.56 4Ф14 1st&2nd 972.08 2Ф24+1Ф14 3rd&4th 915.1 3Ф16+2Ф14 3rd&4th 796.81 3Ф14+3Ф12 roof 356.15 2Ф16 3rd&4th 668.66 3Ф14+2Ф12 roof 225 2Ф12

3rd&4th 639.49 3Ф14+2Ф12 roof 225 2Ф12

3rd&4th 696.39 2Ф14+2Ф16

3rd&4th 525.17 2Ф14+2Ф12 TTBeam 157.5 2Ф12

TTBeam 187.61 2Ф12 TTBeam 159.75 2Ф12 TTBeam 157.5 2Ф12 Head Room 157.5 2Ф12 Head Room 157.5 2Ф12 Head Room 157.5 2Ф12



5.1.2 Pre-cast slab beams

AXIS-A moment LOCATION b d Km KS AS1 Ф(As1 )

15.41 TTBeam 0.25 0.307 25.57 4.007 201.1331 2Ø12

49.82 TTBeam 0.25 0.307 45.98 4.31 699.4274 2Ø16+2Ø14 170.54 1st&2nd 0.3 0.455 52.40 1829.2 3Ø24+2Ø20

66.22 1st &2nd 0.3 0.455 32.65 4.0765 593.2875 3Ø16 156.53 1st &2nd 0.3 0.455 50.20 1599.4 5Ø20 197.12 1st &2nd 0.3 0.455 56.34 2396.13 4Ø24+2Ø20 129.72 3rd&4th 0.3 0.455 45.70 130.95 3rd&4th 0.3 0.455 45.92 4.308 1239.852 4Ø20 177.07 3rd&4th 0.3 0.455 53.39 2014.8 2Ø16+3Ø24+2Ø14

88.64 Gbeam 0.3 0.355 48.42 4.36 1088.649 3Ø14+2Ø20 93.91 Gbeam 0.3 0.355 49.84 1168.59 3Ø20+2Ø12 85.39 Gbeam 0.3 0.355 47.52

AXIS-B

moment LOCATION b d Km KS AS1 Ф(As1 ) 10.83 TTBeam 0.25 0.307 21.44 3.966 139.9081 2Ø12 23.12 TTBeam 0.25 0.307 31.32 4.067 306.2835 2Ø14 194.49 1st&2nd 0.3 0.455 55.96 4Ø24+2Ø20 168.55 1st &2nd 0.3 0.455 52.09 1829.2 3Ø24+2Ø20 245.89 1st &2nd 0.3 0.455 62.92 3260.34 5Ø24+5Ø16

178.456 3rd &4th 0.3 0.455 53.60 2086.4 3Ø24+2Ø16+3Ø14 198.58 3rd&4th 0.3 0.455 56.55 2396.13 4Ø24+2Ø20 154.49 3rd&4th 0.3 0.455 49.87 1654.94 3Ø24+2Ø14 84.374 Gbeam 0.3 0.355 47.24 4.341 1031.74 3Ø14+2Ø20 92.296 Gbeam 0.3 0.355 49.41 1158.51 3Ø20+2Ø12 89.94 Gbeam 0.3 0.355 48.77

AXIS -C moment LOCATION b d Km KS AS1 Ф(As1 )

6.52 TTBeam 0.25 0.307 16.63 min ####### 2Ø12 18.94 TTBeam 0.25 0.307 28.35 4.032 248.7494 1Ø14+1Ø12 196.44 1st&2nd 0.3 0.455 56.24 2371.5 4Ø24+2Ø20 174.54 1st&2nd 0.3 0.455 53.01 1958.3 3Ø24+2Ø20 228.84 1st&2nd 0.3 0.446 61.93 3060.63 4Ø24+4Ø20 161.03 3rd&4th 0.3 0.455 50.92 1744.8 3Ø24+3Ø14

146.9 3rd&4th 0.3 0.455 48.63 1427.68 4Ø20+2Ø12 189.22 3rd&4th 0.3 0.455 55.20 2222.2 4Ø24+3Ø14



83.01 Gbeam 0.3 0.355 46.86 4.324 1011.085 2Ø20+2Ø16 91.4 Gbeam 0.3 0.355 49.17 1180.58 3Ø16+2Ø20 92.33 Gbeam 0.3 0.355 49.42 1195.44 3Ø16+2Ø20

AXIS-D

moment LOCATION b d Km KS AS1 Ф(As1 ) 4.67 TTBeam 0.25 0.307 14.08 min 153 2Φ12 17.43 TTBeam 0.25 0.307 27.20 4.018 228.1229 2Ø12 165.37 4th&3rd 0.3 0.455 51.60 1791.79 3Ø24+3Ø14

143.17 4th&3rd 0.3 0.455 48.01 4.36 1371.915 2Ø24+3Ø14 179.26 4th&3rd 0.3 0.455 53.72 2086.4 3Ø24+2Ø16+3Ø14 196.46 1st&2nd 0.3 0.455 56.24 2371.5 4Ø24+2Ø20 171.23 1st&2nd 0.3 0.455 52.51 1901.71 4Ø24+1Ø12 218.24 1st&2nd 0.3 0.455 59.28 2765.05 4Ø24+3Ø20 81.81 Gbeam 0.3 0.355 46.52 4.323 996.2384 2Ø20+3Ø14

91.12 Gbeam 0.3 0.355 49.09 1180.58 3Ø16+2Ø20 94.02 Gbeam 0.3 0.355 49.87 1205.57 3Ø16+2Ø20

AXIS-E

moment LOCATION b d Km KS AS1 Ф(As1 )

30.99 HEAD ROOM 0.25 0.307 36.27 4.113 415.1852 2Ø14+1Ø12 27.88 HEAD ROOM 0.25 0.307 34.40 4.094 371.7939 2Ø16 28.95 TTBeam 0.25 0.307 35.05 4.101 386.723 2Ø16 18.28 TTBeam 0.25 0.307 27.85 4.026 239.724 1Ø12+1Ø14 1.22 TTBeam 0.25 0.307 7.20 min 153.5 2Ø12 8.45 TTBeam 0.25 0.307 18.94 min 153.5 2Ø12

14.04 TTBeam 0.25 0.307 24.41 3.986 182.2913 2Ø12 2.71 TTBeam 0.25 0.307 10.72 min 153 2Ø12 10.07 TTBeam 0.25 0.307 20.67 3.961 129.926 2Ø12 158.53 4th&3rd 0.3 0.455 50.52 1654.94 3Ø24+2Ø14 123.65 4th&3rd 0.3 0.455 44.62 4.276 1162.038 3Ø20+2Ø12 96.97 4th&3rd 0.3 0.455 39.51 4.162 887.0091 3Ø16+2Ø14

83.29 4th&3rd 0.3 0.455 36.62 4.114 753.088 5Ø14 139.69 4th&3rd 0.3 0.455 47.43 4.346 1334.27 3Ø20+2Ø16 36.74 4th&3rd 0.3 0.455 24.32 3.986 321.8585 3Ø12 87.24 4th&3rd 0.3 0.455 37.48 4.141 793.9799 4Ø16 181.92 1st&2nd 0.3 0.455 54.12 2086.4 3Ø24+2Ø16+3Ø14 135.14 1st&2nd 0.3 0.455 46.65 4.326 1284.87 3Ø24

166.35 1st&2nd 0.3 0.455 51.75 4.463 1631.692 3Ø24+2Ø14 111.05 1st&2nd 0.3 0.455 42.29 4.217 1029.226 2Ø20+2Ø16 110.87 1st&2nd 0.3 0.455 42.25 4.216 1027.314 2Ø20+2Ø16



173.46 1st&2nd 0.3 0.455 52.85 4.498 1714.776 4Ø24 112.42 Gbeam 0.3 0.455 42.55 4.224 1043.653 2Ø20+2Ø16 47.2 Gbeam 0.3 0.355 35.33 4.103 545.5256 2Ø16+1Ø14 98.49 Gbeam 0.3 0.355 51.04 4.436 1230.709 4Ø20 107.95 Gbeam 0.3 0.355 53.43 4.5315 1377.959 4Ø20+1Ø14

108.6 Gbeam 0.3 0.355 53.60 4.54 1388.856 4Ø20+1Ø14 136.06 Gbeam 0.3 0.355 59.99 1926.9 4Ø24+1Ø12

AXIS-H

moment LOCATION b d Km KS AS1 Ф(As1 ) 35.57 TTBeam 0.25 0.307 38.85 4.151 480.9481 2Ø16+1Ø12 26.93 TTBeam 0.25 0.307 33.81 4.088 358.5988 2Ø16 123.6 4th&3rd 0.3 0.455 44.61 4.275 1161.297 3Ø20+2Ø12

107.526 4th&3rd 0.3 0.455 41.61 4.202 993.0203 5Ø16 144.544 4th&3rd 0.3 0.455 48.24 4.36 1385.081 4Ø20+1Ø14

156.45 1st&2nd 0.3 0.455 50.19 1599.4 5Ø20 122.3 1st&2nd 0.3 0.455 44.38 1161.297 3Ø20+2Ø12 164.56 1st&2nd 0.3 0.455 51.47 1631.692 3Ø24+2Ø14 100.8 Gbeam 0.3 0.355 51.63 4.45 1263.549 2Ø24+2Ø16 83.79 Gbeam 0.3 0.355 47.08 4.334 1022.946 2Ø20+2Ø16 89.25 Gbeam 0.3 0.355 48.59 4.375 1099.912 2Ф20+3Ф14

AXIS-4

moment LOCATION b d Km KS AS1 Ф(As1 ) 144.44 1st&2nd 0.25 0.455 52.83 1604.53 4Ø20+2Ø16 104.14 1st&2nd 0.25 0.455 44.86 4.304 985.0957 5Ø16

60.13 1st&2nd 0.25 0.455 34.09 4.091 540.6414 2Ø16+1Ø14 118.76 1st&2nd 0.25 0.455 47.90 4.353 1136.181 3Ø20+2Ø12 100.73 1st&2nd 0.25 0.455 44.12 4.263 943.7626 3Ø20 120.93 1st&2nd 0.25 0.455 48.34 4.36 1158.802 3Ø20+2Ø12 97.79 1st&2nd 0.25 0.455 43.47 4.248 912.9932 3Ø20 124.1 1st&2nd 0.25 0.455 48.97 1206.11 4Ø20

93.55 1st&2nd 0.25 0.455 42.51 4.223 868.2674 3Ø16+2Ø14 125.01 1st&2nd 0.25 0.455 49.15 1214.93 4Ø20 131.28 1st&2nd 0.25 0.455 50.36 1340 3Ø24 140.096 1st&2nd 0.25 0.455 52.03 1516.28 3Ø24+2Ø12 116.75 3rd&4th 0.25 0.455 47.49 4.35 1116.181 2Ø24+2Ø12 81.84 3rd&4th 0.25 0.455 39.77 4.16 748.2514 2Ø20+1Ø14

91.44 3rd&4th 0.25 0.455 42.03 4.211 846.2722 2Ø20+2Ø12 62.82 3rd&4th 0.25 0.455 34.84 4.098 565.7942 3Ø16 30.14 3rd&4th 0.25 0.455 24.13 3.984 263.9072 2Ø14



83.27 3rd&4th 0.25 0.455 40.11 4.172 763.5218 2Ø20+1Ø14 59.01 3rd&4th 0.25 0.455 33.77 4.088 530.1822 2Ø16+1Ø14 93.14 3rd&4th 0.25 0.455 42.42 4.22 863.8479 2Ø20+2Ø12 33.75 3rd&4th 0.25 0.455 25.54 3.994 296.2582 2Ø14 64.06 3rd&4th 0.25 0.455 35.18 4.101 577.3847 3Ø16

66.05 3rd&4th 0.25 0.455 35.72 4.107 596.192 3Ø16 91.94 3rd&4th 0.25 0.455 42.15 4.214 851.5058 2Ø20+2Ø12 95.02 3rd&4th 0.25 0.455 42.85 4.231 883.5816 3Ø16+2Ø14 39.71 TTBeam 0.25 0.307 41.05 4.19 541.9704 2Ø16+1Ø14 17.62 TTBeam 0.25 0.307 27.35 4.019 230.667 2Ø12 39.53 TTBeam 0.25 0.307 40.96 4.189 539.3849 2Ø16+1Ø14

14.15 TTBeam 0.25 0.307 24.51 3.987 183.7656 2Ø12 35.45 TTBeam 0.25 0.307 38.79 4.15 479.2101 2Ø14+1Ø16 9.23 TTBeam 0.25 0.307 19.79 3.955 118.9077 2Ø12 24.97 TTBeam 0.25 0.307 32.55 4.078 331.6862 1Ø16+1Ø14 18.67 TTBeam 0.25 0.307 28.15 4.032 245.2034 2Ø14 8.32 TTBeam 0.25 0.307 18.79 min 153 2Ø12

22.34 TTBeam 0.25 0.307 30.79 4.058 295.2955 2Ø14 4.23 TTBeam 0.25 0.307 13.40 min 153 2Ø12 96.69 Gbeam 0.25 0.357 55.09 4.593 1243.97 4Ø20 75.31 Gbeam 0.25 0.357 48.62 4.379 923.7605 3Ø20 81.12 Gbeam 0.25 0.357 50.46 4.434 1007.524 2Ø20+2Ø16 68.79 Gbeam 0.25 0.357 46.46 4.32 832.4168 2Ø20+2Ø12

83.48 Gbeam 0.25 0.357 51.19 4.456 1041.98 2Ø20+3Ø14 70.06 Gbeam 0.25 0.357 46.89 4.332 850.1398 2Ø20+2Ø12 83.07 Gbeam 0.25 0.357 51.06 4.452 1035.932 2Ø20+2Ø16 76.76 Gbeam 0.25 0.357 49.08 4.392 944.3415 3Ø20 80.23 Gbeam 0.25 0.357 50.18 4.455 1001.189 2Ø20+2Ø16 99.24 Gbeam 0.25 0.357 55.81 4.614 1282.614 2Ø24+2Ø16

AXIS-1

moment LOCATION b d Km KS AS1 Ф(As1 ) 2.74 TTBeam 0.25 0.307 10.78 min 154 2Ø12

13.23 TTBeam 0.25 0.307 23.70 3.981 171.5591 2Ø12 22.64 TTBeam 0.25 0.307 31.00 4.06 299.4085 2Ø14 175.83 1st&2nd 0.25 0.455 58.29 4.481 1853 4Ф24 142.2 1st&2nd 0.25 0.455 52.42 4.483 1401.061 1Ø16+4Ø20 185.74 1st&2nd 0.25 0.446 61.12 2126.2 4Ø24+2Ø16 79.896 3rd&4th 0.25 0.455 39.29 4.158 730.1265 2Ø20+1Ø12

87.07 3rd&4th 0.25 0.455 41.02 4.19 801.8095 4Ø16 108.94 3rd&4th 0.25 0.455 45.88 4.307 1031.219 2Ø20+2Ø16



123.09 Gbeam 0.25 0.355 62.50 2003.4 4Ø24+2Ø12 97.46 Gbeam 0.25 0.355 55.62 4.609 1265.333 3Ø24 124.68 Gbeam 0.25 0.355 62.91 2003.4 4Ø24+2Ø12

AXIS-2

moment LOCATION b d Km KS AS1 Ф(As1 ) 5.87 Head Room 0.25 0.307 15.78 min 153 2Ф12 14.54 Head Room 0.25 0.307 24.84 3.989 188.9253 2Ф12 30.95 Head Room 0.25 0.307 36.24 4.112 414.5485 2Ø14+1Ø12

11.59 TTBeam 0.25 0.307 22.18 3.971 149.915 2Ф12 33.42 TTBeam 0.25 0.307 37.66 4.131 449.7004 3Ø14 133.38 1st&2nd 0.25 0.455 50.76 1340 3Ø24 117.64 1st&2nd 0.25 0.455 47.68 4.352 1125.207 2Ø24+2Ø12 176.79 1st&2nd 0.25 0.446 59.62 1853 4Ø24 77.46 3rd&4th 0.25 0.455 38.69 4.148 706.1628 2Ø16+2Ø14

81.29 3rd&4th 0.25 0.455 39.63 4.164 743.9375 2Ø20+1Ø12 91.79 3rd&4th 0.25 0.455 42.11 4.213 849.9149 2Ø20+2Ø12 100.9 Gbeam 0.25 0.355 56.59 1429.3 1Ø16+4Ø20 94.9 Gbeam 0.25 0.355 54.88 1220.01 4Ø20

108.26 Gbeam 0.25 0.355 58.62 1345.67 4Ø20+1Ø12

AXIS-3

moment LOCATION b d Km KS As1 Ф(As1 ) 16.27 Head Room 0.25 0.307 26.28 4.006 212.305 2Ø12 20.93 Head Room 0.25 0.307 29.80 4.048 275.976 2Ø14 41.28 Head Room 0.25 0.307 41.86 4.207 565.6839 3Ø16

18.53 TTBeam 0.25 0.307 28.04 4.028 243.1233 2Ø14 9.5 TTBeam 0.25 0.307 20.08 3.957 122.4479 2Ø12

11.38 TTBeam 0.25 0.307 21.98 3.97 147.1616 2Ø12 8.83 TTBeam 0.25 0.307 19.36 3.952 113.6683 2Ø12 16.86 TTBeam 0.25 0.307 26.75 4.012 220.3333 2Ø12 17.25 TTBeam 0.25 0.307 27.06 4.016 225.6547 2Ø12

9.25 TTBeam 0.25 0.307 19.81 3.955 119.1653 2Ø12 29.58 TTBeam 0.25 0.307 35.43 4.104 395.4278 2Ø16 35.82 TTBeam 0.25 0.307 38.99 4.153 484.5618 2Ø14+1Ø16 11.77 TTBeam 0.25 0.307 22.35 3.972 152.2816 2Ø12 126.82 1st&2nd 0.25 0.455 49.50 1214.93 4Ø20 110 1st&2nd 0.25 0.455 46.10 4.312 1042.462 2Ø24+1Ø14

110.44 1st&2nd 0.25 0.455 46.19 4.315 1047.36 2Ø24+1Ø14 107.01 1st&2nd 0.25 0.455 45.47 4.297 1010.598 2Ø24+1Ø12 98.47 1st&2nd 0.25 0.455 43.62 4.25 919.7747 2Ø14+2Ø20



106.94 1st&2nd 0.25 0.455 45.46 4.3 1010.642 2Ø24+1Ø12 101.23 1st&2nd 0.25 0.455 44.23 4.267 949.3372 3Ø20 109.9 1st&2nd 0.25 0.455 46.08 4.312 1214.45 4Ø20 103.44 1st&2nd 0.25 0.455 44.71 4.278 972.5633 3Ø12+2Ø20 119.22 1st&2nd 0.25 0.455 47.99 4.36 1142.416 3Ø20+2Ø12

82.61 3rd&4th 0.25 0.455 39.95 4.17 757.107 2Ø20+1Ø14 88.42 3rd&4th 0.25 0.455 41.33 4.198 815.796 2Ø20+1Ø16 58.23 3rd&4th 0.25 0.455 33.54 4.085 522.7902 2Ø16+1Ø14 33.26 3rd&4th 0.25 0.455 25.35 4.001 292.4687 2Ø14 76.67 3rd&4th 0.25 0.455 38.49 4.147 698.7923 2Ø16+2Ø14 56.91 3rd&4th 0.25 0.455 33.16 4.082 510.564 2Ø16+1Ø12

38.72 3rd&4th 0.25 0.455 27.35 4.019 342.0125 2Ø16 76.07 3rd&4th 0.25 0.455 38.34 4.142 692.4878 2Ø16+2Ø14 60.62 3rd&4th 0.25 0.455 34.22 4.092 545.1803 2Ø16+1Ø14 81.59 3rd&4th 0.25 0.455 39.70 4.165 746.8623 2Ø20+1Ø14 51.57 3rd&4th 0.25 0.455 31.57 4.066 460.8431 3Ø14 99.4 3rd&4th 0.25 0.455 43.82 4.256 929.7723 3Ø20

89.94 Gbeam 0.25 0.355 53.43 1317.8 3Ø20+2Ø16 87.35 Gbeam 0.25 0.355 52.65 1246.82 4Ø20 86.16 Gbeam 0.25 0.355 52.29 1246.82 4Ø20 83.54 Gbeam 0.25 0.355 51.49 1160.19 3Ø20+2Ø12 85.72 Gbeam 0.25 0.355 52.16 1246.82 4Ø20 89.12 Gbeam 0.25 0.355 53.19 1317.8 3Ø20+2Ø16

71.8 Gbeam 0.25 0.355 47.74 4.354 880.6118 3Ø16+2Ø14 70.2 Gbeam 0.25 0.355 47.20 4.34 858.2197 2Ø20+2Ø12 68.24 Gbeam 0.25 0.355 46.54 4.324 831.1824 2Ø16+2Ø14 73.15 Gbeam 0.25 0.355 48.18 4.36 898.4056 3Ø16+2Ø14

Inclined beam(SAP) landing beams

LOCATION AS Ф(AS) LOCATION AS Ф(AS) Gbeam 1377.25 4Ф20+1Ø14 G-floor 2172.62 4Ф24+2Ф16 Gbeam 1235.31 4Ф20 G-floor 2002.28 4Ф24+2Ø12 Gbeam 1176.7 2Ø24+1Ф20 G-floor 2291.24 4Ø24+2Ø20 Gbeam 961.86 5Ø16 1st&2nd 1500.52 4Ø20+2Ø14 Gbeam 966.54 5Ø16 1st&2nd 1475.75 4Ø20+2Ø12 1st&2nd 1723.22 4Ø24 1st&2nd 1839 3Ø20+2Ø24 1st&2nd 1426.32 4Ø20+1Ø16 3rd&4th 729.35 4Ø16 1st&2nd 1183.39 2Ø24+1Ф20 3rd&4th 697.65 2Ø16+2Ø14 1st&2nd 991.29 5Ø16 3rd&4th 984.77 5Ø16 1st&2nd 1269.18 3Ø24 roof 343.9 2Ø16 3rd&4th 847.42 2Ø20+2Ф12 roof 225 2Ф12 3rd&4th 745 4Ø16 roof 225 2Ф12



3rd&4th 692.88 2Ø16+2Ø14 roof 225 2Ф12 3rd&4th 520.69 2Ø14+2Ø12 3rd&4th 678.21 2Ø16+2Ø14 TTBeam 159.65 2Ф12 TTBeam 162.19 2Ф12 TTBeam 204.96 2Ф12 TTBeam 157.5 2Ф12 Head Room 157.5 2Ф12 Head Room 157.5 2Ф12 Head Room 157.5 2Ф12

corridor beams added for prec

2.4 0.25 0.455 6.81 min 227 2Ø12 6.15 0.25 0.455 10.90 min 227 2Ø12

3.21 0.25 0.455 7.88 min 227 2Ø12 3.9 0.25 0.455 8.68 min 227 2Ø12 5.65 0.25 0.455 10.45 min 227 2Ø12 16.36 0.25 0.455 17.78 min 227 2Ø12 6.62 0.25 0.455 11.31 min 227 2Ø12

5.1.3 Design of beams for shear and torsion

Shear reinforcement design

Beam sections are subjected to shear forces in addition to flexural actions. Shear is resisted by the combined actions of the following � Shear resistance of concrete in compression zone � Shear reinforcements or stirrups � Dowel action in tension bars across crack � Aggregate interlocking across the inclined crack in tension zone

*ominal reinforcement

The shear force VC carried by the concrete in members with out significant axial forces shall be taken as VC = 0.25fctdK1K2bwd Where K1= (1+50ρ) < 2.0 K2= 1.6-d > 1.0 (d in meters). For members where more than 50%of the bottom reinforcement is curtailed, K2 = 1.

ρmax =0.04



As is the area of tensile reinforcement The ultimate limit state in shear is characterized by either diagonal compression failure of concrete or failure of shear reinforcement due to diagonal tension.

Diagonal compression failure of concrete

To avoid compression failure of concrete the shear resistance of the section , VRD shall not be less than the applied shear force Vd. Where: VRD=0.25 *fcd *bw*d If VRD < Vd ………….increase the concrete section

Diagonal Tension failure of web reinforcement

If the applied shear force Vd < VRD > the shear resistance of the section Vc Shear reinforcement need be provided. The spacing in this case is given by S=(d-d’)Asv*fyk/(Vd-Vc) ( section 4.5 EBCS-2,1995) The shear between the critical section which is at a distance d from the face of the support, and the point beyond which maximum spacing is used is reinforced by the difference of shear capacity of concrete. The region beyond this is reinforced with maximum spacing.( section 4.5-6,EBCS-2,1995,page 43-46)

The maximum spacing Smax between stirrups, in the longitudinal direction should be

= 800 = d

Shear design sample Axis –D 1st &2ndfloor level As, actual =1941.5 mm2, d=446mm ,b= 250 mm ρ=As/bd=0.0174 VC = 0.25fctdK1K2bwd K1 =1+50ρ=1.87 k2=1.6-d=1.154 Then Vc=62.1KN VRD=0.25 *fcd *bw*d=0.25*11.33*250*446=311.1 KN

Taking the design shear at d distance from the face of the column Vd=112.6KN S=(d-d’)Asv*fyk/(Vd-Vc) = 2*50.3*260.87*(446-43)/(112.6-62.1)=209.7 mm But Vd< 2/3Vrd as per EBCS 2-1995 Smax= 0.5d=220mm



Use Φ8 c/c 200mm.Since the minimum reinforcement &the design result are all most similar , so use Φ8 c/c 200mm through out the length The reimaing shear designs are displayed in the reinforcement detail

Torsional reinforcement

Torsion results from the monolithic character of construction; and any assymetric in the loading of the floor slab produces torsion to the supporting beams. Torsion shear stresses create diagonal tension resulting in diagonal crack. Thus, we need to provide both closed stirrups and longitudinal steel to avoid brittle fracture.

Torsional resistance of concrete

Torsional effect may be disregarded whenever the design torque TSD is less than TC given by ( section 4.6.4 EBCS-2, 1995,page 48) TC = 1.2fctdAefhef however, minimum reinforcement may be provided in such away that ρmin= 0.4 /fyk , and the spacing of stirrups shall not exceed Uef /8 More ever, at least one longitudinal bar shall be placed at each corner of the closed stirrup with spacing not exceeding 350mm.

Limiting value of ultimate shear

In order to prevent diagonal compression failure in the concrete the torsional resistance, TRD, of a section shall not be less than the applied torque TSd. Where TRD = 0.8fcdAefhef > Tsd.

Design for torsional reinforcement

When Tsd >Tc……..high torsional moment. Hence ,both longituidinal bars Asl & closed stirrups Astr must be provided.

Combined actions

a) Torsion and bending or torsion and axial forces � Simple super position by separately determining area of reinforcements may be applied.

b) Torsion and shear � limiting values for torsion and shear are TRd, com = βtTRd and VRd,com = βvVRd in which



Further the torsional and shear resistance of the concrete shall be TC, com = βtcTC and VC,com = βvcVC in which

(section 4.6.6 EBCS-2,1995,page 49-50.) AXIS-4 (TORSIO*AL DESIG*)

Applied shear actions , Tsd=6.01kn.m Vsd=32.19kn 350 Equivalent hallow section 250 A=250*350=87.5*103mm2 U=2(250+350)=1200mm Hef=def/5=(350-43)/5=61.4<A/U=72.92 250 Aef=[350-61.4]8[250-61.4]=54429.96mm2 Uef={[350-61.4]+[250-61.4]}*2=954.4mm

Check shear capacity VC = 0.25fctdK1K2bwd ρ=As/bd=[3*201]/[250*307]=0.00689 K1=1+50ρ=1.3446 K2=1.6-d=1.291 Vc=0.25*1.032*1.291*1.3446*250*309=34.6kn VRD=0.25 *fcd *bw*d=218.81kn Torsion TC = 1.2fctdAefhef=4.14kn.m



TRD = 0.8fcdAefhef=30.29kn.m Using combined action Factor for combined action Using the above formula βt=0.8033 βtc=0.842 βv=0.5956 βvc=0.540 Combined section capacity Vc=βvc*Vc=0.540*34.6=18.63kn Vrd,com=Vrd*βv=0.5956*218.81=130.41kn Tc,com=Tc*βtc=0.842*4.41=3.48kn.m Trd,com=Trd*βt=0.8033*30.29=24.32kn.m Check Vsd with VC,com Vsd=32.19>Vc,com=18.63 It requires shear reinforcement S=(d-d’)Asv*fyk/(Vd-Vc) = [2*50.3*260.87*(309-41)]/[13.56*103] =518.67mm 2/3Vrd=86.94 Smax=0.5d=0.5*309=154.5 UseΦ8c/c 150mm Tc=3.486kn.m<Tsd=6.01kn.m needs torsional reinforcement Tef=Tsd-Tc=2.614kn.m Longitudinal reinforcement

Al= =87.85mm2

Al/2=43.93mm2 Top reinforcement=602.1+43.93=646.03mm2 So use 2Φ20 Bottom reinforcement=235.5+43.93=279.43 So use 2Φ14

Spacing S= =546.455mm

Smax=0.5d hence use Φ8c/c 150mm The same procedure is applied for the reimaing torsional action.



Sample reinforcement detail

AXIS-4

5.2 Column design

Columns are axially loaded vertical members, which carry their load primarily in compression. The majority of compression or tension members carry a portion of the load in bending which may arise due to the unbalanced moments in the members connected to their ends. The result of such bending moments in axially loaded members into reduces the range of axial force that the member can carry. For this reason, it is essential to note that the effect of bending in axially loaded members should be considered in designing these columns. 5.2.1 Design Procedure

1. To design a column in a particular frame first the frame is classified wheather it is sway or non sway.

2. To determine the nature of the frame we substitute the beams and columns by one substitute frame

3. The value of the axial force on each substitute frame column is obtained by adding the axial load each column for the story including self weight.



4. the values of the stiffness coefficients of the substitute frame is given by For beams=2*∑Kbi For column =∑Kci Where: Kbi stiffness coefficient of beam Where: Kci stiffness coefficient of column 5. The effective length of the substitute frame is computed for each storey assuming as sway

frame as shown below. The effective length buckling Le of a column in a given plane is obtained from the following approximate equation provided that certain restriction is complied with.

a) Non sway mode Le/L= (αm+0.4)/ (αm+0.8) ≥ 0.8 b) Sway mode: Conservatively: Le/L=√ (1+0.8 αm) ≥ 1.15

Where: αm is a stiffness coefficient which will be discussed Using the following theoretical model.

K12

Kc

K11

K21K22

Kc1

Kc2

α1 =Kc1+Kc

K11+K12

α2 =Kc2+Kc

K21+K22

α1 = α1 + α2

2

• Kc1 and Kc2 are column stiffness coefficients (EI/l) • Kc is the stiffness coefficient of the column being designed

α =1.0 if opposite end elastically or rigidly restrained α= 0.5 if opposite ends are free to rotate α= 0 for cantilever beam



The above approximate equation for effective length calculation is applicable for values of α1 and α 2 not exceeding 10. If a base is designed to resist the column moment may be taken as 1.0.

6. the dimension of the substitute column is computed to find the moment of inertia of the section (Ic)

7. The amount of reinforcement required by the substitute column is computed and the moment of inertia of the reinforcement with respect to the centroid of the concrete section is determined.

In lieu of more accurate determination, the first order moment, Mdl, at critical section of the substitute may be determined using: Mdl = α2+3 HL

α1+ α2 +6 Where: H= the total horizontal reaction at the bottom of the story. L= the story shear

8. The buckling load of a story may be assumed to be equal to that of the substitute Beam-column frame, and may be determined as Ncr= π2 EIe Le2

Where: EIe is the effective stiffness of the substitute column designed Le is the effective length. In lieu of more accurate determination, the effective stiffness of a column may be taken as: EIe= 0.2Ec Ic + Es Is Where Ec= 1100fcd Es is the modulus of elasticity of steel Ic, Is are the moment of inertia of the concrete and reinforcement sections, respectively of the substitute column, with respect to the centroid of the concrete section. Computation of moment of inertia of reinforced concrete section with respect to the centroid of the concrete.



Is = (n (П * r4)/4 + П * r2*d2)

Where

n = number of bars

As/2

As/2

S

S d

Reinforcing the substitute column using the biaxial chart using the following formulas: ν = Nsd * 10

3 Ac *fcd µ = Mdl * 10

6 Ac * fcd *S w = As,tot *fyd Ac *fcd We have designed five columns for solid and six columns for the pre-cast slab systems. Substitute column

Determination of substitute column for each axis. Sample substitute frame is shown below.

AXIS -4



The result of the substitute frames are tabulated as follows AXIS-4 LEVEL α1 α2 H L Le Nsd HL Md1 µ v w

Found 8.92 1.00 301.09 1.50 3.34 1975.36 451.64 113.48 0.04 0.44

min

Ground 2.9 8.92 224.05 3.80 9.10 1903.78 851.39 569.50 0.20

0.43 0.2

1 3.22 2.90 158.88 3.05 5.66 1446.68 484.58 235.89 0.08 0.33

min

2 3.22 3.22 98.67 3.05 5.77 999.10 300.94 150.47 0.05 0.23

min

3 3.22 3.22 50.43 3.05 5.77 502.31 153.81 76.91 0.03 0.11

min

4 4.69 3.22 15.67 3.05 6.23 101.84 47.79 21.37 0.01 0.02

min

As Ǿ Is Ic EIe Ncr Nsd/Ncr condition

3135.008 10Ǿ20 196957002 1.28E+1

0 7.129E+13 63007705.1

8 0.03 non-sway

3403.96 8Ǿ24 226854001 1.28E+1

0 7.727E+13 9210012.38

4 0.21 ''sway''

3135.008 10Ǿ20 196957002 1.28E+1

0 7.129E+13 21917624.0

2 0.07 non-sway

3135.008 10Ǿ20 196957002 1.28E+1

0 7.129E+13 21126915.3

7 0.05 non-sway

3135.008 10Ǿ20 196957002 1.28E+1

0 7.129E+13 21126915.3

7 0.02 non-sway

3135.008 10Ǿ20 196957002 1.28E+1

0 7.129E+13 18127122.2

9 0.01 non-sway

AXIS-2

LEVEL α1 α2 H L Le Nsd HL Md1 µ v w

Found 11.9 1.00 253.85 1.50 3.73 833.87 380.78 80.42 0.07 0.32 min

Ground 4.02 11.94 197.14 3.80 10.33 778.22 749.13 509.75 0.42 0.30 0.79

1 4.46 4.02 140.73 3.05 6.39 627.80 429.23 208.06 0.17 0.24 0.2

2 4.46 4.46 91.53 3.05 6.52 471.96 279.17 139.58 0.11 0.18 0.1

3 4.46 4.46 51.78 3.05 6.52 315.78 157.93 78.96 0.06 0.12 0.02

4 12.6 4.46 23.18 3.05 8.53 166.29 70.70 22.86 0.02 0.06 min



5 6.31 12.61 17.49 3.05 8.93 72.19 53.34 33.42 0.03 0.03 min


1812.608 6Ǿ20 68346169 4.278E+09 2.433E+13 17262278.72 0.05 non-sway

7774.04 10Ǿ32 291981824 4.278E+09 6.906E+13 6385878.969 0.12 ''sway''

1968.111 4Ǿ26 77089269 4.278E+09 2.608E+13 6293839.196 0.10 non-sway

1812.608 6Ǿ20 68346169 4.278E+09 2.433E+13 5647044.625 0.08 non-sway

1812.608 6Ǿ20 68346169 4.278E+09 2.433E+13 5647044.625 0.06 non-sway

1812.608 6Ǿ20 68346169 4.278E+09 2.433E+13 3294931.883 0.05 non-sway

1812.608 6Ǿ20 68346169 4.278E+09 2.433E+13 3009827.243 0.02 non-sway

AXIS-3

LEVEL α1 α2 H L Le Nsd HL Md1 µ v w Found 8.91 1 324.3 1.5 3.34 2061.48 486.41 122.29 0.04 0.46 min Ground 2.9 8.91 270.6 3.8 9.09 1915.2 1028.2 687.59 0.25 0.43 0.33

1 3.22 2.9 200.7 3.05 5.66 1452.15 612.14 297.99 0.11 0.33 min 2 3.22 3.22 123.1 3.05 5.77 1014.74 375.46 187.73 0.07 0.23 min 3 3.22 3.22 59.96 3.05 5.77 583.79 182.88 91.44 0.03 0.13 min

4 6.26 3.22 12.6 3.05 6.68 155.85 38.43 15.44 0.01 0.04 min 5 7.82 6.26 5.44 3.05 7.85 59.35 16.592 7.65 0.00 0.01 min

As Ǿ Is Ic EIe Ncr Nsd/Ncr condition 3135.008 10Ǿ20 196957002 1.28E+10 7.129E+13 63007705.18 0.00 non-sway 5531.435 8Ǿ30 354950030 1.28E+10 1.029E+14 12277159.55 0.00 non-sway 3135.008 10Ǿ20 196957002 1.28E+10 7.129E+13 21940864.41 0.00 non-sway

3135.008 10Ǿ20 196957002 1.28E+10 7.129E+13 21112271.86 0.00 non-sway 3135.008 10Ǿ20 196957002 1.28E+10 7.129E+13 21112271.86 0.00 non-sway 3135.008 10Ǿ20 196957002 1.28E+10 7.129E+13 15751926.29 0.01 non-sway 3135.008 10Ǿ20 196957002 1.28E+10 7.129E+13 11406365.47 0.03 non-sway

AXIS-B LEVEL α1 α2 H L Le Nsd HL Md1 µ v w

Found 14.9 1 319.3 1.5 4.07 2252.2 478.92 87.63 0.07 0.88 0.08 Ground 4.84 14.86 269 3.8 11.32 2108.1 1022.2 710.34 0.26 0.47 0.35

1 5.37 4.84 209.9 3.05 6.88 1566.1 640.1 309.51 0.25 0.61 0.4 2 5.37 5.374 134.4 3.05 7.02 1032.92 409.8 204.90 0.17 0.40 0.13 3 5.37 5.374 72.69 3.05 7.02 540.28 221.7 110.85 0.09 0.21 0.02 4 7.82 5.374 18.75 3.05 7.64 44.99 57.188 24.95 0.02 0.02 0.03




1812.608 6Ǿ20 68346169 4.278E+09 2.433E+13 14518736.79 0.00 non-sway 3444.195 8Ǿ24 226854001 1.28E+10 7.727E+13 5945286.218 0.00 non-sway 3936.223 8Ǿ26 154178539 4.278E+09 4.15E+13 8644145.467 0.00 non-sway 1812.608 6Ǿ20 68346169 4.278E+09 2.433E+13 4868281.781 0.00 non-sway 1812.608 6Ǿ20 68346169 4.278E+09 2.433E+13 4868281.781 0.00 non-sway

1812.608 6Ǿ20 68346169 4.278E+09 2.433E+13 4110202.46 0.02 non-sway

AXIS-E LEVEL α1 α2 H L Le Nsd HL Md1 µ v w Found 4.44 1 473 1.5 2.67 2061.48 709.43 248.05 0.12 0.57 min Ground 1.45 4.44 368.2 3.8 6.96 1915.2 1399 875.39 0.31 0.43 0.47

1 1.61 1.45 290.6 3.05 4.55 1452.15 886.36 435.35 0.21 0.40 0.23 2 1.61 1.61 195.9 3.05 4.61 1014.74 597.62 298.81 0.15 0.28 0.13 3 1.61 1.61 113.7 3.05 4.61 583.79 346.82 173.41 0.08 0.16 0.04 4 1.33 1.61 44.02 3.05 4.5 155.88 134.26 69.23 0.03 0.04 0.03 5 4.23 1.33 14.49 3.05 5.48 59.35 44.195 16.55 0.01 0.02 min

As Ǿ Is Ic EIe Ncr Nsd/Ncr condition 2562.848 6Ǿ24 139106542 8.552E+09 4.914E+13 67961309.81 0.00 non-sway 7999.306 10Ǿ32 504623744 1.28E+10 1.328E+14 27034263.05 0.00 non-sway 3200.122 6Ǿ26 163439197 8.552E+09 5.401E+13 25720151.2 0.00 non-sway 2562.848 6Ǿ24 139106542 8.552E+09 4.914E+13 22797247.4 0.00 non-sway 2562.848 6Ǿ24 139106542 8.552E+09 4.914E+13 22797247.4 0.00 non-sway 2562.848 6Ǿ24 139106542 8.552E+09 4.914E+13 23925401.56 0.01 non-sway 2562.848 6Ǿ24 139106542 8.552E+09 4.914E+13 16133297.64 0.05 non-sway



5.2.2Design of isolated columns

For buildings, a design method may be used which assumes the compression members to be isolated and adopts a simplified shape for the deformed axis of the column.

Total eccentricity The total eccentricity to be used for the design of columns of constant cross section at the critical section is given by: etot= ee+ea+e2 Where

� ee is equivalent constant first-order eccentricity of the design axial load - for first-order eccentricity eo is equal at both ends of a

column ee= eo for first-order moment varying linearly along the length, the equivalent eccentricity is the higher of the following two values

ee =0.6eo2 + 0.4 eo1 ee =0.4 eo2 eo1 and eo2 are first-order eccentricities at the ends eo2 being positive and greater in magnitude than eo1.

� ea is the additional eccentricity to account for geometric imperfection, introduced by increasing the eccentricity of the longitudinal force acting in the most unfavorable direction.



ea = Le/ 300 ≥20mm Le is the effective length of isolated column.

� e2 is the second order eccentricity According to EBCS-2, 1995 Art. 4.4.6(2) second order effects in compressive members need not be taken into account in the following cases

a) for sway frames the greater of λ ≤ 25 ; which ever is maximum d = Nsd/Acfcdע dע√/15

b) for non sway frames λ ≤ 50 – 25 (M1/M2) Where M1 and M2 are the 1

st order (calculated moments at the ends, M2 being always positive and greater

than M1 , and M1 being positive if member is bent in single curvature and negative if bent in double curvature.

For sway frames in the absence of rigorous method the amplified sway moments method can be employed to obtain the sway contribution by multiplying the 1st order moment by magnification factor given by: σs = 1/(1 – Nsd/Ncr) provided; Nsd/Ncr ≤ 0.25

Determination of first order moment

col A-3 Mdy level M1 M2 P eo1 e02 0.6eo2+0.4eo1 0.4eo2 eo M

found -10.62 11.17 1368.42 -

0.0077608 0.00816 0.0017933 0.003265 0.003265 4.468

ground -

115.16 118.57 1076.01 -0.107025 0.11019 0.0233065 0.044078 0.044078 47.428

first -99.46 111.08 806.45 -

0.1233306 0.13774 0.0333114 0.055096 0.055096 44.432

second -37.56 42.01 557.52 -

0.0673698 0.07535 0.018263 0.030141 0.030141 16.804

third -41.94 44.65 314.86 -

0.1332021 0.14181 0.0318046 0.056724 0.056724 17.86 fourth -16.04 43.3 113.28 -0.141596 0.38224 0.1727048 0.152895 0.172705 19.564 Mdx

found -10.87 17.56 1368.42 -

0.0079435 0.01283 0.004522 0.005133 0.005133 7.024

ground -13.75 15.94 1076.01 -

0.0127787 0.01481 0.0037769 0.005926 0.005926 6.376 first -18.35 21.51 806.45 -0.022754 0.02667 0.0069019 0.010669 0.010669 8.604 second -70.31 91.01 557.52 - 0.16324 0.0474996 0.065296 0.065296 36.404



0.1261121

third -62.69 80.18 314.86 -

0.1991044 0.25465 0.07315 0.101861 0.101861 32.072

fourth -10.99 35.68 113.28 -

0.0970162 0.31497 0.1501766 0.125989 0.150177 17.012

column B-3 Mdy level M1 M2 P eo1 e02 0.6eo2+0.4eo1 0.4eo2 eo M found 0.42 0.89 2252.23 0.0001865 0.0004 0.0003117 0.000158 0.000312 0.702

ground -

120.88 131.3 1602.82 -

0.0754171 0.08192 0.018984 0.032767 0.032767 52.52

first -11.14 12.12 1278.28 -

0.0087148 0.00948 0.002203 0.003793 0.003793 4.848

second -2.3 5.93 1032.91 -

0.0022267 0.00574 0.0025539 0.002296 0.002554 2.638

third -1.48 2.82 429.55 -

0.0034455 0.00657 0.0025608 0.002626 0.002626 1.128

fourth -6.08 7.08 44.99 -

0.1351411 0.15737 0.0403645 0.062947 0.062947 2.832 Mdx

found -5.96 9.68 2252.23 -

0.0026463 0.0043 0.0015203 0.001719 0.001719 3.872

ground -24.34 36.7 1602.82 -

0.0151857 0.0229 0.007664 0.009159 0.009159 14.68

first -

113.43 116.88 1278.28 -

0.0887364 0.09144 0.0193666 0.036574 0.036574 46.752

second -56.35 56.89 1032.91 -

0.0545546 0.05508 0.0112246 0.022031 0.022031 22.756

third -71.73 92.79 429.55 -

0.1669887 0.21602 0.0628146 0.086407 0.086407 37.116

fourth -6.39 44.02 44.99 -

0.1420316 0.97844 0.5302512 0.391376 0.530251 23.856



column E-3 Mdy level M1 M2 P eo1 e02 0.6eo2+0.4eo1 0.4eo2 eo M

found -0.67 4.15 1790.15 -

0.0003743 0.00232 0.0012412 0.000927 0.001241 2.222

ground -0.75 5.18 1633.3 -

0.0004592 0.00317 0.0017192 0.001269 0.001719 2.808

first -36.87 37.55 949.05 -

0.0388494 0.03957 0.0081998 0.015826 0.015826 15.02

second -32.36 33.38 671.98 -

0.0481562 0.04967 0.010542 0.01987 0.01987 13.352

third -30.2 32.22 387.46 -

0.0779435 0.08316 0.0187168 0.033263 0.033263 12.888

fourth -16.38 23.42 90.38 -

0.1812348 0.25913 0.082983 0.103651 0.103651 9.368

H.room -13.77 25.07 28.97 -

0.4753193 0.86538 0.3290991 0.346151 0.346151 10.028 Mdx

found -32.76 97.68 1790.15 -

0.0183001 0.05457 0.0254191 0.021826 0.025419 45.504

ground -

101.76 119.28 1633.3 -

0.0623033 0.07303 0.0188967 0.029212 0.029212 47.712

first -141.7 147.18 949.05 -

0.1493072 0.15508 0.033326 0.062033 0.062033 58.872

second -

120.83 129.96 671.98 -

0.1798119 0.1934 0.0441144 0.077359 0.077359 51.984

third -

100.46 112.08 387.46 -

0.2592784 0.28927 0.0698498 0.115707 0.115707 44.832

fourth -34.9 55.16 90.38 -

0.3861474 0.61031 0.2117283 0.244125 0.244125 22.064

H.room -14.95 29.25 28.97 -

0.5160511 1.00967 0.3993787 0.403866 0.403866 11.7

column E-2 Mdy level M1 M2 P eo1 e02 0.6eo2+0.4eo1 0.4eo2 eo M found 1.28 8.38 833.97 0.0015348 0.01005 0.0066429 0.004019 0.006643 5.54 ground 1.7 4.34 456.7 0.0037224 0.0095 0.0071907 0.003801 0.007191 3.284

first -1.24 1.47 461.38 -

0.0026876 0.00319 0.0008366 0.001274 0.001274 0.588

second -3.93 5.69 401.311 -

0.0097929 0.01418 0.00459 0.005671 0.005671 2.276



third -9.19 9.78 297.53 -

0.0308876 0.03287 0.0073673 0.013148 0.013148 3.912

fourth -5.13 9.34 157.38 -

0.0325963 0.05935 0.0225696 0.023739 0.023739 3.736

H.room -9.89 17.57 68.19 -

0.1450359 0.25766 0.0965831 0.103065 0.103065 7.028 Mdx

found -62.05 105.98 833.97 -

0.0744032 0.12708 0.0464861 0.050832 0.050832 42.392

ground -

140.04 144.6 456.7 -

0.3066346 0.31662 0.0673177 0.126648 0.126648 57.84

first -

122.54 126.93 461.38 -

0.2655945 0.27511 0.0588279 0.110044 0.110044 50.772

second -97.43 104.25 401.311 -

0.2427793 0.25977 0.0587524 0.103909 0.103909 41.7

third -68.94 76.62 297.53 -

0.2317077 0.25752 0.0618291 0.103008 0.103008 30.648

fourth -33.02 33.98 157.38 -

0.2098106 0.21591 0.0456221 0.086364 0.086364 13.592

H.room -24.69 32.2 68.19 -

0.3620766 0.47221 0.1384954 0.188884 0.188884 12.88

column H-3 Mdy level M1 M2 P eo1 e02 0.6eo2+0.4eo1 0.4eo2 eo M

found -4.61 19.84 1557.47 -

0.0029599 0.01274 0.0064592 0.005095 0.006459 10.06

ground -1.89 29.48 560.41 -

0.0033725 0.0526 0.0302136 0.021042 0.030214 16.932

first -16.62 22.94 514.99 -

0.0322725 0.04454 0.0138177 0.017818 0.017818 9.176 second 16.68 18.59 434.68 0.0383731 0.04277 0.0410095 0.017107 0.041009 third 9.17 23.29 321.27 0.028543 0.07249 0.0549133 0.028997 0.054913 17.642

fourth -2.9 23.43 240.88 -

0.0120392 0.09727 0.0535453 0.038907 0.053545 12.898

H.room -13.21 16.42 124.59 -

0.1060278 0.13179 0.0366643 0.052717 0.052717 6.568 Mdx found -15.38 92.96 1557.47 -0.009875 0.05969 0.0318619 0.023875 0.031862 49.624

ground -

116.33 165.83 560.41 -

0.2075802 0.29591 0.0945129 0.118363 0.118363 66.332

first -68.08 123.76 514.99 -

0.1321967 0.24032 0.0913105 0.096126 0.096126 49.504



Moment due to imperfection

column E-2 x-dxn level Le eacalc 20 ea Nsd Ma foundation 1.39253 0.004642 0.02 0.02 833.97 16.6794

ground 10.2917 0.034306 0.02 0.0343056 456.7 15.667383 first 2.80135 0.009338 0.02 0.02 461.38 9.2276 second 2.81176 0.009373 0.02 0.02 401.311 8.02622 third 2.81176 0.009373 0.02 0.02 297.53 5.9506 fourth 2.91835 0.009728 0.02 0.02 157.38 3.1476 H.room 2.93109 0.00977 0.02 0.02 68.19 1.3638

y-dxn level Le eacalc 20 ea Nsd Ma foundation 1.23737 0.004125 0.02 0.02 833.97 16.6794 ground 5.36735 0.017891 0.02 0.02 456.7 9.134 first 2.22377 0.007413 0.02 0.02 461.38 9.2276 second 2.24308 0.007477 0.02 0.02 401.311 8.02622

third 2.24308 0.007477 0.02 0.02 297.53 5.9506 fourth 2.49388 0.008313 0.02 0.02 157.38 3.1476 H.room 2.74134 0.009138 0.02 0.02 68.19 1.3638

column E-3 x-dxn 0 level Le eacalc 20 ea Nsd Ma foundation 1.34109 0.00447 0.02 0.02 1790.15 35.803 ground 3.42767 0.011426 0.02 0.02 1633.3 32.666

first 2.56249 0.008542 0.02 0.02 949.05 18.981 second 2.57922 0.008597 0.02 0.02 671.98 13.4396 third 2.57922 0.008597 0.02 0.02 387.46 7.7492 fourth 2.76646 0.009222 0.02 0.02 90.38 1.8076 H.room 2.88328 0.009611 0.02 0.02 28.97 0.5794 y-dxn

level Le eacalc 20 ea Nsd Ma

second -54 97.89 434.68 -

0.1242293 0.2252 0.0854284 0.09008 0.09008 39.156

third -37.45 74.51 321.27 -

0.1165686 0.23192 0.0925265 0.092769 0.092769 29.804

fourth -12.36 25.33 240.88 -

0.0513119 0.10516 0.0425689 0.042062 0.042569 10.254 H.room -17.28 17.41 124.59 -0.138694 0.13974 0.028365 0.055895 0.055895 6.964



foundation 1.29167 0.004306 0.02 0.02 1790.15 35.803 ground 3.27488 0.010916 0.02 0.02 1633.3 32.666 first 2.40302 0.00801 0.02 0.02 949.05 18.981 second 2.42191 0.008073 0.02 0.02 671.98 13.4396 third 2.42191 0.008073 0.02 0.02 387.46 7.7492

fourth 2.64814 0.008827 0.02 0.02 90.38 1.8076 H.room 2.78359 0.009279 0.02 0.02 28.97 0.5794

column A-3 x-dxn level Le eacalc 20 ea Nsd Ma foundation 1.38032 0.004601 0.02 0.02 1368.42 27.3684

ground 3.53444 0.011781 0.02 0.02 1076.01 21.5202 first 2.68623 0.008954 0.02 0.02 806.45 16.129 second 2.70014 0.009 0.02 0.02 557.52 11.1504 third 2.70014 0.009 0.02 0.02 314.86 6.2972 fourth 2.75236 0.009175 0.02 0.02 113.28 2.2656 H.room 0 0 0 0

y-dxn 0 level Le eacalc 20 ea Nsd Ma foundation 1.43125 0.004771 0.02 0.02 1368.42 27.3684 ground 3.65724 0.012191 0.02 0.02 1076.01 21.5202 first 2.84348 0.009478 0.02 0.02 806.45 16.129 second 2.85241 0.009508 0.02 0.02 557.52 11.1504

third 2.85241 0.009508 0.02 0.02 314.86 6.2972 fourth 2.88509 0.009617 0.02 0.02 113.28 2.2656 H.room 0 0 0.02 0.02 0 0

column B-3 x-dxn 0 level Le eacalc 20 ea Nsd Ma foundation 1.34109 0.00447 0.02 0.02 2252.23 45.0446 ground 3.42767 0.011426 0.02 0.02 1602.82 32.0564

first 2.56249 0.008542 0.02 0.02 1278.28 25.5656 second 2.57922 0.008597 0.02 0.02 1032.91 20.6582 third 2.57922 0.008597 0.02 0.02 429.55 8.591 fourth 2.64323 0.008811 0.02 0.02 44.99 0.8998 H.room 0 0 0.02 0.02 0 0 y-dxn 0

level Le eacalc 20 ea Nsd Ma



foundation 1.43125 0.004771 0.02 0.02 2252.23 45.0446 ground 3.65724 0.012191 0.02 0.02 1602.82 32.0564 first 2.84348 0.009478 0.02 0.02 1278.28 25.5656 second 2.85241 0.009508 0.02 0.02 1032.91 20.6582 third 2.85241 0.009508 0.02 0.02 429.55 8.591

fourth 2.88509 0.009617 0.02 0.02 44.99 0.8998

column H-3 level ea Nsd Ma foundation 0.02 1557.47 31.1494 ground 0.02 560.41 11.2082

first 0.02 514.99 10.2998 second 0.02 434.68 8.6936 third 0.02 321.27 6.4254 fourth 0.02 240.88 4.8176 H.room 0.02 124.59 2.4918

Design moment

column E-2

level Mdx Ma Mdxtot Mdy Ma Mdytot foundation 42.392 16.6794 59.07 5.54 16.6794 22.22 ground 62.2952 9.134 71.43 3.53695 15.667383 19.20 first 50.772 9.2276 60.00 0.588 9.2276 9.82 second 41.7 8.02622 49.73 2.276 8.02622 10.30 third 30.648 5.9506 36.60 3.912 5.9506 9.86

fourth 13.592 3.1476 16.74 3.736 3.1476 6.88 H.room 12.88 1.3638 14.24 7.028 1.3638 8.39

colmnE-3

level Mdx Ma Mdxtot 0 Mdy Ma Mdytot foundation 45.504 35.803 81.31 2.222 35.803 38.03 ground 47.712 32.666 80.38 2.808 32.666 35.47 first 58.872 18.981 77.85 15.02 18.981 34.00 second 51.984 13.4396 65.42 13.352 13.4396 26.79 third 44.832 7.7492 52.58 12.888 7.7492 20.64

fourth 22.064 1.8076 23.87 9.368 1.8076 11.18 H.room 11.7 0.5794 12.28 10.028 0.5794 10.61



Column A-3 level Mdx Ma Mdxtot 0 Mdy Ma Mdytot foundation 7.024 27.3684 34.39 4.468 27.3684 31.84 ground 6.376 21.5202 27.90 47.428 21.5202 68.95 first 8.604 16.129 24.73 44.432 16.129 60.56 second 36.404 11.1504 47.55 16.804 11.1504 27.95 third 32.072 6.2972 38.37 17.86 6.2972 24.16 fourth 17.012 2.2656 19.28 19.564 2.2656 21.83

colmn B-3 level Mdx Ma Mdxtot 0 Mdy Ma Mdytot foundation 3.872 45.0446 48.92 0.702 45.0446 45.75 ground 14.68 32.0564 46.74 52.52 32.0564 84.58 first 46.752 25.5656 72.32 4.848 25.5656 30.41 second 22.756 20.6582 43.41 2.638 20.6582 23.30

third 37.116 8.591 45.71 1.128 8.591 9.72 fourth 23.856 0.8998 24.76 2.832 0.8998 3.73

column H-3 level Mdx Ma Mdxtot 0 Mdy Ma Mdytot foundation 49.624 31.1494 80.77 10.06 31.1494 41.21 ground 66.332 11.2082 77.54 16.932 11.2082 28.14 first 49.504 10.2998 59.80 9.176 10.2998 19.48 second 39.156 8.6936 47.85 17.826 8.6936 26.52

third 29.804 6.4254 36.23 17.642 6.4254 24.07 fourth 10.254 4.8176 15.07 12.898 4.8176 17.72 H.room 6.964 2.4918 9.46 6.568 2.4918 9.06



5.2.3 Reinforcement Design

5.2.3.1 solid slab columns

Longitudinal Reinforcement As min = 0.008Ac As max = 0.08Ac

Colmn A-3

level Nsd Mdx Mdy ν µh µb ω As Asmin Asprvd Ф foundn 1368.42 34.39 31.84 1.0 0.07 0.07 0.28 1489.704 980 1489.70 8Ф16 ground 1076.01 27.90 68.95 0.8 0.06 0.14 0.29 1542.907 980 1542.91 8Ф16 first 806.45 24.73 60.56 0.6 0.05 0.12 0.1 532.037 980 980 4Ф12&4Ф14 second 557.52 47.55 27.95 0.4 0.10 0.06 0.06 319.2222 980 980 4Ф12&4Ф14 third 314.86 38.37 24.16 0.2 0.08 0.05 0.045 239.4167 980 980 4Ф12&4Ф14 fourth 113.28 19.28 21.83 0.1 0.06 0.07 0.12 469.0612 720 720 4Ф16

colmn B-3 level Nsd Mdx Mdy ν µh µb ω As Asmin Asprvd Ф foundn 2252.23 48.92 45.75 1.2 0.07 0.06 0.46 3196.565 1280 3196.6 8Ф24 ground 1602.82 46.74 84.58 0.9 0.06 0.12 0.325 2258.443 1280 2258.4 4Ф24&4Ф14

first 1278.28 72.32 30.41 0.9 0.15 0.06 0.32 1702.518 980 1702.5 4Ф20& 4Ф12

second 1032.91 43.41 23.30 0.7 0.09 0.05 0.055 292.6204 980 980 4Ф14&4Ф12 third 429.55 45.71 9.72 0.4 0.15 0.02 0.12 469.0612 720 720 4Ф16 fourth 44.99 24.76 3.73 0.0 0.08 0.01 0.2 781.7687 720 781.77 4Ф16

colmn E-3 level Nsd Mdx Mdy ν µh µb ω As Asmin Asprvd Ф foundn 1790.15 81.31 38.03 1.0 0.11 0.05 0.36 2501.66 1280 2501.7 4Ф24&8Ф12 ground 1633.3 80.38 35.47 0.9 0.11 0.05 0.275 1910.99 1280 1911 4Ф20&4Ф16 first 949.05 77.85 34.00 0.7 0.16 0.07 0.35 1862.13 980 1862.1 4Ф20&4Ф14 second 671.98 65.42 26.79 0.5 0.13 0.06 0.115 611.8426 980 980 4Ф12&4Ф14 third 387.46 52.58 20.64 0.3 0.11 0.04 0.06 319.2222 980 980 4Ф12&4Ф14 fourth 90.38 23.87 11.18 0.1 0.08 0.04 0.115 449.517 720 720 4Ф16 H.room 28.97 12.28 10.61 0.0 0.04 0.03 0.1 390.8843 720 720 4Ф16



5.2.3.2 pre-cast slab columns

Following the same procedure the final out put for the pre-cast slab columns is tabulated below

colum A-3 level Nsd Mdx Mdy ν µh µb ω As Asmin Asprvd Ф foundation 1422.5 33.11 36.90 1.0 0.07 0.08 0.3 1596 980 1596.11 8Ф16 ground 1141.5 70.57 26.12 0.8 0.15 0.05 0.32 1703 980 1702.52 4Ф20+4Ф16 first 850.75 61.16 21.39 0.6 0.13 0.04 0.11 585.2 980 980.00 4Ф12+4Ф14 second 626.26 51.90 17.72 0.5 0.11 0.04 0.02 106.4 980 980.00 4Ф12+4Ф14 third 340.59 40.05 13.36 0.3 0.13 0.04 0.18 703.6 720 720.00 4Ф16 fourth 89.96 13.92 7.08 0.1 0.03 0.01 0.035 136.8 720 720.00 4Ф16

column B-3 level Nsd Mdx Mdy ν µh µb ω As Asmin Asprvd Ф foundation 1751.2 83.70 38.10 1.0 0.12 0.05 0.37 2571 1280 2571.15 4Ф24+4Ф16 ground 1606.5 79.52 36.57 0.9 0.11 0.05 0.27 1876 1280 1876.24 4Ф20+4Ф14 first 1195.3 68.90 28.16 0.7 0.10 0.04 0.065 451.7 1280 1280.00 4Ф16+4Ф14 second 797.91 54.77 18.70 0.4 0.08 0.03 0.01 39.09 1280 1280.00 4Ф16+4Ф14

colmn E-2 level Nsd Mdx Mdy ν µh µb ω As Asmin Asprvd Ф foundn 833.97 59.07 22.22 0.6 0.12 0.05 0.09 478.8333 980 980 4Ф12&4Ф14 ground 456.7 71.43 19.20 0.3 0.15 0.04 0.16 851.2592 980 980 4Ф12&4Ф14 first 461.38 60.00 9.82 0.3 0.12 0.02 0.06 319.2222 980 980 4Ф12&4Ф14 second 401.311 49.73 10.30 0.3 0.10 0.02 0.03 159.6111 980 980 4Ф12&4Ф14 third 297.53 36.60 9.86 0.3 0.12 0.03 0.07 273.619 720 720 4Ф16 fourth 157.38 16.74 6.88 0.2 0.05 0.02 0 0 720 720 4Ф16 H.room 68.19 14.24 8.39 0.1 0.05 0.03 0.06 234.5306 720 720 4Ф16

colmn H-3 level Nsd Mdx Mdy ν µh µb ω As Asmin Asprvd Ф foundn 1557.47 80.77 41.21 0.9 0.11 0.06 0.28 1945.735 1280 1945.7 4Ф20&4Ф16 ground 560.41 77.54 28.14 0.4 0.16 0.06 0.23 1223.685 980 1223.7 4Ф20 first 514.99 59.80 19.48 0.4 0.12 0.04 0.05 266.0185 980 980 4Ф20 second 434.68 47.85 26.52 0.4 0.16 0.09 0.3 1172.653 720 1172.7 4Ф20 third 321.27 36.23 24.07 0.3 0.12 0.08 0.13 508.1497 720 720 4Ф16 fourth 240.88 15.07 17.72 0.2 0.05 0.06 0 0 720 720 4Ф16 H.room 124.59 9.46 9.06 0.1 0.03 0.03 0.04 156.3537 720 720 4Ф16



third 413 45.04 9.70 0.4 0.15 0.03 0.13 508.1 720 720.00 4Ф16 fourth 48.43 20.25 1.66 0.0 0.07 0.01 0.18 703.6 720 720.00 4Ф16

column E-3 level Nsd Mdx Mdy ν µh µb ω As Asmin Asprvd Ф foundation 1526 75.72 33.08 0.8 0.10 0.05 0.16 1112 1280 1280.00 4Ф16+4Ф14 ground 968.71 83.51 25.31 0.5 0.12 0.03 0.045 175.9 1280 1280.00 4Ф16+4Ф14 first 751.83 81.73 23.87 0.4 0.11 0.03 0 0 1280 1280.00 4Ф16+4Ф14 second 545.71 69.51 19.15 0.3 0.10 0.03 0.035 136.8 1280 1280.00 4Ф16+4Ф14 third 331.26 59.24 13.59 0.3 0.19 0.04 0.315 1231 720 1231.29 4Ф16+4Ф12 fourth 96.61 28.24 7.54 0.1 0.09 0.02 0.14 547.2 720 720.00 4Ф16 H.room 30.85 11.95 11.54 0.0 0.04 0.04 0.11 430 720 720.00 4Ф16

column E-2 level Nsd Mdx Mdy ν µh µb ω As Asmin Asprvd Ф foundation 334.26 50.00 12.67 0.2 0.10 0.03 0.08 425.6 980 980.00 4Ф14+4Ф12 ground 413.92 71.97 17.44 0.3 0.15 0.04 0.19 1011 980 1010.87 4Ф14+4Ф12 first 428.13 60.28 10.68 0.3 0.12 0.02 0.075 399 980 980.00 4Ф14+4Ф12 second 377.7 49.76 8.38 0.4 0.16 0.03 0.17 664.5 720 720.00 4Ф16 third 283.8 36.44 7.40 0.3 0.12 0.02 0.075 293.2 720 720.00 4Ф16 fourth 154.59 15.53 5.71 0.2 0.05 0.02 0 0 720 720.00 4Ф16 H.room 66.65 13.81 8.08 0.1 0.05 0.03 0.06 234.5 720 720.00 4Ф16

columnH-3 level Nsd Mdx Mdy ν µh µb ω As Asmin Asprvd Ф foundation 1521.23 80.19 40.40 0.8 0.11 0.06 0.2 1390 1280 1389.81 4Ф16+4Ф14 ground 1437.09 94.95 46.87 0.8 0.13 0.06 0.27 1876 1280 1876.24 4Ф20+4Ф14 first 471.89 64.01 11.33 0.5 0.21 0.04 0.375 1466 720 1465.82 4Ф16+4Ф14 second 448.71 61.02 17.51 0.4 0.20 0.06 0.36 1407 720 1407.18 4Ф16+4Ф14 third 321.21 53.96 22.38 0.3 0.18 0.07 0.345 1349 720 1348.55 4Ф16+4Ф14 fourth 146.81 15.39 10.26 0.1 0.05 0.03 0.06 234.5 720 720.00 4Ф16 H.room 63.26 14.99 25.21 0.1 0.05 0.08 0.13 508.1 720 720.00 4Ф16



column E-1 level Nsd Mdx Mdy ν µh µb ω As Asmin Asprvd Ф foundation 237.74 51.4 6.267 0.2 0.17 0.02 0.26 1016 720 1016.30 4Ф14+4Ф12 ground 239.7 51.31 12.35 0.2 0.17 0.04 0.3 1173 720 1172.65 4Ф16+4Ф12 first 208.25 27.51 9.225 0.2 0.09 0.03 0.05 195.4 720 720.00 4Ф16 second 161.85 9.725 27.44 0.2 0.03 0.09 0.05 195.4 720 720.00 4Ф16 third 103.27 8.393 18.76 0.1 0.03 0.06 0.075 293.2 720 720.00 4Ф16 fourth 28.77 4.683 6.647 0.0 0.02 0.02 0.05 195.4 720 720.00 4Ф16



6. Foundation design



6.1 Footing Design A) Interior column footing design (column at (b3))

Y

a b Using comb-1

My Given L Mx = 5.96 kN.m L’ Mx X My =-0.42 kN.m -Pd =2252.23 kN Assume L = B c d And an allowable bearing capacity for the soil as δall =560 KPa C-25 and S-300

Proportioning

Using unfactored load; Pd = 73.16084.1

23.2252=

mP

Me

mP

Me

d

x

y

d

y

x

00026.073.1608

96.5

0037.073.1608

42.0

===

=−

==

0.89m 1.5m

Since a surface footing, B = L 0.61m

)0037.0

*600026.0

*61(*73.1608

560

)*6*61(*

2 BBB

B

e

B

e

A

p yxd

all

±±=

±±=σ

Solving the equation by trial and error, we get B =1.7m We use B = L = 1.7m

47.562)00094.0013.01(*7.1

73.16082

=++=aultσ kn/m2

42.561)00094.0013.01(*7.1

73.16082

=−+=bultσ kn/m2

)00094.0013.01(*7.1

73.16082

+−=cultσ =548.00 kn/m2



)00094.0013.01(*7.1

73.16082

−−=dultσ =546.96 kn/m2

562.47 561.43 1.7m 1.7m

548

546.96

ultδ avg = 554.7 Kpa

I . Punching shear

According to EBCS-2, 1995 article 4.7.6 the resistance of footing without punching shear reinforcement is give by: Vrd = 0.25 * fctd * k1 * k2 * u * d Where: K1 = 1+50ρ ≤ 2.0 K2 = 1.6 – d ≥ 1.0 (d in meter) Assume ρ = 0.002, k1 = 1.0 + 50 * 0.002 = 1.1 0.4+d L’ U = 4* ( 0.4 + d) = 1.6 + 4d Vrd = 0.25*1043*1.1*1.0*(1.6 + 4*d)*d B’ Vacating = (1.7*1.7 – (0.4 + d)2)*554.7 0 .4+d Then Vrd > Vacting (for safe condition) B’ Hence solving for d d ≥ 0.545 Therefore , D = 549 + 50 + 10 =605mm So use over all depth of 610mm

II.wide beam shear



According to EBCS-2, 1995, article 4.5.3, the shear force Vc carried by the concrete is given by : Vc = 0.3*fctd*k1*k2*bw*d Using 50mm clear cover and φ 16 longitudinal reinforcement bar d= 610 – 50– 8 = 560 mm Vc = 0.3*1043*1.1*1*1.7*0.552 =327.6 kN Vacting = (B/2 - B’/2 - d)*qu*B = 0.09 *561.42*1.7=85.89kN Since Vc > Vacting ..... the section is safe !! So punching governs and the overall depth is found to be 610 mm III.Reinforcement M = 364.18*1*1.05*1.05/2 = 200.75 kN.m Using table No.1 For design

d

b

M

Km = = 19.46

Ks = 3.96 As = Ks * d

M = 3.96* 222.2428

56.0

99.201mm=

Amin = ρmin * b*d = .002*1700*560 = 1904 2mm

s

s

A

bas

*= taking φ 16 mms 140

22.2428

1700*201==

Take φ16 c/c 140 mm (both direction)

No of reinforcement = 12140

)1001700(1 =

−+

Hence provide 12φ 16 c/c 140 mm Similarly the remaining footing and the precast slab footing is done as that of the above procedure. The result is found in the auto cad detail for both cases.



6.2 Mat foundation design

The purpose of designing this mat foundation is due to irregularity of our building and occurrence of small amount of tension at the edge columns. For a building of G+4 with bearing capacity of 560 it is not recommended to use mat foundation but we do it to be safer. And also it is recommended to use cantilever structures to balance the tension by discussing with the architect. since we don’t have this chance we opted to design mat foundation to the local areas in which tension was developed. The design procedure for the precast floor system is presented as follows and for the solid case the results are found in the reinforcement detail and are also tabulated in table.

E G F G 0.5 1

1.3

2

2.7

0.5 m

3 1.5

0.5m 3.54m 0.48m 0.98m 0.53

Case 1 when E-1& F-1 are in tension

Column P Factored p mx My E-1 -143.77 -102.7 -95.52 3.15 F-1 -279.59 -199.71 -93.38 -10.64 E-2 803.13 573.7 -108.53 5.47 G-2 599.8 428.43 -99.51 -12.49 E-3 1525.96 1089.97 -99.8 2.91 H-3 1521.23 1086.6 -94.01 -4.65 R=-102.7-199.71+573.7+428.43+1086.6+1089.97=2876.3 KN Taking moment about axis E

-



e’x =3.15-10.64+5.47-12.49+2.91-4.65-199.71*3.54+428.43*4.02+1086.6*5 2876.3 =2.24 ex=0.5+2.24= 2.74m similarly taking moment about axis 3 ey=1.81m centroid of the area is found to be x= 2.797 m y=2.82m Eccentricities Ex= x-ex= 2.797-2.74 =0.057m Ey =2.82-1.81= 1.01m Then Mx= R*ey= 2876.3*1.01=2905.1 KN-m My =R*ex= 2876.3*0.057= 164.01KN-m Second moment of inertia of the area Ix= 130.76 m4 Iy=52.76 m4

d= ± ± =105.6 ±3.142x ±22.22y

B C A A A D da=105.6 +3.142*2.797+ 22.22*2.82 =177.05 KN/m2 db= 105.6+3.142*2.797-22.22*3.18 =43.73 KN/ m2

dc= 105.6-3.142*1.743-22.22*3.18 =29.5 KN/ m2

dd= 105.6-3.142*3.733+22.22*2.82 =156.53 KN/ m2 Case 2 When E-1&F-1 are in compression

The same procedure is followed to calculate eccentricities & moment

Column P Factored p mx My E-1 1064.74 760.53 93.85 -5.91 F-1 1087.33 776.7 91.5 3.55 E-2 803.13 573.7 -108.53 5.47 G-2 857.76 612.7 -5.87 -86.22 E-3 1525.96 1089.97 -99.8 2.91 H-3 1521.23 1086.6 -94.01 -4.65



d= ± ±

co-ordinates B G C F (-2.797,2.03) ,J (-0.527,-2.83) F H E (-2.797,0.03)

H (2.16,2.03) E I I (2.449,0.03) J G (-0.527,3.18) A D ey=0.56m Mx=Rey=2744.11KN.m ex=0.137 m My=Rex=671.33KN.m p/A=179.9KN/m2 Mx/Ix=20.99KN/m2 My/Ix=12.86KN/m2 dA=179.9+12.86*2.797-20.99*2.82=156 KN/m

2

d B= 179.9+12.86*2.797+20.99*3.18=282.62 KN/m2

dC= 179.9-12.86*1.743+20.99*3.18=224.23 KN/m2

dD= 179.9-12.86*3.73-20.99*2.82=72.7 KN/m2

dF= 179.9+12.86*2.797+20.99*2.03=258.48 KN/m2

dE= 179.9+12.86*2.797+20.99*0.03=216.5 KN/m2

d H= 179.9-12.86*2.16+20.99*2.03=194.73 KN/m2

dI= 179.9-12.86*2.449+20.99*0.33=194.04 KN/m2

dG= 179.9+12.86*0.527+20.99*3.18=253.43 KN/m2

dC= 179.9+12.86*0.527-20.99*2.82=127.5 KN/m2

Since the stress in case 2 greater than that of case 1 so the mat is designed for the compression case X-direction

Strip 1 ∑Pu=760.53+776.7=1537.23 KN A=5.46m2

Qavg=240.015 KN/m2

Q=240.015 KN/m2*5.46m2=1310.48 KN Average load =1310.48 KN+1537.23KN/2=1423.86 KN

Modified soil rxn =Q*( )

STRIP 2

STRIP 3

STRIP 1

STRIP 5

STRIP 4



= 240.02KN/m2*[ ]= 260.79 KN/m2

Load correction factor = =1423.86/1537.23= 0.93

Corrected load for E-1,p= 707.3 KN F-1,P=722.33KN The same procedure is followed for the next strips and the results are tabulated as follows. Strip ∑pu Average soil

rxn Average load

Modified soil rxn

Load correction factor

2 1186.4 204.7 1637.41 160.5 1.38 3 2176.57 148.73 2336.11 139.22 1.07 4 2424.2 205.1 2608.85 191.54 1.08 5 2476 169.5 2897.9 147.96 1.17 *.B. strip 4&5 are spanning in the y- direction

Analysis of individual strips

SAP result for the solid case is presented for sample STRIP 1

SFD

BMD

Strip 2



SFD

STRIP 3

Depth determination (precast case)

Case 1 when one of the edge has no resistance Punching check for the column E-3 which is located at the edge with maximum axial load Vac=p-d(0.4+d)(0.7+0.5d) 0.4+d =1166.3-139.22(0.4+d)(0.7+0.5d) =1127.32-125.3d-69.61d2 0.4m Vres=0.5 fctd (1+50ρ)*(1.8+d)d =1021.68d+1135.2 *d2 0.5 0.2+0.5d equating vact ≤ vres 0.7+0.5d then d = 0.602m 0.7+d 0.5 0.2+d For strip 4 case d=191.54KN/m2 Vact=1166.3-191.54(0.4+d)*(0.7+0.5d) Vact= 112.67-172.4d-95.77d2 Vres ==1021.68d+1135.2 *d2

Equating vact ≤ vres then d= 0.6m



Case when the edge has resistance 0.4+d 0.4+d

Check for the wide beam shear

Maximum wide beam shear =306 KN for strip -1 Vres = 0.3fctd (1+50ρ) bw *d =0.3*1.043*10^3*1.1*1.15*0.788=312 KN Vres < vact ok So use 0ver all depth of 850mm d=850-50-12=78


moment b d km ks As spacing s.provided

Strip-1 364.06 1.15 0.788 22.58 3.974 1835.70 196.71 Φ20c/c190 65.72 1.15 0.788 9.59 min 1812.4 199.24 Strip-2 255.71 2.00 0.788 14.35 min 3152 199.24 Ø20c/c190 113.22 2.00 0.788 9.55 min 3152 199.24 Ø20c/c190 Strip-3 Strip-3 417.34 2.85 0.788 15.36 min 4491.6 199.24 Ø20c/c190 20.31 2.85 0.788 3.39 min 4491.6 199.24 Ø20c/c190 Strip-4 215.48 2.27 0.788 12.36 min 3577.52 199.24 Ø20c/c190 51.95 2.27 0.788 9.585 min 3577.52 199.24 Ø20c/c190 129.49 2.27 0.788 9.585 min 3577.52 199.24 Ø20c/c190 75.58 2.27 0.788 7.323 min 3577.52 199.24 Ø20c/c190 Strip-5 166.46 3.265 0.788 9.06 min 5145.64 199.24 Ø20c/c190 71.22 3.265 0.788 5.93 min 5145.64 199.24 Ø20c/c190 89.81 3.265 0.788 6.66 min 5145.64 199.24 Ø20c/c190 70.72 3.265 0.788 4.91 min 5145.64 199.24 Ø20c/c190



Reinforcement design for solid case

moment b d Km Ks As spacing s.provided Strip-1

436.78 1.15 0.788 24.73 3.988 2210.62 163 Ø20c/c160 79.06 1.15 0.788 10.52 Min 1812.4 199.24 Ø20c/c190

Strip-2

596.5 2.00 0.788 21.92 3.9695 3004.302 209 Ø20c/c190

142.75 2.00 .788 8.02 Min 3152 199.24 Ø20c/c190 Strip-3

1296.38 2.85 0.788 27.066 4.0158 6606.64 135.45 Ø20c/c130 113.62 2.85 0.788 8.01 Min 4491.6 199.24 Ø20c/c190

Strip-4

590.95 2.27 0.788 20.48 3.96 2969.65 240 Ø20c/c190 91.57 2.27 0.788 8.66 Min 3577.52 199.24 Ø20c/c190 96.62 2.27 0.788 8.28 Min 3577.52 199.24 Ø20c/c190 Strip-5 494.10 3.265 0.788 15.61 Min 5145.64 199.24 Ø20c/c190 169.26 3.265 0.788 9.17 Min 5145.64 199.24 Ø20c/c190

The reinforcement detail is attached with AutoCAD



7. Cost estimation

Solid slab

A-SUB STRUCTURE

1. CO*CRETE WORK

1.10 Reinforced concrete quality C-25, 360 kg of cement/m3, filled into formwork and vibrated around rod reinforcement (formwork and reinforcement measured separately)

a) Footing , Grade beam &footing columen m2 53.74 1300.00 69,856.80

1.20 Provide, cut and fix in position sawn zigba wood or steel formwork which ever appropriate.


1.30 Mild steel reinforcement according to structural drawings. Price includes cutting, bending, placing in position and tying wire and required spacers.

a) Φ8-Φ24 mm deformed bar kg 110.20 26.00 2,865.20

b) Φ6 mm plain bar kg 812.44 25.00 20,311.05

TOTAL CARRIED TO

SUMMARY .................... 121,852.55

B-SUPER STRUCTURE

1. CO*CRETE WORK


a) floor slabs m3 121.97 1250.00 152,462.50

b) beams . m3 62.19 1250.00 77,742.75



c) columns . m3 26.61 1250.00 33,262.50


a) Elevation column, beams & floor slabs m2 1250.40 70.00 87,528.00



b) Φ6 mm plain bar kg 357.56 26.00 9,296.56

TOTAL CARRIED TO

SUMMARY .................... 1,082,133.31

Grand total of solid 1,203,989.96

pre-cast ribbed slab

A. super structure

1. CO*CRETE WORK


a) floor slabs

a1)solid part m3 17.51 1250.00 21,891.25

a2)cast in situ m3 51.36 1250.00 64,193.75

a3)beam element m3 7.76 1250.00 9,700.75

b) beams . m3 76.17 1250.00 95,212.50

c) columns . m3 26.29 1250.00 32,862.50

1.20 Class C 200mm thick HCB wall which can satisfy the designed strength , bedded in cement mortar (1:3).Price shall include mortar bed. pcs 4992.00 9.60 47,923.20




a) Elevation column, beams & floor slabs m2 681.86 70.00 47,730.20



b) Φ6 mm plain bar kg 1429.20 26.00 37,159.20

TOTAL CARRIED TO SUMMARY 1,018,322.10

B.sub structure

1. CO*CRETE WORK







b) Φ6 mm plain bar kg 110.70 26.00 2,878.20

TOTAL CARRIED TO SUMMARY 116,902.22

Grand total of pre-cast 1,135,224.32



Conclusion and recommendation Conclusion

The main aim of the project is to compare the total cost variation of pre-cast and solid slab systems. To attain this we have done a detail analysis and design for each case. And finally we have come out with the total cost of each system as shown below.

Total cost(birr)

pre-cast solid difference

concrete work 340,391.97 333,333.95 -7,058.02

reinforcement 721,703.40 754,308.51 32,605.11

form-work 73128.95 116347.5 43,218.55

total 1,135,224.32 1,203,989.96 68,765.64

Total difference = (1,203,989.96-1,135,224.32)*100/(1,203,989.96)=5.7115% As the above data shows the pre-cast slab type is less-costier than that of solid floor type. And also it is clear that the major difference is caused by the cost of form-work and reinforcement instead of concrete cost. Generally using pre-cast slabs is advantageous by minimizing the construction time, work man-ship, construction equipment and attaining quality of materials.

Recommendation

The overall works of the building should be inspected and supervised throughout the entire construction time in order to achieve the design strength.

Care should be taken when handling, casting and placing the precast beam element. Especially the support condition on construction time must be the same as that of previously determined arrangement on the design part.

And also it is better to remove application of concentrated force for the precast floor system, which can cause falling out of the hallow block concrete.

The quality of materials should fulfill the design strength.



References � Ethiopian Building Code Standard 1, 2, 3, 7, & 8 – 1995.

� Gtz technical manual

� Kality steel industry manual of cold framed welded structural & furniture steel tubing

structural design of g+5 building (final year project for bsc in civil engineering)

Documents

design of slab

cast slab design

solid slab design

design of beams

reinforcement design

design of lattice

footing design

design procedure