Structural Design Of G+5 Building (final Year Project For Bsc In Civil Engineering) 474y42

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

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 Mekelle University, Department of Civil Engineering

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June 2008

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

Mekelle University, Department of Civil Engineering

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June 2008

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 . At last but not the least, we would like to thank to our parents for giving their countless material & moral .


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June 2008

Introduction Now a day’s it is being practical to choose types of structural 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 ed 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 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.


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June 2008

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 ing 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


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June 2008

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/m2 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) (e) Where qref =reference wind pressure 2

= ρ/2 Vref …………… (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 Cdir .Ctem .Calt .Vref o = 1*1*1*22m/s 2 qref = ρ/2 Vref =0.5* 0.94Kg/m3*222 =227.48N/m2 Ce=pressure coefficient that s the effect of terrain roughness, topography and height above the ground on the mean wind speed is defined as

Vref

=


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June 2008

  7 * KT 2 Ce(z) = C r ( Z ) * C t ( Z ) * 1 +   C r ( Z ) * Ct ( Z )  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
Case -1 when wind direction 00 I

0.8m

J 6.8

2.6m

H F

0.8m

G

F

2.6m

13m 6.5m

6.5m 26m

Wind θ=00 Mekelle University, Department of Civil Engineering

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Reference height Ze=h=16.91m e=b=26m Area F=16.9m2 H= 20.8m2 I=20.8m2 G= 33.8m2

June 2008

J=67.6m2

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 e= e10 (EBCS 1, 1995 Art. A.2.1)

Pitch angle 15

o

Zone for wind ward direction F G H e,10

e,10

e,10

θ=00 I

J

e,1

e,1

0

0

-0.9

-0.8

-0.3

-0.4

-1.0

0.2

0.2

0.2

_

_

Case-2 when wind direction θ = 900

e/4=1.7m

F H

1.7m

I

G

1.7m

G H

Θ=900

I e/4 =1.7m

F


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e/10=0.68m b=6.8m e= min

Area:

2.72m

b=6.8m 2h=33.82m

June 2008

3.4m

e=6.8m

F = 1.156 m2 G = 1.156m2 H = 9.248 m2 I = 11.56 m2

External pressure coefficient Pitch angle

150

Zone for wind direction θ = 900 F

G

H

I

e,10

e,1

e,10

e,1

e,10

e,10

-1.3

-2.0

-1.3

-2.0

-0.6

-0.5

We = qref Ce(z) e = 227.48*1.602 e = 0.3644e KN/m2 = 0.3644 e K2/m 2 e = e 1 , a <1 m2 e = e1 + ( e10 – e1) logA10 for 1m2 < A <10m2 e = e10 ; a<10 m2 The calculation for the external pressure for each zones are calculated below Case1 θ=00 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 Mekelle University, Department of Civil Engineering

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June 2008

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

Case 2 θ=900 e for F e = e 1 + (e10 – e1) logA10 = -2+ (-1.3+2) log1.156 = -1.96 For G = -1.96 For H=-0.62 Zone F = Zone G = Zone H = Zone I =

0.3644*-1.96 = -0.714 KN/m2 0.3644*-1.96 = -0.714KN/m2 0.3644*-0.62 = -0.226 KN/m2 0.3644 *-0.5 = -0.184 KN/m2

II. Internal wind pressure Wi = qref Ce(zi) i Where i 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 i = 0.8 or i = -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


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June 2008

e calculation for the flat roof The roof is divided as shown below

F e/4=0.675

wind

m

G

H

I

1.35m

F 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 H=1.08*2.7=2.916

External pressure coefficients F Sharp e10 e1 eves -1.8 -2.5

e10 -1.2

G e1 -2

G=1.35*.27=.364m2 I=2.7*5.3=14.31m2

H e10 -0.7

e1 -1.2

I e10 ±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 Mekelle University, Department of Civil Engineering

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June 2008

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)=0.7072*12 *(1+(7*0.24)/(0.707*1)) =1.688 We = qref Ce(z) e =227.48N/m2 (1.688)e =384e N/m2 The calculation for the external pressure for each zones are calculated below Zone F = e1= -2.5 Zone G = e1=-2 Zone H = e = e1 + ( e10 – e1) logA10 for 1m2 < 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) Mekelle University, Department of Civil Engineering

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June 2008

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/m2 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) ST-20

40mm

Ø8 deformed bars

11@410m

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 Mekelle University, Department of Civil Engineering

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June 2008

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 2R = 0.436 For case- 3 R(+ve) = 0.218 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.


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Load Combination COMB 1 = 1(DL) + 1.3(DLp) + LLc COMB 2 = 1(DL + LLD) + 1.3DLP COMB 3 = 1(DLr + WL+) + 1.3DLP COMB 4 = 1(DLr + WL-) + 1.3DLP

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 Bott = 7.4 Critical loads Top = -8.14 Diag tesion = 1.99 Bott = 8.25

June 2008

where:DLr= dead load of roof DLP = dead load of purloin LLc = live load concentrated WL+= wind load +ve WL- = wind load -ve

Diag compression = -1.7

Diag compress = -1.9


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June 2008

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

ii. *egative (suction) wind Reaction from purloin R= -3.51 KN

Rx= 0.23KN Ry= 0.86KN 2Rx= 0.46KN 2Ry= 1.72KN 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-


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June 2008

Analysis result COMB -1

COMB -2

COMB -3

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 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 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 Material: - Fe 430

Fy= 275 MPA Fu= 430 MPA

Diagonal steel member design Design actions

Nsd =12.46 KN


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June 2008

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

1.13

1.13

1.13

0

tan 15 = 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 t = 3mm A= 3.01 cm2 Ix=Iz=3.5 cm4 Wplx = wplz=2.34cm3 rx = rz=1.08 cm

30mm

30mm 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


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June 2008

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 cm2 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 Mekelle University, Department of Civil Engineering

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June 2008

⇒ 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 λλ1= 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=113.9mm2 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 λλ1= 86.4 λx= λz= l/r =1.17*102/1.13 =103.54 Mekelle University, Department of Civil Engineering

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June 2008

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

1.4 Design of 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 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 8.14=0.45*1*A*275/1.1 A=72.36mm2 Nbrd = χβAfy 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 λλ1= 86.4 λx= λz= l/r =0.41*102/0.77 =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 Nsd=8.25KN(tension) take asection of ST-20 with thickness t=1mm A=0.73 I=0.73 Mekelle University, Department of Civil Engineering

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June 2008

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

Check for compression resistance

Φ8 deformed bar buckling length for pin –pin 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 γM1

=0.2677*0.503*10-4m2*260.87*106N/m2 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


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June 2008

=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

pc

ps

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*f ]le yk

=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 Mekelle University, Department of Civil Engineering

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June 2008

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*lx2 Mys =0.0584* 10.31*2.72= 4.36 KN-m Myf =0.044*10.31*2.72 =3.31 KN-m Mxf = 0.0922*10.31*2.72 = 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 7.091

km 20.35

ks 3.96

As 216

Asmin =ρmin*b*d= 0.002*1000*130=260mm2 Asmin
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June 2008

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=0.70750.707*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 rel="nofollow">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 ts since their design action is less than this.


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June 2008

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


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June 2008

Fourth floor slab 1

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

= 94.44mm

4

8

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

= 106.25mm

Ly/Lx = 5/1.65 = 3.03 Mekelle University, Department of Civil Engineering

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June 2008

βa= 12 d ≥ (0.4+0.6*300) 1650 400 12

= 116.88mm

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 s 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 Mekelle University, Department of Civil Engineering

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June 2008

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

2.1.3 Analysis Design moment calculation The and span moment of simply ed (external edges) or fully fixed (contentious edges) are calculated as Mi = αi Pd LX2 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 condition Lx = shorter span of the Ly = longer span of the Fig. Where; s = f = field (span) x = direction of shorter span y = direction of longer span


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June 2008

1

Ly/Lx =1 αxs = 0.039 αys = 0.039 αxs = 0.029 αyf = 0.029 2 DL1 = 6.31 KN/m 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 LX2 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 2,3 and 4

Ly/Lx =1 αxs = 0.032 αys = 0.032 αxs = 0.024 αyf = 0.024 2 DL1 = 6.31 KN/m 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 Mekelle University, Department of Civil Engineering

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June 2008

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 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 Mekelle University, Department of Civil Engineering

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June 2008

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

Equivalent rectangular section 2

2

2

A = ½ ЛD = 0.5*Л*3.8 = 5.67m 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 8

Equivalent rectangular area using Bales theorem

so,

ar =2*((2c + a) * a ) 3 (a + c) br = b – a(a – c) b(a + c) 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)


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June 2008

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 9

Equivalent rectangle ar =2*((2c + a) * a ) 3 (a + c) br = b – a(a – c) b(a + c) ) = 1.043 m so, ar =2*((2* 0.525m + 1.2m) * 1.2 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 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 11


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June 2008

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 12’ 13,14 and 15

Ly/Lx = 5m/ 1.55m = 3.23 > 2 one way slab Pd2 = 16.632 KN/m2 Mys = Pd2 Ly2 = 16.632KN/m *(1.55m)2 = 19.98 KN.m 2 2 17

Pd2 = 16.632 KN/m2 Mys = Pd2 Ly2 2 18

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

Ly/Lx = 4.65m/ 1.1m = 4.23 > 2 one way slab DL2 = 6.31 KN/m2 LL = 5 KN/m2 Mekelle University, Department of Civil Engineering

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June 2008

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 1 Is cantilever slab with length of 1.03m Pd2 = 16.632 KN/m2 Mys = Pd Ly2 = 16.632KN/m *(1.03m)2 = 8.82KN.m 2 2

Adjustment of and span moment 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 1&5 Mxfd = Mxf + Cx ΛM = 11.75 + 0.38*(2.84) =12.83 KN.m 5 Mxfd = Mxf + Cx ΛM = 12.15 + 0.38*(2.84) = 13.58 KN.m


Page 35



June 2008

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June 2008

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

From material used the design constants c1=0.0858 fcd=11.33Mpa c2=3074 fyd= 260.87Mpa m= 28.78 ρb= 0.8Ecu * fcd ( Ecu + Eyd ) fyd b= 1000mm, Ecu= 0.0035, Eyd= (260.87/(200*103) = 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!!


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June 2008

Reinforcement design Moment Km Ks As Asmin S calculated 19.98 35.76 4.108 656.62 212.5 119.55 12.83 28.66 4.03 413.64 212.5 189.78 17.986 33.92 4.09 588.50 212.5 133.39 24.81 39.85 4.16 825.68 212.5 95.07 14.38 30.34 4.05 465.91 212.5 168.49 9.72 24.94 4 311.04 212.5 252.38 12.96 28.8 4.04 418.87 212.5 187.41 14.76 30.73 4.06 479.40 212.5 163.74 15.88 31.88 4.07 517.05 212.5 151.82 13.58 29.48 4.05 439.99 212.5 178.41 2.45 12.52 3.87 75.85 212.5 236.71 8.813 23.75 3.982 280.75 212.5 179.16 6.64 20.65 3.961 210.41 212.5 236.71

S provided Φ10c/c110 Φ10c/c180 Φ10c/c130 Φ10c/c90 Φ10c/c160 Φ10c/c250 Φ10c/c180 Φ10c/c160 Φ10c/c150 Φ10c/c170 Φ8c/c220 Φ8c/c170 Φ8c/c220

Reinforcement detail

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


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June 2008

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 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 manualII the section is recommended as follows

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

220mm

550mm


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June 2008

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 and Ø8 for diagonal

2.2.1Loading A) Initial condition

625mm 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

hf

60 280 220mm

625mm Dead load – Mekelle University, Department of Civil Engineering

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June 2008

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 Mmax=wl2/8=10.154*52/8=31.73KNm

Final condition 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/(c2bd2)) ρ= 0.00305 m=fyd/fcd*0.8=260.87/0.8*11.33=28.78 Mekelle University, Department of Civil Engineering

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June 2008

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 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 Assume s=200mm β= α=67.380 S=2*50.3*260.87*(257-20)(cos67.38+sin67.38)/12.84 S=372.66mm Let’s use Ø8 c/c 200mm

240mm 67.3

0

200mm

Check for initial condition

3-dimentional truss model analysis Mekelle University, Department of Civil Engineering

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June 2008

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 we have modeled the pre-cast beam as 3-D truss whose are pin connected and also we reduced the acting compressive force which is resisted by the concrete section.


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June 2008

2

4 3

1

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 According to EBCS-3,1995 A*fy / γM1 N t,rd ≤ 0.9 Aeff fU/ γM2

γM1 = 1.1 γM2 = 1.25

Since the Top reinforcement bar is ф10 N t,rd

using Fe430

78.5*260.87/1.1=18.62 KN 0.9*78.5*300/1.25=16.96 KN

So take Ntrd = 16.96KN Mekelle University, Department of Civil Engineering

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June 2008

And also the buckling resistance of axial loaded compression 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

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 case 1


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June 2008

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 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
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 and ф8 for the diagonal . 1Ф10

Ф8

2 Ф20


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June 2008

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


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June 2008

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 Mekelle University, Department of Civil Engineering

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June 2008

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 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 Mekelle University, Department of Civil Engineering

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June 2008

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 Mekelle University, Department of Civil Engineering

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June 2008

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


Page 51


June 2008

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 Mekelle University, Department of Civil Engineering

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June 2008

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


Page 53


June 2008

Shear force diagram

Bending moment diagram

Reinforcement design At the 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


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June 2008

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 ing a two way slab distribution on a ing beam is shown in figure 4.5 of EBCS-2, 1995

4.1.1Solid slabs The design loads on beams ing the solid slabs spanning in two directions right angles ing 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 condition of the and Lx is the shortest span of the . The assumed distribution of the load on the ing 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


Page 55


June 2008

Fixed end moment: MFAB= -MF BA=W*S/24(3L2-S2) Span moment: MS =0.75L/2*WL/2-0.076WL2+ (0.75L/2)2*W/2. For the equivalent beam having UDL W| and length L W|

Fixed end moment: MFAB=-MF BA= W|L2/12 Span moment: MS = W|L2/24 Equating the fixed end moment equation W| = 0.914W W*S/24(3L2-S2) = W|L2/12 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 1&5 2,3,4 p6 p7 p8 p9 p10 p11 p12 p13,14,15 p16 p17 p18

type of

βvy

Lx Ly Ly/LX βvxc βvxD βvyc βvyD Pd 3 5 5 1 0.36 0.24 0.36 16.2 1 5 5 1 0.33 0.24 0.33 16.2 cantilever 16.2 cantilever 16.2 cantilever 16.2 cantilever 16.2 cantilever 16.2 cantilever 16.2 cantilever 16.63 cantilever 16.63 cantilever 13.12 cantilever 16.63 cantilever 16.2


Lx vxc vxD vyc 5 27.68 18 27.68 5 25.37 25.37 0.9 14.66 1.5 24.14 1.8 28.45 1 16.9 1.4 21.87 1.4 22.68 1.6 25.78 1.6 25.78 1.7 20.25 1.6 25.78 1.1 17.82

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June 2008

Vertical load on the frames

AXIS-3

AXIS-4


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June 2008

AXIS-A


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June 2008

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


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June 2008

AXIS-E


Page 60


June 2008

AXIS-3


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June 2008

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: =αβγ 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 = C 1 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


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June 2008

β = 1.2 *1.2 =1.84 ≤ 2.5 ok! 2/3 0.691 The parameter, γ, is the behavior factor to 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,

Fi =

( F b − F t )W i h i n

∑W

j

hj

j=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 ing 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.


Page 63


level Ground floor first floor second floor third floor fourth floor roof head room ∑

hi

wihi 1.50 5.30 8.35 11.40 14.45 17.50 20.55

1546.76 12276.74 19082.77 26566.53 35161.19 12704.15 3677.63 111015.8

June 2008

Fi(K*) 13.29 105.45 163.90 228.18 302.00 109.12 31.59

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)e WI=qref Ce(Zi)i 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*222 =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


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June 2008

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
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 Mekelle University, Department of Civil Engineering

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June 2008

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, e Wall zonation: b= 27.75 e=27.75, d <e emin= 2h=32 The zonation is according to EBCS-1 zone d/h=0.425 ≤1 ≥4

A e10 -1 -1

B e10 -0.8 -0.8

D e10 0.8 0.6

E e10 -0.3 -0.3

Determination of external pressures and internal pressure Face external internal D E D E

e10 0.8 -0.3 -0.5 0.8

upper @ 20.3m 0.32 -0.12 -0.2 0.32

Net lower @ 16m upper lower 0.29 0.52 -0.11 -0.44 -0.18 0.47 0.29 -0.4

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


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June 2008

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


Page 67


BLDNG PART

TOTAL WT

wall beam column slab inclined slab landing pvc finishing screed finishing Total

709.69 294.42 218.40 734.59 56.52 19.44 33.19 250.13 2316.37 Xm,Ym

BLDNG PART wall beam column slab inclined slab landing pvc finishing screed finishing Total

June 2008

FIRST FLOOR TOTAL MOMENT WX WY 9876.74 2798.11 3934.78 1001.36 3244.09 1045.84 8986.83 2005.45 1198.14 415.39 464.62 117.13 407.79 170.40 3090.75 677.47 31203.74 8231.15 13.47 3.55

SECOND FLOOR TOTAL WT TOTAL MOMENT WX WY 709.69 9876.74 2798.11 294.42 3934.78 1001.36 187.39 2719.53 876.06 734.59 8986.83 2005.45 56.52 1198.14 415.39 19.44 464.62 117.13 33.19 407.79 170.40 250.13 3090.75 677.47 2285.36 30679.17 8061.37 Xm,Ym


13.42

3.53

Page 68




BLDNG PART wall beam column slab inclined slab

THIRD FLOOR TOTAL WT Wx 732.78 294.42 187.39 744.23 56.52 19.44 40.31 255.30 2330.40 Xm,Ym

June 2008

TOTAL MOMENT Wy 9664.66 3934.78 2719.53 8981.63 1198.14 464.62 422.13 3139.18 30524.65 13.10

FOURTH FLOOR TOTAL WT TOTAL MOMENT Wx Wy 845.74 10937.92 294.42 3934.78 187.39 2719.53 745.32 9053.85 56.52 1198.14 19.44 464.62 40.04 414.53 244.43 2839.08 2433.30 31562.45 Xm,Ym 12.97

2992.85 1001.36 876.06 2053.64 415.39 117.13 157.06 695.70 8309.19 3.57

3060.36 1001.36 876.06 2084.45 415.39 117.13 156.94 690.89 8402.57 3.45

ROOF LEVEL TOTAL WT TOTAL MOMENT Wx Wy 237.21 4578.80 1170.83 212.25 3017.76 713.01 117.12 1904.78 520.01 39.37 793.86 297.03 56.52 1198.14 415.39


Page 69


landing TRUSS+EGA+CHIPWOOD Total

June 2008

19.44 44.05 725.95 Xm,Ym

BLDNG PART beam column slab inclined slab landing Total

HEAD ROOM LEVEL TOTAL WT Wx 52.92 23.42 64.64 28.26 9.72 178.96 Xm,Ym

464.62 577.53 12535.49 17.27

117.13 149.76 3383.17 4.66

TOTAL MOMENT Wy 1138.04 330.90 518.84 148.74 1379.37 407.03 599.07 207.70 232.31 58.56 3867.64 1152.92 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)


Page 70


k1

June 2008

k2

k = I/ L

Kc k3

k2

Kc

k4

k4

k =0.5*k1+k2+k3+k4 Kc

k =0.5*k2+k4 Kc

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

and K = ∑Ktop Kc

for pin ed columns

Calculation of shear center LEVEL Axis Dy Xi DyXi Axis GROUND A 0.000894 0 0 4 B 0.000894 5 0.00447 3 C 0.000894 10 0.00894 2 D 0.000894 15 0.01341 1 E 0.002393 20 0.04785 ∑ F 0.000576 23.54 0.01356 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 A 0.00038 0 0 4 B 0.00038 5 0.0019 3 Mekelle University, Department of Civil Engineering

Dx Yi 0.00299 0 0.003182 5 0.001377 7.7 0.001198 9 0.008746 Ys

DxYi 0 0.01590825 0.01060269 0.01078116 0.0372921 4.26372227

Dx Yi DxYi 0.012172 0 0 0.012976 5 0.06488222 Page 71

Senior project, structural design & cost comparison C D E F G H ∑ 1ST-4th

ROOF

H.ROOM

10 0.0038 0.00038 0.00038 15 0.00571 0.009963 20 0.19925 ∑ 0.002886 23.54 0.06794 0.003373 24.02 0.08101 0.002142 25 0.05355 0.019885 0.41317 Xs 20.7777

Axis A B C D E F G H ∑

June 2008 2 0.004799 7.7 0.03695594 1 0.004908 9 0.0441748 0.034857 0.14601295 Ys 4.18896113

Dy Xi DyXi Axis 0.00038 0 0 4 0.00038 5 0.0019 3 0.00038 10 0.0038 2 0.00038 15 0.00569 1 0.001437 20 0.02875 ∑ 0.000369 23.54 0.00869 0.000429 24.02 0.0103 0.000442 25 0.01105 0.004196 0.07018 Xs 16.7262 Axis Dy Xi DyXi Axis A 0.00028 0 0 4 B 0.00028 5 0.0014 3 C 0.00028 10 0.0028 2 D 0.00028 15 0.0042 1 E 0.001185 20 0.0237 ∑ F 0.000305 23.54 0.00718 G 0.000368 24.02 0.00885 H 0.000334 25 0.00836 ∑ 0.003312 0.05648 Xs 17.0533 Axis Dy Xi DyXi Axis E 0.000268 20 0.00535 3 G 0.000116 24.02 0.0028 2 H 0.000116 25 0.00291 ∑ 0.0005 0.01106 ∑ Xs 22.0981


Dx Yi 0.001574 0 0.001678 5 0.00062 7.7 0.000634 9 0.004505 Ys

DxYi

Dx Yi 0.001212 0 0.001293 5 0.000484 7.7 0.000491 9 0.003479 Ys

DxYi

Dx Yi 0.000206 5 0.00024 7.7 0.000446 Ys

DxYi 0.00103186 0.00184569 0.00287755 6.45086338

0 0.00838865 0.0047703 0.00570805 0.018867 4.18777854

0 0.00646251 0.00372346 0.00441705 0.01460303 4.19713009

Page 72


June 2008

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 FORCE 13.29 105.78 164.42 DDDAXIS VALUE Qi VALUE Qi VALUE Qi 4 0.003 4.543171 0.012 36.9382 0.002 57.44 3 0.0032 4.83463 0.013 39.3783 0.002 61.23 2 0.0014 2.092359 0.005 14.5645 6E-04 22.61 1 0.0012 1.820261 0.005 14.8947 6E-04 23.15 0.0087 0.035 0.005

THIRD 228.27 DVALUE Qi 0.001574 79.74 0.001678 85.007 0.00062 31.39 0.000634 32.135 0.004505

FOURTH 302.12

FLOOR FORCE

D-VALUE 0.00157377 0.00167773 0.00061952 0.00063423 0.00450525

Qi 105.5368 112.508 41.54477 42.53109

ROOF 109.16 DVALUE 0.001212 0.001293 0.000484 0.000491 0.003479

HEADROOM 31.60

Qi D-VALUE Qi AXIS 38.03917 4 40.55121 0.000206372 14.61945 3 15.17151 0.0002397 16.98038 2 15.39791 1 0.000446072

Axes in y-dxn FLOOR FORCE

A B C D E F G H

GROUND 13.29042136 DVALUE Qi 0.0009 1.57154 0.0009 1.57154 0.0009 1.57154 0.0009 1.57154 0.0024 4.206323 0.0006 1.012809 0.0001 0.180896 0.0009 1.604234 0.0076

FIRST 105.7757269 DVALUE Qi 4E-04 2.02353 4E-04 2.02353 4E-04 2.02353 4E-04 2.02353 0.01 52.9951 0.003 15.3529 0.003 17.9401 0.002 11.3935 0.02


SECOND 164.4221758 DVALUE Qi 0.00038 14.87 0.00038 14.87 0.00038 14.87 0.00038 14.87 0.00144 56.32 0.00037 14.47 0.00043 16.81 0.00044 17.33 0.0042

THIRD 228.2715446 DVALUE Qi 0.00038 20.65 0.00038 20.65 0.00038 20.65 0.00038 20.65 0.001437 78.197 0.000369 20.084 0.000429 23.338 0.000442 24.053 0.004196 Page 73


FOURTH 302.1207209 D-VALUE 0.00037955 0.00037955 0.00037955 0.00037955 0.00143729 0.00036915 0.00042895 0.0004421 0.00419571

Qi 27.33061 27.33061 27.33061 27.33061 103.4949 26.58108 30.88771 31.8346

June 2008

ROOF HEADROOM FLOOR 109.1597995 31.59983145 FORCE DVALUE Qi D-VALUE Qi AXIS 0.00028 9.22275 4 0.00028 9.22275 3 0.00028 9.22275 2 0.00028 9.22275 1 0.001185 39.05695 0.00026757 16.89932 0 0.000305 10.05581 0 0.000368 12.13888 0.000116378 7.350258 0 0.000334 11.01716 0.000116378 7.350258 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


Page 74


eccentrities ex actual ey accidental ex ey

June 2008

head room ground first second third fourth roof 0.72 7.22 3.21 3.63 3.76 -0.21 0.49 0.16 0.62 0.64 0.62 0.73 -0.46 0.01 ±1.25 ±1.25 ±1.25 ±1.25 ±1.25 ±1.25 ±0.25 ±0.45 ±0.45 ±0.45 ±0.45 ±0.45 ±0.45 ±0.135

DESIGN ECCENTRICITIES

LEVEL ground first second third fourth roof edx1 1.97 8.47 4.46 4.88 5.01 1.04 edx2 -0.53 5.97 1.96 2.38 2.51 -1.46 edy1 0.61 1.07 1.09 1.07 1.18 -0.01 edy2 -0.29 0.17 0.19 0.17 0.28 -0.91

head room 1.74 -0.76 0.46 -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 yi2) Jy =∑ (Diy xi2) xi = Xi – Xs yi =Ys – Yi


Page 75


June 2008

Ground floor

DI R

AXI S 4

3

2

X

1 A B C D E F G

Y

H

Ys- XsDX(Y DY(X Yi Xi DX DY s-Yi)2 i-Xs)2 4.2 0.054 6 0.003 4 0.7 0.003 0.001 4 2 7 3.4 0.001 0.016 4 4 3 0.001 0.026 4.7 2 9 4 15.01 9E6 04 0.2 10.01 9E6 04 0.09 5.015 9E7 04 0.02 0.015 9E7 04 0 0.00 4.984 2 0.06 6E8.524 04 0.04 1E9.004 04 0.01 9E9.984 04 0.09 0.099 2 0.51 Jx Jy


αy1

αy2

αx,m ax

αy,m ax

αx1 1.01 3

αx2 0.99 4

0.99 8

1.00 1

1.001

0.99 5

1.00 2

1.002

0.99 4

1.00 3

1.003

1.013

1.043 1 1.028 8 1.014 4

0.98 8 0.99 2 0.99 6

1 0.961 7 0.984 2

1

1

1.01 1.00 4 1.00 1 1.00 8

1.01

0.997 0.970 7

1.043 1.029 1.014

1.004 1.001 1.008

Page 76


June 2008

First floor

4

3

2

X

1

4.1 9 0.8 1 3.5 1 4.8 1

E

20.77 8 15.77 8 10.77 8 5.777 7 0.777 7

F

-2.762

G

-3.242

H

-4.222

A B C D

Y

0.012 2

0.213 6

1.06 7

1.01 1

1.06 7

0.013

0.008 5

0.98 6

0.99 8

0.99 8

0.004 8

0.059 2

0.97 8

0.99 6

0.99 6

0.004 9

0.113 6

0.96 9

0.99 5

0.99 5

4E04 4E04 4E04 4E04 0.01 0.00 3 0.00 3 0.00 2

0.1 6 0.0 9 0.0 4 0.0 1 0.0 1 0.0 2 0.0 4 0.0 4 0.394 0.4 2 9 Jx Jy

1.082 4 1.062 5 1.042 7 1.022 9 1.080 7 0.916 9 0.886 1 0.905 8

1.05 8 1.04 4 1.03 1.01 6 1.05 7 0.94 1

1.08 2 1.06 3 1.04 3 1.02 3 1.08 1 0.94 1

0.92 0.93 4

0.92 0.93 4

Second floor 4 3 2 X Y

1 A B

4.19 0.81 3.51 4.81 16.726 11.726

0.0016

0.0276

1.023 1.004

1.023

0.0017

0.0011

0.995 0.999

0.999

0.0006

0.0076

0.992 0.999

0.999

0.0006

0.0147

0.989 0.998

0.998

4E-04 4E-04


0.11 0.05

1.0904 1.04 1.0633 1.028

1.09 1.063 Page 77

Senior project, structural design & cost comparison C D E F G H

4E-04 4E-04 0.001 4E-04 4E-04 4E-04

6.7262 1.7262 -3.274 -6.814 -7.294 -8.274

June 2008

0.02 0 0.02 0.02 0.02 0.03 0.051 0.26 Jx Jy

1.0363 1.0093 0.933 0.9642 0.9555 0.9479

1.016 1.004 0.971 0.984 0.98 0.977

1.036 1.009 0.971 0.984 0.98 0.977

Third floor

X

Y

4.00 3.00 2.00 1.00 A B C D E F G H

4.19 -0.81 -3.51 -4.81

0.00 0.00 0.00 0.00 16.73 11.73 6.73 1.73 -3.27 -6.81 -7.29 -8.27

0.03 0.00 0.01 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.11 0.05 0.02 0.00 0.02 0.02 0.02 0.03 0.05 0.26 Jx Jy


1.02 1.00 0.99 0.99

1.00 1.00 1.00 1.00

1.02 1.00 1.00 1.00 1.10 1.07 1.04 1.01 0.93 0.96 0.95 0.94

1.05 1.03 1.02 1.00 0.96 0.98 0.98 0.97

1.10 1.07 1.04 1.01 0.96 0.98 0.98 0.97

Page 78


June 2008

Fourth floor

X

Y

4.00 3.00 2.00 1.00 A B C D E F G H

4.26 -0.81 -3.51 -4.81

0.00 0.00 0.00 0.00

0.03 0.00 0.01 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

16.73 11.73 6.73 1.73 -3.27 -6.81 -7.29 -8.27

1.03 0.99 0.99 0.99

1.01 1.00 1.00 1.00

0.11 0.05 0.02 0.00 0.02 0.02 0.02 0.03 0.05 0.26 Jx Jy

1.03 1.00 1.00 1.00 1.10 1.07 1.04 1.01 0.93 0.96 0.95 0.94

1.05 1.04 1.02 1.01 0.96 0.98 0.98 0.97

1.10 1.07 1.04 1.01 0.96 0.98 0.98 0.97

Roof 4 3 2 1

X

Y

A B C D E F G H

4.2 -0.8 -3.5 -4.8

0.0012 0.0013 0.0005 0.0005 17.053 12.053 7.0533 2.0533 -2.947 -6.487 -6.967 -7.947

0.0214 0.0008 0.0059 0.0113 3E-04 3E-04 3E-04 3E-04 0.001 3E-04 4E-04 3E-04

0.08 0.04 0.01 0 0.01 0.01 0.02 0.02 0.0394 0.2 Jx Jy


1 1 1 1

0.981 1.004 1.006 1.009

1 1.004 1.006 1.009 1.0207 1.0146 1.0086 1.0025 0.9848 0.9914 0.9889 0.9885

0.971 0.979 0.988 0.996 1.021 1.012 1.016 1.016

Page 79

1.021 1.015 1.009 1.002 1.021 1.012 1.016 1.016


June 2008

Head room

3

X

Y

2

0.000 2

1.4 5 1.2 5

0.000 2

E

2.098 1

G

-1.922

H

-2.902

0.0004

1.0 4

0.96 1

1.04

0.0004

0.9 6

1.03 9

1.03 9

3E04 1E04 1E04

0 0

0.0008 Jx Jy

0 0

1.287 0.885 6 0.827 3

0.87 4

1.28 7

1.05 1.07 6

1.05 1.07 6

Corrected shear forces for torsion Corrected shear forces are given by = αmax * Q LEVEL GROUND Axis 4 3 2 1 A B C D E F G H

αmax*Qi 4.60 4.84 2.10 1.83 1.64 1.62 1.59 1.57 4.25 1.02 0.18 1.62

FIRST

SECOND

αmax αmax*Qi αmax αmax*Qi 1.07 39.42 1.02 58.76 1.00 39.29 1.00 61.18 1.00 14.51 1.00 22.58 1.00 14.82 1.00 23.10 1.08 2.19 1.09 16.22 1.06 2.15 1.06 15.82 1.04 2.11 1.04 15.41 1.02 2.07 1.01 15.01 1.08 57.27 0.97 54.67 0.94 14.45 0.98 14.24 0.92 16.50 0.98 16.48 0.93 10.64 0.98 16.93


THIRD αmax αmax*Qi 1.02 81.54 1.00 84.94 1.00 31.35 1.00 32.08 1.10 22.69 1.07 22.08 1.04 21.47 1.01 20.86 0.96 75.40 0.98 19.70 0.98 22.78 0.97 23.39

Page 80


FOURTH

ROOF

αmax αmax*Qi Qi αmax αmax*Qi Qi 1.03 108.20 1.00 38.03 1.00 112.37 1.00 40.71 1.00 41.46 1.01 15.27 1.00 42.41 1.01 15.54 1.10 30.09 1.02 9.41 1.07 29.27 1.01 9.36 1.04 28.44 1.01 9.30 1.01 27.62 1.00 9.25 0.96 99.61 1.02 39.89 0.98 26.05 1.01 10.18 0.98 30.12 1.02 12.33 0.97 30.91 1.02 11.20

June 2008

HEAD ROOM αmax

αmax*Qi

1.04 1.04

15.21 17.64

1.29 1.05 1.08


LEVEL Axis 4 3 2 1

A B C D 21.75 E F 7.72 G 7.91 H

Page 81


June 2008

Earth quake loading on frames

AXIS-A


Page 82


June 2008

AXIS-E


Page 83


June 2008

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


Page 84


June 2008

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


Page 85


June 2008

5. DESIG* OF BEAMS A*D COLUM*S 5.1 Beam design Beams are flexural 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 +

2

(C1 − 4 M / C 2 bd 2 )

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=0.8ρbd2 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


Page 86


June 2008

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 moment 22.42 12.4 44.97 173.14 102.74 174.08 128.5 71.05 14.31 141.28 96.44 102.44 66.6

LOCATION TTBeam TTBeam TTBeam 1st &2nd 1st &2nd 1st &2nd 3rd&4th 3rd&4th 3rd&4th 3rd&4th Gbeam Gbeam Gbeam

b 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25

AXIS-A d Km KS AS1 0.307 30.85 4.06 296.499 0.307 22.94 3.98 Asmin 0.307 43.69 4.252 622.8418 0.446 59.01 2410.72 0.446 45.45 4.296 989.6212 0.455 58.00 2410.72 0.446 50.83 4.425 1274.916 0.455 37.05 4.12 643.3538 0.455 16.63 3.963 124.6385 0.455 52.25 4.47 1387.96 0.355 55.33 1285.81 0.355 57.02 1275.096 0.355 45.98 4.306 807.8299


Ф(As1 ) 2Ф12 2Ф12 4Ф12+1Ф16 4Ф24+3Ф16 5Ф16 4Ф24+3Ф16 4Ф20 3Ф16+2Ф20 2Ф12 4Ф20+1Ф14 4Ф20 4Ф20 4Ф16

Page 87


June 2008

AXIS-B d Km KS As1 Ф(As1 ) 0.307 26.99 4.015 224.5523 2Ф12 0.307 14.80 min 153.5 2Ф12 0.307 28.90 4.039 258.917 2Ф14 0.445 60.18 4.27 1720.282 4Ф24 0.445 53.34 4.3 1361.216 3Ф24 0.445 64.42 2707.4 6Ф24 0.445 56.32 4.52 1595.204 3Ф24&1Ф20 0.445 42.68 4.22 855.0004 2Ф20 +2Ф12 0.445 56.58 1595.204 3Ф24&1Ф20 0.357 56.22 4.52 1275.096 4Ф20 0.357 56.59 1275.096 4Ф20 0.357 46.61 4.32 837.7412 2Ф20 +2Ф12

moment 17.17 5.16 19.68 179.28 140.87 205.44 157.05 90.16 158.5 100.71 102.03 69.23

LOCATION TTBeam TTBeam TTBeam 1st &2nd 1st &2nd 1st &2nd 3rd&4th 3rd&4th 3rd&4th Gbeam Gbeam Gbeam

b 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25

moment 22.15 9.89 16.01 177.98 114.32 35.44 182.2 166.48 95.32 150.1 115.1 111.28 61.8

LOCATION TTBeam TTBeam TTBeam 1st&2nd 1st&2nd 1st&2nd 1st&2nd 3rd&4th 3rd&4th 3rd&4th Gbeam Gbeam Gbeam

AXIS -C b d Km KS AS1 Ф(As1 ) 0.25 0.307 30.66 3.994 288.1664 3Ф12 0.25 0.307 20.49 3.97 127.8935 2Ф12 0.25 0.307 26.07 4 208.5993 2Ф12 0.25 0.446 59.82 2416.4 5Ф24+1Ф16 0.25 0.446 47.95 4.36 1117.568 4Ф20 0.25 0.455 26.17 4.01 312.3393 2Ф16 0.25 0.455 59.33 2241 4Ф24+3Ф16 0.25 0.446 57.86 1941.5 3Ф24+3Ф16 0.25 0.446 43.78 4.26 910.4556 2Ф20+2Ф14 0.25 0.455 53.85 4.53 1494.402 2Ф24+3Ф16 0.25 0.355 60.44 1550 3Ф24+1Ф20 0.25 0.355 59.43 1550 3Ф24+1Ф20 0.25 0.355 44.29 4.19 729.4141 4Ф16

moment 24.86 12.74 14.44 166.42 96.08 157.49 165.87 105.43

LOCATION TTBeam TTBeam TTBeam 4th&3rd 4th&3rd 4th&3rd 1st&2nd 1st&2nd

b 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25

AXIS-D d Km KS AS1 0.307 32.48 4.07 329.5772 0.307 23.25 3.98 165.1635 0.307 24.76 3.988 187.5789 0.446 57.85 1941.5 0.446 43.96 4.26 917.7148 0.455 55.16 1595.204 0.446 57.75 1941.5 0.446 46.04 4.31 1018.841


Ф(As1 ) 3Ф14 2Ф12 2Ф12 3Ф24+3Ф16 2Ф20+2Ф14 3Ф24&1Ф20 3Ф24+3Ф16 4Ф20 Page 88

Senior project, structural design & cost comparison 80.93 145.5 103.85 99.45 74.01

moment 32.22 6.42 31.25 21.98 13.42 10.41 12.46 3.9 157.15 112.47 121.7 47.81 130.59 81.82 52.57 179.08 120.73 156.16 101.81 146.86 149.72 150.8 100.84 59.44 97.73 85.69 119.53 106.97 130.62

1st&2nd 1st&2nd Gbeam Gbeam Gbeam

LOCATION HEAD ROOM HEAD ROOM TTBeam TTBeam TTBeam TTBeam TTBeam TTBeam 4th&3rd 4th&3rd 4th&3rd 4th&3rd 4th&3rd 4th&3rd 4th&3rd 1st&2nd 1st&2nd 1st&2nd 1st&2nd 1st&2nd 1st&2nd 1st&2nd Gbeam Gbeam Gbeam Gbeam Gbeam Gbeam Gbeam

0.25 0.25 0.25 0.25 0.25

b 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25

0.455 0.455 0.355 0.355 0.355

39.54 53.02 57.41 56.18 48.47

AXIS-E d Km 0.307 36.98 0.307 16.51 0.307 36.42 0.307 30.54 0.307 23.87 0.307 21.02 0.307 23.00 0.307 12.87 0.446 56.22 0.446 47.56 0.446 49.47 0.455 30.39 0.455 50.23 0.455 39.76 0.455 31.87 0.446 60.01 0.446 49.27 0.446 56.04 0.446 45.25 0.446 54.34 0.446 54.87 0.446 55.07 0.335 59.95 0.335 46.03 0.335 59.02 0.335 55.27 0.335 65.27 0.355 58.27 0.355 64.39


June 2008 4.16 4.51

4.37

739.9314 1442.209 1398.54 1398.54 911.0527

KS AS1 4.12 432.3987 Asmin 4.11 418.3632 4.06 290.6801 Asmin Asmin 3.97 161.1277 Asmin 1744.84 4.349 1096.709 4.396 1199.536 4.04 424.5108 4.415 1267.154 4.166 749.1475 4.054 468.3929 1754.68 4.392 1188.893 1744.84 4.29 979.2935 1442.209 1717.45 1717.45 4.275 1286.839 4.09 725.7003 4.28 1248.61 4.2 1074.322 4.386 1564.951 4.32 1301.719 4.43 1629.99

2Ф16+2Ф20 4Ф20+1Ф16 3Ф24 3Ф24 2Ф14+2Ф20

Ф(As1 ) 3Ф14 2Ф12 4Ф12 2Ф14 2Ф12 2Ф12 2Ф12 2Ф12 4Ф24 2Ф24+1Ф16 2Ф24+2Ф14 3Ф14 2Ф24+2Ф16 2Ф20+1Ф12 2Ф14+1Ф16 4Ф24 2Ф24+2Ф14 4Ф24 2Ф20+2Ф16 4Ф20+1Ф16 4Ф24 4Ф24 3Ф20 2Ф20 3Ф20 3Ф20 2Ф24+2Ф14 2Ф20+3Ф14 3Ф20+1Ф24

Page 89

Senior project, structural design & cost comparison AXIS-H d Km KS AS1 0.307 39.16 4.159 489.5969 0.307 22.85 Asmin 0.307 34.45 4.092 372.8119 0.446 55.16 1717.45 0.446 48.51 4.373 1147.471 0.446 40.91 4.18 779.9074 0.446 59.01 2412.33 0.446 55.67 1744.84 0.446 44.09 4.265 924.3383 0.355 56.34 1394.7 0.355 52.42 4.481 1092.607 0.355 51.46 4.435 1042.287

June 2008

moment 36.14 12.3 27.97 151.31 117.03 83.215 173.14 154.14 96.66 100 86.56 83.43

LOCATION TTBeam TTBeam TTBeam 4th&3rd 4th&3rd 4th&3rd 1st&2nd 1st&2nd 1st&2nd Gbeam Gbeam Gbeam

b 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25

moment 186.912 184.18 150.25 174 176.859 180.71 92.19 81.38 71.86 85.69 104.94 155.98 148.96 132.93 134.47 132.34 137.81 82.511 70.31 48.76 67.357 73.61 42.44 37.65

LOCATION 1st&2nd 1st&2nd 1st&2nd 1st&2nd 1st&2nd 1st&2nd 1st&2nd 1st&2nd 1st&2nd 1st&2nd 1st&2nd 3rd&4th 3rd&4th 3rd&4th 3rd&4th 3rd&4th 3rd&4th 3rd&4th 3rd&4th 3rd&4th 3rd&4th 3rd&4th TTBeam TTBeam

AXIS-4 b d Km KS AS1 Ф(As1 ) 0.25 0.446 61.31 4.51 2341 4Ф24+3Ф16 0.25 0.446 60.86 2341 4Ф24+3Ф16 0.25 0.455 53.88 4.53 1495.896 3Ф24+1Ф14 0.25 0.446 59.15 4.51 1759.507 4Ф24 0.25 0.455 58.46 4.51 1753.042 4Ф24 0.25 0.455 59.09 1754.68 4Ф24 0.25 0.455 42.20 4.25 861.1154 2Ф24 0.25 0.455 39.65 4.2 751.2 4Ф16 0.25 0.455 37.26 4.15 655.4264 3Ф14+1Ф16 0.25 0.455 40.69 4.22 794.7512 4Ф16 0.25 0.455 45.03 4.31 994.047 5Ф16 0.25 0.446 56.01 4.52 1580.784 3Ф24+2Ф14 0.25 0.446 54.73 1717.45 4Ф24 0.25 0.455 50.68 4.427 1293.365 2Ф24+2Ф16 0.25 0.455 50.97 4.44 1312.191 3Ф20+2Ф16 0.25 0.455 50.57 4.42 1285.589 4Ф20 0.25 0.455 51.60 4.45 1347.812 2Ф24+3Ф14 0.25 0.455 39.93 4.21 763.4534 4Ф16 0.25 0.455 36.86 4.14 639.7437 1Ф16+3Ф14 0.25 0.455 30.69 4.01 429.731 3Ф14 0.25 0.455 36.08 4.13 611.3943 2Ф16+2Ф12 0.25 0.455 37.71 4.16 673.0057 2Ф12+3Ф14 0.25 0.307 42.44 4.25 587.5244 3Ф12+2Ф14 0.25 0.307 39.97 4.19 513.855 3Ф16


Ф(As1 ) 3Ф16 2Ф12 2Ф16 4Ф24 3Ф20+2Ф12 2Ф20+1Ф14 4Ф24+2Ф20 4Ф24 3Ф20 3Ф24 2Ф24+1Ф16 2Ф20+3Ф14

Page 90

Senior project, structural design & cost comparison 33.94 25.63 17.05 25.89 17.73 13.94 9.27 8.61 5.69 97.3 78.96 81.53 83.34 81.92 22.74 75.44 66.48 68.82 69.32 73.37

moment 21.36 11.92 158.02 177.72 164.47 117.51 104.24 71.82 122.93 122.06 95.75 moment 30.11 14.5 11.27 28.93 32.82

TTBeam TTBeam TTBeam TTBeam TTBeam TTBeam TTBeam TTBeam TTBeam Gbeam Gbeam Gbeam Gbeam Gbeam Gbeam Gbeam Gbeam Gbeam Gbeam Gbeam

0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25

LOCATION TTBeam TTBeam 1st&2nd 1st&2nd 1st&2nd 3rd&4th 3rd&4th

b 0.25 0.25 0.25 0.25 0.25 0.25 0.25

3rd&4th Gbeam Gbeam Gbeam

0.25 0.25 0.25 0.25

LOCATION Head Room Head Room TTBeam TTBeam TTBeam

b 0.25 0.25 0.25 0.25 0.25

0.307 0.307 0.307 0.307 0.307 0.307 0.307 0.307 0.307 0.357 0.357 0.357 0.357 0.357 0.357 0.357 0.357 0.357 0.357 0.357

37.95 32.98 26.90 33.15 27.43 24.32 19.83 19.12 15.54 55.26 49.78 50.58 51.14 50.71 26.72 48.66 45.68 46.47 46.64 47.99

4.15 4.13 4.014 4.082 min min min min min 4.598 4.405 4.425 4.43 4.425 4 4.37 4.29 4.33 4.34 4.34

June 2008 458.798 344.7945 222.9274 344.2442

1253.18 974.2824 1010.561 1034.163 1015.395 254.7899 923.4532 798.8773 834.7076 842.7137 891.949

3Ф16 2Ф16 2Ф12 2Ф12+1Ф14 2Ф12 2Ф12 2Ф12 2Ф12 2Ф12 4Ф20 2Ф20+2Ф16 2Ф20+2Ф16 2Ф20+2Ф16 2Ф20+2Ф16 2Ф14 3Ф20 4Ф16 2Ф20+2Ф12 2Ф20+2Ф12 2Ф24

AXIS-1 d Km KS As1 Ф(As1 ) 0.307 30.11 3.97 276.2189 2Ф14 0.307 22.49 3.96 153.7564 2Ф12 0.455 55.26 4.52 1748 4Ф24 0.455 58.60 1857 5Ф20+2Ф16 0.455 56.37 4.52 1895 5Ф20+2Ф16 0.455 47.65 4.39 1133.778 3Ф20+2Ф12 0.455 44.88 4.282 981.0015 2Ф24+1Ф12 0.455 37.25 4.14 653.4831 0.355 62.46 4.63 1817 0.355 62.24 1817 0.355 55.13 4.57 1232.613 AXIS-2 d Km KS As1 0.307 35.75 4.11 403.1013 0.307 24.81 3.97 187.5081 0.307 21.87 3.96 145.372 0.307 35.04 4.1 386.3616 0.307 37.32 4.15 443.658


3Φ14+2Φ12 4Ф24 4Ф24 4Ф20 Ф(As1 ) 2Ф16 2Ф12 2Ф12 2Ф16 4Ф12 Page 91

Senior project, structural design & cost comparison 177.03 171.09 121.87 115.06 103.82 57.36 118.84 116.89 87.01

moment 15.34 42.74 14.28 22.64 16.53 17.64 27.43 38.55 199.64 178.245 182.77 182.33 148.37 193.54 117.14 87.28 75.44 94.43 72.55 144.86 154.125 154.971 142.89 145.66 107.87 76.46 77.375 77.025 75.474

1st&2nd 1st&2nd 1st&2nd 3rd&4th 3rd&4th 3rd&4th Gbeam Gbeam Gbeam

LOCATION Head Room Head Room TTBeam TTBeam TTBeam TTBeam TTBeam TTBeam 1st&2nd 1st&2nd 1st&2nd 1st&2nd 1st&2nd 1st&2nd 1st&2nd 1st&2nd 1st&2nd 1st&2nd 1st&2nd 3rd&4th 3rd&4th 3rd&4th 3rd&4th 3rd&4th 3rd&4th 3rd&4th 3rd&4th 3rd&4th 3rd&4th

58.48 57.50 48.53 47.15 44.79 33.29 61.42 60.91 52.55

June 2008

0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25

0.455 0.455 0.455 0.455 0.455 0.455 0.355 0.355 0.355

b 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25

AXIS-3 d Km KS As1 Ф(As1 ) 0.307 25.52 3.99 199.37 2Ф12 0.307 42.59 4.23 588.8932 2Ф20 0.307 24.62 4.09 190.245 2Ф12 0.307 31.00 4.434 326.9894 3Ф12 0.307 26.49 4.02 216.4515 2Ф12 0.307 27.36 4.03 231.5609 2Ф14 0.307 34.12 4.09 365.4355 2Ф16 0.307 40.45 4.19 526.1384 2Ф12 +2Ф14 0.446 63.36 4.51 2569 5Ф24+2Ф16 0.446 59.87 4.51 2170 4Ф24+2Ф16 0.446 60.62 2241 4Ф24+3Ф16 0.446 60.55 4.51 2241 4Ф24+3Ф16 0.455 53.54 4.53 1477.178 3Ф24+1Ф14 0.455 61.15 2415.64 4Ф24+2Ф20 0.455 47.57 4.35 1119.91 3Ф20+2Ф12 0.455 41.07 4.2 805.6615 2Ф20+2Ф12 0.455 38.18 4.14 686.4211 3Ф14+2Ф12 0.455 42.71 4.23 877.8877 4Ф16+1Ф12 0.455 37.44 4.15 661.7198 3Ф14+2Ф12 0.446 53.97 4.53 1471.336 2Ф24+2Ф16 0.446 55.67 4.5 1555.073 3Ф24+2Ф12 0.446 55.82 4.51 1567.083 3Ф24+2Ф12 0.446 53.60 4.53 1451.327 4Ф20+1Ф16 0.446 54.12 4.47 1459.866 3Ф24+1Ф12 0.446 46.57 4.28 1035.165 2Ф20+2Ф16 0.455 38.44 4.18 702.4237 2Ф16+2Ф14 0.455 38.67 4.18 710.8297 2Ф16+2Ф14 0.455 38.58 4.18 707.6143 2Ф16+2Ф14 0.455 38.19 4.17 691.7068 2Ф16+2Ф14


4.7 4.41 4.38 4.28 4.05 4.65 4.51

1857 2412.33 1181.202 1107.611 976.5925 510.567 1712 1550 1105.395

5Ф20+2Ф16 4Ф24+2Ф20 2Ф24+2Ф14 2Ф24+2Ф12 2Ф20+2Ф16 2Ф16+1Ф12 3Ф24+2Ф16 3Ф24+1Ф20 2Ф24+2Ф12

Page 92

Senior project, structural design & cost comparison 48.39 95.54 93.45 92.83 114.01 94.49 100.71 68.65 56.89 57.4 55.78 61.71

3rd&4th Gbeam Gbeam Gbeam Gbeam Gbeam Gbeam Gbeam Gbeam Gbeam Gbeam Gbeam

0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25

0.455 0.355 0.355 0.355 0.355 0.355 0.355 0.355 0.355 0.355 0.355 0.355

Inclined beam LOCATION AS Ф(AS) Gbeam 1332.63 3Ф20+2Ф16 Gbeam 1171.31 3Ф20+2Ф12 Gbeam 964.61 2Ф20+2Ф16 Gbeam 1240.9 4Ф20 Gbeam 924.75 2Ф20+2Ф14 1st&2nd 1645.39 3Ф24+2Ф14 1st&2nd 1194.29 2Ф24+2Ф14 1st&2nd 1201.26 2Ф24+2Ф14 1st&2nd 1409.64 4Ф20+1Ф14 1st&2nd 972.08 2Ф24+1Ф14 3rd&4th 796.81 3Ф14+3Ф12 3rd&4th 668.66 3Ф14+2Ф12 3rd&4th 639.49 3Ф14+2Ф12 3rd&4th 3rd&4th TTBeam TTBeam TTBeam TTBeam Head Room Head Room Head Room

696.39 525.17 157.5 187.61 159.75 157.5 157.5 157.5 157.5

30.58 55.07 54.46 54.28 60.16 54.76 56.54 46.68 42.49 42.68 42.08 44.26

June 2008 4.01 4.52 4.52 4.52

426.4701 1253 1239 1230 1550 1252 1416 845.0718 684.2825 690.4169 669.36 749.2115

3Ф14 4Ф20 4Ф20 4Ф20 3Ф24+1Ф20 4Ф20 3Ф24+1Ф12 2Ф20+2Ф12 3Ф14+2Ф12 2Ф14+2Ф16 3Ф14+2Ф12 3Ф16+1Ф14

landing beams LOCATION AS G-floor 2179.44 G-floor 1898.36 G-floor 2221.63 1st&2nd 1560.77 1st&2nd 1357.31 1st&2nd 1728.52 3rd&4th 790.18 3rd&4th 615.56 3rd&4th 915.1 roof 356.15 roof 225 roof 225

Ф(AS) 4Ф24+2Ф16 3Ф24+3Ф16 4Ф24+3Ф14 3Ф24+2Ф12 3Ф24 3Ф24+2Ф16 4Ф16 4Ф14 3Ф16+2Ф14 2Ф16 2Ф12 2Ф12

4.52 4.52 4.37 4.27 4.27 4.26 4.31

2Ф14+2Ф16 2Ф14+2Ф12 2Ф12 2Ф12 2Ф12 2Ф12 2Ф12 2Ф12 2Ф12


Page 93


June 2008

5.1.2 Pre-cast slab beams moment LOCATION 15.41 TTBeam 49.82 170.54 66.22 156.53 197.12 129.72 130.95 177.07 88.64 93.91 85.39

moment 10.83 23.12 194.49 168.55 245.89 178.456 198.58 154.49 84.374 92.296 89.94

moment 6.52 18.94 196.44 174.54 228.84 161.03 146.9 189.22

TTBeam 1st&2nd 1st &2nd 1st &2nd 1st &2nd 3rd&4th 3rd&4th 3rd&4th Gbeam Gbeam Gbeam

LOCATION TTBeam TTBeam 1st&2nd 1st &2nd 1st &2nd 3rd &4th 3rd&4th 3rd&4th Gbeam Gbeam Gbeam

LOCATION TTBeam TTBeam 1st&2nd 1st&2nd 1st&2nd 3rd&4th 3rd&4th 3rd&4th

AXIS-A b d Km KS AS1 Ф(As1 ) 0.25 0.307 25.57 4.007 201.1331 2Ø12 0.25 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3

b 0.25 0.25 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3

0.307 0.455 0.455 0.455 0.455 0.455 0.455 0.455 0.355 0.355 0.355

45.98 4.31 699.4274 2Ø16+2Ø14 52.40 1829.2 3Ø24+2Ø20 32.65 4.0765 593.2875 3Ø16 50.20 1599.4 5Ø20 56.34 2396.13 4Ø24+2Ø20 45.70 45.92 4.308 1239.852 4Ø20 53.39 2014.8 2Ø16+3Ø24+2Ø14 48.42 4.36 1088.649 3Ø14+2Ø20 49.84 1168.59 3Ø20+2Ø12 47.52

d 0.307 0.307 0.455 0.455 0.455 0.455 0.455 0.455 0.355 0.355 0.355

AXIS-B Km KS AS1 21.44 3.966 139.9081 31.32 4.067 306.2835 55.96 52.09 1829.2 62.92 3260.34 53.60 2086.4 56.55 2396.13 49.87 1654.94 47.24 4.341 1031.74 49.41 1158.51 48.77

b 0.25 0.25 0.3 0.3 0.3 0.3 0.3 0.3

Ф(As1 ) 2Ø12 2Ø14 4Ø24+2Ø20 3Ø24+2Ø20 5Ø24+5Ø16 3Ø24+2Ø16+3Ø14 4Ø24+2Ø20 3Ø24+2Ø14 3Ø14+2Ø20 3Ø20+2Ø12

AXIS -C d Km KS AS1 0.307 16.63 min ####### 0.307 28.35 4.032 248.7494 0.455 56.24 2371.5 0.455 53.01 1958.3 0.446 61.93 3060.63 0.455 50.92 1744.8 0.455 48.63 1427.68 0.455 55.20 2222.2


Ф(As1 ) 2Ø12 1Ø14+1Ø12 4Ø24+2Ø20 3Ø24+2Ø20 4Ø24+4Ø20 3Ø24+3Ø14 4Ø20+2Ø12 4Ø24+3Ø14 Page 94

Senior project, structural design & cost comparison 83.01 Gbeam 91.4 Gbeam 92.33 Gbeam

moment 4.67 17.43 165.37 143.17 179.26 196.46 171.23 218.24 81.81 91.12 94.02

moment 30.99 27.88 28.95 18.28 1.22 8.45 14.04 2.71 10.07 158.53 123.65 96.97 83.29 139.69 36.74 87.24 181.92 135.14 166.35 111.05 110.87

LOCATION TTBeam TTBeam 4th&3rd 4th&3rd 4th&3rd 1st&2nd 1st&2nd 1st&2nd Gbeam Gbeam Gbeam

LOCATION HEAD ROOM HEAD ROOM TTBeam TTBeam TTBeam TTBeam TTBeam TTBeam TTBeam 4th&3rd 4th&3rd 4th&3rd 4th&3rd 4th&3rd 4th&3rd 4th&3rd 1st&2nd 1st&2nd 1st&2nd 1st&2nd 1st&2nd

0.3 0.3 0.3

b 0.25 0.25 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3

b 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3

June 2008

0.355 46.86 4.324 0.355 49.17 0.355 49.42

d 0.307 0.307 0.455 0.455 0.455 0.455 0.455 0.455 0.355 0.355 0.355

d 0.307 0.307 0.307 0.307 0.307 0.307 0.307 0.307 0.307 0.455 0.455 0.455 0.455 0.455 0.455 0.455 0.455 0.455 0.455 0.455 0.455

1011.085 2Ø20+2Ø16 1180.58 3Ø16+2Ø20 1195.44 3Ø16+2Ø20

AXIS-D Km KS AS1 14.08 min 153 27.20 4.018 228.1229 51.60 1791.79 48.01 4.36 1371.915 53.72 2086.4 56.24 2371.5 52.51 1901.71 59.28 2765.05 46.52 4.323 996.2384 49.09 1180.58 49.87 1205.57 AXIS-E Km 36.27 34.40 35.05 27.85 7.20 18.94 24.41 10.72 20.67 50.52 44.62 39.51 36.62 47.43 24.32 37.48 54.12 46.65 51.75 42.29 42.25

KS 4.113 4.094 4.101 4.026 min min 3.986 min 3.961


4.276 4.162 4.114 4.346 3.986 4.141 4.326 4.463 4.217 4.216

Ф(As1 ) 2Φ12 2Ø12 3Ø24+3Ø14 2Ø24+3Ø14 3Ø24+2Ø16+3Ø14 4Ø24+2Ø20 4Ø24+1Ø12 4Ø24+3Ø20 2Ø20+3Ø14 3Ø16+2Ø20 3Ø16+2Ø20

AS1 415.1852 371.7939 386.723 239.724 153.5 153.5 182.2913 153 129.926 1654.94 1162.038 887.0091 753.088 1334.27 321.8585 793.9799 2086.4 1284.87 1631.692 1029.226 1027.314

Ф(As1 ) 2Ø14+1Ø12 2Ø16 2Ø16 1Ø12+1Ø14 2Ø12 2Ø12 2Ø12 2Ø12 2Ø12 3Ø24+2Ø14 3Ø20+2Ø12 3Ø16+2Ø14 5Ø14 3Ø20+2Ø16 3Ø12 4Ø16 3Ø24+2Ø16+3Ø14 3Ø24 3Ø24+2Ø14 2Ø20+2Ø16 2Ø20+2Ø16 Page 95

Senior project, structural design & cost comparison 173.46 112.42 47.2 98.49 107.95 108.6 136.06

moment 35.57 26.93 123.6 107.526 144.544 156.45 122.3 164.56 100.8 83.79 89.25

moment 144.44 104.14 60.13 118.76 100.73 120.93 97.79 124.1 93.55 125.01 131.28 140.096 116.75 81.84 91.44 62.82 30.14

1st&2nd Gbeam Gbeam Gbeam Gbeam Gbeam Gbeam

LOCATION TTBeam TTBeam 4th&3rd 4th&3rd 4th&3rd 1st&2nd 1st&2nd 1st&2nd Gbeam Gbeam Gbeam

LOCATION 1st&2nd 1st&2nd 1st&2nd 1st&2nd 1st&2nd 1st&2nd 1st&2nd 1st&2nd 1st&2nd 1st&2nd 1st&2nd 1st&2nd 3rd&4th 3rd&4th 3rd&4th 3rd&4th 3rd&4th

0.3 0.3 0.3 0.3 0.3 0.3 0.3

0.455 0.455 0.355 0.355 0.355 0.355 0.355

b 0.25 0.25 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3

AXIS-H d Km 0.307 38.85 0.307 33.81 0.455 44.61 0.455 41.61 0.455 48.24 0.455 50.19 0.455 44.38 0.455 51.47 0.355 51.63 0.355 47.08 0.355 48.59

b 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25

AXIS-4 d Km 0.455 52.83 0.455 44.86 0.455 34.09 0.455 47.90 0.455 44.12 0.455 48.34 0.455 43.47 0.455 48.97 0.455 42.51 0.455 49.15 0.455 50.36 0.455 52.03 0.455 47.49 0.455 39.77 0.455 42.03 0.455 34.84 0.455 24.13

June 2008

52.85 4.498 1714.776 4Ø24 42.55 4.224 1043.653 2Ø20+2Ø16 35.33 4.103 545.5256 2Ø16+1Ø14 51.04 4.436 1230.709 4Ø20 53.43 4.5315 1377.959 4Ø20+1Ø14 53.60 4.54 1388.856 4Ø20+1Ø14 59.99 1926.9 4Ø24+1Ø12

KS AS1 4.151 480.9481 4.088 358.5988 4.275 1161.297 4.202 993.0203 4.36 1385.081 1599.4 1161.297 1631.692 4.45 1263.549 4.334 1022.946 4.375 1099.912

Ф(As1 ) 2Ø16+1Ø12 2Ø16 3Ø20+2Ø12 5Ø16 4Ø20+1Ø14 5Ø20 3Ø20+2Ø12 3Ø24+2Ø14 2Ø24+2Ø16 2Ø20+2Ø16 2Ф20+3Ф14

KS

Ф(As1 ) 4Ø20+2Ø16 5Ø16 2Ø16+1Ø14 3Ø20+2Ø12 3Ø20 3Ø20+2Ø12 3Ø20 4Ø20 3Ø16+2Ø14 4Ø20 3Ø24 3Ø24+2Ø12 2Ø24+2Ø12 2Ø20+1Ø14 2Ø20+2Ø12 3Ø16 2Ø14

4.304 4.091 4.353 4.263 4.36 4.248 4.223

4.35 4.16 4.211 4.098 3.984


AS1 1604.53 985.0957 540.6414 1136.181 943.7626 1158.802 912.9932 1206.11 868.2674 1214.93 1340 1516.28 1116.181 748.2514 846.2722 565.7942 263.9072

Page 96

Senior project, structural design & cost comparison 83.27 59.01 93.14 33.75 64.06 66.05 91.94 95.02 39.71 17.62 39.53 14.15 35.45 9.23 24.97 18.67 8.32 22.34 4.23 96.69 75.31 81.12 68.79 83.48 70.06 83.07 76.76 80.23 99.24

moment 2.74 13.23 22.64 175.83 142.2 185.74 79.896 87.07 108.94

3rd&4th 3rd&4th 3rd&4th 3rd&4th 3rd&4th 3rd&4th 3rd&4th 3rd&4th TTBeam TTBeam TTBeam TTBeam TTBeam TTBeam TTBeam TTBeam TTBeam TTBeam TTBeam Gbeam Gbeam Gbeam Gbeam Gbeam Gbeam Gbeam Gbeam Gbeam Gbeam

0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25

0.455 0.455 0.455 0.455 0.455 0.455 0.455 0.455 0.307 0.307 0.307 0.307 0.307 0.307 0.307 0.307 0.307 0.307 0.307 0.357 0.357 0.357 0.357 0.357 0.357 0.357 0.357 0.357 0.357

40.11 33.77 42.42 25.54 35.18 35.72 42.15 42.85 41.05 27.35 40.96 24.51 38.79 19.79 32.55 28.15 18.79 30.79 13.40 55.09 48.62 50.46 46.46 51.19 46.89 51.06 49.08 50.18 55.81

LOCATION TTBeam TTBeam TTBeam 1st&2nd 1st&2nd 1st&2nd 3rd&4th 3rd&4th 3rd&4th

b 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25

AXIS-1 d Km 0.307 10.78 0.307 23.70 0.307 31.00 0.455 58.29 0.455 52.42 0.446 61.12 0.455 39.29 0.455 41.02 0.455 45.88

June 2008 4.172 4.088 4.22 3.994 4.101 4.107 4.214 4.231 4.19 4.019 4.189 3.987 4.15 3.955 4.078 4.032 min 4.058 min 4.593 4.379 4.434 4.32 4.456 4.332 4.452 4.392 4.455 4.614

763.5218 530.1822 863.8479 296.2582 577.3847 596.192 851.5058 883.5816 541.9704 230.667 539.3849 183.7656 479.2101 118.9077 331.6862 245.2034 153 295.2955 153 1243.97 923.7605 1007.524 832.4168 1041.98 850.1398 1035.932 944.3415 1001.189 1282.614

2Ø20+1Ø14 2Ø16+1Ø14 2Ø20+2Ø12 2Ø14 3Ø16 3Ø16 2Ø20+2Ø12 3Ø16+2Ø14 2Ø16+1Ø14 2Ø12 2Ø16+1Ø14 2Ø12 2Ø14+1Ø16 2Ø12 1Ø16+1Ø14 2Ø14 2Ø12 2Ø14 2Ø12 4Ø20 3Ø20 2Ø20+2Ø16 2Ø20+2Ø12 2Ø20+3Ø14 2Ø20+2Ø12 2Ø20+2Ø16 3Ø20 2Ø20+2Ø16 2Ø24+2Ø16

KS AS1 Ф(As1 ) min 154 2Ø12 3.981 171.5591 2Ø12 4.06 299.4085 2Ø14 4.481 1853 4Ф24 4.483 1401.061 1Ø16+4Ø20 2126.2 4Ø24+2Ø16 4.158 730.1265 2Ø20+1Ø12 4.19 801.8095 4Ø16 4.307 1031.219 2Ø20+2Ø16


Page 97

Senior project, structural design & cost comparison 123.09 Gbeam 97.46 Gbeam 124.68 Gbeam

moment 5.87 14.54 30.95 11.59 33.42 133.38 117.64 176.79 77.46 81.29 91.79 100.9 94.9 108.26

moment 16.27 20.93 41.28 18.53 9.5 11.38 8.83 16.86 17.25 9.25 29.58 35.82 11.77 126.82 110 110.44 107.01 98.47

LOCATION Head Room Head Room Head Room TTBeam TTBeam 1st&2nd 1st&2nd 1st&2nd 3rd&4th 3rd&4th 3rd&4th Gbeam Gbeam Gbeam

LOCATION Head Room Head Room Head Room TTBeam TTBeam TTBeam TTBeam TTBeam TTBeam TTBeam TTBeam TTBeam TTBeam 1st&2nd 1st&2nd 1st&2nd 1st&2nd 1st&2nd

June 2008

0.25 0.355 62.50 0.25 0.355 55.62 4.609 0.25 0.355 62.91

2003.4 4Ø24+2Ø12 1265.333 3Ø24 2003.4 4Ø24+2Ø12

b 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25

AXIS-2 d Km 0.307 15.78 0.307 24.84 0.307 36.24 0.307 22.18 0.307 37.66 0.455 50.76 0.455 47.68 0.446 59.62 0.455 38.69 0.455 39.63 0.455 42.11 0.355 56.59 0.355 54.88 0.355 58.62

KS AS1 min 153 3.989 188.9253 4.112 414.5485 3.971 149.915 4.131 449.7004 1340 4.352 1125.207 1853 4.148 706.1628 4.164 743.9375 4.213 849.9149 1429.3 1220.01 1345.67

Ф(As1 ) 2Ф12 2Ф12 2Ø14+1Ø12 2Ф12 3Ø14 3Ø24 2Ø24+2Ø12 4Ø24 2Ø16+2Ø14 2Ø20+1Ø12 2Ø20+2Ø12 1Ø16+4Ø20 4Ø20 4Ø20+1Ø12

b 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25

AXIS-3 d Km 0.307 26.28 0.307 29.80 0.307 41.86 0.307 28.04 0.307 20.08 0.307 21.98 0.307 19.36 0.307 26.75 0.307 27.06 0.307 19.81 0.307 35.43 0.307 38.99 0.307 22.35 0.455 49.50 0.455 46.10 0.455 46.19 0.455 45.47 0.455 43.62

KS As1 4.006 212.305 4.048 275.976 4.207 565.6839 4.028 243.1233 3.957 122.4479 3.97 147.1616 3.952 113.6683 4.012 220.3333 4.016 225.6547 3.955 119.1653 4.104 395.4278 4.153 484.5618 3.972 152.2816 1214.93 4.312 1042.462 4.315 1047.36 4.297 1010.598 4.25 919.7747

Ф(As1 ) 2Ø12 2Ø14 3Ø16 2Ø14 2Ø12 2Ø12 2Ø12 2Ø12 2Ø12 2Ø12 2Ø16 2Ø14+1Ø16 2Ø12 4Ø20 2Ø24+1Ø14 2Ø24+1Ø14 2Ø24+1Ø12 2Ø14+2Ø20


Page 98

Senior project, structural design & cost comparison 106.94 101.23 109.9 103.44 119.22 82.61 88.42 58.23 33.26 76.67 56.91 38.72 76.07 60.62 81.59 51.57 99.4 89.94 87.35 86.16 83.54 85.72 89.12 71.8 70.2 68.24 73.15

1st&2nd 1st&2nd 1st&2nd 1st&2nd 1st&2nd 3rd&4th 3rd&4th 3rd&4th 3rd&4th 3rd&4th 3rd&4th 3rd&4th 3rd&4th 3rd&4th 3rd&4th 3rd&4th 3rd&4th Gbeam Gbeam Gbeam Gbeam Gbeam Gbeam Gbeam Gbeam Gbeam Gbeam

0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25

0.455 0.455 0.455 0.455 0.455 0.455 0.455 0.455 0.455 0.455 0.455 0.455 0.455 0.455 0.455 0.455 0.455 0.355 0.355 0.355 0.355 0.355 0.355 0.355 0.355 0.355 0.355

Inclined beam(SAP) LOCATION AS Ф(AS) Gbeam 1377.25 4Ф20+1Ø14 Gbeam 1235.31 4Ф20 Gbeam 1176.7 2Ø24+1Ф20 Gbeam 961.86 5Ø16 Gbeam 966.54 5Ø16 1st&2nd 1723.22 4Ø24 1st&2nd 1426.32 4Ø20+1Ø16 1st&2nd 1183.39 2Ø24+1Ф20 1st&2nd 991.29 5Ø16 1st&2nd 1269.18 3Ø24 3rd&4th 847.42 2Ø20+2Ф12 3rd&4th 745 4Ø16

45.46 44.23 46.08 44.71 47.99 39.95 41.33 33.54 25.35 38.49 33.16 27.35 38.34 34.22 39.70 31.57 43.82 53.43 52.65 52.29 51.49 52.16 53.19 47.74 47.20 46.54 48.18

June 2008 4.3 4.267 4.312 4.278 4.36 4.17 4.198 4.085 4.001 4.147 4.082 4.019 4.142 4.092 4.165 4.066 4.256

4.354 4.34 4.324 4.36

LOCATION G-floor G-floor G-floor 1st&2nd 1st&2nd 1st&2nd 3rd&4th 3rd&4th 3rd&4th roof roof roof


1010.642 949.3372 1214.45 972.5633 1142.416 757.107 815.796 522.7902 292.4687 698.7923 510.564 342.0125 692.4878 545.1803 746.8623 460.8431 929.7723 1317.8 1246.82 1246.82 1160.19 1246.82 1317.8 880.6118 858.2197 831.1824 898.4056

2Ø24+1Ø12 3Ø20 4Ø20 3Ø12+2Ø20 3Ø20+2Ø12 2Ø20+1Ø14 2Ø20+1Ø16 2Ø16+1Ø14 2Ø14 2Ø16+2Ø14 2Ø16+1Ø12 2Ø16 2Ø16+2Ø14 2Ø16+1Ø14 2Ø20+1Ø14 3Ø14 3Ø20 3Ø20+2Ø16 4Ø20 4Ø20 3Ø20+2Ø12 4Ø20 3Ø20+2Ø16 3Ø16+2Ø14 2Ø20+2Ø12 2Ø16+2Ø14 3Ø16+2Ø14

landing beams AS Ф(AS) 2172.62 4Ф24+2Ф16 2002.28 4Ф24+2Ø12 2291.24 4Ø24+2Ø20 1500.52 4Ø20+2Ø14 1475.75 4Ø20+2Ø12 1839 3Ø20+2Ø24 729.35 4Ø16 697.65 2Ø16+2Ø14 984.77 5Ø16 343.9 2Ø16 225 2Ф12 225 2Ф12 Page 99

Senior project, structural design & cost comparison 3rd&4th 3rd&4th 3rd&4th TTBeam TTBeam TTBeam TTBeam Head Room Head Room Head Room

2.4 6.15 3.21 3.9 5.65 16.36 6.62

2Ø16+2Ø14 2Ø14+2Ø12 2Ø16+2Ø14 2Ф12 2Ф12 2Ф12 2Ф12 2Ф12 2Ф12 2Ф12

692.88 520.69 678.21 159.65 162.19 204.96 157.5 157.5 157.5 157.5

0.25 0.25 0.25 0.25 0.25 0.25 0.25

June 2008

roof

225 2Ф12

corridor beams added for prec 0.455 6.81 min 0.455 10.90 min 0.455 7.88 min 0.455 8.68 min 0.455 10.45 min 0.455 17.78 min 0.455 11.31 min

227 227 227 227 227 227 227

2Ø12 2Ø12 2Ø12 2Ø12 2Ø12 2Ø12 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 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 where more than 50%of the bottom reinforcement is curtailed, K2 = 1. ρmax =0.04


Page 100


June 2008

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 , 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 4.56,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 Mekelle University, Department of Civil Engineering

Page 101


June 2008

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 ing 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 , and the spacing of stirrups shall not exceed Uef /8 ρmin= 0.4 /fyk 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 and VRd,com = βvVRd in which TRd, com = βtTRd


Page 102


June 2008

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
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 Mekelle University, Department of Civil Engineering

Page 103


June 2008

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 rel="nofollow">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
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.


Page 104


June 2008

Sample reinforcement detail

AXIS-4

5.2 Column design Columns are axially loaded vertical , which carry their load primarily in compression. The majority of compression or tension carry a portion of the load in bending which may arise due to the unbalanced moments in the connected to their ends. The result of such bending moments in axially loaded 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 should be considered in deg 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. Mekelle University, Department of Civil Engineering

Page 105


June 2008

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

Kc1

K11

Kc K22

K21

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


Page 106


June 2008

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.


Page 107


As/2 S

June 2008

d Is = (n (П * r4)/4 + П * r2*d2) Where n = number of bars

As/2 S

Reinforcing the substitute column using the biaxial chart using the following formulas: ν = Nsd * 103 Ac *fcd µ = Mdl * 106 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 Mekelle University, Department of Civil Engineering

Page 108


June 2008

The result of the substitute frames are tabulated as follows AXIS4 LEVE L

α1

Found Groun d

α2

H

L

Le

Nsd

HL

µ

Md1

v

8.92

1.00

301.09

1.50

3.34

1975.36

451.64

113.48

0.04

2.9

8.92

224.05

3.80

9.10

1903.78

851.39

569.50

0.20

1

3.22

2.90

158.88

3.05

5.66

1446.68

484.58

235.89

0.08

2

3.22

3.22

98.67

3.05

5.77

999.10

300.94

150.47

0.05

3

3.22

3.22

50.43

3.05

5.77

502.31

153.81

76.91

0.03

4

4.69

3.22

15.67

3.05

6.23

101.84

47.79

21.37

0.01

As

Ǿ

Is

Ic

3135.008 10Ǿ20

196957002

3403.96 8Ǿ24

226854001

3135.008 10Ǿ20

196957002

3135.008 10Ǿ20

196957002

3135.008 10Ǿ20

196957002

3135.008 10Ǿ20

196957002

EIe

1.28E+1 0 1.28E+1 0 1.28E+1 0 1.28E+1 0 1.28E+1 0 1.28E+1 0

Nsd/Nc r

Ncr

7.129E+13 7.727E+13 7.129E+13 7.129E+13 7.129E+13 7.129E+13

63007705.1 8 9210012.38 4 21917624.0 2 21126915.3 7 21126915.3 7 18127122.2 9

0.4 4 0.4 3 0.3 3 0.2 3 0.1 1 0.0 2

w mi n 0.2 mi n mi n mi n mi n

condition

0.03 non-sway 0.21 ''sway'' 0.07 non-sway 0.05 non-sway 0.02 non-sway 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


Page 109

Senior project, structural design & cost comparison 5 As

6.31

12.61

Ǿ

Is

1812.608 6Ǿ20

17.49

3.05

June 2008

8.93

Ic

72.19

EIe

53.34

Ncr

33.42

0.03

0.03 min

Nsd/Ncr condition

68346169 4.278E+09 2.433E+13

17262278.72

0.05 non-sway

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

7774.04 10Ǿ32

AXIS-3 LEVEL Found Ground 1 2 3 4 5 As 3135.008 5531.435 3135.008 3135.008 3135.008 3135.008 3135.008

α1 α2 H 8.91 1 324.3 2.9 8.91 270.6 3.22 2.9 200.7 3.22 3.22 123.1 3.22 3.22 59.96 6.26 3.22 12.6 7.82 6.26 5.44 Ǿ Is 10Ǿ20 196957002 8Ǿ30 354950030 10Ǿ20 196957002 10Ǿ20 196957002 10Ǿ20 196957002 10Ǿ20 196957002 10Ǿ20 196957002

L

Le Nsd HL Md1 µ v 1.5 3.34 2061.48 486.41 122.29 0.04 3.8 9.09 1915.2 1028.2 687.59 0.25 3.05 5.66 1452.15 612.14 297.99 0.11 3.05 5.77 1014.74 375.46 187.73 0.07 3.05 5.77 583.79 182.88 91.44 0.03 3.05 6.68 155.85 38.43 15.44 0.01 3.05 7.85 59.35 16.592 7.65 0.00 Ic EIe Ncr Nsd/Ncr condition 1.28E+10 7.129E+13 63007705.18 0.00 non-sway 1.28E+10 1.029E+14 12277159.55 0.00 non-sway 1.28E+10 7.129E+13 21940864.41 0.00 non-sway 1.28E+10 7.129E+13 21112271.86 0.00 non-sway 1.28E+10 7.129E+13 21112271.86 0.00 non-sway 1.28E+10 7.129E+13 15751926.29 0.01 non-sway 1.28E+10 7.129E+13 11406365.47 0.03 non-sway

AXISB LEVEL α1 α2 H Found 14.9 1 319.3 Ground 4.84 14.86 269 1 5.37 4.84 209.9 2 5.37 5.374 134.4 3 5.37 5.374 72.69 4 7.82 5.374 18.75 As Ǿ Is Ic

L

Le 1.5 3.8 3.05 3.05 3.05 3.05

4.07 11.32 6.88 7.02 7.02 7.64 EIe


0.46 0.43 0.33 0.23 0.13 0.04 0.01

w min 0.33 min min min min min

Nsd HL Md1 µ v w 2252.2 478.92 87.63 0.07 0.88 0.08 2108.1 1022.2 710.34 0.26 0.47 0.35 1566.1 640.1 309.51 0.25 0.61 0.4 1032.92 409.8 204.90 0.17 0.40 0.13 540.28 221.7 110.85 0.09 0.21 0.02 44.99 57.188 24.95 0.02 0.02 0.03 Ncr Nsd/Ncr condition Page 110

Senior project, structural design & cost comparison 1812.608 3444.195 3936.223 1812.608 1812.608 1812.608

AXIS-E LEVEL Found Ground 1 2 3 4 5 As 2562.848 7999.306 3200.122 2562.848 2562.848 2562.848 2562.848

6Ǿ20 8Ǿ24 8Ǿ26 6Ǿ20 6Ǿ20 6Ǿ20

68346169 226854001 154178539 68346169 68346169 68346169

α1 α2 H 4.44 1 473 1.45 4.44 368.2 1.61 1.45 290.6 1.61 1.61 195.9 1.61 1.61 113.7 1.33 1.61 44.02 4.23 1.33 14.49 Ǿ Is 6Ǿ24 139106542 10Ǿ32 504623744 6Ǿ26 163439197 6Ǿ24 139106542 6Ǿ24 139106542 6Ǿ24 139106542 6Ǿ24 139106542

4.278E+09 1.28E+10 4.278E+09 4.278E+09 4.278E+09 4.278E+09

2.433E+13 7.727E+13 4.15E+13 2.433E+13 2.433E+13 2.433E+13

June 2008 14518736.79 5945286.218 8644145.467 4868281.781 4868281.781 4110202.46

0.00 0.00 0.00 0.00 0.00 0.02

non-sway non-sway non-sway non-sway non-sway non-sway

L

Le Nsd HL Md1 µ v 1.5 2.67 2061.48 709.43 248.05 0.12 3.8 6.96 1915.2 1399 875.39 0.31 3.05 4.55 1452.15 886.36 435.35 0.21 3.05 4.61 1014.74 597.62 298.81 0.15 3.05 4.61 583.79 346.82 173.41 0.08 3.05 4.5 155.88 134.26 69.23 0.03 3.05 5.48 59.35 44.195 16.55 0.01 Ic EIe Ncr Nsd/Ncr condition 8.552E+09 4.914E+13 67961309.81 0.00 non-sway 1.28E+10 1.328E+14 27034263.05 0.00 non-sway 8.552E+09 5.401E+13 25720151.2 0.00 non-sway 8.552E+09 4.914E+13 22797247.4 0.00 non-sway 8.552E+09 4.914E+13 22797247.4 0.00 non-sway 8.552E+09 4.914E+13 23925401.56 0.01 non-sway 8.552E+09 4.914E+13 16133297.64 0.05 non-sway


0.57 0.43 0.40 0.28 0.16 0.04 0.02

Page 111

w min 0.47 0.23 0.13 0.04 0.03 min


June 2008

5.2.2Design of isolated columns

For buildings, a design method may be used which assumes the compression 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 for geometric imperfection, introduced by increasing the eccentricity of the longitudinal force acting in the most unfavorable direction. Mekelle University, Department of Civil Engineering

Page 112


June 2008

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 need not be taken into in the following cases a) for sway frames the greater of λ≤ 25 ; which ever is maximum 15/√‫ﬠ‬d ‫ﬠ‬d = Nsd/Acfcd b) for non sway frames λ ≤ 50 – 25 (M1/M2) Where M1 and M2 are the 1st 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 level

Mdy M1

found ground

-10.62 115.16

first

M2

P

eo1

e02

11.17

1368.42

0.0077608

0.00816

118.57

1076.01

-99.46

111.08

806.45

second

-37.56

42.01

557.52

third fourth

-41.94 -16.04 Mdx

44.65 43.3

314.86 113.28

found

-10.87

17.56

1368.42

ground first second

-13.75 -18.35 -70.31

15.94 21.51 91.01

1076.01 806.45 557.52

-0.107025 0.1233306 0.0673698 0.1332021 -0.141596 0.0079435 0.0127787 -0.022754 -


0.6eo2+0.4eo1

0.4eo2

eo

0.0017933

0.003265

0.003265

4.468

0.11019

0.0233065

0.044078

0.044078

47.428

0.13774

0.0333114

0.055096

0.055096

44.432

0.07535

0.018263

0.030141

0.030141

16.804

0.14181 0.38224

0.0318046 0.1727048

0.056724 0.152895

0.056724 0.172705

17.86 19.564

0.01283

0.004522

0.005133

0.005133

7.024

0.01481 0.02667 0.16324

0.0037769 0.0069019 0.0474996

0.005926 0.010669 0.065296

0.005926 0.010669 0.065296

6.376 8.604 36.404

Page 113

M


third

-62.69

80.18

314.86

fourth

-10.99

35.68

113.28

June 2008

0.1261121 0.1991044 0.0970162

column B-3 Mdy level M1 M2 P eo1 found 0.42 0.89 2252.23 0.0001865 ground 120.88 131.3 1602.82 0.0754171 first -11.14 12.12 1278.28 0.0087148 second -2.3 5.93 1032.91 0.0022267 third -1.48 2.82 429.55 0.0034455 fourth -6.08 7.08 44.99 0.1351411 Mdx found -5.96 9.68 2252.23 0.0026463 ground -24.34 36.7 1602.82 0.0151857 first 113.43 116.88 1278.28 0.0887364 second -56.35 56.89 1032.91 0.0545546 third -71.73 92.79 429.55 0.1669887 fourth -6.39 44.02 44.99 0.1420316

0.25465

0.07315

0.101861

0.101861

32.072

0.31497

0.1501766

0.125989

0.150177

17.012

e02 0.6eo2+0.4eo1 0.4eo2 eo M 0.0004 0.0003117 0.000158 0.000312 0.702 0.08192

0.018984 0.032767 0.032767

52.52

0.00948

0.002203 0.003793 0.003793

4.848

0.00574

0.0025539 0.002296 0.002554

2.638

0.00657

0.0025608 0.002626 0.002626

1.128

0.15737

0.0403645 0.062947 0.062947

2.832

0.0043

0.0015203 0.001719 0.001719

3.872

0.0229

0.007664 0.009159 0.009159

14.68

0.09144

0.0193666 0.036574 0.036574

46.752

0.05508

0.0112246 0.022031 0.022031

22.756

0.21602

0.0628146 0.086407 0.086407

37.116

0.97844

0.5302512 0.391376 0.530251

23.856


Page 114

Senior project, structural design & cost comparison column E-3 level

Mdy M1

M2

P

eo1

found

-0.67

4.15

1790.15

ground

-0.75

5.18

1633.3

first

-36.87

37.55

949.05

second

-32.36

33.38

671.98

third

-30.2

32.22

387.46

fourth

-16.38

23.42

90.38

H.room

-13.77 Mdx

25.07

28.97

found

-32.76 101.76

97.68

1790.15

119.28

1633.3

-141.7 120.83 100.46

147.18

949.05

129.96

671.98

112.08

387.46

-34.9

55.16

90.38

-14.95

29.25

28.97

ground first second third fourth H.room

column E-2 level found ground first second

0.0003743 0.0004592 0.0388494 0.0481562 0.0779435 0.1812348 0.4753193 0.0183001 0.0623033 0.1493072 0.1798119 0.2592784 0.3861474 0.5160511

Mdy M1 M2 P eo1 1.28 8.38 833.97 0.0015348 1.7 4.34 456.7 0.0037224 -1.24 1.47 461.38 0.0026876 -3.93 5.69 401.311 0.0097929


June 2008

e02

0.6eo2+0.4eo1

0.4eo2

eo

M

0.00232

0.0012412

0.000927

0.001241

2.222

0.00317

0.0017192

0.001269

0.001719

2.808

0.03957

0.0081998

0.015826

0.015826

15.02

0.04967

0.010542

0.01987

0.01987

13.352

0.08316

0.0187168

0.033263

0.033263

12.888

0.25913

0.082983

0.103651

0.103651

9.368

0.86538

0.3290991

0.346151

0.346151

10.028

0.05457

0.0254191

0.021826

0.025419

45.504

0.07303

0.0188967

0.029212

0.029212

47.712

0.15508

0.033326

0.062033

0.062033

58.872

0.1934

0.0441144

0.077359

0.077359

51.984

0.28927

0.0698498

0.115707

0.115707

44.832

0.61031

0.2117283

0.244125

0.244125

22.064

1.00967

0.3993787

0.403866

0.403866

11.7

e02 0.6eo2+0.4eo1 0.4eo2 eo M 0.01005 0.0066429 0.004019 0.006643 5.54 0.0095 0.0071907 0.003801 0.007191 3.284 0.00319

0.0008366 0.001274 0.001274

0.588

0.01418

0.00459 0.005671 0.005671

2.276

Page 115


third

-9.19

9.78

fourth

-5.13

9.34

-9.89 Mdx

17.57

H.room

found

297.53 0.0308876 0.03287 157.38 0.0325963 0.05935 68.19 0.1450359 0.25766

105.98

833.97

144.6

456.7

first

-62.05 140.04 122.54

126.93

461.38

second

-97.43

104.25 401.311

third

-68.94

76.62

297.53

fourth

-33.02

33.98

157.38

H.room

-24.69

32.2

68.19

ground

column H-3 level

Mdy M1

M2

P

found

-4.61

19.84

1557.47

ground

-1.89

29.48

560.41

first second third

-16.62 16.68 9.17

22.94 18.59 23.29

514.99 434.68 321.27

-2.9

23.43

240.88

16.42

124.59

92.96

1557.47

ground

-13.21 Mdx -15.38 116.33

165.83

560.41

first

-68.08

123.76

514.99

fourth H.room found

June 2008

0.0744032 0.3066346 0.2655945 0.2427793 0.2317077 0.2098106 0.3620766

eo1 0.0029599 0.0033725 0.0322725 0.0383731 0.028543 0.0120392 0.1060278 -0.009875 0.2075802 0.1321967


0.0073673 0.013148 0.013148

3.912

0.0225696 0.023739 0.023739

3.736

0.0965831 0.103065 0.103065

7.028

0.12708

0.0464861 0.050832 0.050832 42.392

0.31662

0.0673177 0.126648 0.126648

0.27511

0.0588279 0.110044 0.110044 50.772

0.25977

0.0587524 0.103909 0.103909

0.25752

0.0618291 0.103008 0.103008 30.648

0.21591

0.0456221 0.086364 0.086364 13.592

0.47221

0.1384954 0.188884 0.188884

e02

0.6eo2+0.4eo1

0.4eo2

eo

57.84

41.7

12.88

M

0.01274

0.0064592

0.005095

0.006459

10.06

0.0526

0.0302136

0.021042

0.030214

16.932

0.04454 0.04277 0.07249

0.0138177 0.0410095 0.0549133

0.017818 0.017107 0.028997

0.017818 0.041009 0.054913

9.176 17.642

0.09727

0.0535453

0.038907

0.053545

12.898

0.13179

0.0366643

0.052717

0.052717

6.568

0.05969

0.0318619

0.023875

0.031862

49.624

0.29591

0.0945129

0.118363

0.118363

66.332

0.24032

0.0913105

0.096126

0.096126

49.504

Page 116


second

-54

97.89

434.68

third

-37.45

74.51

321.27

fourth H.room

-12.36 -17.28

25.33 17.41

240.88 124.59

June 2008

0.1242293 0.1165686 0.0513119 -0.138694

0.2252

0.0854284

0.09008

0.09008

39.156

0.23192

0.0925265

0.092769

0.092769

29.804

0.10516 0.13974

0.0425689 0.028365

0.042062 0.055895

0.042569 0.055895

10.254 6.964

Moment due to imperfection column E2 level foundation ground first second third fourth H.room level foundation ground first second third fourth H.room column E3 level foundation ground first second third fourth H.room level

x-dxn Le 1.39253 10.2917 2.80135 2.81176 2.81176 2.91835 2.93109 y-dxn Le 1.23737 5.36735 2.22377 2.24308 2.24308 2.49388 2.74134

x-dxn Le 1.34109 3.42767 2.56249 2.57922 2.57922 2.76646 2.88328 y-dxn Le

eacalc 0.004642 0.034306 0.009338 0.009373 0.009373 0.009728 0.00977

20 ea Nsd Ma 0.02 0.02 833.97 16.6794 0.02 0.0343056 456.7 15.667383 0.02 0.02 461.38 9.2276 0.02 0.02 401.311 8.02622 0.02 0.02 297.53 5.9506 0.02 0.02 157.38 3.1476 0.02 0.02 68.19 1.3638

eacalc 0.004125 0.017891 0.007413 0.007477 0.007477 0.008313 0.009138

20 ea 0.02 0.02 0.02 0.02 0.02 0.02 0.02

0.02 0.02 0.02 0.02 0.02 0.02 0.02

Nsd Ma 833.97 16.6794 456.7 9.134 461.38 9.2276 401.311 8.02622 297.53 5.9506 157.38 3.1476 68.19 1.3638

0 eacalc 0.00447 0.011426 0.008542 0.008597 0.008597 0.009222 0.009611 eacalc

20 ea 0.02 0.02 0.02 0.02 0.02 0.02 0.02

Nsd Ma 0.02 1790.15 35.803 0.02 1633.3 32.666 0.02 949.05 18.981 0.02 671.98 13.4396 0.02 387.46 7.7492 0.02 90.38 1.8076 0.02 28.97 0.5794

20 ea


Nsd

Ma

Page 117

Senior project, structural design & cost comparison foundation ground first second third fourth H.room

column A3 level foundation ground first second third fourth H.room level foundation ground first second third fourth H.room column B3 level foundation ground first second third fourth H.room level

1.29167 3.27488 2.40302 2.42191 2.42191 2.64814 2.78359

x-dxn Le 1.38032 3.53444 2.68623 2.70014 2.70014 2.75236 0 y-dxn Le 1.43125 3.65724 2.84348 2.85241 2.85241 2.88509 0

x-dxn Le 1.34109 3.42767 2.56249 2.57922 2.57922 2.64323 0 y-dxn Le

0.004306 0.010916 0.00801 0.008073 0.008073 0.008827 0.009279

0.02 0.02 0.02 0.02 0.02 0.02 0.02

eacalc 0.004601 0.011781 0.008954 0.009 0.009 0.009175

20 ea 0.02 0.02 0.02 0.02 0.02 0.02

eacalc 0.004771 0.012191 0.009478 0.009508 0.009508 0.009617 0

20 ea 0.02 0.02 0.02 0.02 0.02 0.02 0.02

June 2008 0.02 1790.15 0.02 1633.3 0.02 949.05 0.02 671.98 0.02 387.46 0.02 90.38 0.02 28.97

0.02 0.02 0.02 0.02 0.02 0.02 0 0

35.803 32.666 18.981 13.4396 7.7492 1.8076 0.5794

Nsd Ma 1368.42 27.3684 1076.01 21.5202 806.45 16.129 557.52 11.1504 314.86 6.2972 113.28 2.2656 0 0

Nsd Ma 0.02 1368.42 27.3684 0.02 1076.01 21.5202 0.02 806.45 16.129 0.02 557.52 11.1504 0.02 314.86 6.2972 0.02 113.28 2.2656 0.02 0 0

0 eacalc 0.00447 0.011426 0.008542 0.008597 0.008597 0.008811 0 eacalc

20 ea 0.02 0.02 0.02 0.02 0.02 0.02 0.02

0.02 0.02 0.02 0.02 0.02 0.02 0.02 0

20 ea


Nsd Ma 2252.23 45.0446 1602.82 32.0564 1278.28 25.5656 1032.91 20.6582 429.55 8.591 44.99 0.8998 0 0 Nsd

Ma

Page 118

Senior project, structural design & cost comparison foundation ground first second third fourth

1.43125 3.65724 2.84348 2.85241 2.85241 2.88509

0.004771 0.012191 0.009478 0.009508 0.009508 0.009617

column H3 level foundation ground first second third fourth H.room

0.02 0.02 0.02 0.02 0.02 0.02

June 2008 0.02 0.02 0.02 0.02 0.02 0.02

2252.23 1602.82 1278.28 1032.91 429.55 44.99

45.0446 32.0564 25.5656 20.6582 8.591 0.8998

ea Nsd Ma 0.02 1557.47 31.1494 0.02 560.41 11.2082 0.02 514.99 10.2998 0.02 434.68 8.6936 0.02 321.27 6.4254 0.02 240.88 4.8176 0.02 124.59 2.4918

Design moment column E2 level foundation ground first second third fourth H.room

Mdx Ma Mdxtot 42.392 16.6794 59.07 62.2952 9.134 71.43 50.772 9.2276 60.00 41.7 8.02622 49.73 30.648 5.9506 36.60 13.592 3.1476 16.74 12.88 1.3638 14.24

colmnE-3 level foundation ground first second third fourth H.room

Mdx Ma Mdxtot 45.504 35.803 81.31 47.712 32.666 80.38 58.872 18.981 77.85 51.984 13.4396 65.42 44.832 7.7492 52.58 22.064 1.8076 23.87 11.7 0.5794 12.28


Mdy Ma Mdytot 5.54 16.6794 22.22 3.53695 15.667383 19.20 0.588 9.2276 9.82 2.276 8.02622 10.30 3.912 5.9506 9.86 3.736 3.1476 6.88 7.028 1.3638 8.39

0 Mdy Ma Mdytot 2.222 35.803 38.03 2.808 32.666 35.47 15.02 18.981 34.00 13.352 13.4396 26.79 12.888 7.7492 20.64 9.368 1.8076 11.18 10.028 0.5794 10.61

Page 119


June 2008

Column A-3 level foundation ground first second third fourth

Mdx Ma Mdxtot 7.024 27.3684 34.39 6.376 21.5202 27.90 8.604 16.129 24.73 36.404 11.1504 47.55 32.072 6.2972 38.37 17.012 2.2656 19.28

0 Mdy Ma Mdytot 4.468 27.3684 31.84 47.428 21.5202 68.95 44.432 16.129 60.56 16.804 11.1504 27.95 17.86 6.2972 24.16 19.564 2.2656 21.83

colmn B-3 level foundation ground first second third fourth

Mdx Ma Mdxtot 3.872 45.0446 48.92 14.68 32.0564 46.74 46.752 25.5656 72.32 22.756 20.6582 43.41 37.116 8.591 45.71 23.856 0.8998 24.76

0 Mdy Ma Mdytot 0.702 45.0446 45.75 52.52 32.0564 84.58 4.848 25.5656 30.41 2.638 20.6582 23.30 1.128 8.591 9.72 2.832 0.8998 3.73

column H3 level foundation ground first second third fourth H.room

Mdx Ma Mdxtot 49.624 31.1494 80.77 66.332 11.2082 77.54 49.504 10.2998 59.80 39.156 8.6936 47.85 29.804 6.4254 36.23 10.254 4.8176 15.07 6.964 2.4918 9.46

0 Mdy Ma Mdytot 10.06 31.1494 41.21 16.932 11.2082 28.14 9.176 10.2998 19.48 17.826 8.6936 26.52 17.642 6.4254 24.07 12.898 4.8176 17.72 6.568 2.4918 9.06


Page 120


June 2008

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

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

colmn B-3 level foundn ground

Ф 8Ф16 8Ф16 4Ф12&4Ф14 4Ф12&4Ф14 4Ф12&4Ф14 4Ф16

first second third fourth

Nsd Mdx Mdy ν µh µb ω As Asmin Asprvd Ф 2252.23 48.92 45.75 1.2 0.07 0.06 0.46 3196.565 1280 3196.6 8Ф24 1602.82 46.74 84.58 0.9 0.06 0.12 0.325 2258.443 1280 2258.4 4Ф24&4Ф14 4Ф20& 1278.28 72.32 30.41 0.9 0.15 0.06 0.32 1702.518 980 1702.5 4Ф12 1032.91 43.41 23.30 0.7 0.09 0.05 0.055 292.6204 980 980 4Ф14&4Ф12 429.55 45.71 9.72 0.4 0.15 0.02 0.12 469.0612 720 720 4Ф16 44.99 24.76 3.73 0.0 0.08 0.01 0.2 781.7687 720 781.77 4Ф16

colmn E-3 level foundn ground first second third fourth H.room

Nsd Mdx Mdy ν µh µb ω As Asmin Asprvd 1790.15 81.31 38.03 1.0 0.11 0.05 0.36 2501.66 1280 2501.7 1633.3 80.38 35.47 0.9 0.11 0.05 0.275 1910.99 1280 1911 949.05 77.85 34.00 0.7 0.16 0.07 0.35 1862.13 980 1862.1 671.98 65.42 26.79 0.5 0.13 0.06 0.115 611.8426 980 980 387.46 52.58 20.64 0.3 0.11 0.04 0.06 319.2222 980 980 90.38 23.87 11.18 0.1 0.08 0.04 0.115 449.517 720 720 28.97 12.28 10.61 0.0 0.04 0.03 0.1 390.8843 720 720


Ф 4Ф24&8Ф12 4Ф20&4Ф16 4Ф20&4Ф14 4Ф12&4Ф14 4Ф12&4Ф14 4Ф16 4Ф16

Page 121


June 2008

colmn E-2 level foundn ground first second third fourth H.room

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

colmn H-3 level foundn ground first second third fourth H.room

Nsd Mdx Mdy ν µh µb ω As Asmin Asprvd 1557.47 80.77 41.21 0.9 0.11 0.06 0.28 1945.735 1280 1945.7 560.41 77.54 28.14 0.4 0.16 0.06 0.23 1223.685 980 1223.7 514.99 59.80 19.48 0.4 0.12 0.04 0.05 266.0185 980 980 434.68 47.85 26.52 0.4 0.16 0.09 0.3 1172.653 720 1172.7 321.27 36.23 24.07 0.3 0.12 0.08 0.13 508.1497 720 720 240.88 15.07 17.72 0.2 0.05 0.06 0 0 720 720 124.59 9.46 9.06 0.1 0.03 0.03 0.04 156.3537 720 720

Ф 4Ф20&4Ф16 4Ф20 4Ф20 4Ф20 4Ф16 4Ф16 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 foundation ground first second third fourth

Nsd 1422.5 1141.5 850.75 626.26 340.59 89.96

column B3 level foundation ground first second

Nsd Mdx Mdy ν µh µb ω As Asmin Asprvd 1751.2 83.70 38.10 1.0 0.12 0.05 0.37 2571 1280 2571.15 1606.5 79.52 36.57 0.9 0.11 0.05 0.27 1876 1280 1876.24 1195.3 68.90 28.16 0.7 0.10 0.04 0.065 451.7 1280 1280.00 797.91 54.77 18.70 0.4 0.08 0.03 0.01 39.09 1280 1280.00

Mdx 33.11 70.57 61.16 51.90 40.05 13.92

Mdy 36.90 26.12 21.39 17.72 13.36 7.08

ν µh 1.0 0.07 0.8 0.15 0.6 0.13 0.5 0.11 0.3 0.13 0.1 0.03


µb ω As Asmin Asprvd Ф 0.08 0.3 1596 980 1596.11 8Ф16 0.05 0.32 1703 980 1702.52 4Ф20+4Ф16 0.04 0.11 585.2 980 980.00 4Ф12+4Ф14 0.04 0.02 106.4 980 980.00 4Ф12+4Ф14 0.04 0.18 703.6 720 720.00 4Ф16 0.01 0.035 136.8 720 720.00 4Ф16

Ф 4Ф24+4Ф16 4Ф20+4Ф14 4Ф16+4Ф14 4Ф16+4Ф14 Page 122

Senior project, structural design & cost comparison third fourth

413 48.43

45.04 20.25

9.70 1.66

0.4 0.0

0.15 0.07

June 2008 0.03 0.01

0.13 0.18

508.1 703.6

720 720

720.00 4Ф16 720.00 4Ф16

column E3 level foundation ground first second third fourth H.room

Nsd Mdx Mdy ν µh µb ω As Asmin Asprvd 1526 75.72 33.08 0.8 0.10 0.05 0.16 1112 1280 1280.00 968.71 83.51 25.31 0.5 0.12 0.03 0.045 175.9 1280 1280.00 751.83 81.73 23.87 0.4 0.11 0.03 0 0 1280 1280.00 545.71 69.51 19.15 0.3 0.10 0.03 0.035 136.8 1280 1280.00 331.26 59.24 13.59 0.3 0.19 0.04 0.315 1231 720 1231.29 96.61 28.24 7.54 0.1 0.09 0.02 0.14 547.2 720 720.00 30.85 11.95 11.54 0.0 0.04 0.04 0.11 430 720 720.00

Ф 4Ф16+4Ф14 4Ф16+4Ф14 4Ф16+4Ф14 4Ф16+4Ф14 4Ф16+4Ф12 4Ф16 4Ф16

column E2 level foundation ground first second third fourth H.room

Nsd Mdx Mdy ν µh µb ω As Asmin Asprvd 334.26 50.00 12.67 0.2 0.10 0.03 0.08 425.6 980 980.00 413.92 71.97 17.44 0.3 0.15 0.04 0.19 1011 980 1010.87 428.13 60.28 10.68 0.3 0.12 0.02 0.075 399 980 980.00 377.7 49.76 8.38 0.4 0.16 0.03 0.17 664.5 720 720.00 283.8 36.44 7.40 0.3 0.12 0.02 0.075 293.2 720 720.00 154.59 15.53 5.71 0.2 0.05 0.02 0 0 720 720.00 66.65 13.81 8.08 0.1 0.05 0.03 0.06 234.5 720 720.00

Ф 4Ф14+4Ф12 4Ф14+4Ф12 4Ф14+4Ф12 4Ф16 4Ф16 4Ф16 4Ф16

columnH-3 level foundation ground first second third fourth H.room

Nsd Mdx Mdy ν µh µb ω As Asmin Asprvd 1521.23 80.19 40.40 0.8 0.11 0.06 0.2 1390 1280 1389.81 1437.09 94.95 46.87 0.8 0.13 0.06 0.27 1876 1280 1876.24 471.89 64.01 11.33 0.5 0.21 0.04 0.375 1466 720 1465.82 448.71 61.02 17.51 0.4 0.20 0.06 0.36 1407 720 1407.18 321.21 53.96 22.38 0.3 0.18 0.07 0.345 1349 720 1348.55 146.81 15.39 10.26 0.1 0.05 0.03 0.06 234.5 720 720.00 63.26 14.99 25.21 0.1 0.05 0.08 0.13 508.1 720 720.00

Ф 4Ф16+4Ф14 4Ф20+4Ф14 4Ф16+4Ф14 4Ф16+4Ф14 4Ф16+4Ф14 4Ф16 4Ф16


Page 123

Senior project, structural design & cost comparison column E1 level foundation ground first second third fourth

Nsd 237.74 239.7 208.25 161.85 103.27 28.77

Mdx 51.4 51.31 27.51 9.725 8.393 4.683

Mdy 6.267 12.35 9.225 27.44 18.76 6.647

June 2008

ν µh µb ω As Asmin Asprvd Ф 0.2 0.17 0.02 0.26 1016 720 1016.30 4Ф14+4Ф12 0.2 0.17 0.04 0.3 1173 720 1172.65 4Ф16+4Ф12 0.2 0.09 0.03 0.05 195.4 720 720.00 4Ф16 0.2 0.03 0.09 0.05 195.4 720 720.00 4Ф16 0.1 0.03 0.06 0.075 293.2 720 720.00 4Ф16 0.0 0.02 0.02 0.05 195.4 720 720.00 4Ф16


Page 124


June 2008

6. Foundation design


Page 125


June 2008

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 My =-0.42 kN.m -Pd =2252.23 kN Assume L = B

L’

c

Mx

X

d

And an allowable bearing capacity for the soil as δall =560 KPa C-25 and S-300 Proportioning Using unfactored load; Pd = ex =

My Pd

=

2252.23 = 1608.73 1 .4

− 0.42 = 0.0037 m 1608.73

M 5.96 ey = x = = 0.00026m Pd 1608.73

0.89m

Since a surface footing, B = L

1.5m

0.61m

ey pd e * (1 ± 6 * x ± 6 * ) A B B 1608.73 0.00026 0.0037 560 = * (1 ± 6 * ± 6* ) 2 B B B

σ all =

Solving the equation by trial and error, we get B =1.7m We use B = L = 1.7m 1608 .73 σ ult a = * (1 + 0.013 + 0.00094 ) = 562.47 kn/m2 2 1 .7 1608.73 σ ult b = * (1 + 0.013 − 0.00094) = 561.42 kn/m2 2 1 .7 1608.73 σ ult c = * (1 − 0.013 + 0.00094 ) =548.00 kn/m2 2 1 .7 Mekelle University, Department of Civil Engineering

Page 126


σ ult d =

June 2008

1608.73 * (1 − 0.013 − 0.00094) =546.96 kn/m2 2 1 .7

562.47

561.43

1.7m

1.7m

548 546.96

δ ult 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


Page 127


June 2008

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

Km =

M b d

= 19.46

M 201.99 = 3.96* = 2428.22mm 2 d 0.56 Amin = ρmin * b*d = .002*1700*560 = 1904 mm2 a *b 201 * 1700 s= s taking φ 16 s= = 140mm As 2428.22 Ks = 3.96

As = Ks *

φ16 c/c 140 mm (both direction) 1700 − 100) N o of reinforcement = 1 + ( = 12 140 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. Take


Page 128


June 2008

6.2 Mat foundation design The purpose of deg 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 0.5

G

F

G

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 E-1 F-1 E-2 G-2 E-3 H-3

P -143.77 -279.59 803.13 599.8 1525.96 1521.23

Factored p -102.7 -199.71 573.7 428.43 1089.97 1086.6

mx -95.52 -93.38 -108.53 -99.51 -99.8 -94.01

My 3.15 -10.64 5.47 -12.49 2.91 -4.65

R=-102.7-199.71+573.7+428.43+1086.6+1089.97=2876.3 KN Taking moment about axis E Mekelle University, Department of Civil Engineering

Page 129


June 2008

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

C

B

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 Column P Factored p mx E-1 1064.74 760.53 93.85 F-1 1087.33 776.7 91.5 E-2 803.13 573.7 -108.53 G-2 857.76 612.7 -5.87 E-3 1525.96 1089.97 -99.8 H-3 1521.23 1086.6 -94.01 The same procedure is followed to calculate eccentricities & moment Mekelle University, Department of Civil Engineering

My -5.91 3.55 5.47 -86.22 2.91 -4.65

Page 130


E

STRIP 1

G

H

STRIP 2

J STRIP 3

co-ordinates F (-2.797,2.03) ,J (-0.527,-2.83) E (-2.797,0.03)

C

STRIP 5

B F

±

STRIP 4

d= ±

June 2008

I

A

H (2.16,2.03) I (2.449,0.03) G (-0.527,3.18) D

ey=0.56m Mx=Rey=2744.11KN.m ex=0.137 m My=Rex=671.33KN.m 2 p/A=179.9KN/m Mx/Ix=20.99KN/m2 My/Ix=12.86KN/m2 dA=179.9+12.86*2.797-20.99*2.82=156 KN/m2 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*(

)


Page 131


= 240.02KN/m2*[ Load correction factor =

June 2008

]= 260.79 KN/m2

=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. Load correction Modified soil Strip ∑pu Average soil Average factor rxn load rxn 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


Page 132


June 2008

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

0.4+d 0.4m 0.5 0.2+0.5d 0.7+0.5d

Vac=p-d(0.4+d)(0.7+0.5d) =1166.3-139.22(0.4+d)(0.7+0.5d) =1127.32-125.3d-69.61d2 Vres=0.5 fctd (1+50ρ)*(1.8+d)d =1021.68d+1135.2 *d2 equating vact ≤ vres 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


Page 133


June 2008

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

Reinforcement design moment Strip-1 364.06 65.72 Strip-2 255.71 113.22 Strip-3 417.34 20.31 Strip-4 215.48 51.95 129.49 75.58 Strip-5 166.46 71.22 89.81 70.72

b

d

km

ks

As

spacing

s.provided

1.15 1.15

0.788 0.788

22.58 9.59

3.974 min

1835.70 1812.4

196.71 199.24

Φ20c/c190

2.00 2.00 Strip-3 2.85 2.85

0.788 0.788

14.35 9.55

min min

3152 3152

199.24 199.24

Ø20c/c190 Ø20c/c190

0.788 0.788

15.36 3.39

min min

4491.6 4491.6

199.24 199.24

Ø20c/c190 Ø20c/c190

2.27 2.27 2.27 2.27

0.788 0.788 0.788 0.788

12.36 9.585 9.585 7.323

min min min min

3577.52 3577.52 3577.52 3577.52

199.24 199.24 199.24 199.24

Ø20c/c190 Ø20c/c190 Ø20c/c190 Ø20c/c190

3.265 3.265 3.265 3.265

0.788 0.788 0.788 0.788

9.06 5.93 6.66 4.91

min min min min

5145.64 5145.64 5145.64 5145.64

199.24 199.24 199.24 199.24

Ø20c/c190 Ø20c/c190 Ø20c/c190 Ø20c/c190


Page 134


June 2008

Reinforcement design for solid case moment Strip-1 436.78 79.06 Strip-2 596.5 142.75 Strip-3 1296.38 113.62 Strip-4 590.95 91.57 96.62 Strip-5 494.10 169.26

b

d

Km

Ks

As

spacing

s.provided

1.15 1.15

0.788 0.788

24.73 10.52

3.988 Min

2210.62 1812.4

163 199.24

Ø20c/c160 Ø20c/c190

2.00 2.00

0.788 .788

21.92 8.02

3.9695 Min

3004.302 3152

209 199.24

Ø20c/c190 Ø20c/c190

2.85 2.85

0.788 0.788

27.066 8.01

4.0158 Min

6606.64 4491.6

135.45 199.24

Ø20c/c130 Ø20c/c190

2.27 2.27 2.27

0.788 0.788 0.788

20.48 8.66 8.28

3.96 Min Min

2969.65 3577.52 3577.52

240 199.24 199.24

Ø20c/c190 Ø20c/c190 Ø20c/c190

3.265 3.265

0.788 0.788

15.61 9.17

Min Min

5145.64 5145.64

199.24 199.24

Ø20c/c190 Ø20c/c190

The reinforcement detail is attached with AutoCAD


Page 135


June 2008

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. a) Footing , Grade beam &footing columen

m2

384.26

75.00

28,819.50

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

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

TOTAL CARRIED TO SUMMARY ....................

121,852.55

B-SUPER 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) floor slabs

m

3

b) beams .

m

3


121.97 1250.00

152,462.50

62.19 1250.00

77,742.75 Page 136


June 2008

m

c) columns .

3

26.61 1250.00

33,262.50

1.20 Provide, cut and fix in position sawn zigba wood or steel formwork which ever appropriate. a) Elevation column, beams & floor slabs

m2

1250.40

70.00

87,528.00


kg

28873.64

25.00

721,841.00

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 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) 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

76.17 1250.00

95,212.50

26.29 1250.00

32,862.50

b) beams .

m

3

c) columns .

m

3

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. Mekelle University, Department of Civil Engineering

pcs

4992.00

9.60

47,923.20 Page 137


June 2008

1.30 Provide, cut and fix in position sawn zigba wood or steel formwork which ever appropriate. a) Elevation column, beams & floor slabs

m2

681.86

70.00

47,730.20


kg

26465.95

25.00

661,648.75

b) Φ6 mm plain bar

kg

1429.20

26.00

37,159.20


1,018,322.10

TOTAL CARRIED TO SUMMARY

B.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

52.78 1300.00

68,608.02

1.20 Provide, cut and fix in position sawn zigba wood or steel formwork which ever appropriate. a) Footing , Grade beam &footing columen

m2

338.65

75.00

25,398.75


kg

800.69

25.00

20,017.25

b) Φ6 mm plain bar

kg

110.70

26.00

2,878.20


TOTAL CARRIED TO SUMMARY

Grand total of pre-cast


116,902.22 1,135,224.32

Page 138


June 2008

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

73128.95

116347.5

43,218.55

1,135,224.32 1,203,989.96

68,765.64

form-work total

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 manship, 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 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.


Page 139


June 2008

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


Page 140

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