Tall Building Data Sheet

8/3/2019 Tall Building Data Sheet

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Structures & Tall Buildings Data Page 1

A. REINFORCED CONCRETE DESIGN FORMULAE (For fcu 40 MPa)(Based on Hong Kong Code of Practice for the Structural Use of Concrete 2004, and moment

redistribution < 10%)

A1. Lever Arm (Singly reinforced section)

9.025.05.0 kdz

A2. Bending Reinforcement

,2

cufbd

MK

zf

MA

y

s87.0

For d/x < 0.43, compressive stress in steel = 0.87fy

ForK 0.156, compression steel required.

,'87.0

156.0'

2

ddf

fbdKA

y

cus

dzA

zf

bdfA s

y

cus

775.0and'87.0

156.0 2

Min. 18.0100

bh

As for bw / b < 0.4

Min. 13.0100 bhAs for bw / b 0.4

Max. 0.4100

bh

As

Min. 2.0'100

bh

As , Max. 0.4'100

bh

As

A3.1 Bending Moments for Two-way Spanning Simply Supported Slabs

22 and, xsysyxsxsx lnmlnm

A3.2 Bending Moments for Restrained Two-way Spanning Solid Slabs

and2

xsxsxlnm 2

xsysy lnm

A3.3 Loads on Supporting Beams of Restrained Two-way Slabs

andxvxsxlnV

xvysy lnV


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A4. Deflection

bprovs

reqsy

ss

tA

Aff

bd

M

fm

1

3

2,2

9.0120

47755.0

,

,

2

5.1'100

3

'100

1,

,

bd

A

bd

A

mprovs

provs

c

A5.1 Shear Reinforcement for Beam & Slab

yvv

sv

yv

c

v

sv

f

b

s

A

f

vvb

s

A

87.0

4.0,

87.0

,

A5.2 Punching Shear Reinforcement for Slab

cyv

csv vv

f

udvvA 6.1ewher

87.0sin

or cc

yv

csv vvv

f

udvvA 21.6ewher

87.0

7.05sin

in either case 87.0

4.0sin

yv

svf

udA

m

s

c

dbd

A

v

4/13/1400100

79.0

, m = 1.25;

bd

As100 should not be taken as greater than 3;

d

400should not be less than 0.67 for members without shear reinforcement,

d

400should not be less than 1 for members with shear reinforcement providing minimum links.

For characteristic concrete strengths greater than 25 N/mm2, the values ofvc may be multiplied by (fcu/

25)1/3. The value offcu should not be taken as greater than 80.

Note: All the terms and symbols bear their usual meanings.


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Table 1: Lever Arm Factor (b 0.9)

K= M/bd2fcu

0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.043 0.156

0.950 0.7750.941 0.928 0.915 0.901 0.887 0.873 0.857 0.842 0.825 0.807 0.789la = z/d

Table 2 Area of Steel Reinforcement

Steel Reinforcement

Bar Size Area of one Bar (mm2)

8 50.3

10 78.512 113

16 201

20 314

25 491

32 804

40 1257

Table 3 Area of Steel Reinforcement Per Meter

Table 4 Asv / sv Ratio for Shear Link

Steel Reinforcement - Area per one meter (mm2/m)

Bar Spacing

in mm

Bar

Size

100 125 150 175 200 225 250 275 300 350

8 503 402 335 287 251 223 201 183 168 144

10 785 628 524 449 393 349 314 286 262 224

12 1131 905 754 646 565 503 452 411 377 323

16 2011 1608 1340 1149 1005 894 804 731 670 574

20 3142 2513 2094 1795 1571 1396 1257 1142 1047 898

25 4909 3927 3273 2805 2454 2182 1964 1785 1636 1403

32 8042 6434 5362 4596 4021 3574 3217 2925 2681 2298

40 12566 10053 8378 7181 6283 5585 5027 4570 4189 3590

Asv/sv Ratio for Shear Link (2 legs)

Spacing of Links in (mm)

Link Size (mm)80 100 125 150 175 200 225 250 275 300 325 350

8 1.257 1.005 0.804 0.670 0.574 0.503 0.447 0.402 0.366 0.335 0.309 0.287

10 1.964 1.571 1.257 1.047 0.898 0.785 0.698 0.628 0.571 0.524 0.483 0.449

12 2.827 2.262 1.810 1.508 1.293 1.131 1.005 0.905 0.823 0.754 0.696 0.646

16 5.027 4.021 3.217 2.681 2.298 2.011 1.787 1.608 1.462 1.340 1.237 1.149


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Shear

Reproduced from Hong Kong Code of Practice for Structural Use of Concrete (2004)


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Deflection:



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Deflection:

Effective Flange Width


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Force Coefficients:

Table 6.5 Bending moment coefficients for slabs spanning in two directions at right

angles, simply supported on four sides

ly / lx 1.0 1.1 1.2 1.3 1.4 1.5 1.75 2.0

sx 0.062 0.074 0.084 0.093 0.099 0.104 0.113 0.118

sy 0.062 0.061 0.059 0.055 0.051 0.046 0.037 0.029



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Two-Way Spanning Slabs:



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Two-Way Spanning Slabs:



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B. Design Formulae for Prestressed Concrete Structures

B1.1 Concrete Stresses at transfer:

'min

ftZ

iM

tZ

ei

P

cA

iP and '

maxf

bZ

iM

bZ

ei

P

cA

iP

B1.2 Concrete stresses at service:

maxf

tZ

sM

tZ

ei

P

cA

iP and

minf

bZ

sM

bZ

eiP

cA

iP

B2. Section modulus:

min'max ff

iMsM

tZ

and

minmax' ff

iMsM

bZ

B3. Prestressing force based on allowable stresses:

)min'max'

(

tZbZ

ftZfbZcA

iP or )min

max(

tZbZ

fbZftZcA

iP

The greater value of Pi obtained from the above equations should be used.

B4. Prestressing force and eccentricity:

)/(

min'

ec

At

Z

iMf

tZ

iP

iP

iMfZ

iP

cA

tZ

e

t

)

min'(

)/(

max'

e

c

A

b

Z

iMf

bZ

iP

i

P

iMfZ

iP

cA

bZ

e

b

)max'(

)/(

max

ec

At

Z

sMftZ

iP

i

P

sMfZiP

cA

tZ

e

t

)max(

)/(

min

ec

Ab

Z

sMfbZ

iP

i

P

sMfZiP

cA

bZ

e

b

)

min(


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B5. Prestress Loss:

B5.1 Relaxation:

Loss of prestress =1000 hr

relaxationx

relaxation

factorx

initial prestress

in steel

Table 1 Relaxation Factor

Wires and strands

Class 1 Class 2 Bars

Normal Relaxation Low Relaxation

Pre-tensioning 1.5 1.2 -

Post-tensioning 2.0 1.5 2.0

B5.2 Elastic Deformation:

I

eM

r

eA

Am

ff i

ps

c

pi

co

)1(2

2

at mid-span

Loss = m fco for pre-tensioned member

Loss = m fco for post-tensioned member with sequential tensioning

B5.3 Shrinkage:

CS = Cs kL kC ke kj in microstrains

Loss of prestress = CS Es

B5.4 Creep:

28E

fccc

= kL km kc ke kjLoss of prestress = cc Es

B5.5 Anchorage Draw-in:

p

pssad

A

AEx


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B5.6 Friction due to Curvature and 'Wobble' effect:

)(

0

KxR

x

x ePP or )](1[0 Kx

R

xPPx

R = L2

/ 8 dr

where dr

is the drape

B6. Moment Capacity:

Neutral axis depth trial: ' = (1 + 2c

s

F

F) /3

Strain in steel: 0.0035/x = p/(d-x)

B7. For unbonded tendons in rectangular section or flanged section in which stress block lies within

the flange.

bdf

Af

dl

ffcu

pspupepb 7.11

7000

df

f

bdf

Afx

pu

pb

cu

pspu47.2

B8. Shear Resistance

Uncracked Shear resistance:

tcp2tvco f0.8ffh0.67bV where ft = 0.24 fcu

Cracked Shear resistance:

cuv

0

vcpu

pe

cr fd0.1bthanlessnotbutVM

M

db)vf

f

0.55(1V

Mo =0.8 [fptI/y]

d)(0.87f

V-V

s

A

yv

c

v

sv if V - Vc > 0.4 b d


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B9. Deflection

Deflection due to uniformly distributed load :

EI

wLy

4

384

5 Deflection due to prestress force from straight tendon :

EI

PeLy

8

2

Deflection due to prestress force from symmetrical parabolic tendon profile: EI

LPey c

2

48

5

Table 2 Short Term Elastic Modulus of Concrete (Hong Kong)

Characteristic Strength Modulus of

at Age Considered (N/mm2) Elasticity (N/mm

2)

20 18900

25 20200

30 21700

40 24000

45 26000

50 2740055 28800

60 30200



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C. Design Formulae for Water Retaining Structures

C1. Allowable steel stresses in direct or flexural tension for SLS (Table 3.1 of BS 8007)

Design crack width Allowable stress (N/mm2)

(mm) Plain bars Deformed bars

0.1 85 100

0.2 115 130

C2 Elastic design

Depth of neutral axis:

dxe

e

121

Level Arm3

xdz

Moment of resistance zfbxzfAM cbssr 5.0

C3.1 Crack width calculations (direct tension)

Steel: yss

ys ff

E

f8.0or

8.0

Average strain 21 m andssEA

T1 For a limiting design surface crack width of 0.2 mm:

ss

t

AE

hb

3

22

For a limiting design surface crack width of 0.1 mm:

2ss

t

AE

hb

The design surface crack width mcraw 3


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C3.2 Crack width calculations (flexure)

Concrete: cucb ff 45.0

Steel: yss

ys ff

E

f8.0or

8.0

Average strain 21 m and ss

E

f

xd

xh 1


xdAE

xaxhb

ss

t

3

'2


xdAE

xaxhb

xdAE

xaxhb

ss

t

ss

t

2

'or

3

'5.122

The design surface crack width

xh

ca

aw

cr

mcr

min21

3

Where222

22

csacr

C3.3 Crack width calculations (Temperature and moisture effects)

Crack width max21 sTTRw

C4. Critical Steel:y

ctcrit

crit

s

f

f

bh

A

C5. Maximum crack spacing:

cb

ct

f

fss

22max

For Type 2 deformed bar,b

ctf

f= 3

2



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Typical value of T1 ( C ) for Hong Kong condition

Cement content

(kg/m3)

Steel Formwork 18 mm Plywood

Formwork

Winter Summer Winter Summer

300 12 18 20 28350 15 23 27 35

400 17 27 32 43

T2 = 20C in summer and 10C in winter

Restraint Factor R

Restraint condition Restraint Factor

R

External : Base cast onto blinding 0.2

Edge restraint in box typedeck cast in stages

0.5

Wall cast onto base 0.6

Edge element cast onto slab 0.8

Infill bays 1.0

Internal : 0.5

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