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Design of Simply Supported Slab

Slab design Example 02 Design of simply supported slab (Two way

spanning)

Span of slab 4.5m & 6.3m

Variable load 5 kN/mm2

Slab thickness 200 mm

Fck 25 N/mm2 fyk 500 N/mm2

Cover to the reinforcements 25mm

Office building

No Moment re-distribution

Ly/Lx =6.3/4.5

=1.4

Therefore slab is two way

Slab loading

Self weight = 200x25x10-3

= 5kN/mm2

Ultimate load = 1.35gk+1.5qk

= 1.35x5+1.5x5

n = 14.25 kN/mm2

Bending moment coefficients for mid span

sx = 0.099

sy = 0.051

Bending moment in short span

Msx = sxn(lx)^2

= 0.099*14.25*4.5^2

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= 28.57 kN/mm2

Bending moments at long span

Msy = syn(lx)^2

= 0.051*14.25*4.5^2

= 14.72 kN/mm2

Assume T12 bars used for short span and T10 bars for long span

Effective depth at short span

= 200-25-6

= 169mm

Effective depth at long span

= 200-25-12-5

= 158mm

Reinforcement for short span

K = Msx/bd2fck

= 28.57x10^6/1000x169^2x25

= 0.04

K = 0.60-0.182-0.21

No redistribution ,Therefore

= 1

k = 0.21

k>k

Compression reinforcement is not required

Z = (d/2)*(1+(1-3.53k)^0.5) 0.95d

= (169/2)*(1+(1-3.530.04)^0.5) 0.95169

= 162.81 160.55

Therefore

Z = 160.55

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As = Msx/0.87fyk*Z

= 28.57*10^6/(0.87*500*160.55)

= 409 mm2/m

Provide T10 @ 150mm C/C (As pro. = 523mm2/m)

Check for deflection

Allowable span/d eff. = (l/d)*F1*F2*F3

= As req. /bd

For simply supported slab

K = 1

o = (fck ^.5)/1000

= (25 ^.5)/1000

= 0.005

= 445/ (1000*169)

= 0.00263

0 >

Then

l/d = K{11+[1.5(fck^0.5) o/ + 3.2(fck^0.5)*( 0/ )-1]^1.5}

= K{11+[1.5*(25^0.5)0.005/0.00263]+ 3.2*(25^0.5)*

*[(0.005/0.00263)- 1]^1.5}

= 38.95

Normal slab

F1 = 1

Span is less than 7m

F2 = 1

F3 = 310/s 1.5

s = (fyk/s)(As,req/As,prov)(SLS Loads / ULS loads)(1/)

= (fyd)(As,req/As,prov)(gk+ 2qk) /(G gk + Qqk)(1/)

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= (500/1.15)(409/523)(5+0.3*5) /(1.35*5 + 1.5*5)(1/1)

= 155.09 N/mm2

F3 = 310/155.09

= 2.0 1.5

Hence,

F3 = 1.5

Allowable span/d eff. = 38.95*1*1*1.5

= 58.43

Actual span/ d eff. = 4500/169

= 26.63

Deflection check is ok

Reinforcement for long span

K = Msy/bd2fck

= 14.72x10^6/1000x158^2x25

= 0.024

K = 0.60-0.182-0.21

No redistribution, Therefore

= 1

k = 0.21

k>k

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Compression reinforcement is not required

Z = (d/2)*(1+(1-3.53k)^0.5) 0.95d

= (158/2)*(1+(1-3.530.024)^0.5) 0.95158

= 154.58 150.1

Therefore

Z = 150.1

As = Msx/0.87fyk*Z

= 14.72*10^6/ (0.87*460*150.1)

= 245 mm2/m

Provide T10 @ 200mm C/C (As provided 293mm2/m)

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Labels: Simply Supported Slab Design

Thursday, November 4, 2010

Design of Simply Supported Slab (one way spanning)

Slab design Example 01 Design of simply supported slab (one way

spanning)

Span of slab 4.5m

Variable load 4kN/mm2

Floor finishes and Ceiling load 1kN/mm2

Fck 25N/mm2 fyk 500N/mm2

Office building

No re-distribution of moments ( = 1)

Assume slab thickness 200mm

d = 200-25-5

= 170mm

Slab loading

Self weight = 200x25x10-3

= 5kN/m2

Total permanent load = 1+5

= 6kN/m2

Ultimate load = 1.35gk+1.5qk

= 1.35x5+1.5x6

Bending Moment = wl2/8

= (1.35x5+1.5x6)x4.5^2/8

= 31.9kNm

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Reinforcement

K = M/bd2fck

= 31.9x10^6/1000x170^2x25

= 0.044

K = 0.60-0.182-0.21

No redistribution ,Therefore

= 1

k = 0.21

k>k

Compression reinforcement is not required

Z = (d/2)*(1+(1-3.53k)^0.5) 0.95d

= (170/2)*(1+(1-3.530.049)^0.5) 0.95170

= 162.3 161.5

Therefore

Z = 161.5

As = M/0.87fykz

= 35.69*10^6/(0.87*500*161.5)

= 508 mm2

Provide T10 @ 150mm C/C (As pro. = 523mm2/m

Check for deflection

Allowable span/d eff. = (l/d)*F1*F2*F3

= As req. /bd

For simply supported slab

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K = 1

o = (fck ^.5)/1000

= (25 ^.5)/1000

= 0.005

= 508/ (1000*170)

= 0.00299

0 >

Then

l/d = {11+[1.5*(fck^0.5) o/ + 3.2(fck^0.5)*( 0/ )-1]^1.5}

={11+[1.5*(25^0.5)0.005/0.00299]+ 3.2*(25^0.5)*[(0.005/0.00299)-1]^1.5}

= 32.36

Normal slab

F1 = 1

Span is less than 7m

F2 = 1

Steel ratio

F3 = 310/s 1.5

s = (fyk/s)(As,req/As,prov)(SLS Loads / ULS loads)(1/)

= (fyd)(As,req/As,prov)(gk+ 2qk) /(G gk + Qqk)(1/)

= (500/1.15)(508/525)(5+0.3*6) /(1.35*5 + 1.5*6)(1/1)

= 151.85 N/mm2

F3 = 310/151.85

= 2.04 1.5

Hence,

F3 = 1.5

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Allowable span/d eff. = 32.36*1*1*1.5

= 48.54

Actual span/ d eff. = 4500/170

= 26.47

Deflection check is OK

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Labels: Simply Supported Slab Design

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