Plain & Reinforced Concrete-1

CE-313

Analysis and Design of Slabs

Sixth TermCivil Engineering

Plain & Reinforced Concrete-1

Example: Design a cantilever projecting out from a room slab extending 1.0m and to be used as balcony (LL = 300 kg/m2). A brick wall of 250 mm thickness including plaster of 1.0m height is provided at the end of cantilever

fc’ = 17.25 MPa fy = 300 MPa

Slab thickness of room = 125 mm. Slab bottom steel in the direction of cantilever is # 13 @ 190 mm c/c

Plain & Reinforced Concrete-1

Solution:

1m

125 mm

cantilever

2

h1000L

mm10632

1251000L

Plain & Reinforced Concrete-1

Solution: (contd…)

min

106389

12 12

lh mm

Let’s use the same thickness as of the room

minhmm125h

d

mm98720125d Main steel in cantilever is at the top

Plain & Reinforced Concrete-1

Solution: (contd…)

Slab Load

2m/kg30024001000

125Self weight of

slab

75 mm brick ballast/ screed

2m/kg13518001000

75

60 mm floor finishes

2m/kg13823001000

60

Total dead load 2m/kg573138135300

Plain & Reinforced Concrete-1

Solution: (contd…)

Slab Load2m/kg300Live Load

1000

81.93006.15732.1ωu

2u m/kN46.11ω

m/kN46.11ωu For a unit strip

1000

81.919301125.02.1Pu

kN65.5Pu

Plain & Reinforced Concrete-1

Solution: (contd…)

2

LωLPM

2u

uu

kN65.5Pu

1.063m

m/kN46.11ωu

2

063.111.46063.165.5M

2

u

mkN48.12Mu Per meter width

3.1981000

1048.12

bd

M2

6

2u

0488.0f

'f85.0ω

y

c

0.0052ρ

Plain & Reinforced Concrete-1

Solution: (contd…)

2s 510mm9810000.0052A

d

# 13 @ 380 mm c/c already available in the form half the bent up bar from the room slab

2s mm342Ac/c380@13#

Plain & Reinforced Concrete-1

Solution: (contd…)

2168mm342-510 Remaining steel required at the top

c/c400@10#

Use

c/c380@10#

Distribution steel

2mm2501251000002.0

c/c280@10#

Plain & Reinforced Concrete-1

Solution: #13 @ 380 c/c

#10 @ 380 c/c

#10 @ 280 c/c

1500 mm

Slab bottom steel

Plain & Reinforced Concrete-1

Two-Way Edge Supported Slabs

Plain & Reinforced Concrete-1

Two-Way SlabsSlab resting on walls or sufficiently deep and rigid beams on all sides. Other options are column supported slab e.g. Flat slab, waffle slab.

5.0L

Lm

y

x

Two-way slabs have two way bending unlike one-way slab.

Plain & Reinforced Concrete-1Design Methods

1. ACI co-efficient method2. Direct design method3. Equivalent frame method4. Finite element method

Notes

1. In two-way slabs shorter direction strip carry greater %age of load.

2. Steel will be more in shorter direction.3. Shorter direction steel will be placed near the

outer edge to get more “d” means more lever arm to get more flexural capacity.

Lx

Ly

Plain & Reinforced Concrete-1ACI Co-efficient Method

Unit width strip is taken in both directions. The strip is designed separately for +ve and –ve moment

2nuu LωCM

C = ACI co-efficientωu = Slab load

“C” depends upon the end conditions of slab and the aspect ratioThree tables are available for “C”

• Dead load positive moment

• Live load positive moment

• -ve moment

M+ coefficients are increased by 25 % and M- coefficients are reduced by 10 % to get the result more closer to accurate solution.

Plain & Reinforced Concrete-1

Minimum Depth of 2-Way Slab for Deflection ControlAccording to ACI-318-1963

hmin = (inner perimeter of slab panel)/180 ≥ 90 mm

For fy = 300 MPa

180

LL2h yx

min

For fy = 420 MPa

165

LL2h yx

min

According to ACI-318-2005

9m36

1500f8.0Lh yn

min

y

x

L

Lm

Ln = clear span in short direction

Plain & Reinforced Concrete-1Example: Design the 4 marked slab panels of an ordinary house. Use US customary bars. fc’= 17.25 MPa fy = 300 MPa

4500 x 7000

6000 x 7000

3500 x 6000

6000 x 6000

1 2

3 4

Wall thickness = 228 mm

Plain & Reinforced Concrete-1

Solution: Panel Edge Conditions

Panel # 1Lx = 4.5m , Ly = 7.0mm = 0.64 > 0.5, 2-way slab Panel # 2Lx = 6.0m , Ly = 7.0mm = 0.86> 0.5, 2-way slab Panel # 3Lx = 3.5m , Ly = 6.0mm = 0.58 > 0.5, 2-way slab Panel # 4Lx = 6.0m , Ly = 6.0mm = 1 > 0.5, 2-way slab

Plain & Reinforced Concrete-1

Solution: (contd…)

Slab Thickness

Generally same depth is preferred for one monolithic slab Calculate hmin for all the panels and select the largest value

9m36

1500f8.0Lh yn

min

Panel # 1

mm140

964.036

15003008.04500hmin

Panel # 2

mm150986.036

15003008.06000hmin

Plain & Reinforced Concrete-1

Solution: (contd…)

Panel # 3

mm117958.036

15003008.03500hmin

Panel # 4

mm1339136

15003008.06000hmin

mm150h

Plain & Reinforced Concrete-1Solution: (contd…)

Effective depth

mm12327hd1 For longer direction steel

d2 d1

Long direction steel

Short direction steel

mm1122101320hd2

For short direction steel

Plain & Reinforced Concrete-1

Solution: (contd…)

Slab Load

2m/kg36024001000

150Self weight of

slab

75 mm brick ballast/ screed

2m/kg13518001000

75

60 mm floor finishes

2m/kg13823001000

60

Total dead load 2m/kg633138135360

Plain & Reinforced Concrete-1

Solution: (contd…)

Slab Load2m/kg200Live Load

1000

81.96332.11.2ωd

2d m/kN45.71.2ω

2L

9.811.6ω 1.6 200 3.14 /

1000kg m

2u m/kN59.1014.345.7ω

Plain & Reinforced Concrete-1

Solution: (contd…)

Minimum Steel

bh002.0A mins

1501000002.0A mins 2

mins mm300A For a unit strip

Concluded