This document provides methods for designing reinforced concrete slabs using working stress design and ultimate strength design. It discusses one-way and two-way slab design, including defining characteristics, load calculations, moment calculations, depth checks, and steel calculations. Formulas are provided for slab thickness selection, elastic constant calculation, load calculations considering dead and live loads, moment determination using code coefficients, minimum steel requirements, and distribution steel spacing.

1. [Date]
Priodeep Chowdhury;Lecturer;Dept. of CEE; Uttara University// Slab Design
1
This method directs attention to stress conditions within the structural member under
working loads.
Working stress design is based on just such a stress distribution, on the grounds that elastic
stress limits are not exceeded at working loads.
 By working-stress methods, allowable stresses are established as some fraction of the stress
capacities of the materials i.e. the yield strength of the steel and the cylinder strength of the
concrete.
 Members are proportioned so that these allowable stresses are not exceeded when working
loads are applied.
 Working load is defined as the sum of the actual dead load of the structure and an estimate of
the maximum live load, which will be superimposed at some time during its life.
This method focuses on the strength capacity of the member at conditions corresponding
to failure and is known as ultimate-strength design. This design is based on the nonlinear
compressive- stress variation, which is obtained before a member fails.
USD method, base the design of members on conditions just before failure. Members are
proportioned so that the lull strength of the cross-section is just utilized when the ultimate load is
applied.
The ultimate load is obtained by multiplying the actual dead load and the anticipated live load
by separate overload factors greater than unit.

2. [Date]
Priodeep Chowdhury;Lecturer;Dept. of CEE; Uttara University// Slab Design
2
In reinforced concrete structures, slabs are used to provide flat, useful
surfaces. A reinforced concrete slab is a broad, flat plate usually horizontal
with top and bottom surfaces parallel or nearly so. Reinforced concrete
beams, may support it by masonry or reinforced concrete walls, by
structural steel members, directly by columns or continuously by the
ground.
Types of slab:
According to distribution of load along side, slabs are of two types –
1. One way slab
2. Two way slab
There are other types of slabs, such as flat plate slab, flat stab, folded plate slab, reinforced
brick slab, ribbed slab, hollow slab etc.
One Way Slab:
Slabs may be supported on two opposite sides only in which case, the structural action of
the slab is essentially one- way the loads being carried by the slab in the direction perpendicular to
the supporting beams, then the slab is called one way slab.
Slabs may be supported on all four sides in which case if the ratio of length to width of one slab
panel is larger than 2, most of the load is carried in short direction and to the supporting members
and one- way action is obtained. In one way, slab main reinforcement is placed in the shorter
direction.
Two way slab
If the slab in two directions is essentially in two ways and the load carrying the structural
action of the slab then the slab is called two- way slabs. If the ratio of length to width of one panel
is equal or smaller than 2 then the slab is two way. In two ways, slab main reinforcement is provided
in both the shorter and longer direction.
One way slab design formulae
Method: Working Stress Design (W S D)
1. Design data
» La = Clear span in short direction in ft
» Lb = Clear span in long direction in ft
» f’y = Yield strength of steel, psi
» f’c = Crushing strength of concrete, psi
» DL = Sum of all Dead Load [ excluding self weight ]
» LL = Live load, psf
2. Condition:
Lb/La > 2

3. [Date]
Priodeep Chowdhury;Lecturer;Dept. of CEE; Uttara University// Slab Design
3
3. Elastic constant calculation:
» Es = 29 x 106
psi
» Ec = 57000√ fc'
» fs = 0.4f’y
» fc = 0.45f’c
» r = fs/fc
» n = Es/Ec
» k = n/(n+ r)
» j = 1-k/3
4. Selection of slab thickness:
Minimum slab thickness from deflection point of view. (According to ACI Code)
» Assume, slab thickness = t inch
» Effective depth, d= t – 1
5. Load calculation:
o Calculation, self-weight, SW = t/12 x 150
o Total load W = DL+ LL+ SW
6. Moment calculation:
Moment from ACI code moment co-efficient
M = C x W x La
2
(C = ACI code moment co-efficient)
7. Depth check:
dreq = √
𝐌
𝐑𝐛
[ b = 12 inch]
d = t- 1
If, d> dreq. Hence; depth is ok.
[If, d<dreq. Change slab thickness and repeat from step (4) to (7)]
8. Steel calculation:
As = (
𝐌
𝐟𝐬𝐣𝐝
)
Asmin = 0.0025bt
If As< Asmin then As = Asmin
9. Distribution steel:
As = 0.002bt
[*Specification: Maximum spacing = 2t.]

4. [Date]
Priodeep Chowdhury;Lecturer;Dept. of CEE; Uttara University// Slab Design
4
One way slab design formulae
Method: Ultimate Strength Design (U S D)
1. Design data: Mentioned as above
2. Condition: Lb/La> 2
3. Elastic constant calculation:
If f’c= 4000 psi then β1 = 0.85
If f’c> 4000 psi then β1 = 0.8
Balance steel ratio –
4. Selection of slab thickness: Mentioned as above.
5. Load calculation:
DL = Dead load (including self-weight)
LL = Live load
Total load, W = 1.4 x (DL+ SW) + 1.7 x LL
6. Moment calculation:
Moment from ACI code moment co-efficient
M = C x W x La
2
C = ACI code moment co- efficient.
7. Depth check:
If d > dreq; Depth is OK.
If d < dreq; increase slab thickness.
8. Steel calculation:
9. Temperature and shrinkage steel:
 If f’y= 50000 psi then, Asmin = 0.002bt
 If f’y=60,000 Asmin = 0.0018bt
 If f’y> 60000 psi then Asmin = 0.0018 x 60000 x bt/fy

5. [Date]
Priodeep Chowdhury;Lecturer;Dept. of CEE; Uttara University// Slab Design
5
Two way slab design formulae
Method: Ultimate Strength Design (U S D)
1. Selection of slab thickness:
Minimum slab thickness, tmin= 2(La + Lb) / 180 inch
Assume slab thickness = t
Effective depth in short direction; dsor = t-1 inch
Effective depth in long direction; dlon = t –1.5 inch
2. Load calculation:
Total load W = DL + LL + SW (Self weight) [ For WSD]
Total load W = DL x 1.4 + LL x 1.7 + SW x 1.4 (Self weight) [ For USD]
3. Moment calculation:
Panel ratio, m = La/Lb
(a) Negative moment at continuous edges:
Maneg = Caneg x W x La2
Mbneg = Cbneg x W x Lb2
Caneg, Cbneg = Co- efficient for negative moments in slabs from panel ratio and support condition.
(b) Positive moment at mid span:
Ma.pos.dl = Capdl x DL x La2
Ma.pos.ll = Capll x LL x La2
Ma.pos.tot = Mapos.dl + Mapos.ll
Mb.pos.dl = Cbpdl x DL x Lb2
Mb.pos.ll = Cbpll x LL x Lb2
Mb.pos.tot = Mbpos.dl + Mbpos.ll
»» Ca.dl, Cbdl = Co- efficient for dead load positive moments.
»» Ca.ll, Cbll = Co- efficient for live load positive moments.
(c) Negative moments at discontinuous ends:
Ma.neg = 1/3 x Mapos.tot
Mb.neg = 1/3 x Mb.pos.tot
4. Depth check:
Find Mmax

6. [Date]
Priodeep Chowdhury;Lecturer;Dept. of CEE; Uttara University// Slab Design
6
If, dreq.< dsor then depth is Ok.
If dreq.>dsor then increase the depth and repeat depth check
5. Steel calculation:
Calculate steel for long and short direction.
(a) For continuous ends
(b) For mid span
(c) For discontinuous ends
6. Temperature and shrinkage steel