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Reinforced Concrete Design

One way slab design example

Example 1: Design of interior three span slab as shown below

Design code: ACI 318-05

Design data:

Number of span: 3

Length of spans: L1 = 20 ft, L2 = 24 ft, L3 = 20 ft

Thickness of slab: 6 in

Live load: WL = 50 psf

Superimposed dead load: WSD = 10 psf

Concrete compressive strength: fc' = 4000 psi

Yield strength of steel: fy = 60 ksi

Requirement: design slab reinforcement use ACI factors and check deflection

1. Check if two adjacent spans differ more than 20%.

    L2/L1 = 120%,     L2/L3 = 120 %        O.K.

Weight of slab: Ws = 75 psf

Total dead load: WD = 75 + 10 = 85 psf

Live load to dead load ratio: WL/WD = 0.6   < 3 O.K.

Calculate slab moments using ACI factors:

Assume 1 ft width of slab for calculation, b = 1 ft

Factored load: Wu = (1.2*85+1.6*50) * 1 = 182 lb/ft    (ACI 318-02, 05)

Positive moment:

Exterior span: Mu1 = 182*202 / 14 /1000 = 5.2 ft-kip

Interior span: Mu2 = 182*242 / 16 /1000 = 6.6 ft-kip

Negative moment:

Exterior face of first interior support: Mu3 = 182*202 / 10 /1000 = 7.3 ft-kip

Interior face of first interior support: Mu4 = 182*242 / 11 /1000 = 9.5 ft-kip

Interior face of Exterior support: Mu1 = 182*202 / 24 /1000 = 3.0 ft-kip

Design Positive moment reinforcement

Exterior span

Factored moment: Mu1 = 5.2 ft-kip

Concrete cover: 0.75"  for interior slab

Effective depth: d = 6 - 0.75-0.5 = 4.75 in

Factor: Rn = Mu1/(0.9 b d2 ) = 256.1 psi    m = fy/(0.85 fc') = 17.7

Reinforcement ratio, r = 1/m [ 1 - ( 1 - 2 m Rn / fy )]  = 0.00444

Area of reinforcement, As = r b d = 0.253 in2.

Use #5 at 12" O.C. area of reinforcement = 0.3 in2.

Interior span

Factored moment: Mu2 = 6.6 ft-kip

Factor: Rn = 322.7 psi    m = 17.7

Reinforcement ratio, r = 0.0057

Area of reinforcement, As = r b d = 0.323 in2.

Use #5 at 11" O.C. area of reinforcement = 0.327 in2.

Negative moment reinforcement

Design negative reinforcement for first interior support, 

Factored moment: Mu4 = 9.5 ft-kip

Factor: Rn = 469.3 psi    m = 17.7

Reinforcement ratio, r = 0.00845

Area of reinforcement, As = r b d = 0.482 in2.

Use #6 at 10" O.C. area of reinforcement = 0.528 in2.

Design negative reinforcement for Exterior support

Factored moment: Mu4 = 3.0 ft-kip

Factor: Rn = 149.4 psi    m = 17.7

Reinforcement ratio, r = 0.00255

Use minimum reinforcement, area of reinforcement, As = 1.33 r b d = 0.194 in2.

Use #4 at 12" O.C. area of reinforcement = 0.2 in2.

Temperature reinforcement: As = 0.0018*6*12 = 0.13 in2.

Use #4 at 18" O.C., area of reinforcement 0.133 in2.