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Reinforced Concrete Design

Design of concrete slab on grade

Slab Reinforcement and spacing of control joints.

When concrete slab are poured on grade, steel reinforcement and control joints are used to control shrinkage and expansion.  When concrete slab shrink or expansion, it will drag the soil beneath the slab with it.  Friction at bottom of slab is trying to prevent the slab from moving.  Steel reinforcement inside the slab is also trying to prevent the slab from shrink or expansion.  It is not practical to place large amount of reinforcement to completely prevent slab from shrink or expanse. Therefore, Control joints are normal placed at a distance to allow for the slab to shrink or expanse.  

Subgrade drag equation

PCA recommends that the area of steel per linear foot of slab width for slab on grade is

As = F L w / (2 fs)                                                    [1]

Where 

As = area of steel (in2) per linear foot of slab width.

F = coefficient of subgrade friction (F = 1.2 to 2 for pavement, F = 1.5 for concrete slab on grade)

L = Length of slab between control joint (feet)

w = weight of slab (lb/ft2)

fs = allowable working stress of reinforcement (lb/in2) is usually 0.67fy to 0.75 fy, fy is yield strength of reinforcing steel)

 

Example:

 

Given:

Length between Joint: 30 ft

Thickness of pool slab: 6 in

Slab reinforcement in the long direction:

Weight of slab: w = 150 lb/ft3 x 6 in = 75 lb/ft2

Yield strength of steel: 60 ksi

Allowable stress of reinforcement: fs = 0.75 x 60 ksi = 45 ksi

Coefficient of subgrade fraction: F = 1.5

Reinforcement required, As = F L w / (2 fs) = 0.037 in2/ft

Use Welded Wire fabric, WWW 6x6, W2.0xW2.0, Area = 0.04 in2/ft.