Question

A cement concrete pavement slab is 3.75 m wide, 15 m long and 200 mm thick. The concrete weighs 2400 kg/m${}^3,$ working stress in the steel is 1400 kg/cm${}^2.$ Coefficient of friction is 1.5. The total cross-sectional area of longitudinal reinforcing steel bars required is ___cm${}^2.$

• A. 7.23
• B. 14.46
• C. 9.64
• D. 28.92

Answer 1

The correct option is B 14.46


Assuming the longitudinal reinforce takes the entire tensile force in the slab, caused by the frictional resistance of subgrade, then
$A_s\times S_e=f\times b\times \frac{L_c}{2}\times \frac{h}{100}\times \gamma$
$\Rightarrow A_s=\frac{b\times h\times f\times \gamma \times L_C}{200\times S_s}$
Where, $A_s=$ Area of steel per m length of joint in cm ${}^2$
f = Coefficient of friction between pavement and subgrade
b = Distance between joint and nearest free edge in m
h = thickness of pavement in cm
$\gamma$ = unit weight of cement concrete in $kg/m^3$
$S_s$ = allowable working stress in tension for steel in kg/cm${}^2$
$L_c=$ length of the slab in metre
$Hence,A_s=\frac{3.75\times 0.2\times 1.5\times 2400\times 15}{200\times 1400}{m}^2$
$A_s=14.46c{m}^2$