The thickness of a PCC pavement is 24 cm and width of lane is 3.5 m. Find length of a tie bar system along longitudinal joints if allowable working stress in concrete is 1250 kg/cm², unit weight of concrete is 2400 kg/m³, coefficient of friction is 1.5, allowable bond stress in deformed bars is 24.6 kg/cm² and allowable tensile stress in deformed bars is 2000 kg/cm².

There is a set procedure given by IRC to find the length of a tie bar system and it is carried out below.
Step 1: Cross-sectional area of the tie bar
\(A_s=\frac{fWbh×10^{-2}}{s_s}\)
Where A_s is the cross-sectional area
f is the coefficient of friction = 1.5
W is the unit weight of concrete = 2400 kg/m³
b is the width of the slab = 3.5 m
h is the thickness of the slab = 24 cm
S_s is the allowable tensile stress in deformed bars = 2000 kg/cm²
Substituting these in the equation,
\(A_s=\frac{1.5×2400×3.5×24×10^{-2}}{2000}\)=1.51 cm²
Step 2: Length of the tie bar
\(L_t=\frac{S_s d}{2S_b}\)
Where L_t is the length of the tie bar
S_s is the allowable tensile stress in deformed bars = 2000 kg/cm²
d is the diameter of the tie bar and it is assumed as 1.2 cm
S_b is the allowable bond stress in deformed bars = 24.6 kg/cm²
After substituting these in the equation,
\(L_t=\frac{2000×1.2}{2×24.6}=48.78?50\) cm