A good joint is supposed to have certain requirements. They are that joint must be free to move, it must prevent any sort of infiltration and it must not protrude beyond general level of slab.

\(L_e=\frac{?}{100C(T_2-T_1)}\) is equation used to find spacing of expansion joints. As per question,
δ =2.5/2=1.25 cm C=10×10^-6/°C T₁=14°C T₂=50°C
Therefore, \(L_e=\frac{?}{100C(T_2-T_1)} =\frac{1.25}{100×10×10^{-6}×(50-14)}\)=34.72 m

The load stress decreases in order at corner, edge and interior part of pavement. The temperature stress, on or hand, increases in that order. Therefore, corner of pavement experiences least stress due to wheel loads.

The equivalent wheel load is obtained by considering equivalency of load to 2268 kg load. It is obtained by dividing 105000 by number of repetitions corresponding to load that is considered. The equivalency in question is 105000/22500 = 4.66. The equivalent wheel load can be written as closest power of 2, i.e. equivalent load factor would be 4.

To find length of dowel bar sum L_d + δ is used, where L_d is embedded length and ? is width of joint. The equation to find embedded length is given by:
\(L_d=5d\left(\frac{F_f}{F_b} ×\frac{L_d+1.5?}{L_d+8.8?}\right)^{1/2}\)
Where, F_f is allowable flexural stress = 1400 kg/cm²
F_b is allowable bearing stress in concrete = 100 kg/cm²
d is diameter of dowel bar and it can be assumed as 2.5 cm
δ is width of joint = 2.5 cm
After substituting all values in equation,
\(L_d=5×2.5\left(\frac{1400}{100}×\frac{L_d+1.5×2.5}{L_d+8.8×2.5}\right)^{1/2}\)
\(L_d=12.5\left(14×\frac{L_d+3.75}{L_d+22}\right)^{1/2}\)
The next step is to find value of Lsub>d using trial and error method. This is in accordance with method prescribed by IRC 58:1988.
Assuming L_d = 45 cm for first trial,
\(L_d=12.5\left(14×\frac{45+3.75}{45+22}\right)^{1/2}\)=39.89 cm
39.89 is less than 45 cm, now assume 39.5 cm
\(L_d=12.5\left(14×\frac{39.5+3.75}{39.5+22}\right)^\frac{1}{2}\)=39.22 cm
39.22 cm is less than 39.5 cm, now assume 39.2 cm,
\(L_d=12.5\left(14×\frac{39.2+3.75}{39.2+22}\right)^{1/2}=39.18 ?39.2\) cm
Therefore, L_d is obtained as 39.2 cm.
The length of dowel bar would be = L_d + δ = 39.2 + 2.5 = 41.7 cm

The fatigue life and stress ratio can be related to each or using different equations for range of stress ratio. When stress ratio is less than 0.45, fatigue life is considered to be unlimited. For condition 0.45 ≤stress ratio≤ 0.55, re is an equation and for stress ratio > 0.55, re is anor equation.

\(L_e=\frac{?}{100C(T_2-T_1)}\) is equation used to find spacing of expansion joints. In equation, term ? represents half width of joint, C is coefficient of rmal expansion of concrete and T₂-T₁ indicates rise in temperature during expansion.

The equation to \(f_{cr}=0.49f_{ck}^{0?55}\) find flexural strength of concrete was given by Croney and Croney when gravel aggregates are used. The equation can be slightly modified for crushed aggregates as \(f_{cr}=0.36f_{ck}^{0?7}\) .

The maintenance requirements in case of rigid pavement is reduced to almost half of that required in flexible pavements. The main area of pavement that needs to be checked and maintained is joints. These are weak points and are prone to damage.

A joint sealer is provided atop filler in between joints to prevent entry of debris and it must be durable to do that. It must also possess extensibility so that it doesn?t break easily and need maintenance. It must have adhesion with cement concrete edges for sealant to serve its purpose.