Q. Calculation of crack widths arising from thermal movement

In the calculation of thermal movement, the below formula is used in most codes:

w_max=s x a x (T₁+T₂)/2 

Where w_max = maximum crack width; s = maximum crack spacing 

a = coefficient of thermal expansion of mature concrete

T1= fall in temperature amid peak of hydration and ambient temperature

T2= fall in temperature owing to seasonal variation

For T1 it signifies the situation when freshly placed concrete is under hydration process. As the occurrence of high creep strain to immature concrete tends to offset the effect of early thermal movement, a factor of 0.5 is purposely introduced to take into account such effect.

For T2 it refers to seasonal drop in temperature for mature concrete. Because of the maturity of concrete in this stage, effect of creep on concrete is decreased accordingly. As the ratio of tensile strength of concrete (f_ct) to average bond strength between concrete and steel (f_b) increases with maximum crack spacing, lower values of f_ct/ f_b in mature concrete results in smaller crack spacing. Consequently the increased number of cracks helps to decrease the effect of thermal movement brought about by seasonal variation. Hereafter T2 is decreased by one-half to cater for further creep and bond effects in mature concrete.