What is the purpose of reducing the seasonal and hydration temperature by one-half in the calculation of crack widths arising from thermal movement?

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

w_max=sa(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 between peak of hydration and ambient
temperature
T₂= fall in temperature due to seasonal variation

For T₁, it represents the situation when the freshly placed concrete is under hydration process. Since the occurrence of high creep strain to the 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 the seasonal drop in temperature for the mature concrete. Owing to the maturity of concrete in this stage, the effect of creep on concrete is reduced accordingly. Since the ratio of tensile strength of concrete (fct) to average bond strength between concrete and steel (fb) increases with maximum crack spacing, the lower values of f_ct/ f_b in mature concrete leads to smaller crack spacing. Therefore, the increased number of cracks helps to reduce the effect of thermal movement brought about by seasonal variation. Hence, T₂ is reduced by one-half to cater for further creep and bond effects in mature concrete.

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