A highway is made of concrete slabs that are 14.0 m long at 20° C.
(a) If the temperature range at the location of the highway is from -17.8° C to +40.8° C, what size expansion gap should be left (at 20° C) to prevent buckling of the highway?
(b) How large are the gaps at -17.8° C?
To calculate the size of the expansion gap, we need to consider the coefficient of thermal expansion of the concrete slabs. The coefficient of thermal expansion measures how much a material expands or contracts with a change in temperature.
(a) Let's calculate the expansion gap required at 20°C to prevent buckling.
1. Determine the coefficient of thermal expansion: The coefficient of thermal expansion for concrete typically ranges from 10 to 12 x 10^-6 per °C. Let's assume a value of 11 x 10^-6 per °C for this calculation.
2. Calculate the change in length: To find the change in length of the concrete slabs, we multiply the coefficient of thermal expansion by the change in temperature. In this case, the change in temperature is 40.8°C - 20°C = 20.8°C.
Change in length = coefficient of thermal expansion * change in temperature
Change in length = 11 x 10^-6 per °C * 20.8°C
3. Calculate the expansion gap: The expansion gap should be large enough to accommodate the change in length of the slabs. Thus, the expansion gap size is equal to the change in length.
Expansion gap size = Change in length
Expansion gap size = 11 x 10^-6 per °C * 20.8°C
(b) Now, let's calculate the size of the gaps at -17.8°C.
1. Calculate the change in length: Similar to part (a), we multiply the coefficient of thermal expansion by the change in temperature. In this case, the change in temperature is -17.8°C - 20°C = -37.8°C since we are subtracting a negative temperature.
Change in length = coefficient of thermal expansion * change in temperature
Change in length = 11 x 10^-6 per °C * -37.8°C
2. Calculate the gap size: The gap size is equal to the change in length.
Gap size = Change in length
Gap size = 11 x 10^-6 per °C * -37.8°C
Note: The negative sign indicates a contraction in length due to cooling.