Calculating Thermal StressConcrete blocks are laid out next to each other on a highway without any space between them, so they cannot expand. The construction crew did the work on a winter day when the temperature was 5 °C . Find the stress in the blocks on a hot summer day when the temperature is 38 °C . The compressive Young’s modulus of concrete is Y = 20 × 109 N/m2 .StrategyAccording to the chapter on static equilibrium and elasticity, the stress F/A is given by FA = Y ΔLL0, where Y is the Young’s modulus of the material—concrete, in this case. In thermal expansion, ΔL = αL0 ΔT.We combine these two equations by noting that the two ΔL’s are equal, as stated above. Because we are not given L0 or A, we can obtain a numerical answer only if they both cancel out.
Calculating Thermal Stress
Concrete blocks are laid out next to each other on a highway without any space between them, so they cannot expand. The construction crew did the work on a winter day when the temperature was 5 °C . Find the stress in the blocks on a hot summer day when the temperature is 38 °C . The compressive Young’s modulus of concrete is Y = 20 × 109 N/m2 .
Strategy
According to the chapter on static equilibrium and elasticity, the stress F/A is given by FA = Y ΔLL0, where Y is the Young’s modulus of the material—concrete, in this case. In thermal expansion, ΔL = αL0 ΔT.
We combine these two equations by noting that the two ΔL’s are equal, as stated above. Because we are not given L0 or A, we can obtain a numerical answer only if they both cancel out.
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