The 'temperature stress' in a bar fixed at both ends is:
Choose the correct answer
σ = E×α×ΔT×L (includes length)
σ = E×α×ΔT (compressive) — restrained expansion creates stress proportional to thermal strain
Zero (temperature causes no stress)
σ = α×ΔT only (no E needed)
Correct Answer
B. σ = E×α×ΔT (compressive) — restrained expansion creates stress proportional to thermal strain
Why is this the answer?
Temperature stress: bar fixed at both ends, temperature rises by ΔT. Free thermal strain = αΔT, but restrained → compressive stress developed = E×αΔT (compressive because bar wants to expand but cannot). No strain in bar. If one end is free: expansion ΔL = αΔTL, no stress. For prestress: temperature stress important in bridges where expansion joints are limited.
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