Thermal Stress in a Restrained Member
Hardthermal stressrestraint
A steel member is held between rigid supports so it cannot expand, then heated by 40 °C. Taking α = 12 × 10⁻⁶ per °C and E = 200 GPa, the magnitude of the induced axial stress is most nearly:
- A48 MPa
- B96 MPa
- C192 MPa
- D240 MPa
Show solutionHide solution
Answer: B. 96 MPa
Full restraint means the free thermal strain αΔT is entirely converted into stress: σ = EαΔT = (200,000 MPa)(12 × 10⁻⁶)(40) = 96 MPa, in compression because the bar is prevented from growing. The member length never enters — a common misconception, since a longer restrained bar develops the same stress.
Practice this deckUntimed, one problem at a time, with your progress saved.
Related problems
- Axial Normal Stress from Load and Area · Stress & Strain
- Axial Strain from Stress and Modulus · Stress & Strain
- Elongation of an Axially Loaded Bar · Stress & Strain