Thermal Stress and Deformation

Problem 1: Thermal Stress and Deformation (Unrestrained and Restrained)

A metal bar is 4m long at 30ºC. If the temperature rises to 85ºC, determine the following if its coefficient of thermal expansion is 11.6x10^-6mm/mmºC.
a. The total length (m) of the bar at 85ºC.
b. The stress (MPa) on the bar.
c. If the ends of the bar are prevented from expanding, how much stress (MPa) is produced on the bar? Use E = 200GPa.

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Problem 2: Steel Rod Stretched between Two Supports with Stress Conditions

A steel rod 3ft long with a cross-sectional area of 0.25in² is stretched between two fixed points. The tensile force is 1200lb at 40ºF. Using E=29x10⁶psi and α=6.5x10^-6mm/mmºF, determine the following:
a. The temperature at which the stress in the bar is 10ksi.
b. The temperature at which the stress in the bar is zero.
c. The temperature at which the stress in the bar is 3200psi.

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Problem 3: Statically Indeterminate Members and Yielding of Support

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Problem 4: Bar with Gap at the Support

The bronze bar 3m long with a cross-sectional area of 350mm² is placed between two rigid walls. At a temperature of -20ºC, there is a gap Δ=2.2mm, as shown in the figure. Find the temperature at which the compressive stress in the bar will be 30MPa. Use α=18.0x10^-6/ºC and E = 80GPa

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Problem 5:

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Problem 6:

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Problem 7:

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Problem 8:

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