Thermal Stress and Spring Systems

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SUMMARY

The discussion focuses on calculating the force in an A-36 steel rod with a diameter of 0.25 inches and a length of 4 feet when subjected to thermal stress. The rod is attached to springs with a spring constant of k=10,000 lb/in, initially compressed by 0.5 inches at 40°F. To find the force at 160°F, the thermal deformation is calculated using the equation Thermal Deformation = alpha * change in temp * length, followed by applying F = kx to determine the force, which is confirmed to be 163 lbs.

PREREQUISITES
  • Understanding of thermal expansion principles, specifically linear thermal expansion.
  • Familiarity with Hooke's Law and spring constants.
  • Basic knowledge of material properties, particularly for A-36 steel.
  • Ability to perform unit conversions and apply temperature changes in calculations.
NEXT STEPS
  • Study the concept of linear thermal expansion and its formula.
  • Learn more about Hooke's Law and its applications in mechanical systems.
  • Investigate the properties of A-36 steel, including its thermal expansion coefficient.
  • Practice solving similar problems involving thermal stress and spring systems.
USEFUL FOR

Mechanical engineers, materials scientists, and students studying thermal stress analysis in mechanical systems will benefit from this discussion.

christina12345
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The rod is made of A-36 steel and has a diameter of 0.25 in and a length of 4 ft. Attached to each end of the rod is a spring which is fixed to a wall. If the springs are compressed 0.5 in. when the temperature of the rod is T=40 F, determine the force in the rod when its temperature is T=160 F. It is given that k=10,000 lb/in.

Equations: F=kx, Thermal Deformation=alpha*change in temp*length

Attempted Solution: Find the thermal deformation in the rod at T=160 F, then use this in F=kx to solve for F.

I know the correct answer is 163 lbs, but I don't understand why.
 
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