Determine the stress experienced by the member if it is cooled and heated from room temperature. 9.9 A steel member is fully restrained against tension and compression. At room temperature(70°F), the member has a tensile stress of 11 830 lb/in².(a) Determine the stress experienced by the member if it is cooled from room tempera-ture to 50°F.(b) Determine the stress experienced by the member if it is heated from room tempera-ture to 100°F.(c) Determine the stress experienced by the member if it is heated from room tempera-ture to 150°F.

The member experiences stress due to thermal change only when it is restrained. This stress is because the length of the member is not changed with the change in temperature. This produces stresses in the member. When restrained, cooling produces tensile stresses while heating produces compressive stresses. Steel has a fairly high expansion and contraction due to temp changes as compared to other metals.We have to calculate the stresses in the steel member. For this we need to use the standard properties of the material namely Modulus of Elasticity and Coefficient of Thermal Expansion. For Steel the standard values for these are: E = 29000 ksi α = 0.00000645 / oF The standard equation for the stress developed due to temp change is: σ = Eα∆T where, E is the modulus of elasticity α is the coefficient of thermal expansion T is the change in temperature The member already has an initial stress which will be added to the thermal stress to get the final stress in member. Therefore, for part a σt = Eα∆Tσt = 29000×103×6.45×10-6×70-50σt = 3741 lbs/in2 σ = 3741+11830σ = 15571 lbs/in2 Temperature drops below the normal, the rod is in tension, Therefore the final stress in member will be 15571 lbs/in2. for part b σt = Eα∆Tσt = 29000×103×6.45×10-6×70-100σt = -5611.5 lbs/in2σ = -5611.5+11830σ = 6218.5 lbs/in2 Temperature rises above the normal, the rod will be in compression. Therefore the final stress in member will be 6218.5 lbs/in2. for part c σt = Eα∆Tσt = 29000×103×6.45×10-6×70-150σt = -14964 lbs/in2σ = -14964+11830σ = -3134 lbs/in2 Therefore the final stress in member will be 3134 lbs/in2.