FE Civil Mechanics of Materials Practice Problems

The current FE Civil specification assigns 7-11 of the 110 exam questions to Mechanics of Materials. Form A contains 8 original problems in this area. The sample below is published in full, with the same worked-solution format used throughout the book.

A straight steel member with a cross-sectional area of 8.0 in^2 is fully restrained against axial deformation between two bridge abutments. The coefficient of thermal expansion is $6.5 \times 1 0^{- 6}$ per degree F, and the modulus of elasticity is $29 \times 1 0^{6}$ psi. For a uniform temperature rise of 70 degrees F, the compressive force developed in the member is most nearly:

(A)13.2 kips
(B)58.6 kips
(C)106 kips
(D)190 kips

Show worked solution

Answer: (C)

Restrained thermal strain converts entirely to stress: $σ = E α Δ T = 13, 195$ psi, which over 8.0 in^2 is $105, 600$ lb — about 106 kips.

Left free, the member would expand by $α Δ T$ ; the abutments deny all of it.

ϵ_{t} = α Δ T = (6.5 \times 1 0^{- 6}) (70) = 4.55 \times 1 0^{- 4}

That denied strain returns as elastic stress.

σ = E α Δ T = (29 \times 1 0^{6}) (4.55 \times 1 0^{- 4}) = 13, 195 psi

F = σ A = (13, 195) (8.0) = 105, 600 lb \approx 106 kips

FE Reference Handbook — Mechanics of Materials: Thermal Deformations

Why the other choices appear

(A)Stopped at the restraint stress, 13,195 psi = 13.2 ksi, and reported it as a force in kips.
(B)Converted the 70 degree F rise to 38.9 degrees C while keeping alpha per degree F, giving (188.5)(38.9)(8.0) = 58.6 kips.
(D)Used the SI coefficient 11.7e-6 per degree C with the Fahrenheit temperature rise, giving 23,751 psi times 8.0 in^2 = 190 kips.