Stress and strain, thermal stress, torsion, shear and moment diagrams, bending, deflection, columns and combined stress: the mechanics behind FE Civil structural design.
NCEES lists these Mechanics of Materials topics for the FE Civil: shear and moment diagrams; stresses and strains: axial, torsion, bending, shear, thermal; deformations; combined stresses, principal stresses and Mohr’s circle; elastic and plastic deformation; columns.
Choose any section below to get a free FE Civil practice problem. Work it with the FE Reference Handbook open, tap your answer, then check the solution.
Normal stress is force over area, σ = P/A; shear stress is τ = V/A.
A bar with ν = 0.3 has an axial strain of 0.001. What is its lateral strain?
εlat = −νε = −0.3(0.001) = −0.0003.
Mechanics of MaterialsStress and StrainPoisson’s RatioThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Start your 3-day free trial →
A free bar heated by ΔT grows δ = αLΔT.
A 1 m diameter tank with 10 mm walls holds 2 MPa. What is the longitudinal stress?
σL = pD/4t = 2(1000)/40 = 50 MPa, half the hoop stress.
Thermal DeformationsThin-Walled Pressure VesselsThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Start your 3-day free trial →
A shaft under torque T has shear stress τ = Tr/J, largest at the outer surface.
If a solid shaft’s diameter is doubled under the same torque, the maximum shear stress becomes:
τ = 16T/(πd3), so doubling d divides τ by 23: ⅛ as large.
Torsionangle of twistpolar momentThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Start your 3-day free trial →
Shear and moment diagrams show where a beam works hardest.
A 4 m simply supported beam (E = 200 GPa, I = 8 × 106 mm4) carries 10 kN at midspan. What is the maximum deflection?
δ = PL3/48EI = 10,000(4000)3/(48 × 200,000 × 8 × 106) = 8.33 mm.
BeamsShearing Force and Bending MomentBeam DeflectionThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Start your 3-day free trial →
Long slender columns fail by buckling, not crushing.
A 3 m column has a radius of gyration of 20 mm. What is its slenderness ratio (K = 1)?
KL/r = 3000/20 = 150.
ColumnsEulerMohr’s CircleThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Start your 3-day free trial →
Newton’s Notes FE Civil has 18 chapters (11 shared with Mechanical, 7 Civil-only) with lessons, worked examples and 420+ FE-style practice problems with full solutions, 171 of them Civil-only. Pro adds a timed full-length FE Civil practice exam (110 problems), a custom test builder and Ask Newton, the AI tutor. Try it free for 3 days, no card to start.
Start your 3-day free trialSee plans →