Skip to main content
ExamWize
Sign up

FE · 9% of the exam

Strength of Materials practice questions

10 free Strength of Materials questions for the FE Other Disciplines Exam (FE) exam, each with the correct answer and an explanation for every option.

Start the questionsFree 10-question FE quiz

What this domain covers

How loaded members deform and carry stress: axial, torsional and bending loads, combined stresses, deflection and buckling.

Exam weight
9%
On a real exam
≈ 10 questions
In our bank
54 questions

Topics that come up most

  • Stress, strain and Hooke's law
  • Shear force and bending moment diagrams
  • Torsion of circular shafts
  • Combined stress and Mohr's circle
  • Beam deflection and column buckling

How to study it

Sketch shear and bending moment diagrams for a range of standard beams until you can find the maximum moment quickly; bending stress questions depend on it.

Sample Strength of Materials questions

Try each one before opening the answer. Original questions written to the official exam objectives.

  1. Question 1

    For Euler buckling, a column fixed at one end and free at the other has an effective length factor K of:

    • A0.5
    • B1.0
    • C2.0
    • D0.7
    Show answer and explanation

    Answer: C) 2.0

    • AIncorrect. That's fixed-fixed.
    • BIncorrect. That's pinned-pinned.
    • CCorrect. It's the weakest common end condition.
    • DIncorrect. That's fixed-pinned.

  2. Question 2

    A simply supported beam with uniform load has midspan deflection 5wL⁴/(384EI). If the span doubles, the deflection becomes:

    • A16 times larger
    • B2 times larger
    • C4 times larger
    • D8 times larger
    Show answer and explanation

    Answer: A) 16 times larger

    • ACorrect. Deflection varies with L⁴.
    • BIncorrect. It varies with L⁴.
    • CIncorrect. It varies with L⁴.
    • DIncorrect. It varies with L⁴.

  3. Question 3

    If the length of a pinned-pinned column is doubled, its Euler critical buckling load becomes:

    • AOne-fourth as large
    • BHalf as large
    • CTwice as large
    • DUnchanged
    Show answer and explanation

    Answer: A) One-fourth as large

    • ACorrect. \(P_{cr} = \pi^2EI/L^2\).
    • BIncorrect. It varies with \(1/L^2\).
    • CIncorrect. Longer columns buckle more easily.
    • DIncorrect. It depends on length.

  4. Question 4

    A bar in uniaxial tension carries a normal stress of 100 MPa. The maximum shear stress in it is:

    • A0 MPa
    • B100 MPa, equal to the normal stress
    • C50 MPa
    • D200 MPa
    Show answer and explanation

    Answer: C) 50 MPa

    • AIncorrect. Shear exists on inclined planes.
    • BIncorrect. The maximum shear is half.
    • CCorrect. It acts on planes at 45°.
    • DIncorrect. That doubles it.

  5. Question 5

    A point has σx = 80 MPa, σy = 20 MPa and no shear stress. The maximum in-plane shear stress is:

    • A100 MPa
    • B60 MPa
    • C50 MPa
    • D30 MPa
    Show answer and explanation

    Answer: D) 30 MPa

    • AIncorrect. Use the difference, not the sum.
    • BIncorrect. Divide the difference by 2.
    • CIncorrect. That's the average normal stress.
    • DCorrect. τ_max = (σx − σy)/2 = 60/2.

  6. Question 6

    For an otherwise identical beam, using a material with half the elastic modulus makes the deflection:

    • AFour times as large
    • BHalf as large
    • CUnchanged
    • DTwice as large
    Show answer and explanation

    Answer: D) Twice as large

    • AIncorrect. It's inversely proportional, not squared.
    • BIncorrect. Lower stiffness increases deflection.
    • CIncorrect. E affects deflection.
    • DCorrect. Deflection is inversely proportional to E.

  7. Question 7

    A rectangular beam section is 0.1 m wide and 0.2 m deep. Its area moment of inertia about the centroidal axis parallel to the width is:

    • A6.67 × 10⁻⁵ m⁴
    • B1.67 × 10⁻⁵ m⁴
    • C8.00 × 10⁻⁴ m⁴
    • D3.33 × 10⁻⁴ m⁴
    Show answer and explanation

    Answer: A) 6.67 × 10⁻⁵ m⁴

    For a rectangle about its centroidal axis parallel to the width, I = bh³/12 with h the depth: (0.1)(0.2)³/12 = 6.67 × 10⁻⁵ m⁴.

    • ACorrect. I = bh³/12 = (0.1)(0.2)³/12 = 0.0008/12 = 6.67 × 10⁻⁵ m⁴, where h is the depth perpendicular to the bending axis.
    • BIncorrect. This is hb³/12 = (0.2)(0.1)³/12, the moment of inertia about the other centroidal axis (parallel to the depth).
    • CIncorrect. This is bh³ = (0.1)(0.008) without dividing by 12.
    • DIncorrect. This is bh²/12 = (0.1)(0.04)/12, which squares the depth instead of cubing it.

  8. Question 8

    A solid circular shaft has a diameter of 0.05 m. Its polar moment of inertia is most nearly:

    • A9.8 × 10⁻⁶ m⁴
    • B3.1 × 10⁻⁷ m⁴
    • C6.1 × 10⁻⁷ m⁴
    • D1.2 × 10⁻⁶ m⁴
    Show answer and explanation

    Answer: C) 6.1 × 10⁻⁷ m⁴

    For a solid circular section, J = πd⁴/32 = πr⁴/2. With d = 0.05 m this gives about 6.1 × 10⁻⁷ m⁴, which is twice the area moment I = πd⁴/64.

    • AIncorrect. This puts the 0.05-m diameter into J = πr⁴/2 as if it were the radius.
    • BIncorrect. This is πd⁴/64, the area moment of inertia about a diameter. That is half the polar moment.
    • CCorrect. J = πd⁴/32 = π(0.05)⁴/32 ≈ 6.14 × 10⁻⁷ m⁴.
    • DIncorrect. This is πd⁴/16, which is twice the correct polar moment of inertia.

  9. Question 9

    An aluminum part (E = 70 GPa) is loaded in uniaxial tension within its elastic range, and the measured normal strain is 0.002. What is the normal stress in the part?

    • A140 MPa
    • B14 MPa
    • C1,400 MPa
    • D1.4 MPa
    Show answer and explanation

    Answer: A) 140 MPa

    In the elastic range, σ = Eε. With E = 70 GPa and ε = 0.002, the stress is 140 MPa.

    • ACorrect. Hooke's law: σ = Eε = (70 × 10⁹ Pa)(0.002) = 1.4 × 10⁸ Pa = 140 MPa.
    • BIncorrect. This reads the strain as 0.0002 (one decimal place off): (70 GPa)(0.0002) = 14 MPa.
    • CIncorrect. This reads the strain as 0.02 (2%) instead of 0.002 (0.2%): (70 GPa)(0.02) = 1,400 MPa. That is far above aluminum's elastic range.
    • DIncorrect. This treats 0.002 as a percentage (0.002% = 2 × 10⁻⁵): (70 GPa)(2 × 10⁻⁵) = 1.4 MPa.

  10. Question 10

    A steel rod (E = 200 GPa) 2 m long with a 500-mm² area carries 50 kN. Its elongation is:

    • A0.1 mm
    • B1.0 mm
    • C2.0 mm
    • D10 mm
    Show answer and explanation

    Answer: B) 1.0 mm

    • AIncorrect. That's off by a factor of 10.
    • BCorrect. \(\delta = PL/(AE)\).
    • CIncorrect. That doubles it.
    • DIncorrect. That's off by a factor of 10.

Strength of Materials: FAQs

How much of the FE exam is Strength of Materials?

Strength of Materials is 9% of the FE exam by the official exam guide's weighting, which on a 110-question form works out to roughly 10 questions. The real exam's exact split varies by form.

What does the Strength of Materials domain cover?

How loaded members deform and carry stress: axial, torsional and bending loads, combined stresses, deflection and buckling.

How should I study Strength of Materials for FE?

Sketch shear and bending moment diagrams for a range of standard beams until you can find the maximum moment quickly; bending stress questions depend on it.

Where can I practise more Strength of Materials questions?

This page has 10 free Strength of Materials questions with answers. The ExamWize FE question bank has 54 questions in this domain. Every practice exam result breaks your score down by domain, and Review Mode re-drills the questions you missed.

Other FE topics

Also: 15 free questions across all topics, the FE cheat sheet and the study guide.

Get Strength of Materials exam-ready

The full FE bank has 54 Strength of Materials questions. Timed practice exams match the real exam's length and domain weights, every result shows your score per domain, and Review Mode re-drills the questions you missed.

See the full FE practice examsTake the free diagnostic

Not affiliated with NCEES; questions are original, written from the official exam outline, and never copied from the real exam.