Skip to main content
ExamWize
Sign up

FE · 9% of the exam

Mechanics of Materials practice questions

10 free Mechanics of Materials questions for the FE Mechanical 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 stress and deform: axial, torsion, bending and shear, combined stresses and buckling.

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

Topics that come up most

  • Shear force and bending moment diagrams
  • Bending, torsional and axial stress
  • Mohr's circle and principal stresses
  • Beam deflection and statically indeterminate members
  • Column buckling

How to study it

Practise drawing shear and moment diagrams quickly from a loaded beam; many stress and deflection questions depend on finding the maximum moment first.

Sample Mechanics of Materials questions

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

  1. Question 1

    Along a cantilever carrying only a point load P at its free end, the shear force is:

    • AZero everywhere along the beam
    • BConstant and equal to P
    • CLinearly increasing toward the support
    • DMaximum at the free end only
    Show answer and explanation

    Answer: B) Constant and equal to P

    • AIncorrect. The load must be resisted by shear.
    • BCorrect. The moment varies linearly.
    • CIncorrect. That's the moment diagram.
    • DIncorrect. It's constant along the span.

  2. Question 2

    A simply supported 2-m beam (E = 200 GPa, I = 1 × 10⁶ mm⁴) carries 10 kN at midspan. The midspan deflection is about:

    • A0.83 mm
    • B2.08 mm
    • C13.3 mm
    • D8.33 mm
    Show answer and explanation

    Answer: D) 8.33 mm

    • AIncorrect. Recheck the powers of ten.
    • BIncorrect. Use 48EI, not 192EI.
    • CIncorrect. Recheck the denominator.
    • DCorrect. \(PL^3/(48EI) = 10{,}000(2{,}000)^3/[48(200{,}000)(10^6)]\).

  3. Question 3

    Superposition of beam deflections from separate loads is valid when the beam is:

    • AYielding plastically
    • BLinear elastic with small deflections
    • CBuckled
    • DMade of two materials only
    Show answer and explanation

    Answer: B) Linear elastic with small deflections

    • AIncorrect. Superposition needs linear behavior.
    • BCorrect. Effects then add linearly.
    • CIncorrect. Superposition needs linear behavior.
    • DIncorrect. It needs linear behavior.

  4. Question 4

    An element in pure shear has τ = 50 MPa. Its principal stresses are:

    • A+50 MPa and −50 MPa
    • B+50 MPa and 0
    • C+100 MPa and −100 MPa
    • D+25 MPa and −25 MPa
    Show answer and explanation

    Answer: A) +50 MPa and −50 MPa

    • ACorrect. On planes at 45°.
    • BIncorrect. Pure shear gives equal and opposite principals.
    • CIncorrect. They equal τ in magnitude.
    • DIncorrect. They equal τ in magnitude.

  5. Question 5

    A shaft (G = 80 GPa, J = 1 × 10⁶ mm⁴, L = 1 m) carries a torque of 500 N·m. Its angle of twist is:

    • A0.0625 rad
    • B0.00625 rad
    • C0.000625 rad
    • D6.25 rad
    Show answer and explanation

    Answer: B) 0.00625 rad

    • AIncorrect. Recheck the powers of ten.
    • BCorrect. \(\phi = TL/(GJ) = 5\times10^5(1{,}000)/[80{,}000(10^6)]\).
    • CIncorrect. Recheck the powers of ten.
    • DIncorrect. Recheck the units.

  6. Question 6

    A member carries 100 MPa of axial compression plus 50 MPa of bending stress at its extreme fiber. The maximum compressive stress is:

    • A100 MPa
    • B150 MPa
    • C50 MPa
    • D112 MPa
    Show answer and explanation

    Answer: B) 150 MPa

    • AIncorrect. Add the bending stress.
    • BCorrect. Superpose axial and bending stresses.
    • CIncorrect. That's the minimum fiber stress.
    • DIncorrect. Stresses add directly.

  7. Question 7

    Along a beam, the slope of the bending moment diagram at any point equals:

    • AThe applied load intensity
    • BThe shear force at that point
    • CThe deflection
    • DZero everywhere
    Show answer and explanation

    Answer: B) The shear force at that point

    • AIncorrect. That's the slope of the shear diagram, with a sign.
    • BCorrect. The relationship is dM/dx = V.
    • CIncorrect. That isn't the relationship.
    • DIncorrect. It equals the shear.

  8. Question 8

    A thin-walled tube encloses a mean area of 0.01 m² and carries 1,000 N·m of torque. The shear flow is:

    • A20 N/m
    • B100,000 N/m
    • C10 N/m
    • D50,000 N/m
    Show answer and explanation

    Answer: D) 50,000 N/m

    • AIncorrect. Recheck the formula.
    • BIncorrect. Include the factor of 2.
    • CIncorrect. Recheck the formula.
    • DCorrect. \(q = T/(2A_m) = 1{,}000/0.02\).

  9. Question 9

    A plane-stress element has σx = 80 MPa, σy = 20 MPa, and τxy = 0. On Mohr's circle, the center lies on the normal-stress axis at:

    • A60 MPa
    • B30 MPa
    • C100 MPa
    • D50 MPa
    Show answer and explanation

    Answer: D) 50 MPa

    The center of Mohr's circle is the average normal stress, (σx + σy)/2 = 50 MPa. The radius here is (σx − σy)/2 = 30 MPa, so the principal stresses are 80 and 20 MPa.

    • AIncorrect. 60 MPa is σx − σy = 80 − 20. The difference sets the size of the circle, not where its center is.
    • BIncorrect. 30 MPa is (σx − σy)/2. With τxy = 0 this is the radius R = √[((σx − σy)/2)² + τxy²], not the center.
    • CIncorrect. 100 MPa is σx + σy. The center is the average of the two normal stresses, so this sum still has to be divided by 2.
    • DCorrect. C = (σx + σy)/2 = (80 + 20)/2 = 50 MPa.

  10. Question 10

    A material with G = 80 GPa carries a shear stress of 40 MPa within the elastic range. The shear strain is:

    • A0.0005 rad
    • B0.005 rad
    • C2,000 rad, inverting the ratio
    • D0.00005 rad
    Show answer and explanation

    Answer: A) 0.0005 rad

    • ACorrect. \(\gamma = \tau/G\).
    • BIncorrect. That's off by a factor of 10.
    • CIncorrect. That reverses it.
    • DIncorrect. That's off by a factor of 10.

Mechanics of Materials: FAQs

How much of the FE exam is Mechanics of Materials?

Mechanics 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 Mechanics of Materials domain cover?

How loaded members stress and deform: axial, torsion, bending and shear, combined stresses and buckling.

How should I study Mechanics of Materials for FE?

Practise drawing shear and moment diagrams quickly from a loaded beam; many stress and deflection questions depend on finding the maximum moment first.

Where can I practise more Mechanics of Materials questions?

This page has 10 free Mechanics 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 Mechanics of Materials exam-ready

The full FE bank has 54 Mechanics 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.