FE Civil Practice Question Solution included after investigation
CASE E-114 Β· FE

The Shaft That Reached 50.9 MPa, Not 25.5

The polar moment was correct, but shear stress was evaluated at half the outer radius. Maximum torsional stress occurs at the outside surface and was 50.9 MPa.

β–Ά INTERACTIVE CASE FILE β€’ 5–10 MIN β€’ CLICK TO INVESTIGATE

Inspect, commit, prove, fix, and sign off.

Case E-114 engineering failure visual
HOW THIS WORKS

Think like
a real engineer.

Follow the investigation process used in the field β€” in five guided steps.

1

Inspect

Review the problem, diagram, and evidence.

2

Commit

Choose your hypothesis.

3

Prove

Run calculations and test your idea.

4

Fix

Select and validate a safe correction.

5

Sign Off

See the full debrief and key takeaways.

Case Brief

SAME PRINCIPLES. HIGHER STANDARDS.
PROBLEM STATEMENT

A solid circular steel shaft has diameter d=50 mm and transmits torque T=1.25 kNΒ·m. Determine maximum torsional shear stress. A note evaluates stress at r=12.5 mm instead of the 25 mm outer radius and reports about 25.5 MPa.

Mechanics Of Materials Civil Design Verification Root Cause Analysis Safe Correction
E-114
INVESTIGATION WORKSPACE WORK THROUGH THE CASE β€” YOUR CHOICES MATTER.
πŸ”’
DEBRIEF (LOCKED)

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Find the root cause, confirm the fix, and see how this connects to the exam.

πŸ”’Root causeComplete the case
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πŸ”’Correct fixComplete the case
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πŸ”’Exam takeawayComplete the case
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CASE CLOSED Β· ENGINEERING VERDICT

What actually failed β€” and what should change.

What failed

The stress was evaluated at an interior radius.

What was missed

Torsional shear increases linearly from the center to the surface.

Corrected model

Use Ο„max=16T/(Ο€dΒ³) for a solid circular shaft.

QUICK ANSWER

Ο„max=16T/(Ο€dΒ³)=16(1.25Γ—10^6)/(Ο€50Β³)=50.93 MPa.

ENGINEERING TAKEAWAY

In a solid circular shaft, Ο„=Tr/J and the maximum occurs at the outer radius c=d/2.

CASE QUESTIONS

Questions this case should settle.

Where does maximum torsional shear occur in a solid circular shaft?

At the outer surface.

NEXT FE PRACTICE QUESTION

The Plate That Peaked at 92.4 MPa, Not 110

Mechanics Of Materials Β· 5–10 min

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WHAT YOU’LL LEARN

Real failures. Lasting skills.

Each case is designed to build the judgment, analysis, and confidence you need for engineering exams β€” and beyond.

  • Apply core engineering concepts to real-world problems
  • Practice structured troubleshooting and analysis
  • Strengthen exam-ready thinking through realistic scenarios
COMMON QUESTIONS
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What happens after I complete a case?

The sealed debrief unlocks with the root cause, corrected reasoning, fix, and takeaway.