FE Mechanical Practice Question Solution included after investigation
CASE E-057 · FE

The 50 mm Shaft That Saw 81.5 MPa of Shear

The torque was only 2 kN·m, but the outer surface of the 50 mm shaft reached about 81.5 MPa shear stress.

▶ INTERACTIVE CASE FILE • 5–10 MIN • CLICK TO INVESTIGATE

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

Case E-057 engineering failure visual
HOW THIS WORKS

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Follow the investigation process used in the field — 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 steel shaft of diameter 50 mm transmits 2.0 kN·m torque. A quick review divides torque by shaft area and reports an invalid stress measure. Calculate the maximum torsional shear stress at the outer surface and identify the correct section property.

Mechanical Design Analysis Mechanical Design Verification Root Cause Analysis Safe Correction
E-057
INVESTIGATION WORKSPACE WORK THROUGH THE CASE — YOUR CHOICES MATTER.
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CASE CLOSED · ENGINEERING VERDICT

What actually failed — and what should change.

What failed

Torque was treated like a direct force.

What was missed

Torsional stress distribution and polar moment of inertia.

Corrected model

Use τ=Tc/J for circular shafts.

QUICK ANSWER

For a solid circular shaft, τmax=16T/(πd³). With T=2.0 kN·m and d=50 mm, the maximum torsional shear stress is about 81.5 MPa.

ENGINEERING TAKEAWAY

Use τ=Tc/J; for a solid circular shaft J=πd^4/32 and c=d/2, giving τmax=16T/(πd^3).

CASE QUESTIONS

Questions this case should settle.

What is the maximum shear stress formula for a solid circular shaft?

τmax=16T/(πd³).

Where is torsional shear stress maximum in a solid shaft?

At the outer surface.

NEXT FE PRACTICE QUESTION

The 30 kW Shaft That Needed 239 N·m of Torque

Mechanical Design Analysis · 5–10 min

Continue Practice →
WHAT YOU’LL LEARN

Real failures. Lasting skills.

Each case is designed to build the judgment, analysis, and confidence you need for engineering exams — 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.