FE Mechanical Practice Question Solution included after investigation
CASE E-059 Β· FE

The Thin-Wall Vessel That Saw 100 MPa Hoop Stress

At 2 MPa internal pressure, the vessel's hoop stress reached 100 MPaβ€”twice the longitudinal stress.

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

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

Case E-059 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 thin-walled cylindrical vessel has internal pressure 2.0 MPa, internal diameter 1.0 m, and wall thickness 10 mm. A design note uses 50 MPa for both membrane directions. Calculate hoop and longitudinal stresses and identify which direction governs.

Mechanical Design Analysis Mechanical Design Verification Root Cause Analysis Safe Correction
E-059
INVESTIGATION WORKSPACE WORK THROUGH THE CASE β€” YOUR CHOICES MATTER.
πŸ”’
DEBRIEF (LOCKED)

Complete the investigation
to unlock the full debrief.

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

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

What actually failed β€” and what should change.

What failed

Both vessel stress directions were assigned the same value.

What was missed

Different membrane-force equilibrium in hoop and longitudinal cuts.

Corrected model

Use Οƒh=pD/(2t) and ΟƒL=pD/(4t).

QUICK ANSWER

For a thin-walled closed cylinder, Οƒh=pD/(2t) and ΟƒL=pD/(4t). With p=2 MPa, D=1 m, and t=10 mm, hoop stress is 100 MPa and longitudinal stress is 50 MPa.

ENGINEERING TAKEAWAY

For a thin-walled closed cylinder, hoop stress is twice longitudinal stress.

CASE QUESTIONS

Questions this case should settle.

Which stress is larger in a thin-walled cylindrical vessel?

Hoop stress; it is twice the longitudinal stress in the idealized closed-cylinder model.

How does wall thickness affect hoop stress?

Hoop stress is inversely proportional to wall thickness.

NEXT FE PRACTICE QUESTION

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

Mechanical Design Analysis Β· 5–10 min

Continue Practice β†’
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
Do I need prior knowledge to use these cases?

Basic subject familiarity helps, but every case is designed to teach through the investigation itself.

How long does a case take?

Most cases are designed for a focused 5–10 minute investigation.

Are the cases aligned with engineering exams?

Each case is mapped to a verified exam, subject, topic, and misconception before publication.

What happens after I complete a case?

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