FE Other Disciplines Practice Question Solution included after investigation
CASE E-098 · FE

The 2 m Bar That Grew 2.3 mm, Not 1.15

The thermal strain was correct, but it was applied as if the bar were only 1 m long. The 2 m bar expanded 2.3 mm.

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

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

Case E-098 engineering failure visual
HOW THIS WORKS

Think like
a real engineer.

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 free aluminum bar is 2.0 m long with coefficient of thermal expansion alpha=23×10^-6 /°C. Its temperature rises by 50°C. A note reports 1.15 mm expansion by treating alpha delta T as the full length change. Determine the correct expansion.

Materials Other Disciplines Design Verification Root Cause Analysis Safe Correction
E-098
INVESTIGATION WORKSPACE WORK THROUGH THE CASE — YOUR CHOICES MATTER.
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DEBRIEF (LOCKED)

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

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🔒Correct fixComplete the case
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🔒Exam takeawayComplete the case
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CASE CLOSED · ENGINEERING VERDICT

What actually failed — and what should change.

What failed

Thermal strain was reported as total length change.

What was missed

The bar was 2 m long.

Corrected model

Use delta L=alpha L delta T.

QUICK ANSWER

delta L=alpha L delta T=(23×10^-6)(2.0)(50)=0.00230 m=2.3 mm.

ENGINEERING TAKEAWAY

Free thermal expansion is delta L=alpha L delta T.

CASE QUESTIONS

Questions this case should settle.

What is the linear thermal expansion formula?

delta L=alpha L delta T for free expansion.

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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 — 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.