FE Other Disciplines Practice Question Solution included after investigation
CASE E-097 · FE

The Alloy That Was 40% Beta, Not 57%

Dividing the overall composition by the beta composition gave 57%, but phase fractions come from tie-line segment lengths. The beta fraction was 40%.

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

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

Case E-097 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

At a specified temperature, a binary alloy lies in the alpha+beta region. The tie line gives Calpha=20 wt% B and Cbeta=70 wt% B. The overall alloy composition is C0=40 wt% B. Determine the alpha and beta mass fractions.

Materials Other Disciplines Design Verification Root Cause Analysis Safe Correction
E-097
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

Overall composition was divided by one phase composition.

What was missed

The opposite tie-line segment and both phase endpoints.

Corrected model

Use the lever rule and verify component mass balance.

QUICK ANSWER

Wbeta=(40-20)/(70-20)=0.40 and Walpha=0.60. The alloy is 40% beta and 60% alpha by mass.

ENGINEERING TAKEAWAY

Use opposite tie-line segment lengths: Wbeta=(C0-Calpha)/(Cbeta-Calpha) and Walpha=1-Wbeta.

CASE QUESTIONS

Questions this case should settle.

What is the lever rule for beta fraction?

Wbeta=(C0-Calpha)/(Cbeta-Calpha).

NEXT FE PRACTICE QUESTION

The Stronger Material That Made the Heavier Tie Rod

Materials · 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 — 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.