FE Civil Practice Question Solution included after investigation
CASE E-043 · FE

The Truss Diagonal That Carried More Than the Support Reaction

Each support reaction was only 6 kN, yet each inclined top member carried about 8.49 kN.

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Case E-043 engineering failure visual
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Case Brief

SAME PRINCIPLES. HIGHER STANDARDS.
PROBLEM STATEMENT

A symmetric triangular truss spans 6 m and has an apex 3 m above the supports, so each inclined top member is at 45°. A 12 kN downward load acts at the apex. By symmetry the support reactions are 6 kN each. A review then labels each diagonal member as 6 kN. Determine the actual axial force in each inclined member and identify whether it is in tension or compression.

Statics Civil Design Verification Root Cause Analysis Safe Correction
E-043
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CASE CLOSED · ENGINEERING VERDICT

What actually failed — and what should change.

What failed

The member axial force was set equal to its vertical contribution.

What was assumed

Support reaction magnitude and diagonal member-force magnitude were treated as identical.

Corrected model

Use method of joints and resolve axial member forces along the member directions.

QUICK ANSWER

At the symmetric apex joint, the two 45° member forces must satisfy 2F sin45°=12 kN. Therefore F≈8.49 kN in each inclined member. Each contributes 6 kN vertically, while the full axial force is larger.

ENGINEERING TAKEAWAY

A truss member carries axial force along its own axis. Resolve that force into components at the joint before comparing it with external forces.

CASE QUESTIONS

Questions this case should settle.

Why is the truss member force greater than 6 kN?

Because 6 kN is only the vertical component of the inclined axial force.

Are the inclined top members in tension or compression in this case?

Compression; their forces must push upward on the loaded apex joint.

NEXT FE PRACTICE QUESTION

The Beam Reactions That Refused to Split 50-50

Statics · 5–10 min

Continue Practice →
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