GATE CE 2021 Set 1 — Question 48
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Structural Engineering → Determinate Structures & Energy Methods → Simple Stress & Strain
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Question
Refer the truss as shown in the figure (not to scale).
If load, kN, moment of inertia, mm, area of cross-section, mm, and length, m for all the members of the truss, the compressive stress (in kN/m, in integer) carried by the member Q-R is __________

Correct answer
490 to 510
Solution
1.Reactions: Due to symmetry, the vertical reactions at supports P and S are kN.
2.Geometry: Since all members have length , the triangles PQT, TRS, and QTR are equilateral. The height of the truss is m.
3.Force in QR: Using the method of sections, cut through members QR, QT, and PT. Taking moments about joint T for the left part:
kN (Compression).
4.Stress in QR: The area of member QR is given as .
mm m m.Area of QR m.
Compressive stress kN/m.
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