60 solved GATE ME questions on Strength of Materials, drawn from 9 exam years and grouped by year. Every question shows the official answer and a step-by-step solution.
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Study Stress, Strain & Elastic Constants through equilibrium, material response, and displacement constraints. These original axial-bar exercises build selected foundations; beams, columns, and material testing need separate study.
Our study notes and original examples support the PYQs below; they are not official exam questions or a replacement for the current syllabus.
Cut the bar conceptually and balance forces. Internal force N stays constant between applied loads when distributed axial loading is absent. For a singly restrained bar, equilibrium determines the reaction.
Check yourself: Does your segment satisfy axial equilibrium?
Away from end disturbances, uniform axial stress is σ = N/A using original area. Engineering strain ε = δ/L uses original length. Stress has force-per-area units; strain is dimensionless and signed.
Check yourself: Have you distinguished total extension from extension per unit length?
Uniaxial linear elasticity gives σ = Eε within the elastic range. Homogeneity makes material properties spatially constant. This simple uniaxial model requires traction-free lateral surfaces and excludes local end disturbances.
Check yourself: Is the material response assumed linear, and are lateral constraints absent?
For a uniform segment, δ = NL/(AE). Add signed extensions for segments in series: interface displacements match, but strains need not. A second axial restraint introduces another displacement constraint, not a freely extending endpoint.
Check yourself: Which displacement is fixed, and which endpoint may move?
Temperature changes add free thermal strain αΔT; restraint may create stress. Here uniform unchanged temperature eliminates thermal strain. Centric loading excludes bending; neglected end effects exclude local stress concentrations from these calculations.
Check yourself: Are thermal strain or eccentric loading being silently omitted?
Original teaching example · not a PYQ
Original example: a straight uniform bar has L = 1000 mm, A = 100 mm², and E = 200 GPa. Its left end is restrained only axially; a slowly applied centric tensile force of 10 kN acts at the movable right end. Assume homogeneous isotropic linear elasticity, small strain, traction-free sides, constant uniform 20 °C, and no initial stress. Neglect weight, friction, and end effects. Find stress, strain, and extension.
Tensile stress = 100 MPa; strain = 0.0005; extension = 0.5 mm.
Separate original check: two perfectly joined series segments each have length 500 mm and E = 100 GPa. Their areas are 100 and 200 mm². Fix only the left axial displacement; apply 10 kN centric right-end tension, with no interface load. Use the same linear-elastic, small-strain, traction-free, friction-free, weightless model at unchanged uniform 20 °C, neglecting junction and end effects. Find total extension.
Total extension = 0.75 mm.
Both segments carry 10000 N. With E = 100000 N/mm², extensions are 10000 × 500/(100 × 100000) = 0.5 mm and 10000 × 500/(200 × 100000) = 0.25 mm. Compatibility requires adding them.
Supplemental reading, not an official GATE reading list or an endorsement of these notes.
Free supplemental module by David Roylance introducing elastic response, stress, and strain. Rebuild the force-to-extension reasoning before studying more complex loading.
This page shows 60 recent questions from the released archive, newest first. For older questions and complete papers, browse all GATE ME papers. Questions can carry more than one subject tag; counts are not marks weightage.
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