60 solved GATE ME questions on Machine Design, drawn from 12 exam years and grouped by year. Every question shows the official answer and a step-by-step solution.
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Determine the type of loading (static, fluctuating, or impact), compute the relevant stress, and compare it against the appropriate material strength using the correct failure theory. These selected foundations cover static and fatigue design of common machine elements. They are not a complete syllabus; detailed bearing life, gear-tooth analysis, and weld design 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.
For ductile materials under static loading, use the maximum shear stress theory (Tresca) or distortion energy theory (von Mises). Tresca: τ_max = S_y/(2n). Von Mises: σ' = √(σ₁² - σ₁σ₂ + σ₂²) ≤ S_y/n for plane stress with principal stresses σ₁, σ₂. For brittle materials, use the maximum normal stress theory.
Check yourself: Is the material ductile or brittle, and have you found the principal stresses?
Geometric discontinuities (holes, fillets, notches) raise local stress by a factor Kt: σ_max = Kt × σ_nominal. For static loading of ductile materials, local yielding redistributes stress, so Kt is often not applied to static strength. For fatigue, use the fatigue stress concentration factor Kf ≤ Kt.
Check yourself: Is this a static or fatigue calculation, and is the material ductile?
Fluctuating stress has mean σ_m and alternating σ_a components. The endurance limit S_e of steel is roughly 0.5 S_ut for S_ut ≤ 1400 MPa, modified by surface, size, reliability, and other factors. The modified Goodman line connects (S_e, 0) on the σ_a axis to (S_ut, 0) on the σ_m axis: σ_a/S_e + σ_m/S_ut = 1/n.
Check yourself: Have you applied all endurance-limit modifying factors before using the Goodman diagram?
A shaft under combined bending moment M and torque T experiences bending stress σ = 32M/(πd³) and shear stress τ = 16T/(πd³). For static design, combine using distortion energy theory. For fatigue, treat bending as alternating and torque as mean stress when the shaft rotates under constant loads.
Check yourself: Is the bending fully reversed (zero mean) under shaft rotation?
A preloaded bolt with stiffness k_b and clamped members with stiffness k_c share an external tensile load P. The bolt sees additional force Pb = P × k_b/(k_b + k_c), while the clamp force decreases by P × k_c/(k_b + k_c). Separation occurs when the clamp force drops to zero.
Check yourself: Have you identified both the bolt stiffness and the clamped-member stiffness?
Original teaching example · not a PYQ
Original example: a solid circular shaft transmits a torque T = 500 N·m under static loading. The material has S_y = 250 MPa. Using the maximum shear stress theory with a safety factor n = 2, find the minimum shaft diameter.
Minimum diameter ≈ 34.4 mm; select the next larger standard diameter.
A machine component experiences σ_max = 200 MPa and σ_min = 0 (repeated loading). Find σ_m and σ_a.
σ_m = 100 MPa; σ_a = 100 MPa.
Mean stress: σ_m = (200 + 0)/2 = 100 MPa. Alternating stress: σ_a = (200 - 0)/2 = 100 MPa. This is a repeated (zero-to-max) loading pattern, not fully reversed.
Supplemental reading, not an official GATE reading list or an endorsement of these notes.
Free supplemental course materials on mechanical element design including shafts, bearings, and fatigue. Covers design methodology relevant to GATE ME.
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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