GATE ME 2022 Set 2 — Question 53
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.NAT+2 / -0HardTheories of FailureStatic & Dynamic LoadingMachine DesignShafts, Keys & CouplingsMachine Elements
Machine Design → Machine Elements → Shafts, Keys & Couplings
Last updated
Question
A shaft AC rotating at a constant speed carries a thin pulley of radius m at the end C which drives a belt. A motor is coupled at the end A of the shaft such that it applies a torque about the shaft axis without causing any bending moment. The shaft is mounted on narrow frictionless bearings at A and B where AB = BC = m. The taut and slack side tensions of the belt are N and N, respectively. The allowable shear stress for the shaft material is 80 MPa. The self-weights of the pulley and the shaft are negligible. Use the value of available in the on-screen virtual calculator. Neglecting shock and fatigue loading and assuming maximum shear stress theory, the minimum required shaft diameter is _______ mm (round off to 2 decimal places).
Correct answer
23.6 to 24.2
Solution
1.Calculate the torque ():
The torque transmitted by the belt drive is the difference in tensions multiplied by the pulley radius:2.Calculate the bending moment ():
The net vertical force acting on the pulley at C is N.The shaft is supported at bearings A and B. Taking moments about A to find the reaction at B ():
The maximum bending moment occurs at bearing B:
3.Calculate the equivalent torque ():
According to the maximum shear stress theory (Guest's theory):4.Calculate the shaft diameter ():
The maximum shear stress is given by:Rounding to two decimal places, the minimum required shaft diameter is 23.94 mm.
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE ME question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Machine Elements
2026 Set 1 Q19A closely coiled helical compression spring of mean coil diameter and wire diameter , is…2026 Set 1 Q21A rectangular plate is perfectly welded to a gusset plate with parallel fillet weld joints as shown…2026 Set 1 Q34A steel plate having yield strength of 550 MPa, is subjected to biaxial state of stress as…2025 Set 1 Q22The yield stress of a metal in uniaxial tension is MPa. According to von Mises yield…2025 Set 1 Q30A shaft carries a helical spur gear. Which one of the following bearings can NOT be used to support…