GATE CE 2014 Set 1 — Question 41
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.NAT+2 / -0MediumEnergy MethodsDeterminate Structures & Energy MethodsStructural Engineering
Structural Engineering → Determinate Structures & Energy Methods → Energy Methods
Last updated
Question
For the cantilever beam of span (shown below), a concentrated load of applied at the free end causes a vertical displacement of at a section located at a distance of from the fixed end. If a concentrated vertically downward load of is applied at the section located at a distance of from the fixed end (with no other load on the beam), the maximum vertical displacement in the same beam (in mm) is __________
Correct answer
1 to 1
Solution
According to Maxwell's Reciprocal Theorem, the deflection at point due to a load at point is equal to the deflection at point due to the same load at point .Let point 1 be at from the fixed end and point 2 be at the free end ( from the fixed end).Case 1: Load is applied at point 2. The deflection at point 1 is .
The deflection at point 1 due to a unit load at point 2 is:Case 2: A load is applied at point 1. We need to find the maximum vertical displacement, which occurs at the free end (point 2), denoted as .
By Maxwell's Reciprocal Theorem:Thus, the deflection at point 2 due to at point 1 is:
The deflection at point 1 due to a unit load at point 2 is:Case 2: A load is applied at point 1. We need to find the maximum vertical displacement, which occurs at the free end (point 2), denoted as .
By Maxwell's Reciprocal Theorem:Thus, the deflection at point 2 due to at point 1 is:
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 CE 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 Determinate Structures & Energy Methods
2026 Set 1 Q13A thin-walled spherical gas balloon of radius and wall thickness () is subjected…2026 Set 2 Q14A rectangular singly reinforced concrete beam has a width of 300 mm and an effective depth of 550…2026 Set 1 Q14Black dot shown in the figure qualitatively represents the shear centre of the angle section. The…2026 Set 2 Q15As per IS:800-2007, design of a cantilever steel beam section for its moment capacity requires…2026 Set 1 Q15Which one of the following is utilized to determine the long-term deformation of concrete under…