GATE CE 2026 Set 2 — Question 38
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67MediumInfluence LinesIndeterminate Analysis & Influence LinesStructural EngineeringMuller-Breslau Principle
Structural Engineering → Indeterminate Analysis & Influence Lines → Influence Lines
Last updated
Question
A simply supported, linearly elastic, homogeneous, prismatic beam of length and flexural rigidity is shown in the figure.
The expression for the Influence Line Diagram (ILD) of the rotation at the support B is
Correct answer
(B) (1)/(6EIL)(x³ - L²x)
Solution
By the Muller-Breslau principle, the ILD for the rotation at B, , is the deflected shape of the beam when a unit rotation is applied at B. This is equivalent to the deflection of the beam due to a unit moment applied at B.
For a unit moment at B, the moment at any section is .
Using the differential equation of the elastic curve:
Integrating once:
Integrating again:
Boundary conditions:
Thus, .
For a unit moment at B, the moment at any section is .
Using the differential equation of the elastic curve:
Integrating once:
Integrating again:
Boundary conditions:
1.At
2.At
Substituting back: Thus, .
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 Indeterminate Analysis & Influence Lines
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…