GATE CE 2020 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 / -0.67MediumStrain EnergyDeterminate Structures & Energy MethodsStructural Engineering
Structural Engineering → Determinate Structures & Energy Methods → Strain Energy
Last updated
Question
A prismatic linearly elastic bar of length , cross-sectional area , and made up of a material with Young's modulus , is subjected to axial tensile force as shown in the figures. When the bar is subjected to axial tensile forces and , the strain energies stored in the bar are and , respectively.
If is the strain energy stored in the same bar when subjected to an axial tensile force , the correct relationship is
Correct answer
(D) U U₁ + U₂
Solution
The strain energy in a linearly elastic bar is given by .
For the first two cases:
For the third case, the force is :
Since and are both tensile forces (positive), the term .
Therefore, .
For the first two cases:
For the third case, the force is :
Since and are both tensile forces (positive), the term .
Therefore, .
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…