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Assertion (A): In a simply supported beam subjected to a concentrated load P at mid-span, the elastic curve slope becomes zero under the load.
Reason (R): The deflection of the beam is maximum at mid-span.
  • a)
    Both A and R are individually true and R is the correct explanation of A
  • b)
    Both A and R are individually true but R is NOT the correct explanation of A
  • c)
    A is true but R is false
  • d)
    A is false but R is true
Correct answer is option 'A'. Can you explain this answer?
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Assertion (A): In a simply supported beam subjected to a concentrated ...
Explanation:



Assertion (A): In a simply supported beam subjected to a concentrated load P at mid-span, the elastic curve slope becomes zero under the load.



This assertion is true. When a simply supported beam is subjected to a concentrated load P at mid-span, the elastic curve slope becomes zero under the load. This means that the slope of the deflected beam at mid-span is zero or horizontal. This can be explained by considering the bending moment diagram of the beam. The bending moment diagram is symmetrical about the mid-span of the beam when it is subjected to a concentrated load at mid-span. The slope of the elastic curve is related to the bending moment by the equation: slope = M/EI, where M is the bending moment, E is the modulus of elasticity of the material, and I is the moment of inertia of the cross-section of the beam. At mid-span, the bending moment is zero, hence the slope of the elastic curve at mid-span is also zero.



Reason (R): The deflection of the beam is maximum at mid-span.



This reason is also true. When a simply supported beam is subjected to a concentrated load P at mid-span, the deflection of the beam is maximum at mid-span. This can be explained by considering the slope-deflection equation of the beam. The slope-deflection equation relates the deflection of the beam to the slope of the elastic curve by the equation: d = (5PL^4)/(384EI), where d is the deflection, P is the load, L is the span of the beam, E is the modulus of elasticity of the material, and I is the moment of inertia of the cross-section of the beam. At mid-span, the load P is maximum, hence the deflection of the beam is also maximum at mid-span.



Therefore, both Assertion (A) and Reason (R) are individually true and R is the correct explanation of A.
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Assertion (A): In a simply supported beam subjected to a concentrated ...
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Assertion (A): In a simply supported beam subjected to a concentrated load P at mid-span, the elastic curve slope becomes zero under the load.Reason (R): The deflection of the beam is maximum at mid-span.a)Both A and R are individually true and R is the correct explanation of Ab)Both A and R are individually true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false but R is trueCorrect answer is option 'A'. Can you explain this answer?
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Assertion (A): In a simply supported beam subjected to a concentrated load P at mid-span, the elastic curve slope becomes zero under the load.Reason (R): The deflection of the beam is maximum at mid-span.a)Both A and R are individually true and R is the correct explanation of Ab)Both A and R are individually true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false but R is trueCorrect answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Assertion (A): In a simply supported beam subjected to a concentrated load P at mid-span, the elastic curve slope becomes zero under the load.Reason (R): The deflection of the beam is maximum at mid-span.a)Both A and R are individually true and R is the correct explanation of Ab)Both A and R are individually true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false but R is trueCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assertion (A): In a simply supported beam subjected to a concentrated load P at mid-span, the elastic curve slope becomes zero under the load.Reason (R): The deflection of the beam is maximum at mid-span.a)Both A and R are individually true and R is the correct explanation of Ab)Both A and R are individually true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false but R is trueCorrect answer is option 'A'. Can you explain this answer?.
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