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A beam having uniform cross-section carries a uniformly distributed load of intensity q per unit length over its entire span, and its mid-span deflection is δ.The value of mid-span deflection of the same beam when the same load is distributed with intensity varying from 2q unit length at one end to zero at the other end is:?
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A beam having uniform cross-section carries a uniformly distributed lo...
Solution:
Given:
To find: Mid-span deflection with load varying from 2q at one end to zero at the other end.
Approach:
Principle of superposition:
Deflection equation:
Conclusion:
Given:
- Uniformly distributed load = q per unit length
- Mid-span deflection with uniformly distributed load = δ
To find: Mid-span deflection with load varying from 2q at one end to zero at the other end.
Approach:
- Use the principle of superposition to obtain the deflection equation for the given load variation.
- Integrate the equation to get the mid-span deflection.
Principle of superposition:
- The deflection due to a combination of loads acting on a beam is the sum of the deflections due to each load acting alone.
- This principle is valid only for linearly elastic materials and small deflections.
Deflection equation:
- Let L be the span of the beam.
- For the uniformly distributed load, the deflection equation is given by δ = (5qL^4)/(384EI).
- For the load varying from 2q at one end to zero at the other end, the deflection equation is given by y = (qL^4)/(48EI) * (x^2 - 3Lx^3/4 + L^3x/4), where x is the distance from one end of the beam.
- The deflection at mid-span is obtained by setting x = L/2 in the above equation. Therefore, the mid-span deflection is y = (5qL^4)/(384EI).
Conclusion:
Therefore, the mid-span deflection of the beam with load varying from 2q at one end to zero at the other end is equal to the mid-span deflection of the beam with uniformly distributed load, which is δ = (5qL^4)/(384EI).
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A beam having uniform cross-section carries a uniformly distributed load of intensity q per unit length over its entire span, and its mid-span deflection is δ.The value of mid-span deflection of the same beam when the same load is distributed with intensity varying from 2q unit length at one end to zero at the other end is:?
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A beam having uniform cross-section carries a uniformly distributed load of intensity q per unit length over its entire span, and its mid-span deflection is δ.The value of mid-span deflection of the same beam when the same load is distributed with intensity varying from 2q unit length at one end to zero at the other end is:? 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 A beam having uniform cross-section carries a uniformly distributed load of intensity q per unit length over its entire span, and its mid-span deflection is δ.The value of mid-span deflection of the same beam when the same load is distributed with intensity varying from 2q unit length at one end to zero at the other end is:? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A beam having uniform cross-section carries a uniformly distributed load of intensity q per unit length over its entire span, and its mid-span deflection is δ.The value of mid-span deflection of the same beam when the same load is distributed with intensity varying from 2q unit length at one end to zero at the other end is:?.
A beam having uniform cross-section carries a uniformly distributed load of intensity q per unit length over its entire span, and its mid-span deflection is δ.The value of mid-span deflection of the same beam when the same load is distributed with intensity varying from 2q unit length at one end to zero at the other end is:? 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 A beam having uniform cross-section carries a uniformly distributed load of intensity q per unit length over its entire span, and its mid-span deflection is δ.The value of mid-span deflection of the same beam when the same load is distributed with intensity varying from 2q unit length at one end to zero at the other end is:? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A beam having uniform cross-section carries a uniformly distributed load of intensity q per unit length over its entire span, and its mid-span deflection is δ.The value of mid-span deflection of the same beam when the same load is distributed with intensity varying from 2q unit length at one end to zero at the other end is:?.
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