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The maximum deflection due to a uniformly distributed load w/unit length over entire span of a cantilever of length L and of flexural rigidity EI, is
- a)wL3/3EI
- b)wL4/3EI
- c)wL4/8EI
- d)wL4/12EI
Correct answer is option 'C'. Can you explain this answer?
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The maximum deflection due to a uniformly distributed load w/unit leng...
Formula Used:
The equation for the maximum deflection due to a uniformly distributed load w/unit length over the entire span of a cantilever is given by:
δmax = (5/384)wL^4/EI
where,
δmax = maximum deflection
w = uniformly distributed load
L = length of the cantilever
E = modulus of elasticity
I = moment of inertia
Solution:
Given, a cantilever of length L and of flexural rigidity EI, subjected to a uniformly distributed load w/unit length over the entire span.
Using the formula mentioned above, we can calculate the maximum deflection as:
δmax = (5/384)wL^4/EI
On solving this equation, we get:
δmax = wL^4/8EI
Therefore, the correct answer is option C, i.e., wL^4/8EI.
Conclusion:
The maximum deflection due to a uniformly distributed load w/unit length over the entire span of a cantilever of length L and of flexural rigidity EI is given by the equation δmax = wL^4/8EI. This equation can be easily derived using the basic principles of mechanics and is useful in determining the maximum deflection of cantilever beams under different loading conditions.
The equation for the maximum deflection due to a uniformly distributed load w/unit length over the entire span of a cantilever is given by:
δmax = (5/384)wL^4/EI
where,
δmax = maximum deflection
w = uniformly distributed load
L = length of the cantilever
E = modulus of elasticity
I = moment of inertia
Solution:
Given, a cantilever of length L and of flexural rigidity EI, subjected to a uniformly distributed load w/unit length over the entire span.
Using the formula mentioned above, we can calculate the maximum deflection as:
δmax = (5/384)wL^4/EI
On solving this equation, we get:
δmax = wL^4/8EI
Therefore, the correct answer is option C, i.e., wL^4/8EI.
Conclusion:
The maximum deflection due to a uniformly distributed load w/unit length over the entire span of a cantilever of length L and of flexural rigidity EI is given by the equation δmax = wL^4/8EI. This equation can be easily derived using the basic principles of mechanics and is useful in determining the maximum deflection of cantilever beams under different loading conditions.
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