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A cantilever 8 m long carries uniformly distributed load of intensity w kN/m run, starting from free end up to the middle of its length. If the maximum bending moment in the cantilever is 240 kN-m, what is magnitude of w?
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A cantilever 8 m long carries uniformly distributed load of intensity ...
Given:


  • Length of cantilever (L) = 8 m

  • Distributed load intensity (w) = ? kN/m

  • Maximum bending moment (M) = 240 kN-m

  • Load starts from free end and runs up to the middle of the length



Calculating Load Intensity (w)

For a cantilever beam with distributed load, the maximum bending moment occurs at the fixed end. In this case, the maximum bending moment is given as:

M = (wL^2)/8

Substituting the given values:

240 = (w*8^2)/8

240 = 8w

w = 30 kN/m


Explanation


  • A cantilever beam is a type of beam that is fixed at one end and free at the other end.

  • The distributed load on the cantilever starts from the free end and runs up to the middle of its length.

  • The maximum bending moment in the cantilever occurs at the fixed end.

  • The formula for calculating the maximum bending moment in a cantilever beam with distributed load is M = (wL^2)/8.

  • We can use this formula to calculate the load intensity (w) when the maximum bending moment (M) is given.

  • In this case, the load intensity is calculated to be 30 kN/m.

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A cantilever 8 m long carries uniformly distributed load of intensity w kN/m run, starting from free end up to the middle of its length. If the maximum bending moment in the cantilever is 240 kN-m, what is magnitude of w?
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