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A beam 6 m long is fixed at it ends ┬╖ It carries a udl of 5 kN/m. find the maximum bending moment in the beam.
15 kNm
20 kNm
35 kNm
10 kNm
15 kNm
Given: Length of the fixed beam L = 6 m, Uniformly Distributed Load w = 5 kN/m.
Length of the fixed beam L = 6 m, Uniformly Distributed Load w = 5 kN/m.
MmaxтАЛ=12w├ЧL2тАЛ
Identify beam type and load
The beam is fixed at both ends (encastre) and is subjected to a Uniformly Distributed Load (UDL) ┬╖ The formula for the maximum bending moment in a fixed-fixed beam under UDL occurs at the supports.
MsupportтАЛ=12wL2тАЛ
Substitute the given values
Given w=5┬аkN/m and L=6┬аm, substitute these into the bending moment formula.
M=125├Ч62тАЛ
Calculate the result
Simplify the expression to find the maximum bending moment value.
M=125├Ч36тАЛ=5├Ч3=15┬аkNm
A is correct because the maximum bending moment at the supports of a fixed beam under UDL is calculated as 15 kNm.
In Structural Mechanics, remember that for a simply supported beam the max moment is 8wL2тАЛ, whereas for a fixed beam the supports take 12wL2тАЛ and the center takes 24wL2тАЛ.