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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.
Mmax=12w×L2
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.
Msupport=12wL2
Substitute the given values
Given w=5 kN/m and L=6 m, substitute these into the bending moment formula.
M=125×6°2
Calculate the result
Simplify the expression to find the maximum bending moment value.
M=125×36=5×3=15 kNm
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 8wL2, whereas for a fixed beam the supports take 12wL2 and the center takes 24wL2.