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A fixed beam 5 m long span, It carries a concentrated load of 15 kN at mid point of span, find the maximum bending moment in the beam.
10.375 kNm
375 kNm
475 kNm
75 kNm
375 kNm
Given: Length of the beam L = 5 m, Concentrated load at midpoint P = 15 kN
Length of the beam L = 5 m, Concentrated load at midpoint P = 15 kN
M=8PLтАЛ
Identify beam type and load condition
The problem describes a fixed-fixed beam with a point load acting at the center of the span.
L=5┬аm,P=15┬аkN
Apply formula for fixed end moment
For a fixed beam with a central point load, the bending moment at the supports and the center are determined by the standard fixed-beam formulas ┬╖ The fixed end moment is MfixedтАЛ=PL/8.
M=8PLтАЛ
Calculate the bending moment
Substitute the values into the formula: M=815├Ч5тАЛ.
M=875тАЛ=9.375┬аkNm
B is correct because the maximum bending moment for a fixed beam with a central point load is given by PL/8, which calculates to $9.375 \text{ kNm}$.
This concept is fundamental to the 'Force Method' or 'Consistent Deformation' method used in indeterminate structures; always identify if the beam is determinate or indeterminate before applying force-based formulas.