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The fixed beam carrying a udl of w kN/m of overall span l, the equation of fixed end moment for this beam is
12wl2тАЛ
4WlтАЛ
8WlтАЛ
8wl2тАЛ
12wl2тАЛ
For a beam fixed at both ends and subjected to a uniformly distributed load (UDL) of w per unit length over its entire span l, the fixed-end moments (FEM) develop to maintain zero slope at the supports ┬╖ Using the principle of superposition or the moment-area method, the fixed end moment at both supports is determined to be 12wl2тАЛ.
For a beam fixed at both ends and subjected to a uniformly distributed load (UDL) of w per unit length over its entire span l, the fixed-end moments (FEM) develop to maintain zero slope at the supports ┬╖ Using the principle of superposition or the moment-area method, the fixed end moment at both supports is determined to be 12wl2тАЛ.
MFEMтАЛ=12wl2тАЛ тАФ Fixed end moment for UDL
MmaxтАЛ=24wl2тАЛ тАФ Maximum sagging moment at center
Due to the end fixity, the beam is statically indeterminate to the second degree ┬╖ The internal moments generated at the supports counteract the rotation that would otherwise be caused by the UDL ┬╖ Specifically, the fixed-end moment MABтАЛ=MBAтАЛ=12wl2тАЛ ensures the slope at both ends remains zero, satisfying the displacement boundary condition of a clamped support.
A fixed beam is statically indeterminate of the 2nd degree.
The hogging moment occurs at the supports, while the sagging moment occurs at the center.
The internal resistance at the supports prevents both rotation and deflection.
The value 12wl2тАЛ is a standard result derived from the slope-deflection method or Castigliano's theorem.
Higher stiffness compared to simply supported beams.
Reduces maximum deflection at mid-span.
Sensitive to support settlement.
Thermal stresses may develop if expansion is constrained.
Rigid frame construction.
Continuous slab systems in reinforced concrete buildings.
For a concentrated load W at the center, the FEM is 8WlтАЛ.
Option D (8wl2тАЛ) is the maximum bending moment for a simply supported beam with UDL, which is a common distractor.
A is correct тАФ The fixed-end moment for a beam with UDL w over span l is calculated as 12wl2тАЛ.
Always distinguish between 'Fixed End Moment' (which is 12wl2тАЛ) and 'Maximum Bending Moment' of a simply supported beam (which is 8wl2тАЛ) to avoid confusion in competitive exams.