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Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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The fixed beam having a length l and point load W kN at its mid point of the span, the equation of fixed end moment for this beam is
12wl2
4Wl
8Wl
8wl2
8Wl
For a fixed-fixed beam of length l subjected to a central point load W, the fixed end moments (MA and MB) arise due to the rotational restraint at the supports. Using the theorem of consistent deformation or the moment-area method, the fixed end moment is calculated as 8Wl.
For a fixed-fixed beam of length l subjected to a central point load W, the fixed end moments (MA and MB) arise due to the rotational restraint at the supports. Using the theorem of consistent deformation or the moment-area method, the fixed end moment is calculated as 8Wl.
MF=8Wl — Fixed end moment for central point load
MF=12wl2 — Fixed end moment for Uniformly Distributed Load (UDL)
In a statically indeterminate beam with fixed ends, the supports prevent rotation. Applying a point load W at the center causes a downward deflection. The fixed ends generate restraining moments MF that oppose this rotation, ensuring the slope remains zero at the supports. By symmetry, the moments at both ends are equal, and equilibrium requires the internal resisting moment to counteract the externally induced bending moment.
Fixed beams are statically indeterminate to the second degree.
The fixed end moment for a central point load is independent of the flexural rigidity (EI) as long as the beam is uniform.
Bending moment at the center of the beam is 8Wl.
Higher stiffness compared to simply supported beams.
Significant reduction in maximum mid-span deflection.
Sensitive to support settlements, which induce additional stresses.
Temperature changes induce internal thermal stresses.
Rigidly connected frames in high-rise buildings.
Continuous beam bridge decks.
Option A (12wl2) is the fixed end moment for a beam subjected to a UDL.
Option B (4Wl) is the maximum bending moment for a simply supported beam with a central point load.
Option D (8wl2) is the maximum bending moment for a simply supported beam with a UDL.
C is correct — The fixed end moment for a beam of length l with a central point load W is 8Wl.
Always distinguish between 'W' (point load) and 'w' (load per unit length) as examiners often use them to differentiate between point load and UDL formulas.