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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
12wl2тАЛ
4WlтАЛ
8WlтАЛ
8wl2тАЛ
8WlтАЛ
For a fixed-fixed beam of length l subjected to a central point load W, the fixed end moments (MAтАЛ and MBтАЛ) 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 8WlтАЛ.
For a fixed-fixed beam of length l subjected to a central point load W, the fixed end moments (MAтАЛ and MBтАЛ) 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 8WlтАЛ.
MFтАЛ=8WlтАЛ тАФ Fixed end moment for central point load
MFтАЛ=12wl2тАЛ тАФ 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 MFтАЛ 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 8WlтАЛ.
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 (12wl2тАЛ) is the fixed end moment for a beam subjected to a UDL.
Option B (4WlтАЛ) is the maximum bending moment for a simply supported beam with a central point load.
Option D (8wl2тАЛ) is the maximum bending moment for a simply supported beam with a UDL.
C is correct тАФ The fixed end moment for a beam of length l with a central point load W is 8WlтАЛ.
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.