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In deflection of a continuous beam, when loaded there will be convexity upwards over _________ supports.
End
Altermate
Intermediate
Every
Intermediate
In a continuous beam, the bending moment at intermediate supports is negative (hogging). Negative bending moment causes the beam to curve such that the top fiber is in tension and the bottom fiber is in compression, resulting in convexity upwards.
In a continuous beam, the bending moment at intermediate supports is negative (hogging). Negative bending moment causes the beam to curve such that the top fiber is in tension and the bottom fiber is in compression, resulting in convexity upwards.
M=тИТ12wL2тАЛ тАФ Typical hogging moment at fixed/continuous support
dx2d2yтАЛ=тИТEIMтАЛ тАФ Relation between curvature and bending moment
Due to the continuity of the beam over intermediate supports, the rotation at these points is restrained, inducing a hogging (negative) moment. According to the sign convention for bending moments, a negative moment results in a concave-down shape when viewed from the top, which geometrically manifests as 'convexity upwards' at the support cross-section.
Hogging moment occurs at intermediate supports of a continuous beam.
The beam profile becomes concave downwards (or convex upwards) in the vicinity of negative moments.
End supports for a simply supported beam exhibit zero moment, thus no convexity upwards at the ends.
Reduces the maximum span bending moment compared to simply supported beams.
Provides structural redundancy and better load distribution.
Sensitive to support settlement.
Requires complex reinforcement detailing (top bars at supports).
Multi-span highway bridges.
Continuous slab-beam floor systems in buildings.
At the end supports, if the beam is simply supported, the moment is zero and the deflection shape is concave upwards (sagging).
Option B (Alternate) is incorrect as convexity upwards occurs at every intermediate support, not just alternate ones.
C is correct тАФ Continuous beams experience negative bending moments at intermediate supports, leading to upward convexity (hogging).
Always visualize the Elastic Curve: Hogging (Negative M) = Convexity Upwards; Sagging (Positive M) = Convexity Downwards.