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At the centre of simply supported beam, deflection is _________ and slope is _________.
Maximum, Maximum
Zero, Maximum
Maximum, Zero
Zero, Zero
Maximum, Zero
In a simply supported beam subjected to symmetric loading (like a point load at the center or uniform distributed load), the deflected shape is symmetric about the mid-span. Due to this symmetry, the tangent to the elastic curve at the center is horizontal, resulting in zero slope, while the vertical displacement reaches its maximum value.
In a simply supported beam subjected to symmetric loading (like a point load at the center or uniform distributed load), the deflected shape is symmetric about the mid-span. Due to this symmetry, the tangent to the elastic curve at the center is horizontal, resulting in zero slope, while the vertical displacement reaches its maximum value.
╬┤maxтАЛ=48EIWL3тАЛ тАФ Maximum deflection for a central point load
╬╕=dxdyтАЛ тАФ Definition of slope as the first derivative of deflection
The beam undergoes bending such that the curvature is concave downward (or upward depending on loading). At the center, the internal bending moment is at its peak; since slope (theta=fracdydx) represents the rate of change of deflection, and the deflection curve reaches a stationary point (peak) at the center, the derivative is zero. Thus, theta=0 and delta=deltamaxтАЛ.
Symmetry in loading and support conditions leads to zero slope at the center of a simply supported beam.
The maximum deflection occurs where the shear force changes sign (which is at the center for a central point load).
Slope is maximum at the supports of a simply supported beam.
Predictable structural behavior under symmetric loading.
Allows for simplified calculation of deflection and slope using double integration or area-moment methods.
Does not hold true for asymmetric loading where the point of zero slope shifts.
Assumes linear elastic material behavior (Hooke's Law).
Structural design of beams in buildings and bridges.
Mechanical design of shafts and machine components.
For a central point load W, slope ╬╕=0 at x=L/2.
Option B is incorrect because slope is maximum at the supports, not the center.
C is correct тАФ At the center of a symmetric simply supported beam, the deflected shape is horizontal, meaning the slope is zero and the deflection is at its peak.
Always verify loading symmetry before assuming zero slope at the center; if the load is eccentric, the point of zero slope (maximum deflection) will shift away from the mid-span.