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A simply supported beam of span l, carrying udl of w on entire span, deflection at centre will be
16EIWl2тАЛ
48EIWl3тАЛ
24EIwl3тАЛ
384EI5wl4тАЛ
384EI5wl4тАЛ
For a simply supported beam of span l subjected to a uniformly distributed load (udl) of intensity w per unit length over its entire span, the maximum deflection occurs at the centre of the span.
For a simply supported beam of span l subjected to a uniformly distributed load (udl) of intensity w per unit length over its entire span, the maximum deflection occurs at the centre of the span.
╬┤maxтАЛ=384EI5wl4тАЛ тАФ Maximum deflection for simply supported beam under UDL
╬╕endтАЛ=24EIwl3тАЛ тАФ Maximum slope at the supports
The deflection is derived from the differential equation of the elastic curve, EIdx2d2yтАЛ=MxтАЛ. Integrating twice using the boundary conditions y=0 at x=0 and x=l yields the expression for deflection at any point x. At x=2lтАЛ, the value evaluates to 384EI5wl4тАЛ.
Deflection depends inversely on the flexural rigidity (EI).
For a point load W at the centre, the deflection is 48EIWl3тАЛ.
The deflection is maximum where the slope of the elastic curve is zero.
Uniform load distribution prevents stress concentrations.
Easier to analyze using standard integration techniques.
Higher mid-span deflection compared to a propped cantilever.
Susceptible to structural vibration under dynamic loads.
Design of floor joists in buildings.
Bridge girders subjected to uniform dead loads.
Note that w represents load per unit length (e.g., kN/m), whereas W typically represents total load (kN).
Option B represents the deflection due to a point load at mid-span.
Option C represents the slope at the supports under UDL.
D is correct тАФ The central deflection of a simply supported beam under a uniformly distributed load is 384EI5wl4тАЛ.
Always verify if the load given is total load (W) or intensity per unit length (w); failure to distinguish this is a common trap in structural mechanics exams.