iniform simply supported beam, span Z, carries a distributed loading which varies according to a parabolic law across the span. The load intensity is zero at botch ends of the beam and w, at its mid- point. The loading is normal to a principal axis of the beam cross section and the relevant flexural rigidity is EI. Assuming that the deflected shape of the beam can be represented by the series inx a; sin L find the coefficients a; and the deflection at the mid-span of the beam using only the first term in this series. Ans 4=32u 1LEG77 (G odd) u 1/94 4FI

Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
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This question is of Chapter- Virtual Work and Energy Methods.

A uniform simply supported beam, span L, carries a distributed loading which varies according to a
parabolic law across the span. The load intensity is zero at both ends of the beam and w, at its mid-
point. The loading is normal to a principal axis of the beam cross section and the relevant flexural
rigidity is EI. Assuming that the deflected shape of the beam can be represented by the series
izx
a; sin
L
find the coefficients a, and the deflection at the mid-span of the beam using only the first term in
this series.
Ans. a;=32w,L´IEIn’i (i odd), w,Lʻ194.4EI.
Transcribed Image Text:A uniform simply supported beam, span L, carries a distributed loading which varies according to a parabolic law across the span. The load intensity is zero at both ends of the beam and w, at its mid- point. The loading is normal to a principal axis of the beam cross section and the relevant flexural rigidity is EI. Assuming that the deflected shape of the beam can be represented by the series izx a; sin L find the coefficients a, and the deflection at the mid-span of the beam using only the first term in this series. Ans. a;=32w,L´IEIn’i (i odd), w,Lʻ194.4EI.
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