A simply supported beam AB of span L and uniform section carries a distributed load of intensity varying from zero at A to w,Junit length at B according to the law 2w,x w=- L 2L per unit length. If the deflected shape of the beam is given approximately by the expression 2nx v= aj sin-+a2 sin- L L evaluate the coefficients aj and a, and find the deflection of the beam at mid-span. Ans. a,-2w,Lª (x’+4)/Eln", az--w,L*/16EIn*, 0.00918w,L*/EI.

A simply supported beam AB of span L and uniform section carries a distributed load of intensity varying from zero at A to w,Junit length at B according to the law 2w,x w=- L 2L per unit length. If the deflected shape of the beam is given approximately by the expression 2nx v= aj sin-+a2 sin- L L evaluate the coefficients aj and a, and find the deflection of the beam at mid-span. Ans. a,-2w,Lª (x’+4)/Eln", az--w,L/16EIn, 0.00918w,L*/EI.

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Methods to Determine Vertical Stress

The load applied to the soil is transferred to the underground. The presence of water at soil pores and solid grains above the soil are the primary components that are responsible for the effective load transfer. Due to the load acting, the internal component of the soil or the underground formations undergoes deformations or a tectonic shift. The amount of deformation depends upon the amount of load acting on the soil surface, which indeed, depends on the weight of everything present above the soil. Due to this, the underground soil element develops internal stresses which try to resist the tectonic changes.

Question

A simply supported beam AB of span L and uniform section carries a distributed load of intensity
varying from zero at A to wJunit length at B according to the law
2w,x (1
w=
L
2L
per unit length. If the deflected shape of the beam is given approximately by the expression
2лх
v= aj sin-+az sin-
L
evaluate the coefficients aj and a, and find the deflection of the beam at mid-span.
Ans. a,-2w,L“ (x'+4)/Elx², az--w.L*/16EI*, 0.00918w,L*IEI.

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