Question

A simple beam $A B$ is subjected to a distributed load of intensity $q(x)=q_{0} \sin \pi x / L,$ where $q_{0}$ is the maximum intensity of the load (see figure). Derive the equation of the deflection curve, and then determine the deflection $\delta_{\max }$ at the midpoint of the beam. Use the fourth-order differential equation of the deflection curve (the load equation).

          A simple beam $A B$ is subjected to a distributed load of intensity $q(x)=q_{0} \sin \pi x / L,$ where $q_{0}$ is the maximum intensity of the load (see figure).

Derive the equation of the deflection curve, and then determine the deflection $\delta_{\max }$ at the midpoint of the beam. Use the fourth-order differential equation of the deflection curve (the load equation).

Added by Ana C.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adriano Chikande

05/12/2022

Step 1

Step 1: The load equation is given by: EI * y'''' = q(x) where EI is the flexural rigidity of the beam, y is the deflection of the beam, and q(x) is the distributed load. Show more…

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A simple beam $A B$ is subjected to a distributed load of intensity $q(x)=q_{0} \sin \pi x / L,$ where $q_{0}$ is the maximum intensity of the load (see figure). Derive the equation of the deflection curve, and then determine the deflection $\delta_{\max }$ at the midpoint of the beam. Use the fourth-order differential equation of the deflection curve (the load equation).