The beam shown is subjected to a uniformly distributed load of magnitude q. The following shape...

 

Transcribed Image Text:

The beam shown is subjected to a uniformly distributed load of magnitude q. The following shape function has been suggested to be used in a one-term RRG approximation for the vertical deflection v(x) L πχ L p(x) = sin². q X (a) Verify that this shape function satisfies the support-conditions at both ends of the beam. If it doesn't, the method cannot be applied. For example, the shape function x(x − L) is unsuitable for this purpose. b) Obtain the function v(x) according to the RRG method. Plot the result (c) Recalling the relation between the bending moment M(x) and the deflection v(x), obtain the bending moment and shear force diagrams that correspond to your approximate solution. (d) Compare the results obtain in parts (b) and (c) with the exact solution and comment on the results. The beam shown is subjected to a uniformly distributed load of magnitude q. The following shape function has been suggested to be used in a one-term RRG approximation for the vertical deflection v(x) L πχ L p(x) = sin². q X (a) Verify that this shape function satisfies the support-conditions at both ends of the beam. If it doesn't, the method cannot be applied. For example, the shape function x(x − L) is unsuitable for this purpose. b) Obtain the function v(x) according to the RRG method. Plot the result (c) Recalling the relation between the bending moment M(x) and the deflection v(x), obtain the bending moment and shear force diagrams that correspond to your approximate solution. (d) Compare the results obtain in parts (b) and (c) with the exact solution and comment on the results.