Question

A propped cantilever beam EF is subjected to a unit moving load as shown in the figure. The sign convention for positive shear force at the left and right sides of any section is also shown. 
 

The CORRECT qualitative nature of the influence line diagram for shear force at G is 

• A. A
• B. B
• C. C
• D. D

Hint:

For influence lines in structural analysis, the shear force at a point can be determined by considering how the load moves along the beam. The sign conventions and beam reactions play a key role in determining the shape of the influence line.

Answer 1

The Correct Option is B

The influence line diagram is a graphical representation that shows how the shear force (or any other internal force) at a point changes as a unit moving load is applied across the length of a beam. The diagram helps in understanding how the internal shear force at a particular point varies with the position of the applied load.
Step 1: Analyze the problem setup.
We are given a propped cantilever beam EF with a unit moving load applied across the length of the beam. The point of interest is at section G of the beam, and we are asked to determine the qualitative nature of the influence line for shear force at this point. The sign conventions for positive shear force are also provided.
Step 2: Influence line for shear force at G.
For a beam subjected to a unit moving load, the influence line for shear force at a particular point can be determined by considering the following: - The shear force at a point in the beam changes as the position of the applied load moves along the beam. - When the moving load passes over the section of interest (in this case, at G), the shear force at that point will experience a change. - The qualitative shape of the influence line can be inferred from the beam's reaction and loading conditions. For a propped cantilever beam with a unit load moving from left to right: - The shear force starts positive at the left end (at E) and decreases as the load moves towards the point G. - As the load passes over G, the shear force decreases and becomes negative as the load moves beyond G. Thus, the qualitative nature of the influence line is a line that starts positive and then decreases to negative as the load passes from left to right. Step 3: Conclusion.
The correct influence line diagram corresponds to option (B), where the shear force starts positive and decreases as the moving load passes over the point G. Final Answer: (B) + -