Unit Load Method for curved determinate structure

[Caution]

Homework Statement

A uniform curved beam ABC of radius R is fixed at C and is free at end A, and carries a vertical load W at B, as shown in Fig. 3.2. Considering only bending action of W, derive expressions for the vertical and horizontal displacements as well as the rotation at end A in terms of W, R and flexural rigidity EI of the beam. Ignore the self-weight of the beam.

Use unit load method, 1.  U * .

Homework Equations

I had uploaded the qns and solution provided, but there is one part where moment about AB =0 which i do not understand.

The Attempt at a Solution

I understand the whole solution except for one part, which is moment about AB for real load analysis.Why is it 0 and not WRcostheta? Thanks in advance : )

 

[KataKoniK]

I would approach this forum post by first acknowledging the importance of understanding the solution provided and addressing any confusion or questions about it. In this case, it is important to clarify the concept of moment and how it applies to this specific problem.

Moment is a measure of the tendency of a force to rotate an object about an axis. In this problem, the moment about AB is the tendency of the load W to rotate the beam about the fixed point C. However, in this case, the beam is fixed at C and therefore cannot rotate about that point. This means that the moment about AB is zero.

To further understand this concept, we can consider the equilibrium of forces and moments at point B. The vertical force W is balanced by the reaction force at point C, and the horizontal reaction force at point C creates a moment that counteracts the moment created by W. This results in a net moment of zero about point B.

In summary, the moment about AB is zero because the beam is fixed at point C and cannot rotate about that point. The horizontal reaction force at point C creates a moment that balances the moment created by the load W, resulting in a net moment of zero about point B.