- #1

fonseh

- 529

- 2

## Homework Statement

In the link at 12:35 , the author show the equation of the displacement of the beam without explaining , can someone try to explain why we need to use 3 Φ , 2EI / L , 2

**θa and 2**

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- Thread starter fonseh
- Start date

- #1

fonseh

- 529

- 2

In the link at 12:35 , the author show the equation of the displacement of the beam without explaining , can someone try to explain why we need to use 3 Φ , 2EI / L , 2

- #2

- 38,457

- 7,967

In the left hand picture, we have a beam subject to a moment M at x=0.

For equilibrium, there would also be an upward force F at x=0 and downward at x=L. To balance the moments we have M=FL.

Consider a point at x. The moments from the left of that are Fx-M, so EI y" = Fx-M. Integrating, EI y' = Fx

For small angles, tan θ≈θ, so from the boundary condition at x=0, the constant is EI θ

Integrating again, EI y = Fx

The boundary condition (L, 0) gives θ

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