Problem # p040

Constrained Beam, method of integration

A beam is pinned horizontally into a wall on either end at the same height. It is subject to the continuous load wo [N/m]. In the following assume the wo, the length L, the modulus of elasticity E, and the central moment of inertia I of the beam's cross-section are given.


  1. What is (are) the boundary condition(s) for the deflection curve at point A ?

  2. What is (are) the boundary condition(s) for the deflection curve at point C ?

  3. How many boundary conditions do you have all together for the deflection curve ?

  4. In the figure above, indicate and label the force and moment the left wall is exerting on the beam at point A.

  5. In the figure above, indicate and label the force and moment the right wall is exerting on the beam at point C.

  6. Find the equation for the internal moment M(x) in terms of the length L, the continuous load wo, and the unknown force and moment the wall is exerting on the beam at point A. Hint : draw a free body diagram for the section to the left of your cut at location x.

  7. Integrate the moment equation once to find EI dy/dx

  8. Integrate a second time to find the equation for EIy(x)

  9. Which quantities in the equation for EIy(x) are unknown to you ?

  10. Do you have enough boundary conditions to solve for the unknowns ?

  11. Write out the equations you would solve to find all unknowns (including the integration constants).

This is the end of this problem. Do NOT solve for the unknowns.