Problem # p043

Constrained Beam

A beam is pinned horizontally into a wall on either end and subject to a single load P. In the following assume the force P, the lengths a and L as well as the modulus of elasticity E and the moment of inertia I of the beam's cross-section to be 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 forces and/or moments the left wall is exerting on the beam at point A.

  5. In the figure above, indicate and label the forces and/or moments 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 lengths a and L, the force P and the force and moment acting on the beam at point A. Use bracket functions if you like.

  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.