PROBLEM STATEMENT

DISCUSSION THREAD

Hints:
Since this is a determinate beam, you are able to determine the reactions on the beam at B and C straight away from equilibrium considerations. It is recommended that you use the second-order approach for the integration process for finding rotations and displacements. For this, consider the two sections of the beam BC and CD.

• Make a mathematical cut through the beam between B and C, and from equilibrium considerations, determine the bending moment M(x). Integrate once and twice to get the rotation θ(x) and displacement v(x):
  θ(x) = θ(0) + (1/EI) ∫M(x)dx
  v(x) = v(0) +  ∫θ(x)dx
  where θ(0) and v(0) are integration constants.
• Make a mathematical cut through the beam between C and D, and from equilibrium considerations, determine the bending moment M(x). Integrate once and twice to get the rotation θ(x) and displacement v(x):
  θ(x) = θ(a) + (1/EI) ∫M(x)dx
  v(x) = v(a) +  ∫θ(x)dx
  where θ(a) and v(a) are integration constants. θ(a) and v(a) are found from the results of integrating from B to C.
• Enforce the displacement boundary condition at x = a to determine the unknown integration constant.

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