Hints and Discussion Thread
It should come as no surprise to you that this is an indeterminate problem (if you remove the roller support at C, the beam can still be in equilibrium, thereby saying that the problem is over constrained). Let’s review the four-step plan for indeterminate problems.
- Equilibrium: Draw the FBD for the beam. You will have two equilibrium equations from that FBD and three unknown reactions (bending moment at B, reaction force at B and reaction force at C. This supports the conclusion drawn above that the problem is statically indeterminate.
- Load/deflection: Here you are asked to use the superposition approach to develop the load/deflection equation for the beam. Here you will break down the loading and one of the three unknown reactions (recommend that you use the reaction at C) into three sub-problems, and using superposition to represent the overall deflection of the beam.
- Compatibility: Enforcing the boundary conditions provides the additional equations to determine unknown reaction.
- Solve: Now you can solve the equilibrium equations for the remaining two reactions.
Any questions? Ask (and answer) questions here.