Example 6: For the cantilever beam and loading shown, determine the reactions at the support.

Solution: We begin our analysis by first drawing the freebody diagram of the beam. Once we have the unknown reaction loads identified, we solve for them using the equilibrium equations.
FreeBody Diagram of Beam: The beam is fixed at point A. Therefore, there are two reaction forces and one reaction moment at this point as shown below.
We assume a direction for each reaction load. Also to simplify the calculations, the distributed force is represented by its resultant acting at its centroid.,
Reaction loads: As shown in the freebody diagram, there are three unknown reactions that need to be solved for using the equilibrium condition. Since this represents a twodimensional force system, we can only make use of three equilibrium equations.
We begin the solution by using the equilibrium of moments with point A as the moment center. We choose point A as it would eliminate the contributions of the two unknown reaction forces.
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Negative sign indicates the direction of QA is opposite to that shown in the freebody diagram. Now we proceed with solving the two reaction forces. Using the equilibrium of forces in the x direction gives
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The horizontal reaction force at A is zero as there is no other horizontal force acting on the beam.
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Verification of Results: We can verify the solution by summing moments about D or any other point to see if it is equal to zero.
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With e being zero, we have confidence that there are no errors in the solution.
Unlike in examples 4 and 5, the entire load is supported at point A. The fixed support also develops a moment reaction as the beam is restrained from rotation. This element is an important factor in design of beams.