Step 1: calculate the reactions at the supports
The reactions at the encastré support of this cantilever beam can be determined by equilibrium calculations only, so the beam is statically determinate. The support provides a vertical reaction and a moment reaction. The equilibrium equations I will use are those for vertical equilibrium and moment equilibrium. The equilibrium calculations are made easier if I convert the uniformly distributed load in to an equivalent point load.
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Step 2: form imaginary cut and draw free body diagram
In order to be able to calculate the shear force and bending moment at D, I introduce an imaginary cut in to the beam at D. This splits the actual beam in to two imaginary free bodies. It also splits the uniformly distributed load in to two, one for each free body. I’ll choose to analyse the left hand section A to D, and draw it’s free body diagram. As before, I turn the uniformly distributed load on this section in to an equivalent point load.
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Step 3: calculate force and moment at the imaginary cut
I will calculate the shear force and bending moment at D using my free body diagram and the equilibrium equations for vertical equilibrium and moment equilibrium. This is a similar process to what I did in step 1 to calculate the reactions at the encastré support.
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Step 4: check calculation by analysing the second free body
In the check calculation, I choose to analyse the right hand section D to C. This must give me the same values I have already found for the shear force and bending moment at D, if I’ve already calculated these correctly. This calculation is actually easier than the one I already did.
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