How to Calculate Deflection & Bending Stress in Steeped Beam with Uniformly Distributed Load..??
The easy way to handle it is by area-moment method. The key is on the moment diagram. Draw the moment diagram by parts and then revise your diagram by dividing the moment at each segment by EI that corresponds to the segment. Note that the degree of curve of the diagram won't change.
Here is an example:
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