# Macaulay's Beam deflection

I have calculated one of the 2 questions successfully with it being a simply supported beam, now i am stuck on the remaining question. Previously i have used the double integration method.

It is as follows:

"A cantilever beam, 15m long has a UDL of 25N/m acting along its entire length and a point load of 250N at the free end. If EI for the beam = 100MN/m^2 calculate the slope and deflection of the beam at the free end "

How do i include 2 different load values which are of a different format UDL & point load? and how should the answer be carried out?

## Answers and Replies

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Generally, superposition is the key. I have not looked at at mechanics in awhile, but I recall this being the trick.

Find the solution to one of the loadings, then find the solution due to the other loading, then sum the two solutions.

Whether you should use integration or tabulated formulas I don't know.

That depends on what your prof wants.

There is a book called Strength of Materials by J. P. Den Hartog (Dover edition) that contains a table/page for rotations and deflections of a cantilever beam subject to different loadings. I do not have my book handy with me, but the formulas are so straight-forward that they can be memorized by anyone vaguely familiar with the subject:

moment ML/EI ML^2/2EI
Point load at end PL^2/2EI PL^3/3EI
UDL wL^3/6EI wL4/8EI

The rotations and deflections refer, of course, to the free end of the cantilever.

You can get a description of the book at :
https://www.amazon.com/dp/0486607550/?tag=pfamazon01-20

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