# 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?

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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.

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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