Expert: Veto Varma - 5/23/2006

Question
Hi, I am a high school student studying physics and writing a big paper on the Euler-Bernoulli beam theory.

In the Euler-Bernoulli beam equation
                                                        is it possible to make w , the deflection of the beam, the subject of the equation?

Also, is p, the line pressure load, in the case of cantilevers with a free tip load, constant, or is it dependent on x, the distance along the beam?

Thank you very much in advance,
Tsuyoshi Onda


Answer
Hello Tsuyoshi,

You can derive deflection directly using the Euler Bernoulli equation. Solution of the beam can start with
EI d4y/dx4=-w(x), if moment of inertia and E is constant.
then by putting suitable boundary conditions one can derive deflections.

If a cantilever beam is subjected to uniformly distributed load of intensity p per unit length, then the load at x distance from the free tip of cantilever will be p times x and you should use this value in the equation.


Regards
Veto