how can we find out the deflection (sagging) of a beam when it is uniformly loaded and supported at two ends?

Answer 1

Formulas are available in textbooks on solid mechanics or engineering handbooks.

Answer 2

Assuming a pin and roller config, u can use:

delta(max) = -(w*L^3)/(384*E*I)

where:

w = weight per unit run (kN/m),
L=length,
E=young modulus,
I = second moment of area

Dependign on the exact config, there are some standard formulae in any good structures book, this is the one i use:

M S Williams & J D Todd. "STRUCTURES: Theory and analysis"

ISBN: 0333677609

Also if you need to check your answers there's a really good program called ruckzuck made by mursoft, which is simple to use, can't find a demo of it online, but it'd be on ur uni/college computers.

Answer 3

you can calculate it, with a numerical shooting method. i think it has the form of a tanh function.