# Deflection at any point in fixed beam

1. Jan 8, 2009

### sunil.hk1

give formula or reference for finding deflection at any point in beam (fixed at both ends) due to couple acting intermediate in the beam? its urgent........

2. Jan 8, 2009

CS

3. Jan 8, 2009

### L62

I think the easiest thing is to define the loading using singularity functions, set it equal to EIy'''' (where E = elastic mod, I = moment of inertia, y'''' = fourth derivative of deflection); then successively integrate to get the shear force, moment, and finally the deflection as a function of x (the position along the beam). and determining the integration constants from the boundary conditions (such as at x = 0 and x = l, y = 0).

example of the singularity functions
http://www.roymech.co.uk/Useful_Tables/Beams/Singularity.html

(this is assuming small deflections by the way)

Last edited: Jan 8, 2009