# Partial distributed load over fully fixed beam

1. Mar 10, 2014

### aqpahnke

I am trying to figure out the deflection in a fully restrained beam. A diagram of the beam can be found here on this website.
http://civilengineer.webinfolist.com/fb/fbcalcu.php

I have been able to find the reactionary forces as well as the moments at each end of the beam for any distributed load at any position on the beam.
I would like to relate this to the deflection of the beam at any point and am completely stuck.

Aric

2. Mar 10, 2014

### SteamKing

Staff Emeritus
If you have determined the reaction forces and moments which keep the loaded beam in equilibrium, then you can calculate the deflection curve of the beam by integrating the bending moment curve twice w.r.t. length and applying the boundary conditions to determine the unknown constants of integration, just like any other beam problem.

3. Mar 11, 2014

### aqpahnke

Okay.. lets say that on that particular beam that the reactionary force for one direction is R1= (q*d/L^3)[(2b+L)a^2-((a-b)/4)d^2)]
I get stuck on the particulars. I don't really know where to integrate in this equation

4. Mar 11, 2014

### aqpahnke

Okay.. lets say that on that particular beam that the reactionary force for one direction is R1= (q*d/L^3)[(2b+L)a^2-((a-b)/4)d^2)]
I get stuck on the particulars. I don't really know where to integrate in this equation

5. Mar 11, 2014

### SteamKing

Staff Emeritus
'Reactionary' means something else than what you assume. The proper terminology in English is 'reaction force'.

http://en.wikipedia.org/wiki/Reactionary

You misunderstand the procedure to follow in analyzing beams to determine deflections. Once you have determined the end reactions and moments, you construct the bending moment diagram for the beam, using the end reactions and moments. This bending moment diagram, or the functions which generate it, is integrated twice w.r.t. the length coordinate, say x. After each integration, an unknown constant of integration is obtained, which constants can be calculated by applying the boundary conditions for the beam. In this case, both the slope and deflection of the beam will be equal to zero at each end.

Have you studied any strength or materials courses?