Not sure what beam deflection formula to use...
Not sure what beam deflection formula to use...
(OP)
I've been through my Machinery's and Marks', but can't find a beam bending diagram for a beam that is loaded at 2 points, one on the cantilever end and one between two other supports, sort of like this:
W W
----------------------------------
R R
Where "W" are the loads, and "R" are the supports. I realize that I may not have the most complete set of beam diagrams with these two books. How would you go about determining the maximum deflection in this beam?
W W
----------------------------------
R R
Where "W" are the loads, and "R" are the supports. I realize that I may not have the most complete set of beam diagrams with these two books. How would you go about determining the maximum deflection in this beam?





RE: Not sure what beam deflection formula to use...
2 ways you can do this:
1. 3 separate calculations, 1 for the cantilever, 1 for the u.d.l on the span, and one for the span with a moment on the end then add the relevant deflection/rotations up to get the total.
2. formulas are
cantilever deflection = (wa/(24EI))x(3a^3 +4a^2Xl - l^3)
span deflection = (wl^2/(384EI))x(5l^2-12a^2)
where a = cantileveer (an not more than l/2),l = span.
Be aware that this is for uniform load on the whole beam only and if you have only partial load then the deflection will be more.
RE: Not sure what beam deflection formula to use...
If it's structurally determinant, I would instead find the reactions and draw the shear force (V) and bending moment (M) diagrams. Bending moment at a given location is the area under the shear force diagram up to that point (M=∫V and V=∫[loading diagram].
RE: Not sure what beam deflection formula to use...
RE: Not sure what beam deflection formula to use...