force method structural analysis examples

Just like the evenly distributed load affected the right side of the shear/moment diagram, we can use the same concept on the moment diagram.

The first half of the moment diagram is a slam dunk.

We find the slope of the shear by subtracting Ra from Rb and dividing by the acting length (L/2) At L/2 we know the shear force must change linearly as the evenly distributed load acts form L/2 to L.

Now that we have Ra, we know the shear force from support A to L/2.

To find the reactions, we place a statically equivalent load in the middle and sum the forces and moments about on of the support locations and calculate Ra and Rb.

Both ends are pinned so there can be no moment at either end.

The simply supported beam above is subjected to a evenly distributed load from L/2 to L.

In case a refresher is needed on internal and external indeterminacy: external indeterminacy means you can't find the support reactions using only the equilibrium equations internal indeterminacy means you can't solve for the members' internal forces using only equilibrium equations. I honestly don't remember how to use the force method, so I'd certainly use the displacement method. This is why almost all structural analysis software uses the displacement method.įor structures which are only slightly externally indeterminate (by one or two degrees of freedom) and which aren't very complex (or which can be decomposed into simple sub-structures), the force method might be useful if you're doing things by hand.įor internally indeterminate structures. Obviously, indeterminate structures will have more complicated solutions, but the basic working is all the same.

The displacement method is useful in that it is agnostic to such things, statically determinate and indeterminate structures are identical, as far as the method is concerned. Depends on your definition of 'better' and on the specific truss being analyzed.

Force method structural analysis examples