Calculating Nodal Forces in a Simple Truss: Homework Solution

[Aerstz]

Homework Statement

Calculate nodal forces in truss (illustrated below).

Homework Equations

Force (horizontal) = FCosTheta

The Attempt at a Solution

Force in node A (horizontal) = FCosTheta = (5000)(Cos60) = 2500 N
Force in node A (vertical) = 5000/2 = 2500 N

Force in node B (vertical = 5000 N
(no horizontal force in B)

Force in node C (vertical) = 5000 N
(no horizontal force in C)

Forces in D are the same as in A.

 

[PhanthomJay]

The net forces at each node must always sum to 0 in the x and y directions. The problem asks (not clearly) to find the forces of each member (or support) at that node such that their vector sum is 0. Always calculate the end support reactions first (2500 N up in this case). Then start at the simplest joint (where there are 2 unknown forces or less), like at A. Since AC cannot take vertical forces, the vert comp of the force in AB must be 2500 N acting down on the joint, and the horiz comp of the force in AB must be 2500/tan 60 acting to the left on the joint. Thus, the force in AC (horizontal) must be 2500/tan 60 acting to the right on the joint. Continue on to the other joints.

 

[Aerstz]

Many thanks for your help. Values found using your solution are in agreement with values determined using graphical truss analysis, so I now feel more confident with truss problems and am grateful for your assistance.