Calculating Nodal Forces in a Simple Truss: Homework Solution

In summary, the problem involves calculating the nodal forces in a truss. The net forces at each node must sum to 0 in the x and y directions. The solution involves calculating the end support reactions first, starting at the simplest joint, and working through the other joints. This method was found to be in agreement with graphical truss analysis and helped increase confidence in solving truss problems.
  • #1
Aerstz
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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.
 

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  • #2
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.
 
  • #3
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.
 

1. What is a simple truss?

A simple truss is a structural system made up of interconnected members, typically made of steel or timber, joined together at their ends to form a series of triangles. It is used to support loads and distribute forces in a structure.

2. What are nodal forces in a simple truss?

Nodal forces, also known as joint forces, are the forces acting on the joints or connection points of a simple truss. These forces can be either tensile (pulling apart) or compressive (pushing together) and are essential for determining the stability and strength of the truss.

3. How are nodal forces calculated in a simple truss?

Nodal forces are calculated using the method of joints, which involves analyzing each joint in the truss individually. The forces acting on a joint must be in equilibrium, meaning that the sum of all forces in the x and y directions must equal zero. By setting up and solving equations for each joint, the nodal forces can be determined.

4. What factors affect the nodal forces in a simple truss?

The nodal forces in a simple truss are affected by several factors, including the magnitude and direction of external loads, the geometry and size of the truss, and the materials used for the truss members. Changes in any of these factors can alter the distribution and magnitude of nodal forces.

5. How do nodal forces affect the design of a simple truss?

Nodal forces are crucial in determining the strength and stability of a simple truss, and therefore play a significant role in its design. Engineers must ensure that the nodal forces are within safe limits for all joints in the truss, as excessive forces can lead to failure or collapse of the structure. The design of the truss must also take into account the type and distribution of nodal forces to ensure the truss can adequately support the intended loads.

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