# How to Determine the Strength of Trusses

Written by lenna allen
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Calculating the strength of trusses is used in two ways: to determine the viability of an existing bridge or to design a new bridge. While the determination of truss strength uses basic skills, it is the combination of those skills coupled with the ability to analyse structures that engineers possess. In the final design process, to determine the strength required of the trusses in a bridge (combination of trusses), you must also consider the expected 'live' loading (weight of traffic, pedestrians, etc.).

Skill level:
Easy

### Things you need

• Scientific calculator
• Graph paper
• Straight edge

## Instructions

1. 1

Use the equation 2J = M + 3, to determine if the truss is determinate. In this equation, J equals the number of joints in the truss and M equals the number of members in the truss.

2. 2

Continue with the analysis, if the equation is satisfied. If 2J < M + 3, the structure is indeterminate and cannot be analysed without advanced engineering mechanics.

3. 3

If 2J > M + 3, the structure is unstable and will collapse.

1. 1

Draw a free-body diagram on graph paper with x-y axis coordinates. To make a structural analysis of a simple truss, certain assumptions are required: that all members of the truss are perfectly straight, all joints in the truss are frictionless and all loads and reaction occur only at the joints.

2. 2

Make a simple line sketch of the truss. Show all members. Include the length of each member and all angles formed at joints.

3. 3

Draw and label the supports. Indicate the type of support -- fixed, rolling, etc.

4. 4

Indicate all the loads applied to truss. Include angles, amount of load and direction of force.

1. 1

Calculate reactions. Reactions are the component vectors of any force that is applied to a truss. Each force in this example will be either directed on the x-axis or the y-axis. For a truss to be at equilibrium (safe/strong), the sum of forces in the x-axis = 0 and the sum of forces in the y-axis = 0. With this in mind, look at the truss and determine loads as given and the distribution to each joint. For example, consider the weight of a truss is 680 Kilogram. This would be a force along the x-axis in the downward direction, distributed evenly across the truss (dead load). Any live loads must be indicated in the given problem.

2. 2

Calculate internal member forces. Isolate one joint truss, and draw a free-body diagram of that joint using basic trigonometry and geometry:

Each force vector of an internal force has x-component and y-component determined by the angle at which the truss members come into the joint. Using the following calculations, calculate the components:

Force y-component (Fy) = External Load (F) x sin of the angle formed by the truss member and the x-axis.

Force x-component (Fx) = F x cos of the angle formed by the truss member and the x-axis.

Again, sum of all forces = 0

Therefore, F + Fy + Fx = 0. Be careful of signs of loads because the final sign determines whether the member is in compression (-) or tension (+).

3. 3

Determine strength of truss. To determine this, you must have information regarding the building materials of each member. Using the member forces calculated in Step 2 and strength graphs for the given material, you can determine whether the truss is strong enough. The material graphs show member width on the x-axis, and tensile or compressive strength on the y-axis. Each graph has a corresponding Trend Line. Draw a straight line from the y-axis at the tensile/compressive force value calculated in Step 2 until it intersects with the Trend Line. Drop a line vertically to the x-axis from the intersection on the Trend Line to show the required minimum width of the member.

#### Tips and warnings

• Always check your calculations to catch simple math errors.
• Brush up on your math and physics skills.
• Be aware that every type of material has its own graph.
• This method assumes that the truss is in equilibrium, with no moment forces applied.
• This is an analysis of dead load only.

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