Truss calculation method of joints - example solutions

In this article you will learn how to use the method of joints to calculate the internal member forces in a truss system

1. Method of Joints

2. Truss solution instructions

3. Method of Joints - example solution

Method of Joints

The method of joints is one of the methods used to solve truss systems. This is an analytical method considered by many people to be the easiest, but at the same time time-consuming and involves a lot of calculations, especially if the truss has a large number of nodes and bars.

Other methods are:

• Method of sections - Ritter's method - analytical - graphical

• Cremona method - graphical

The method of joints involves calculating the normal forces in the truss bars by sequentially separating nodes (points where the bars meet).

It is important that the node we are calculating has a maximum of two bars for which we do not know the normal forces. Since we have two equilibrium equations (horizontal forces and vertical forces).

Truss solution instructions

Below you will find the recipe and step-by-step instructions for solving the truss:

1. Node designation - consecutive numbers (1,2,3..) or letters of the alphabet (A,B,C..)

2. Bar designation - usually consecutive numbers (1,2,3..)

3. Determination of reactions in supports

4. Calculation of support reactions from equilibrium equations (Fx, Fy, Mi)

5. Separating nodes and calculating forces in members from the equilibrium equations (Fx, Fy)

6. Check for the last node - optional

7. Summary in table (Bar No. -> Normal force)

Method of Joints - example solution

Below I have included a diagram of the truss that we will solve. The truss consists of 6 nodes and 9 members. It is loaded with three point loads P1 = 2 kN, P2 = 6 kN and P3 = 3 kN.

I marked the nodes with numbers from 1 to 6. Support reaction forces have been added R1 for roller support in node 1. H4 and V4 for the pin support in node 4.

Fig.1 Truss diagram - method of joint example solution

In the next step, we will calculate the support reactions from the equilibrium equations.

Fig.2 Determining the reaction - truss method of joint

All examples used in this post were created in my Truss Calculator . In this application, you will determine support reactions and normal forces in truss bars. Design your own trusses, and the software will provide interactive, step-by-step calculations using the method of joints.

Once we have calculated the values of the support reactions, we can proceed to the next stage, i.e. separation of nodes. In our case, we will start from node No. 1. In this node we have two unknown bars, N1-5 and N1-2. The 45-degree angle results from the geometry of members system.

Fig.3 Calculation of forces in truss members for node 1

The drawing above shows the drawing of forces for node 1 and the calculation of forces in bars 1-2 and 1-5. These forces are calculated from the equilibrium conditions: the sum of the projections of the horizontal forces and the sum of the projections of the vertical forces must be zero. Bar 1-2 is stretched because the force value is positive. However, rod 1-5 is in compression because the force value is negative.

The next node we will deal with is node number 4. In this node we also have two unknown forces for rod 4-3 and 4-6. We also use the equilibrium equations: the sum of projections of horizontal forces and the sum of projections of vertical forces.

Fig.4 Calculation of forces in truss members for node 4

When drawing forces for subsequent nodes, remember about the reactions or external forces applied to the node. A common mistake in node balancing solutions is to ignore these forces.

We proceed in the same way with subsequent nodes, remembering that the maximum number of unknown forces in the rod is two.

Fig.5 Calculation of forces in truss members for node 3

Fig.6 Calculation of forces in truss members for node 2

Fig.7 Calculation of forces in truss members for node 5

After calculating all normal forces in the bars, tables with summary is prepared.

Fig.8 Summary of normal forces in truss bars

This is where we will end the entry Truss calculation method of joints - example solutions.

Thank you.