Stop Struggling with Mechanics: Master Force Systems Once and for All!

Engineering school is a non-stop battle with vectors, and mechanics exams are the stuff of nightmares. The biggest issue? We often misidentify force systems, leading to wrong equations right from the start. Today, we’re breaking it all down to show you how to make your life much easier.

1. Convergent or arbitrary? You need to distinguish between the two!
2. Conditions of equilibrium - where is the difference?
3. Example tasks

1. Concurrent or General? You MUST know the difference!

Before you get to calculations, you need to classify your system correctly. This will determine how many equations you will have to write down and whether you are faced with counting moments.

Concurrent Force Systems:

• Coplanar Concurrent Force Systems - In mechanics, a planar concurrent force system is one in which all force vectors act in a single plane, and their lines (directions) intersect exactly at the single point. Each individual node of the truss is considered precisely as a planar system of convergent forces

• Spatial Concurrent Force Systems - A system of forces, applied to a rigid body, whose directions of action intersect at the single point.

General Force Systems (Non-Concurrent):

• It is a situation in which forces are dispersed. Their lines of action have no single point of contact. Such a system can not only move the body up, down or sideways, but most importantly -. can cause a turnover. Such a system can be planar when all forces lie in one plane or spatial where forces lie on different planes.

2. Equilibrium Conditions – Where’s the difference?

Depending on which system you are dealing with, you need to write the appropriate number of equations. A convergent force system is in equilibrium if the force vectors form a closed polygon.

Feature	Concurrent System	Non-Concurrent System
Coplanar	$\F_x = 0$ $\F_y = 0$	$\F_x = 0$ $\F_y = 0$ $\M_o = 0$
Spatial	$\F_x = 0$ $\F_y = 0$ $\F_z = 0$	$\F_x = 0$ $\M_x = 0$ $\F_y = 0$ $\M_y = 0$ $\F_z = 0$ $\M_z = 0$

In a coplanar general force system, a third equation is introduced – the sum of moments about a chosen point. This is where most errors occur, as it's easy to lose track of the moment's direction (sign) or the force's lever arm.

3. Example Problems

Below you will find an example of a task with a concurrent system of forces.

You can train the solutions of flat force systems tasks in my free tool Coplanar Force Resultant & Moment Calculator

The examples shown above are generated in this program for solving tasks of plane force systems, where you can calculate the resultant and principal moment of a force system.