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Section 1: Types of Force

Forces impact structures in a variety of different ways depending on how they are applied. Forces can move a structure slightly or cause damage by changing its shape. Sometimes the changes are almost impossible to see — for example, a bridge will sag slightly when a vehicle drives over it. Forces can also make an object move or change direction.

There are five types of force you need to know:

Compression

The supporting columns of the Queensferry Crossing experience a huge downward force from the cables. The ground exerts an upward reaction force on the bases of the columns. These two opposing forces try to squash or shorten the column — the column is said to be in compression. A weightlifter's body experiences compression in the same way: the weights push down, the ground pushes up.

Tension

Tension is the opposite of compression. A structure under tension is being pulled apart. In a tug of war, both teams pull the rope in opposite directions — the rope is in tension. Wire ropes, cables and chains are typically in tension.

Bending

Structures that carry loads across their length are subject to bending forces. A weightlifting bar bends due to the downward forces of the weights at each end. Beams in buildings and bridges experience bending.

Shear

Shear forces can be described as tearing or cutting forces. A pair of scissors cuts a ribbon using shear — the two blades push in opposite directions across the material. A lawn mower blade shears the grass.

Torsion

Torsion (also called torque) forces twist or turn a structure. A screwdriver being twisted to drive a screw applies torsion to the screw. A spanner turning a bolt applies torsion to the bolt.

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Section 2: Levers

A lever is a simple machine that can amplify force. By using a pivot point (called a fulcrum) and a rigid bar, a small effort force can move a large load. The further from the fulcrum the effort is applied, the easier it is to move the load.

A lever system changes an input force and input motion into an output force and output motion:

When a counterbalance weight is attached to one side of a lever to assist the user, it is known as a counterbalance. Cranes and diggers use counterbalances to prevent them toppling over.

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Section 3: Moments

When a force acts at a distance from a pivot, it creates a turning effect called a moment. Moments are measured in Newton-metres (Nm).

Equilibrium and the Principle of Moments

When a system is in a steady, balanced state it is said to be in equilibrium. For a lever to be in equilibrium, the clockwise moments must equal the anticlockwise moments.

The Principle of Moments states:

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Section 4: Free-Body Diagrams

A free-body diagram is a simplified diagram that shows all the forces acting on a structure or body. It isolates the structure from its surroundings and replaces real components with arrows representing the forces they exert.

To draw a free-body diagram:

1. Draw a simple outline of the structure (or just a line or box)
2. Replace all connections and supports with arrows showing the force they exert
3. Label each force with a letter or value
4. Show downward forces (loads, weight) acting through their point of application
5. Show upward reaction forces at support points

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Section 5: Beams and Reactions

A beam is a structural member that carries loads across its length. For a horizontal beam to be in equilibrium, two conditions must be satisfied simultaneously:

The upward forces at the support points are called reactions (R₁ and R₂). To find both reactions, we use the Principle of Moments and the force balance equation together.

Method for finding beam reactions

1. Take moments about one reaction (R₁) — this eliminates R₁ from the equation, allowing you to solve for R₂
2. Use the force balance (∑ up = ∑ down) to find R₁
3. Check: R₁ + R₂ should equal the sum of all downward forces

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Vectors

Force is a vector quantity — it has both magnitude (size) and direction. Vectors can be represented as drawn lines where:

• The length of the line (drawn to scale) represents the magnitude of the force
• The direction and arrowhead show the direction of the force

When multiple forces act along the same line, they can simply be added or subtracted. For example: a cyclist pedalling with 800 N, assisted by a tailwind of 400 N, but with 200 N road friction, has a net force of 800 + 400 − 200 = 1 000 N.

Resultant of two angled forces

When two forces act at an angle to each other, their combined effect is a single force called the resultant. The resultant can be found graphically using the parallelogram of forces:

1. Choose a suitable scale and draw both force vectors from a common point C
2. From the tip of each vector, draw a line parallel to the other vector
3. The point where these lines intersect (D) completes the parallelogram
4. Draw the line from C to D — this is the resultant
5. Measure the length of C to D and convert using your scale to find the magnitude
6. Measure the angle to find the direction

Conditions for Equilibrium

For a structure or body to be in equilibrium (a balanced, stable state), three conditions must all be satisfied:

Condition	Meaning
∑ upward forces = ∑ downward forces	Vertical forces balance — no net vertical movement
∑ leftward forces = ∑ rightward forces	Horizontal forces balance — no net horizontal movement
∑ CWM = ∑ ACWM	Moments balance — no net rotation

Graphical solution for forces in members

For a structure such as a crane or frame, the forces in individual members can be found graphically by drawing a triangle of forces:

1. Identify the joint where the known load acts
2. Draw the known force to scale
3. From each end of this line, draw lines parallel to the unknown force members
4. Where the lines intersect completes the triangle
5. Measure each side to find the forces (following arrowheads round the triangle indicates compression or tension)