Members in tension (ties) and compression (struts), and finding the internal forces in a pin-jointed framework by resolving forces at a joint in equilibrium.

What this key area is asking

The SQA wants you to identify structural members as ties (in tension) or struts (in compression), and to find the internal forces in a simple pin-jointed framework by resolving forces at a joint that is in equilibrium. Once the support reactions are known, this is how you find whether each member is being pulled or pushed, and by how much.

Ties and struts

The distinction drives the design. A tie only resists being pulled apart, so it can be slender, even a cable or rod. A strut resists being crushed and, more importantly, buckling (bowing out sideways under compression), so it is usually a thicker or hollow section to stay stiff. A cable can act as a tie but never as a strut. Working out which members are ties and which are struts is therefore the first design decision in a framework.

Pin-jointed frameworks

A pin-jointed framework (a truss) is built from straight members connected at pinned joints that can rotate freely. Because the joints cannot transmit a turning moment, each member carries only an axial force along its length, either tension or compression. This is what makes a truss easy to analyse: every member is simply a tie or a strut with a single force value.

Resolving forces at a joint

Each joint is in equilibrium, so the forces meeting at it must balance both horizontally and vertically. To use this, resolve each member force into components:

The method is: pick a joint where only one or two member forces are unknown, resolve all forces at it into horizontal and vertical components, and set each direction's sum to zero. Two equations let you solve for up to two unknown member forces. Choosing a joint with a known external load (or reaction) gets you started.

Putting it together

Structural analysis runs in order: first find the support reactions (the previous key area, using equilibrium and moments), then work joint by joint resolving forces to find each member's internal force, classifying it as a tie or strut. The member forces then feed the next stage, materials, where you check that each member's stress is within safe limits. Each step depends on the structure being in equilibrium, the single idea underpinning the whole of structures.

Examples in context

A roof truss is a classic framework: the sloping rafters are often struts in compression carrying the roof load down, while a horizontal tie beam across the bottom is in tension, stopping the walls being pushed apart. A crane jib uses a tie (a cable or rod) to hold the jib up and a strut (the jib itself) in compression. A bridge truss combines ties and struts so that each member carries only axial load, which is why trusses are such an efficient way to span a gap with little material. Identifying ties and struts and finding their forces is exactly what lets an engineer size each member safely.

Try this

Q1. State whether a member in tension is a tie or a strut. [1 mark]

• Cue. A tie (tension stretches it).

Q2. A force of 200 N acts at 30 degrees to the horizontal. Find its vertical component. [2 marks]

• Cue. $F\sin\theta = 200 \times \sin 30^\circ = 200 \times 0.5 = 100\ \text{N}$.

Q3. At a joint, a single angled member must balance a 600 N vertical load and acts at 90 degrees (vertical). State its force and type. [1 mark]

• Cue. A vertical member takes the full 600 N; if it holds the joint up against the load it is a tie in tension (600 N).