Structural forces and members

Once you know what loads a structure must carry, the next question is how its members carry them. Every member in a building, whether a cable, a column, a beam or a wall, resists load through internal forces. There are only a few kinds of internal force: tension, compression, bending, shear and torsion. Learning to recognize them in real members, and to sketch the forces acting on a piece of structure, is the core skill of structures literacy.

This lesson introduces equilibrium, free-body diagrams, the basic internal forces, stress and strain, and the way different materials respond. It uses simple arithmetic only. The aim is not to design members but to understand why they are shaped and connected the way they are, and why changing them on site can be dangerous.

Forces and equilibrium

A force has size, direction and a point of application. In structures we usually describe forces by their components: vertical and horizontal. A structure that is standing still, which is what we want from buildings, is in equilibrium. That means three things must be true for any part of it in a two-dimensional view.

• The sum of all vertical forces is zero: upward forces balance downward forces.
• The sum of all horizontal forces is zero: forces to the left balance forces to the right.
• The sum of all moments about any point is zero: the turning effects balance.

A moment is the turning effect of a force about a point, equal to the force multiplied by its perpendicular distance from the point. A 1 kN force acting 2 m from a point produces a moment of 2 kN·m. Moments explain why a long cantilever is harder to hold up than a short one, and why a crane outrigger must be farther from the crane's centre as the lift gets heavier or longer.

Free-body diagrams

A free-body diagram (FBD) is a sketch of one part of a structure, cut free from everything around it, with every force that acts on it drawn as an arrow. Engineers use FBDs to work out unknown forces. Constructors can use simple FBDs to reason about temporary works: what holds up a shore, what keeps a wall brace from sliding, or what forces act on an outrigger pad.

To draw an FBD, isolate the object, draw its outline, add the known loads (weights, applied forces) and then add the reactions where it touches supports. Supports are modelled by what they resist: a roller resists only a force perpendicular to its surface; a pin resists vertical and horizontal forces but not rotation; a fixed support resists forces and rotation.

The basic internal forces

When a member carries load, it develops internal forces that hold its parts together.

• Tension: the member is pulled and tends to stretch. Cables, hangers, the bottom chord of a truss and steel tie rods work in tension. Tension members can be slender because they cannot buckle.
• Compression: the member is pushed and tends to shorten. Columns, struts, shores and the top chord of a truss work in compression. Slender compression members can buckle sideways at loads far below the material's crushing strength.
• Bending: the member is loaded across its length and curves. One face is stretched (tension) and the other squeezed (compression). Beams, slabs and lintels work mainly in bending.
• Shear: one part of the member tends to slide past the next. Shear is high near the supports of beams and around columns in flat slabs, where it can cause punching shear failure.
• Torsion: the member is twisted, as in a spandrel beam carrying a slab on one side or a balcony cantilever.

Stress and strain

Stress is internal force divided by the area that carries it. It tells you how hard the material is working. Strain is the change in length divided by the original length. For most structural materials, stress and strain are proportional up to a limit; the ratio is the modulus of elasticity (E).

In SI units stress is measured in megapascals (MPa), where 1 MPa = 1 N/mm². Typical values: structural steel yields at about 350 MPa (CSA G40.21 350W) and has E ≈ 200,000 MPa; normal concrete is specified at 25 to 50 MPa in compression, has a tensile strength only about a tenth of that and E ≈ 25,000 to 30,000 MPa; reinforcing bars yield at 400 MPa (CSA G30.18 Grade 400).

How materials behave

Materials differ in strength, stiffness and how they fail, and that drives how structures are designed and built.

Ductility is a structure's ability to deform a lot before it fails, giving warning. Ductile behaviour is designed in deliberately, through steel reinforcing in concrete, through steel connections that yield before they fracture and through seismic detailing. A brittle failure, such as a shear failure in a beam with missing stirrups or a punching failure in a flat slab, can happen suddenly without warning. This is why seemingly small site errors in reinforcing detail can matter so much.

Common structural members

Each common member type works mainly in one or two ways.

• Columns and posts: compression, with some bending from eccentric loads or frames.
• Beams, girders, joists and lintels: bending and shear.
• Slabs and decks: bending in one or two directions, and shear around columns.
• Walls: compression from gravity loads, in-plane shear from lateral loads (shear walls) and out-of-plane bending from wind or soil.
• Trusses: members in pure tension or compression, connected at joints, carrying bending of the whole truss efficiently.
• Braces: tension or compression, depending on load direction.
• Cables and hangers: tension only.
• Arches and domes: mainly compression, pushing outward at their supports.

The last example has a practical lesson for rigging and temporary bracing: the flatter the angle of a sling, tie or brace, the higher the force in it for the same load. That is why rigging tables limit sling angles and why braces are usually set at 45° to 60° rather than lying almost flat.

Connections

Members are only as good as their connections. Loads must pass from one member to the next through bolts, welds, nails, screws, bearing plates, anchors or concrete reinforcing that laps or develops into the next element. Many structural failures, during construction and in service, are connection failures: a missing bolt, a short weld, a hanger rod with a changed detail, a bar lap that was too short or an anchor set in weak concrete.

Constructors control connection quality directly. Bolting and welding must follow approved shop drawings and inspection requirements. Anchors must be installed to the manufacturer's instructions, often with special inspection. Reinforcing laps, hooks and development lengths must match the drawings. Lesson 12 returns to the Hyatt Regency walkway collapse of 1981, in which a change to a hanger connection doubled the load on a critical detail.

For constructors, the practical value of these ideas is in reading situations quickly: seeing which member of a temporary frame is in compression and might buckle, which tie is carrying tension and must not be removed, and where a load will travel when a support is taken away.