A3.2 — Introduction to structural systems (HL)

Key concepts

A structure is anything that carries a load — a chair holding a person, a bridge holding traffic, a bottle holding pressure. Structural design is the art of making something stand up, stay strong, and resist failure without using more material than necessary.

Forces and loads

A force is a push or pull, measured in newtons (N). A load is an applied force or weight on a structure. Structures experience several types of load:

• Tension — pulled apart. Cables, ropes, suspension bridge stays.
• Compression — pushed together. Columns, table legs, walls.
• Bending — curved by a transverse load. Beams, shelves, bicycle frames.
• Shear — layers sliding past each other. Scissors cutting paper, bolts under load.
• Torsion — twisted. Drive shafts, screwdriver shafts, wrench handles.

Real loads are usually combinations. A bicycle frame experiences bending (rider weight), torsion (pedalling forces), and compression (when hitting a kerb) simultaneously.

Structural forms

Different geometries carry loads differently:

• Columns and struts carry compression along their length. Must resist buckling as well as crushing.
• Ties carry tension along their length. Usually the most efficient structural member — material used fully.
• Beams carry transverse loads by bending. Top surface compresses, bottom stretches (or vice versa). Material at the neutral axis does little work.
• Arches convert vertical loads into compression along curved members. Used since Roman aqueducts.
• Trusses replace solid beams with triangulated members, saving material. Each member is purely in tension or compression.
• Shells and monocoques carry loads through a curved or closed surface. Used in car bodies, aircraft fuselages, eggshells.

Stress, strain and deformation

Stress (σ) is force per unit area (N/m², or Pa): σ = F / A. Strain (ε) is change in length divided by original length: ε = ΔL / L.

Stress describes how hard the material is working. Strain describes how much it is deforming. A thin wire under a small load can have the same stress as a thick cable under a large load.

Young's modulus (E) relates the two in the elastic region: E = σ / ε. High-modulus materials (steel, CFRP) are stiff. Low-modulus materials (rubber, foam) deform easily.

Structural optimisation

The best structure uses the minimum material to do the job safely. Strategies include:

• Triangulation — triangles are inherently rigid (unlike rectangles)
• Hollow sections — tubes are nearly as strong as solid bars for a fraction of the mass
• I-beams — concentrate material where bending stress is highest (top and bottom flanges)
• Ribbing and corrugation — thin sheet plus ribs is stiffer than thicker flat sheet
• Topology optimisation — software removes material from low-stress regions

Structural testing

Real structures are tested before deployment:

• Static load testing — apply known load, measure deflection, verify within limits.
• Destructive testing — load to failure to find true safety margins.
• Fatigue testing — repeated cyclic loading to reveal long-term failure modes.
• Finite element analysis (FEA) — software simulates stress distribution under load.

Case studies

Eiffel Tower — an open lattice truss using wrought iron. Uses minimal material for enormous height because every member is in pure tension or compression, and wind loads pass through the open lattice. Topology optimised by hand in 1889.

Airbus A350 wing spar — CFRP composite optimised through FEA. Wing flexes several metres in flight without fatigue, demonstrating high-cycle fatigue resistance impossible to achieve with aluminium at the same weight.

Bicycle frames — classic diamond frame uses triangulation. Modern CFRP frames use monocoque construction with varying wall thickness, placing material precisely where stress analysis demands.

Egg carton — thin paper pulp moulded into conical/pyramidal forms. Demonstrates shell structures: the curved surfaces convert point loads into distributed membrane stresses, making the carton far stronger than flat paper.

Glossary

• Structure — an assembly designed to carry loads.
• Tension — force pulling a member apart.
• Compression — force pushing a member together.
• Bending — load causing curvature in a member.
• Shear — force causing layers to slide past one another.
• Torsion — twisting force.
• Beam — a horizontal or transverse member resisting bending.
• Column — a vertical member resisting compression.
• Truss — a triangulated frame where members carry only tension or compression.
• Monocoque — a shell structure that derives strength from its outer surface.
• Stress — force per unit cross-sectional area.
• Strain — ratio of deformation to original length.
• Young's modulus — material property relating stress to strain in the elastic region.
• Buckling — sudden sideways failure of a slender compression member.
• Finite element analysis (FEA) — computational method simulating stress distribution in a structure.

Check your understanding

1. Distinguish between tension, compression, bending, and shear, with a product example of each.

Tension pulls a member apart — a bicycle brake cable. Compression pushes a member together — a chair leg. Bending curves a member through a transverse load — a bookshelf under a row of books. Shear causes adjacent layers to slide past each other — the blades of scissors cutting paper. Real structures usually experience combinations.

2. Explain why a truss uses less material than a solid beam of equivalent span and load capacity.

In a solid beam, only the top and bottom surfaces carry significant stress (compression and tension respectively); material in the middle (near the neutral axis) is lightly loaded. A truss removes this under-used material and replaces the core with diagonal members that transfer load through pure tension and compression. Every triangulated member is fully loaded, so the structure achieves equivalent performance with a fraction of the mass.

3. Define stress and strain and explain how Young's modulus relates them.

Stress is force per unit cross-sectional area (σ = F/A, measured in pascals). Strain is the proportional change in length (ε = ΔL/L, dimensionless). Young's modulus (E = σ/ε) is the material's intrinsic stiffness in the elastic region — it is a property of the material independent of geometry. Steel has a Young's modulus of about 200 GPa; rubber around 0.01 GPa.

4. A student claims their CFRP skateboard deck is "stronger" than an equivalent timber deck. Critique this claim.

"Stronger" is ambiguous — it conflates several distinct properties. CFRP has much higher tensile strength and stiffness per unit mass than timber, so a CFRP deck of equal weight will flex less under load. However, CFRP typically has lower impact toughness — it can fail catastrophically under a sudden point load whereas timber fails progressively (bending, splintering). The correct comparison depends on failure mode: CFRP is stronger in stiffness and strength-to-weight, timber is tougher in absorbing impacts.

Teacher's notes — additional examples and activities

Structures in nature vs built environment

Nature has evolved highly efficient structures over millions of years. Designers learn by imitating:

Biomimicry — designing by copying nature's solutions.

Three structural classifications

1. Frame structures — beams and columns, lightweight, hollow or open, need bracing. Examples: bicycle frames, tent poles, truss bridges, skyscraper steel frames.

2. Shell structures — 3D hollow forms with thin walls relative to overall size. Distribute forces smoothly across the surface. Examples: helmets, car body panels, plastic bottles, Pantheon dome, O2 Arena, clamshell packaging.

3. Solid structures — few internal spaces, resist deformation by bulk. Examples: dam walls, road surfaces, tool handles, brick walls.

Strengthening a structure — five strategies

When a structure fails or flexes too much, designers can:

1. Change the material — e.g. plastic → aluminium
2. Add reinforcements — ribs, gussets, cross-bracing
3. Change the shape — arches, domes, triangulated frames
4. Increase thickness — at stress concentration points only
5. Combine structures — frame + shell (e.g. bike frame with rigid shell casing)

Stress-strain graph — key points

A stress-strain graph shows how a material behaves when loaded:

• Straight-line region = elastic (returns to shape)
• Slope = Young's modulus (steep = stiff like steel; shallow = flexible like rubber)
• Yield point — where plastic (permanent) deformation begins
• After yield — necking (thinning) may occur
• Final point = fracture

Safety Factor

Safety Factor (SF) = Ultimate Load ÷ Allowable Load

Engineers specify an SF to ensure structures handle more than the maximum expected load. Higher SF = more margin but more material. Aircraft ~1.5; consumer products 2–3; lifting equipment up to 10.

Free body diagrams (force diagrams)

A free body diagram shows: - All forces acting on an object (direction and magnitude) - The object isolated from its environment - Reaction forces at supports or contact points

Essential for analysing structural loading. Students should be able to draw free body diagrams for simple loaded members.

Practical challenge — cantilever beam

A classic workshop exercise: using 6mm plywood, screws, and glue, build the strongest cantilever beam that supports 2 kg at the free end without flexing. Weigh the structure to measure strength-to-weight ratio. Iterate through multiple designs documenting each change. Excellent for teaching structural optimisation hands-on.