Introduction to Structural Systems | A3.2

Students must be able toAnalyse and interpret a variety of human-made and natural structures.

A structure is any object or assembly that supports a load without undergoing unacceptable deformation or failure. Structures are found everywhere, from the bones of a skeleton to the steel frame of a skyscraper, from a spider's web to a suspension bridge.

In nature, evolution has optimised structures over millions of years. Examples include:

• Bones: hollow tubes of dense cortical bone surrounding a lattice of spongy trabecular bone. Lightweight yet strong in both compression and bending.
• Eggshells: thin, dome-shaped shells that resist compressive forces by distributing them across their curved surface.
• Honeycombs: hexagonal cells use minimal wax while providing maximum compressive strength. Nature's own corrugation.
• Tree trunks and branches: tapered cantilevers that are wider at the base where bending forces are greatest.

In the built environment, designers learn from nature but also from the properties of manufactured materials:

• Great Wall of China solid masonry structures filled with earth and stone.
• Eiffel Tower: open lattice steel frame; triangulated geometry provides rigidity with minimal material.
• Shipping Container: Intentionally formed steel plates are welded together to form a rigid shell structure
• Bicycle frame: welded tubular triangles; geometry is the source of strength, not material mass.

Real products and buildings combine structure types. A motor vehicle has a frame chassis, shell body panels, and solid engine block components: analysing each helps designers understand the load paths and select appropriate materials.

Students must be able toDiscuss frame, shell and solid structures, and how they are used in the design of products.

The three primary structural classifications are:

Solid structures are formed from a single, continuous mass of dense material. They resist forces primarily by sheer bulk and mass rather than by geometry. Solid structures are extremely strong in compression but tend to be heavy and material-intensive.

• Examples: Concrete dams and retaining walls, hammer heads, brick walls, the pyramids, paperweights, door handles.
• Design implication: Suitable where weight is not a constraint and where forces act from many unpredictable directions.

Frame structures consist of a skeleton of interconnected beams, rods, or struts. Strength comes from the geometry of the arrangement (especially triangles) rather than material mass. Frame structures are lightweight and efficient.

• Examples: Bicycle frames, steel skyscrapers, scaffolding, chairs, the Eiffel Tower, roof trusses.
• Design implication: Excellent strength-to-weight ratio; ideal when reducing mass matters (transport, long spans).

Shell structures are thin, curved surfaces that enclose a space or wrap around a form. Their curvature transfers forces across the entire surface, not through a concentrated path. This allows great strength with very little material.

• Examples: Eggshells, domes, car body panels, motorcycle helmets, aircraft fuselages, shipping containers
• Design implication: Highly efficient for enclosing volumes; curved geometry is critical, as flat panels are much weaker than curved ones.

Combination structures use elements of all three types. An automobile combines a space frame (chassis), shell panels (body), and solid components (engine block, axles). Analysing which part is which helps designers understand load paths and optimise material placement.

Students must be able toIdentify simply supported beams, fixed beams, cantilever beams, continuously supported beams and columns, and explain their function.

Larger structures are built from individual structural members: elements designed to carry specific types of load in specific ways. The four primary beam types and columns are:

Simply supported beam: Rests freely on supports at both ends, with no resistance to rotation at those supports. The beam can bend between the two points. This is the most common beam type and the simplest to analyse.

• Examples: A shelf resting on two brackets, a plank across two bricks, a bridge span resting on piers.

Fixed beam: Rigidly attached (built-in) at both ends. The supports resist not only vertical force but also rotation (bending moment). Fixed beams deflect less than simply supported beams under the same load, because the rigid ends counteract bending.

• Examples: Reinforced concrete beams cast monolithically into walls, structural floor joists welded into a rigid frame.

Cantilever beam: Fixed at only one end, with the other end projecting freely with no support. All the bending moment is resisted at the single fixed point. Cantilevers are efficient for overhangs but require strong, rigid fixing.

• Examples: Diving boards, balconies, aircraft wings, shop signs, traffic lights on single poles. The Junkers J 1 (1915) was the first aircraft to use cantilever wings, eliminating the external bracing wires of earlier biplanes and demonstrating that internal structure alone could carry the load.

Continuously supported beam: Spans across more than two supports. The multiple supports share the load and reduce maximum bending moments, allowing longer spans. Analysis is more complex because it is statically indeterminate.

• Examples: Cable-stayed bridge decks, continuous floor beams over multiple columns, railway rails.

Columns are vertical structural members that carry compressive loads downward to the foundations. They are primarily loaded in compression (unlike beams, which are loaded in bending). Long slender columns are vulnerable to buckling (sudden lateral deflection under compressive load), which is why I-sections and hollow tubes are preferred over solid rods.

• Examples: Building columns, table legs, struts in a bicycle frame.

Students must be able toExplain how compression, tension, torsion, bending and shear forces act within a structure, and differentiate between static and dynamic forces.

Static forces are constant, non-changing loads. Also called dead loads, they include the permanent weight of the structure itself and any fixed attachments. A bridge's own weight is a static force. Static forces do not change with time and are relatively straightforward to design for.

Dynamic forces are changing or moving loads. Also called live loads, they include traffic, wind gusts, people moving, earthquakes, and machinery vibration. Dynamic forces are harder to predict precisely, which is one reason safety factors (see 3.2.9) are built into structural designs.

There are five fundamental types of force that can act within a structure:

1. Compression: A squashing force that pushes material together, shortening it. Columns under vertical load are in compression. Concrete is strong in compression (20–40 MPa) but weak in tension, which is why it is reinforced with steel. Example: Chair legs under a sitting person; arch bridges convert loads into compression throughout the arch.
2. Tension: A pulling or stretching force that tries to elongate a material. Suspension bridge cables carry loads primarily in tension. Steel is very strong in tension. Example: Tug-of-war rope; tie rods in a truss; bungee cord.
3. Torsion: A twisting force that rotates a structural member around its longitudinal axis. Drive shafts in cars are in torsion while transmitting torque from the engine to the wheels. Example: Turning a screwdriver; wringing out a wet towel; propeller shaft.
4. Bending: A force that creates a curved deflection, combining compression on one face and tension on the opposite face simultaneously. A beam loaded at its centre compresses the top fibres and stretches the bottom fibres (or vice versa for a cantilever). Example: A shelf sagging under books; a ruler pressed from one end.
5. Shear: A force that causes adjacent layers of material to slide in opposite directions. Scissors cut by applying shear. Bolts and rivets joining structural components are often loaded in shear. Example: Cutting paper with scissors; the web of an I-beam resists shear between flanges.

In practice, most structural members experience combinations of these forces simultaneously. A beam under a central load experiences bending (tension + compression) and shear at the supports. A drill bit experiences both torsion (turning) and compression (pushing).

Tacoma Narrows Bridge

A steady wind and a bridge that tore itself apart.

Read case study →

Students must be able toDescribe the relationship between stress and strain on a material under stress, and outline Young's Modulus, yield strength, ultimate strength and fracture in the context of a stress-strain graph.

When a force is applied to a material, two things happen simultaneously: the material experiences stress (internal resistance) and strain (deformation).

Stress (σ) is the force per unit cross-sectional area:

σ = F / A    [units: Pa or MPa; 1 MPa = 10⁶ Pa = 1 N/mm²]

Where F is the applied force in newtons and A is the cross-sectional area in m² (or mm² for MPa).

Strain (ε) is the fractional change in length:

ε = ΔL / L₀    [dimensionless, no units]

Where ΔL is the change in length and L₀ is the original length. Strain has no units; it is often expressed as a percentage or in microstrain (με).

A stress-strain graph shows how a material responds from first loading to final fracture. Key points on the graph:

1. Linear elastic region: stress and strain are proportional (Hooke's Law). If the load is removed, the material returns to its original shape. The slope of this region is Young's Modulus (E = σ/ε).
2. Yield strength (σ_y): the stress at which the material begins to deform plastically (permanently). Below this point, deformation is elastic; above it, permanent set remains after unloading. For most metals, the yield strength is close to but slightly below the proportionality limit.
3. Ultimate tensile strength (UTS, σ_u): the maximum stress the material can withstand before necking begins (localised thinning). This is the peak of the stress-strain curve for ductile materials.
4. Fracture point: the stress at which the material breaks completely. In ductile materials (like steel), there is significant plastic deformation before fracture. In brittle materials (like glass or cast iron), fracture occurs with little or no plastic deformation; the curve drops steeply from near the UTS.

Young's Modulus (E) measures stiffness: how much a material resists elastic deformation per unit stress:

E = σ / ε    [units: GPa or MPa]

A high Young's Modulus means the material is very stiff (little strain per unit stress). A low E means the material is flexible (large strain per unit stress). Note: stiffness is not the same as strength; a stiff material resists deformation, while a strong material resists fracture.

Students must be able toCompare materials with a high Young's Modulus and those with a low Young's Modulus in terms of how they react under stress, and explain why this is important when designing structures.

Young's Modulus spans many orders of magnitude across the material families. The table below shows approximate values for key engineering materials:

High E materials (steel, CFRP, titanium) deform very little under load. They maintain their shape under high stress, making them ideal for structural members in buildings, bridges, and aircraft where maintaining precise geometry matters. Under the same load, a steel beam deflects far less than a timber or polymer one of the same dimensions.

Low E materials (rubber, soft plastics) undergo large elastic deformations under relatively small loads. This is not a weakness: it is useful when compliance and energy absorption are required. Vehicle tyres must flex to absorb road irregularities; rubber seals must deform to create a watertight joint; foam cushioning deflects to protect fragile contents.

Design implications:

• A structure where deflection must be minimised (bridge deck, shelf, aircraft wing) demands high E material.
• A component that must absorb energy or vibration (engine mount, sports shoe sole) benefits from low E material.
• Composite structures (steel-reinforced concrete, CFRP laminates) can combine a high-E reinforcement with a lower-E matrix to achieve both stiffness and fracture resistance.

Students must be able toDescribe when a structure is in equilibrium and identify the conditions where a structure will fail.

A structure is in static equilibrium when it is stationary and all forces and moments acting on it are balanced. Two conditions must both be satisfied:

ΣF = 0    (the sum of all forces is zero in every direction)

ΣM = 0    (the sum of all moments about any point is zero)

When ΣF = 0 but ΣM ≠ 0, the structure will rotate. When ΣF ≠ 0, the structure will accelerate. Only when both conditions hold is the structure truly stable and stationary.

Conditions that disrupt equilibrium and can cause structural failure:

1. Overloading: The applied load exceeds the structure's designed capacity. Stress in a member exceeds yield strength (permanent deformation) or ultimate strength (fracture). Example: Too many people on a balcony; a lorry exceeding bridge weight limits.
2. Uneven force distribution: Load concentrates in one region, creating a local stress concentration that exceeds the material's strength even when total load is within limits. Example: A crack or notch in a structural member acts as a stress concentrator; the stress at the tip of a notch can be many times the average stress.
3. Foundation instability: Soil beneath the structure settles unevenly or erodes, changing the support conditions. This introduces unexpected moments that the structure was not designed for. Example: The Leaning Tower of Pisa; buildings on clay that shrinks when dried.
4. Dynamic impact: A sudden impulse load (earthquake, explosion, impact) creates forces far exceeding the static load. Structures may fail not because the peak force exceeds strength, but because resonance amplifies oscillations. Example: The Tacoma Narrows Bridge (1940): wind-induced resonance caused the bridge deck to oscillate and tear itself apart despite the wind speed being well within static design limits.
5. Fatigue: Repeated cycles of stress below the yield strength gradually introduce micro-cracks that grow until sudden fracture occurs. Even though each individual load cycle is safe, cumulative damage builds. Example: Metal fatigue in aircraft structures (the de Havilland Comet pressurisation cycle failures, 1954).

Students must be able toExplain how structures can be strengthened by using struts, shape, lamination and composite materials.

Designers have four primary strategies for increasing structural strength and stiffness without simply using more material:

1. Struts and triangulation

A strut is a compression member added to a frame to stabilise it against lateral forces or to share loads between members. When struts are arranged to create triangles, the structure becomes inherently rigid: a triangle is the only polygon whose shape cannot be changed without changing the length of its sides.

• Roof trusses use diagonal struts to convert a long horizontal span into a series of triangles. Each triangle carries load by pure compression or tension in its members, with no bending; this is far more efficient than a simple beam.
• Bicycle frames use triangulated tube arrangements (main triangle + rear triangle) to create a rigid, lightweight structure.
• Tower cranes and transmission pylons use lattice frameworks of triangulated struts.

2. Shape optimisation

The cross-sectional shape of a structural member dramatically affects its resistance to bending and buckling, independent of the material used:

• I-beams (universal beams): Concentrate material in the flanges (top and bottom), where bending stresses are highest, while the thin web between resists shear. This gives a high moment of inertia with minimal material. I-beams resist bending more efficiently than solid rectangular or circular sections of the same area.
• Hollow tubes and sections: For columns and members in torsion, hollow sections (square or circular) provide better resistance to buckling and twisting than solid rods of the same weight.
• Arches and domes: Convert loads into compression throughout their depth, making use of materials like masonry and concrete that are strong in compression but weak in tension. The Roman Pantheon dome (c. 125 CE) has stood for nearly 2,000 years.
• Corrugation: Folding a flat sheet into a corrugated profile dramatically increases its second moment of area (resistance to bending) without adding mass. Corrugated iron roofing, cardboard packaging, and corrugated steel decking all exploit this principle.

3. Lamination

Bonding multiple layers of material together, often with the layers' grain or fibre orientation varied between plies, creates composites that outperform any single layer:

• Glued laminated timber (glulam): Thin timber boards are glued together with grain alternating direction. Glulam can span longer distances than solid timber and achieves a specific strength (strength per unit weight) comparable to or exceeding steel. A 10 m glulam beam weighing 100 kg can carry loads that would require a much heavier steel beam.
• Laminated safety glass: Two panes of glass with a PVB (polyvinyl butyral) interlayer. When broken, the interlayer holds fragments together, preventing shattering. Used in vehicle windscreens and structural glazing.
• Plywood: Thin wood veneers glued with alternating grain directions. Cross-lamination distributes forces in both directions, eliminating the directional weakness of solid timber along the grain.
• Carbon fibre reinforced polymer (CFRP): Layers of carbon fibre fabric impregnated with epoxy resin, with fibre orientations chosen to resist specific load directions. Used in aircraft, racing cars, and high-performance sporting equipment.

Concept: Second Moment of Area

The second moment of area (also called the moment of inertia of a cross-section) is a geometric property that measures how a member's cross-sectional area is distributed relative to its bending axis. The further material sits from that axis, the more it contributes, because each small area's contribution is weighted by the square of its distance from the axis. This is why an I-beam, which concentrates material into flanges far from the centre, resists bending far better than a solid rectangular bar of the same mass.

This connects directly to the stiffness ideas introduced for Young's Modulus: bending resistance depends on both the material's Young's Modulus (a property of the material itself) and the cross-section's second moment of area (a property of its shape). Two beams made of identical steel can have very different bending stiffness purely because one is shaped to place material further from the bending axis, which is exactly the logic behind I-beams, corrugation, and box sections.

Students must be able toDefine a safety factor as a ratio of a structure's absolute strength to the allowable load, and explain why structures are designed to include a safety factor.

A safety factor (SF) is the ratio of the load at which a structure would fail to the maximum load it is designed to carry in service:

SF = Failure load / Maximum service load

A safety factor of 2 means the structure is built to withstand twice its intended maximum load before failing. A safety factor of 1 means the structure fails exactly at its design load, with zero margin for error.

Why do structures require SF > 1? Real-world conditions are imperfect in ways that pure calculation cannot fully capture:

1. Material variability: Real materials have natural flaws, impurities, and microstructural variations. Laboratory test specimens are ideal; production materials are not. The actual strength of a structural member may be 5–15% below the theoretical value.
2. Load unpredictability: Actual loads in service may exceed design estimates. Crowds may be denser than anticipated; storms may be more severe; accidents can apply sudden impact loads. Dynamic loads (wind gusts, earthquakes) are particularly hard to predict with precision.
3. Wear, fatigue, and ageing: Structures degrade over time due to corrosion, fatigue micro-cracks, UV degradation of polymers, and repeated loading cycles. A bridge designed for 50 years must have sufficient margin to remain safe as materials weaken over its life.
4. Human safety: Lives depend on structural integrity. A bookshelf that collapses wastes books; a bridge that collapses kills people. Society demands a significant margin between design load and failure load wherever human safety is at risk.
5. Modelling assumptions: Structural calculations use simplified mathematical models. Real load paths, connection stiffness, material isotropy, and boundary conditions are all approximations. The SF absorbs the inevitable gap between model and reality.

Students must be able toOutline what a safety factor of 1 means for a structure, and explain why most structures have a safety factor above 1.

A safety factor of 1 means the structure is designed to fail precisely at its maximum service load. Any additional load, any material imperfection, or any dynamic amplification will cause failure. No engineering structure intended for human use is designed with SF = 1. Even temporary structures on remote construction sites carry SF > 1.

The typical SF varies significantly by application, balancing the consequences of failure against the cost of over-engineering:

SF and material choice: A high SF does not just require a stronger material; it may allow the use of a lower-grade, cheaper material. A designer choosing between high-grade steel (SF 1.5) and mild steel (SF 3) might find that mild steel at SF 3 is lighter and cheaper for a given load case, because the mild steel section can be made thicker to compensate for its lower strength, while the higher SF makes the structure safer overall.

SF and sustainability: Over-engineering (excessively high SF) wastes material, increases weight, costs energy to manufacture and transport, and may shorten service life by introducing additional mass-related stresses. Sustainable structural design seeks the minimum SF consistent with safety, no more and no less.