A3.2 Introduction to Structural Systems

How do structures carry loads, resist forces and remain stable?

Learning goals

recognise structures in nature and designed products;
distinguish frame, shell and solid structures;
identify structural members, loads and the five main forces;
use stress, strain, Young's modulus and safety factor in design decisions.

Starter · Look around the classroom

Find one structure that is mainly a frame, one that behaves like a shell, and one solid component. Be ready to justify each choice.

3.2.1 Structures in Nature and the Built Environment

A structure is a system of parts designed to support loads, resist forces and maintain its shape. Structures are not limited to buildings: a leaf, a bicycle and the human skeleton all depend on an organised arrangement of material.

A structure is defined by what it does, not only by what it looks like.

Nature as a designer

Natural structures often achieve high performance with little material. Their form has developed in response to a function:

Natural structure	What to notice	Structural benefit
Spider web	radial and spiral threads	carries tension with very little material
Honeycomb	repeated hexagonal cells	encloses space efficiently and shares loads
Leaf veins	branching network	supports the leaf and transports nutrients
Eggshell	thin, curved surface	protects the contents and spreads load

Four examples of efficient natural structures: a spider web, honeycomb, leaf veins and an eggshell cross-section — **Figure 1.** Spider web, honeycomb, leaf veins and eggshell. In each case, geometry reduces the amount of material required.

Spot it

Trace the load path with your finger: where does an applied force travel, and which parts finally support it?

Human-made structures

Designed structures respond to a purpose and a context. A bridge spans a gap; a building provides shelter; a dam holds back water; a chair supports a user. Designers balance:

form · function · materials · forces · culture · cost

Think like a designer

Do not write only, “It is strong.” Explain why: “The curved shell spreads the load over its surface, so a thin layer of material can resist the force.”

A six-question analysis routine

What is its purpose?
What loads act on it?
Where are the supports?
How does the shape carry the load?
Why is this material suitable?
Where might it deform or fail?

Common mistake

Naming a structure is description. Explaining how its parts, shape and material resist forces is analysis.

3.2.2 Classification of Structures

The three main structural types are frame, shell and solid. Many real products combine more than one type.

Frame

A skeleton of interconnected members.

Strength comes from: arrangement and joints.

Clue: you can see spaces between the members.

Shell

A thin surface that encloses a space.

Strength comes from: surface and shape.

Clue: the skin carries and spreads the load.

Solid

A mass of material that resists through its bulk.

Strength comes from: material and cross-section.

Clue: little or no internal empty space.

Frame structure · bicycle

Road bicycle showing its triangular frame — **Figure 2.** A bicycle frame connects the wheels, saddle and handlebars.

The tubes form interconnected triangles. This provides rigidity and load distribution while keeping mass low. Frames are useful when the goal is high strength with low weight.

Look for the same principle in scaffolding, cranes, roof trusses, furniture and skeletons.

Shell structure · drinks can

Thin cylindrical aluminium drinks can — **Figure 3.** The curved wall of a can spreads forces across its surface.

A can uses a very thin sheet of aluminium. Its cylindrical form creates rigidity, encloses liquid and distributes loads. Shells are useful for protection, enclosure, aerodynamics and watertightness.

Other examples include helmets, eggshells, domes, vehicle bodies and aircraft skins.

Solid structure · dam and engine block

A concrete dam and a dense metal engine block as examples of solid structures — **Figure 4.** Solid structures resist large forces through material strength and bulk.

Solid structures are usually stable, durable and difficult to deform, but they often have greater mass, material use and cost. Examples include dams, foundations, hammer heads, teeth and machine parts.

Quick check

A crash helmet has a hard outer skin and a thick foam liner. Is it frame, shell or solid? Answer: it is a combination—the outer shell spreads impact while the foam behaves as a solid energy-absorbing layer.

Why combine types?

Product	Frame	Shell	Solid
Car	chassis	body panels	engine block
Building	columns and beams	cladding	foundations
Aircraft	fuselage ribs	external skin	landing gear components
3D printer	rigid gantry	enclosure	motor housings

Classification depends on how each part carries load; one product may contain all three types.

3.2.3 Structural Components

Structural members create a path that transfers loads safely to the supports and, eventually, to the ground.

Beams and columns

A beam usually carries loads across a horizontal distance.
A column usually carries compressive loads vertically towards the foundations.

Steel I-section beam shown horizontally on a white background — **Figure 5 · Beam.** A beam carries loads across a span and transfers them to its supports. In an I-section, the flanges resist most of the bending while the web resists shear.

A row of vertical reinforced-concrete columns supporting a concrete slab — **Figure 6 · Column.** Columns carry loads mainly in compression, transferring the weight of slabs and beams down towards the foundations.

Beam type	How it is supported	Easy-to-recognise example
Simply supported	support at both ends; ends may rotate	shelf resting on two brackets
Fixed	rigidly fixed at both ends	beam cast into concrete walls
Cantilever	fixed at one end; other end is free	balcony or diving board
Continuous	extends over more than two supports	long multi-span bridge deck

Photo challenge · Identify the beam type

Photograph A: a short bridge deck spanning between two concrete abutments — A

Photograph B: a projecting balcony connected to a wall and supported by diagonal stays — B

Photograph C: a long bridge deck carried by several concrete piers — C

Photograph D: a steel I-beam rigidly connected to a concrete wall — D

Identify the beam types

Which beam type is shown in each photograph A–D? Choose the best description from simply supported, fixed, cantilever or continuously supported.

For each answer, justify your decision by describing:

the number and position of the supports;
whether either end appears free to move or rotate;
any additional support that makes the real structure more complex than the simplified model.

Suggested analysis

A — Simply supported: the bridge deck spans between supports at each end.
B — Stayed cantilever: the balcony projects from the building, but diagonal tension stays provide additional support. It is not a pure cantilever.
C — Continuously supported: one deck extends across several piers, so the load is shared between multiple supports.
D — Insufficient evidence from this view: the visible end is rigidly fixed. If the unseen end is free, it is a cantilever; it is a fixed beam only if the other end is also fixed.

Recognition technique

Cover the object itself and inspect only its supports. Beam names describe the support condition, not the material or appearance.

Columns

Columns are vertical structural members designed primarily to transfer compressive loads.

They carry loads from above, such as:

roofs,
upper floors,
beams.

These forces are transferred downward towards the foundations.

Columns therefore contribute to the stability of the complete structure.

Examples

columns in classical Greek temples,
timber or steel columns in buildings,
table legs,
chair legs.

In residential buildings, columns can replace some load-bearing walls, allowing designers to create more open interior spaces.

Key Idea

Beams mainly carry loads across horizontal distances, while columns transfer loads vertically towards the foundations.

Load-path example

Person on a balcony → balcony beam → fixed connection → building frame → foundations → ground

The free end of a cantilever needs no column below it, but the fixed connection must resist a large bending effect.

Check your understanding

Why is a diving board a cantilever but a shelf on two brackets is usually simply supported?

Answer

The diving board is fixed at one end and free at the other. The shelf transfers load to supports near both ends.

3.2.4 Static, Dynamic and Structural Forces

A load is an external action on a structure. Loads create internal forces and stresses in its members.

Static and dynamic loads

Static	Dynamic
constant or slowly changing	changes with time or movement
little impact or vibration	may include impact or vibration
roof weight, books on a shelf	traffic, wind gusts, a person jumping

Important distinction

“Static” does not mean “small,” and “dynamic” does not mean “large.” The distinction is whether the load changes significantly with time.

The five actions

Action	What the material does	Everyday memory cue
Compression	shortens or squashes	chair leg
Tension	lengthens or pulls apart	rope in tug-of-war
Bending	curves; one side compresses and the other stretches	diving board
Torsion	twists around an axis	screwdriver shaft
Shear	adjacent parts slide in opposite directions	scissors cutting paper

Visual comparison of compression, tension, bending, torsion and shear, with force arrows and everyday examples — **Figure 7 · The five structural actions.** The arrows show how each action affects a material; the photographs connect each action to an everyday example.

Push = compression · Pull = tension · Curve = bending · Twist = torsion · Slide = shear

Use your hands

Mime each action while saying its name. Linking a technical term to a physical movement makes it easier to retrieve later.

Forces act together

When a beam bends, the inside of the curve is in compression and the outside is in tension. Bolts at its connection may also experience shear. Analyse the complete load path rather than assigning only one force to an entire product.

A simply supported beam bending under a central load, showing compression above the neutral axis and tension below it — **Figure 8 · Forces acting together.** Bending creates compression above the neutral axis and tension below it; stress increases with distance from the neutral axis.

Bending always creates tension on one side and compression on the other.

3.2.5 Stress, Strain and Material Failure

Force alone does not tell us how severely a material is loaded. The same force becomes more critical when it acts through a smaller area.

Stress

Stress $σ$ is the applied force divided by the cross-sectional area carrying that force:

Stress = Force Cross-sectional area

Using symbols, the same relationship is:

σ = F A

Stress is measured in pascals (Pa):

1 P a = 1 N / m 2

The prefix mega (M) means one million:

1 M P a = 1, 000, 000 P a = 1 N / m m 2

For this reason, MPa and N/mm² are commonly used in product design and engineering.

Worked example

A 10,000 N tensile force acts on a rod with an area of 200 mm².

σ = 10000200 = 50 N / m m 2 = 50 M P a

Strain

Strain $ε$ compares the change in length with the original length:

ε = Δ L L 0

Strain has no unit because it is a ratio of two lengths.

Connecting stress, strain and stiffness

Stress describes how intensely a material is loaded; strain describes how much it deforms in response. Comparing them tells us how easily the material changes shape.

Within the elastic region:

E = stress strain

This ratio is Young's modulus. A high value means that a large stress produces only a small strain, so the material is stiff. A low value means that the material deforms more easily and is therefore more flexible.

Reading a stress–strain graph

Typical stress-strain curve showing the elastic limit, yield point, ultimate tensile strength, necking, plastic zone and fracture — **Figure 9 · Reading a stress–strain graph.** Stress is plotted vertically and strain horizontally. The curve shows the transition from reversible elastic deformation to permanent plastic deformation, necking and final fracture.

Elastic region: deformation is reversible; when the load is removed, the specimen returns to its original length.
Yield strength: permanent deformation begins. From this point, the specimen will not fully return to its original shape.
Plastic region: the specimen continues to stretch permanently while still carrying an increasing tensile load.
Ultimate tensile strength (UTS): the highest engineering tensile stress recorded during the test.
Necking and fracture: after UTS, deformation becomes concentrated in a narrow region. The specimen carries less load until it finally separates.

Ultimate tensile strength (UTS)

UTS is the maximum engineering tensile stress a material reaches during a tensile test. It is calculated using the greatest tensile load and the specimen's original cross-sectional area:

U T S = F max A 0

At UTS, the material has reached its peak load-carrying capacity. Necking normally begins after this point, but the specimen has not broken yet. Fracture occurs later, when the remaining section can no longer carry the load.

Yield → permanent deformation begins · UTS → highest engineering tensile stress · Fracture → the specimen separates

Do not confuse UTS with fracture

UTS is the peak of the engineering stress–strain curve, not the breaking point. A ductile material can continue stretching and necking between UTS and final fracture.

Common mistake

Stiffness is resistance to elastic deformation. Strength is resistance to yielding or failure. A material can be stiff but brittle, or flexible but strong.

3.2.6 Young's Modulus and Material Selection

Young's modulus $E$ measures stiffness in the linear elastic region:

E = stress strain = σ ε

High Young's modulus	Low Young's modulus
steep stress–strain slope	shallow stress–strain slope
small elastic deformation under load	larger elastic deformation under load
useful for frames, beams and precision machines	useful for seals, cushions and flexible components

Comparison of stress-strain curves for materials with high and low Young's modulus — **Figure 10 · High and low Young’s modulus.** A steep initial slope indicates a stiff material with a high Young’s modulus; a shallow slope indicates a more flexible material with a low Young’s modulus.

Reference table of typical Young's modulus values and applications for common material groups — **Figure 11 · Typical Young’s modulus values.** These approximate ranges help compare material stiffness; actual values depend on composition, processing, orientation and test conditions.

A high Young's modulus means stiff, not automatically strong.

Material-selection sentence frames

Complete both sentences before opening the model answers:

High Young's modulus: “I would select ___ because its high Young's modulus means it will ___ under the expected load, which is important because ___.”
Low Young's modulus: “I would select ___ because its low Young's modulus means it will ___ under the expected load, which is important because ___.”

Show model answers

High Young's modulus — machine frame: “I would select steel because its high Young's modulus means it will deform very little under the expected load, which is important because the machine must remain rigid and accurate.”
Low Young's modulus — sealing strip: “I would select rubber because its low Young's modulus means it will deform easily and conform to the surfaces under the expected load, which is important because it must create an effective air- and watertight seal.”

Design context matters

An earthquake-resistant building needs strength but may also need controlled flexibility and energy dissipation. The “best” material is therefore not always the stiffest one: designers balance stiffness, strength, toughness, mass, cost and manufacturing.

3.2.7 Equilibrium and Structural Stability

A structure is in equilibrium when its forces and moments are balanced, so it has no overall linear or rotational acceleration. Both conditions below must be satisfied at the same time.

Translational equilibrium

The resultant force is zero:

\sum F = 0

Upward reactions balance downward loads, and horizontal reactions balance horizontal loads.

Rotational equilibrium

The resultant moment about any point is zero:

\sum M = 0

Clockwise moments balance anticlockwise moments.

Moment reminder

$Moment = Force \times perpendicular distance from the pivot$

When can a structure fail?

A structure may fail when equilibrium is lost or when its load-carrying capacity is exceeded. Failure does not always mean immediate collapse: it may begin as excessive movement, permanent deformation, cracking, buckling or foundation settlement.

Cause of failure	How it affects the structure	Possible result or example
Overloading	The applied load produces internal stresses greater than the strength of a member or connection.	Permanent deformation, buckling or collapse; for example, a floor carrying more weight than it was designed for.
Uneven force distribution	Loads become concentrated in one area or act away from the centre, creating excessive local stress or an unbalanced turning moment.	Local cracking, twisting or overturning; for example, a shelf loaded heavily at one end.
Foundation instability	A support shifts, sinks or rotates, changing the reactions and disrupting the intended load path.	Tilting, cracking and possible progressive collapse; for example, uneven settlement in soft ground.
Dynamic impacts	Sudden or changing loads create acceleration, vibration and inertia forces faster than the structure can respond safely.	Oscillation, connection failure or collapse during an earthquake, wind gust, collision or impact.

Four visual comparisons showing structural failure caused by overloading, uneven force distribution, foundation instability and dynamic impacts — **Figure 12 · Common causes of structural failure.** Each comparison shows how a change in load, load position, support condition or dynamic action can disrupt the intended structural behaviour.

Important distinction

A structure can be in external equilibrium and still fail if its members are not strong or stiff enough. Equilibrium describes balance; strength describes whether the structure can resist the resulting internal stresses.

Failure risk increases when: loads are too large · loads are badly distributed · supports move · forces change suddenly

3.2.8 Strengthening Structures

Structures can be strengthened without simply adding more material. Designers improve the way a structure carries and distributes loads by using four main techniques:

struts · shape · lamination · composite materials

Efficient strengthening places material and geometry where they contribute most to the load path.

1. Struts

A strut is a structural member designed mainly to resist compression. Struts reinforce frames by creating additional load paths.

They can:

distribute loads through different parts of a structure;
reduce stress concentrations at individual joints;
prevent long members from bending or buckling;
increase the rigidity and stability of a frame.

From a rectangle to triangles

Adding a diagonal strut divides a rectangular frame into triangles:

Without a diagonal strut	With a diagonal strut
The rectangle can distort into a parallelogram.	The frame is divided into two triangles.
Loads may concentrate at the joints.	The diagonal provides a new compression load path.
The frame has low resistance to sideways deformation.	The frame becomes much more rigid and stable.

This works because a rectangle can change shape without changing the length of its sides, whereas a triangle is geometrically stable unless one of its members changes length.

Typical applications include roof trusses, truss bridges and aircraft structures.

Key idea · Struts

Struts strengthen a structure by resisting compression, distributing loads and preventing deformation or buckling.

Check your understanding

Why does adding a diagonal strut make a rectangular frame more stable?

Show answer

The diagonal creates triangular sections. Triangles resist changes in shape, while the strut carries compressive force through the frame and away from individual joints.

2. Shape

The geometry of a structure can greatly increase its strength and stiffness without necessarily increasing the amount of material. Different shapes control forces in different ways.

Triangles

Triangles are geometrically stable and resist distortion. This is why they are widely used in trusses, bridges, bicycle frames and roof structures.

Arches and domes

Arches and domes redirect much of an applied load into compression and transfer it towards their supports. This reduces the bending that would occur in a flat beam spanning the same opening.

Corrugation

Folding a thin sheet into a corrugated profile increases its depth and makes it much more resistant to bending. The amount of material may be almost unchanged, but its geometry produces far greater stiffness.

Typical examples are corrugated cardboard and metal roofing.

I-beams

An I-beam places most of its material away from the neutral axis, where bending stresses are greatest:

the upper and lower flanges provide most of the bending resistance;
the central web resists much of the shear force and keeps the flanges apart.

This creates a high resistance to bending without using a completely solid section, giving an efficient strength-to-weight ratio.

Structural shape	Main mechanism	Typical example
Triangle	prevents a frame changing shape	roof truss
Arch or dome	redirects loads through compression	stone bridge or stadium roof
Corrugation	increases section depth and bending stiffness	cardboard or roof sheet
I-section	positions material away from the neutral axis	steel floor beam

Key idea · Shape

Shape strengthens a structure by using geometry to distribute forces efficiently and resist deformation without necessarily adding more material.

3. Lamination

Lamination means bonding multiple layers of material together to form a stronger and more reliable structural material.

Lamination can:

increase strength and stiffness;
improve toughness;
slow or redirect the propagation of cracks;
allow different layers to perform different functions;
combine useful levels of strength and flexibility.

Loads are shared between the bonded layers, so a weakness in one layer can be supported by the others.

Plywood

Plywood is made by bonding thin sheets of wood veneer. The grain direction of adjacent layers is usually rotated:

Layer 1 → → → → → Layer 2 ↑ ↑ ↑ ↑ ↑ Layer 3 → → → → →

Natural timber is much stronger in some directions than others. Crossed grain directions make plywood more dimensionally stable and resistant in more than one direction.

Cross-laminated timber (CLT)

CLT uses thicker timber layers arranged crosswise to adjacent layers. The crossed arrangement produces large structural panels with increased rigidity and strength.

Key idea · Lamination

Lamination strengthens a structure by bonding layers so that loads are shared and weaknesses or cracks in individual layers are less likely to continue through the whole material.

4. Composite materials

A composite material combines two or more different materials whose properties complement each other. The aim is to obtain structural performance that the materials cannot provide as effectively on their own.

Composites can provide:

a high strength-to-weight ratio;
strength and stiffness in selected directions;
improved durability;
improved corrosion resistance.

In fibre-reinforced composites, designers can orientate the fibres to resist forces in the directions where strength and stiffness are most needed.

Reinforced concrete

Reinforced concrete clearly demonstrates complementary material properties:

Material	Performs well in	Function in a reinforced-concrete member
Concrete	compression	carries much of the compressive stress and protects the reinforcement
Steel reinforcement	tension	carries tensile stress where concrete would crack

Concrete — strong in compression + Steel — strong in tension → Reinforced concrete

When a reinforced-concrete beam bends, concrete carries much of the compression while steel bars positioned in the tensile region help prevent tensile failure.

Carbon-fibre composite

A carbon-fibre-reinforced polymer combines:

carbon fibres, which provide strength and stiffness;
a polymer matrix, which holds the fibres together, protects them and transfers loads between them.

The fibres can be orientated to match the direction of the expected forces, allowing high performance with relatively low mass.

Key idea · Composite materials

Composite materials strengthen structures by combining materials with complementary properties, allowing each material to perform the function it does best.

Comparing the four strengthening techniques

Technique	How it strengthens the structure	Simple example
Struts	resist compression, distribute loads and prevent deformation or buckling	roof truss
Shape	uses geometry to distribute forces efficiently and increase rigidity	triangle, arch, corrugation or I-beam
Lamination	bonds layers so loads are shared and weaknesses or crack propagation are reduced	plywood or CLT
Composite materials	combines materials with complementary properties	reinforced concrete or carbon fibre

Choose the strengthening technique

Identify the main technique in each example: a corrugated cardboard box, a plywood panel, a roof truss and a reinforced-concrete beam.

Show answer

Corrugated cardboard box → shape.
Plywood panel → lamination.
Roof truss → struts and triangulation.
Reinforced-concrete beam → composite materials.

3.2.9 Safety Factor

The factor of safety compares the load that causes failure with the maximum expected working load:

S F = failure load working load

Worked example

A hook fails at 12 kN and is rated for a 3 kN working load:

S F = 123 = 4

The failure load is four times the intended working load.

Why include a margin?

Real conditions contain uncertainty:

variation in material properties and dimensions;
manufacturing defects;
unexpected or uneven loads;
impact, vibration and fatigue;
corrosion, wear and ageing;
errors in use, inspection or maintenance.

Important

A higher safety factor is not free: it can increase mass, cost and environmental impact. The required value depends on consequences of failure, uncertainty, standards and the design method used.

3.2.10 Designing Above the Required Load

A safety factor of $1$ means the predicted failure load equals the expected maximum load. This leaves no allowance for uncertainty or deterioration.

Safe design separates normal working conditions from failure.

A balanced decision

The designer must balance:

safety · reliability · mass · cost · material use · regulation

Values should come from the applicable engineering standards and evidence—not from a universal table applied to every product.

Exit ticket · 60 seconds

Choose one classroom product and write three sentences:

classify its structural type;
identify its main load and internal force;
explain one way to strengthen it without adding unnecessary mass.

Topic recap

Structures support loads, resist forces and maintain shape.
Frame, shell and solid structures obtain strength in different ways.
Supports determine the behaviour of beams; columns transfer compression vertically.
Loads may be static or dynamic and can create compression, tension, bending, torsion and shear.
Stress describes force per area; strain describes relative deformation.
Young's modulus measures stiffness in the elastic region.
Equilibrium requires balanced forces and moments.
Geometry, lamination and composites can strengthen structures efficiently.
Safety factors provide a margin between working conditions and failure.

You should now be able to...

Analyse a product by tracing its load path, naming the structural system and forces, and justifying material and strengthening choices with technical evidence.