Structures: forces, stability, strength, frameworks, reinforcement

Structures – Forces, Stability, Strength & Reinforcement (IGCSE Design & Technology 0445)

This note summarises everything required for the Structures component of the Cambridge IGCSE Design & Technology syllabus (specialist option – Systems & Control). It is organised to match the syllabus headings, includes the mandatory common‑content points, and provides exam‑friendly formulas, examples and checklists.

1. Types of Structure

Structures are classified by origin and by the way they carry loads.

Origin	Typical Examples (IGCSE level)	Load‑Carrying Principle
Natural	Tree trunk, bone, spider web, seashell	Geometry (cylindrical, curved) + fibre orientation gives strength and stiffness.
Man‑made	Wooden bridge, steel portal frame, concrete slab, aluminium aircraft wing, FRP sports racket	Engineered members (beams, columns, trusses) and connections (pinned, fixed, braced).

2. Materials for Structures

The five material families required by the syllabus are listed below with typical uses, a representative property value and a brief note on sustainability.

Material Family	Typical Structural Uses	Key Property (representative)	Sustainability / Environmental Note
Wood	Frames, joists, trusses, furniture, timber bridges	Modulus of Elasticity ≈ 10 GPa	Renewable, low embodied energy, but vulnerable to moisture & decay.
Metals (steel, aluminium)	Beams, columns, bridges, chassis, portal frames	Modulus ≈ 70 GPa (steel), ≈ 70 GPa (Aluminium)	High recyclability; steel production is energy‑intensive, aluminium has high embodied energy.
Concrete (plain & reinforced)	Columns, slabs, foundations, walls, precast units	Compressive strength ≈ 30 MPa (plain), ≈ 35 MPa (reinforced)	Low tensile strength; cement production generates CO₂ – consider supplementary cementitious materials.
Plastics (PVC, acrylic, polycarbonate)	Light‑weight panels, housings, pipework, protective covers	Modulus ≈ 3 GPa	Often derived from fossil fuels; can be recycled but recycling rates vary.
Composites (FRP, carbon‑fibre)	High‑performance panels, aerospace parts, sports equipment, bridge decks	Modulus ≈ 100 GPa (carbon‑fibre)	Very high specific strength; fibre production is energy‑intensive, but material usage is low.

3. Loads, Load Paths & Load Classifications

• Dead load (permanent) – Self‑weight of the structure and any fixed services.
• Live load (variable) – Occupants, furniture, movable equipment, vehicles.
• Environmental loads – Wind pressure, snow, rain, seismic forces, thermal expansion.
• Applied loads – Any external force deliberately placed on the structure (e.g., a machine).
• Reaction forces – Forces supplied by supports or foundations that keep the structure in equilibrium.

Load paths show how each load is transferred from the point of application, through members, joints and finally to the foundations. In exam diagrams, clearly label the path with arrows and indicate whether the load is a dead or live load.

4. Stability of Structures

Stability ensures a structure remains upright and does not undergo uncontrolled deformation.

4.1 Static (Equilibrium) Stability

• Sum of vertical forces = 0: \(\sum F_y = 0\)
• Sum of horizontal forces = 0: \(\sum F_x = 0\)
• Sum of moments about any point = 0: \(\sum M = 0\)

4.2 Geometric (Buckling) Stability

Critical for slender columns. Euler’s formula is used in the IGCSE:

\[ P_{cr}= \frac{\pi^{2}EI}{(K L)^{2}} \]

• \(E\) – Modulus of Elasticity (Pa)
• \(I\) – Second moment of area (mm⁴)
• \(L\) – Unsupported length (mm)
• \(K\) – Effective length factor (1.0 for pinned‑pinned, 0.7 for fixed‑fixed, etc.)

4.3 Dynamic (Vibration) Stability

Natural frequency of a simple system:

\[ f = \frac{1}{2\pi}\sqrt{\frac{k}{m}} \] where \(k\) is stiffness and \(m\) is mass. For the IGCSE, it is enough to recognise that excessive vibration can be reduced by increasing stiffness or adding damping (e.g., bracing).

5. Strength of Materials & Allowable Stresses

Property	Definition	Typical Units
Compressive Strength	Maximum compressive stress before crushing	MPa
Tensile Strength	Maximum tensile stress before rupture	MPa
Shear Strength	Maximum shear stress before sliding	MPa
Modulus of Elasticity (E)	Stress ÷ strain in the elastic region	GPa

For design calculations the allowable stress is used:

\[ \sigma_{allow}= \frac{\sigma_{material}}{SF} \] where \(SF\) (safety factor) is typically:

• Timber – 1.5 – 2.0
• Steel – 1.2 – 1.5
• Concrete – 1.5 – 2.0

6. Structural Systems, Joints & Simple Truss Analysis

6.1 Common Systems

• Triangulation – The most efficient way to achieve rigidity; a triangle cannot change shape without changing side lengths.
• Truss – Network of straight members forming triangles; joints are usually pinned (no moment resistance).
• Rigid (Moment‑Resisting) Frame – Members joined with fixed or semi‑fixed connections; can carry bending moments.
• Space Frame – 3‑D triangulated lattice, high strength‑to‑weight.
• Shell – Curved thin surface (e.g., dome, arch) that distributes loads through membrane stresses.

6.2 Joint Types (IGCSE relevance)

Joint	Behaviour	Typical Use
Pinned (hinged)	Allows rotation, transfers only axial forces.	Truss connections, simple supports.
Fixed (rigid)	Resists rotation, transfers axial + bending moments.	Portal frames, cantilever bases.
Roller	Restrains movement in one direction only.	Expansion joints, sliding supports.

6.3 Basic Truss Analysis (Method of Joints)

1. Draw a clear free‑body diagram of the whole truss and calculate the support reactions.
2. Isolate a joint where only two unknown forces act (so they can be solved using \(\sum F_x = 0\) and \(\sum F_y = 0\)).
3. Proceed joint‑by‑joint until all member forces are known.
4. Indicate whether each member is in tension (draw a “pulling” arrow) or compression (draw a “pushing” arrow).

For exam purposes, a short worked example (e.g., a simple 3‑panel roof truss) can be included in revision notes.

7. Reinforcement Techniques

• Steel reinforcement in concrete – Bars or mesh placed before casting to resist tension.
• Fiber‑Reinforced Polymers (FRP) – Glass or carbon fibres embedded in a polymer matrix; used for light, high‑strength panels.
• Post‑tensioning – Steel tendons are tensioned after concrete has set, introducing a compressive pre‑stress that counteracts tensile forces.
• Bracing – Diagonal members (X‑braces, knee braces) that increase lateral stability and raise the buckling load.

7.1 Reinforced Concrete Design (IGCSE formula)

For a rectangular beam or column subjected to a bending moment \(M\):

\[ A_s = \frac{M}{f_y \, d} \]

• \(A_s\) – Required area of steel reinforcement (mm²)
• \(M\) – Factored bending moment (N·mm)
• \(f_y\) – Yield stress of the steel (typically 250 MPa for mild steel)
• \(d\) – Effective depth from the extreme compression fibre to the centroid of the tensile steel (mm)

Use the allowable stress approach: first calculate the required steel area, then check that the concrete stress does not exceed its allowable compressive stress.

8. Design Process Checklist (Exam‑Friendly & Syllabus‑Aligned)

1. Define the problem – State functional requirements, site constraints and all relevant loads (dead, live, environmental).
2. Plan & record – Sketch initial ideas, keep a design journal, note assumptions, and decide on a CAD/CAM tool if required.
3. Select material family – Use the table in Section 2; justify choice with properties, cost and sustainability.
4. Choose a structural system – Truss, rigid frame, shell, etc.; explain why the system suits the load path.
5. Calculate section properties
   • Determine bending moment \(M\) (use simple beam formulas or statics).
   • Find required section modulus \(S = M/\sigma_{allow}\).
   • Check Euler buckling for columns: \(P_{applied} < P_{cr}\).
6. Design reinforcement (if concrete) – Compute \(A_s\) with the formula above; specify bar size and spacing.
7. Apply safety factors – Show the factor used for each material and reference the syllabus or a standard (e.g., 1.5 for timber).
8. Health & Safety & Sustainability
   • Identify any hazards (sharp edges, heavy lifting, fire risk).
   • Consider waste reduction, material recycling and energy use.
9. Produce clear communication
   • Free‑body diagrams with labelled forces (magnitude & direction).
   • Section views showing reinforcement layout.
   • Dimensions, units, significant figures.
   • Use correct technical terminology and CAD drawings if required.
10. Evaluate – Comment on strengths, possible weaknesses, and suggest improvements (e.g., alternative material, additional bracing).

9. Examination Tips for IGCSE

• Read the command word carefully: Explain → give reasons; Justify → link choice to properties; Calculate → show all steps.
• Draw neat, labelled free‑body diagrams before starting calculations.
• Keep units consistent (N, mm, MPa). Convert only once and keep the same number of significant figures throughout.
• State the safety factor you are using and why it is appropriate for the material.
• When using formulas, define every symbol in a short footnote or beside the equation.
• Show all required calculations:
  • Stress \(\sigma = F/A\)
  • Section modulus \(S = M/\sigma_{allow}\)
  • Euler buckling check
  • Reinforcement area \(A_s\)
• Conclude with a brief evaluation (strengths, limitations, possible refinements).
• If CAD is part of the task, include a clear, labelled drawing and a short note on the software used.