Sources and References

Primary texts — Schodek, D. L. and Bechthold, M. Structures, 7th ed. Pearson, 2013. Allen, E. and Iano, J. The Architect’s Studio Companion: Rules of Thumb for Preliminary Design, 6th ed. Wiley, 2017.

Supplementary texts — Ambrose, J. and Tripeny, P. Simplified Engineering for Architects and Builders, 12th ed. Wiley, 2016. Billington, D. P. The Tower and the Bridge. Princeton University Press, 1985. Salvadori, M. Why Buildings Stand Up. W. W. Norton, 1990.

Online resources — CISC design guides on floor vibration and long-span structures; Canadian Wood Council Wood Design Manual companion educational content; Structural Engineers Association international case studies; NIST Building Materials reference database; MIT OpenCourseWare 4.462 Building Technology Workshop.

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Chapter 1: Vocabulary of Structural Systems

Architectural form and structural system are intertwined. A dome, a vault, a truss, a cable net, or a flat plate each carries load differently and produces a different spatial experience. Before any member is sized, the designer chooses a system whose behaviour suits the span, occupancy, and building economy. This chapter surveys the principal systems and introduces the criteria by which systems are compared.

1.1 Load Paths

Every structural system defines a path from applied load to foundation. Gravity loads flow downward through some combination of slabs, beams, trusses, columns, walls, and foundations. Lateral loads flow horizontally through diaphragms to vertical elements (moment frames, braced frames, shear walls) and then to foundations. A system is regular if the load paths are continuous, direct, and predictable; irregularity (transfer slabs, discontinuous walls, setbacks) creates stress concentrations and seismic vulnerability.

1.2 Selection Criteria

System selection weighs occupancy type, span requirements, height, seismic exposure, fire rating, construction speed, local labour skills, geography, and sustainability. A warehouse with 30 m bays and 10 m height is not the same problem as a hospital or a high-rise residential tower.

Chapter 2: Concrete Systems

2.1 Flat Plate and Flat Slab

A flat plate is a uniform-thickness concrete slab supported directly on columns, with no beams or drop panels. It achieves the minimum structural depth for a given span, simplifies formwork, and leaves ceilings flat for unobstructed mechanical routing. Punching shear at columns governs; for spans above roughly 7.5 m, shear reinforcement or drop panels (flat slab) become necessary. Typical thickness is span/30 for flat plate.

2.2 One-Way and Two-Way Joist Systems

Long spans with moderate loads (30 kN/m² or less) favour ribbed systems. One-way joists (pan joists) span between beams at regular intervals; two-way joists (waffle slabs) form an orthogonal grid. Material is concentrated where flexural stress requires it, leaving lightweight voids. Total depth is span/20 to span/24.

2.3 Post-Tensioned Slabs

Post-tensioned concrete embeds high-strength steel tendons in plastic ducts (unbonded) or grouted ducts (bonded) and stresses them after the concrete has cured. The compressive prestress offsets service-load tension, allowing thinner slabs and longer spans. A 225 mm post-tensioned flat plate can span 10 m where a conventional flat plate requires 260 mm at 7.5 m.

2.4 Walls and Cores

Concrete shear walls and elevator/stair cores provide the primary lateral resistance in most concrete buildings. The core also houses vertical services (plumbing, HVAC risers, elevators). Dual systems combine cores with perimeter moment frames; outrigger systems couple the core to perimeter columns at mechanical floors to engage the full building width in lateral resistance.

Chapter 3: Steel Systems

3.1 Wide-Flange Framing

Hot-rolled W-shapes form the backbone of most steel buildings. Girders at column lines carry infill beams; both support composite metal deck slabs. Spans of 9 to 15 m are routine; longer spans use deeper wide-flanges, castellated or cellular beams, or trusses.

3.2 Trusses and Open-Web Joists

Open-web steel joists achieve long span with minimal material by triangulating the web. Spans of 15 to 30 m are typical; the flat top chord supports decking and the diagonal webs define the depth. Depth-to-span ratio near 1:20 produces a competitive system for warehouses, big-box retail, and large institutional rooms.

Plate girders and deep Warren or Pratt trusses extend the reach to 50 m or more, used in stadiums, airport terminals, and industrial buildings.

3.3 Lateral Systems in Steel

Concentrically braced frames (X, chevron, diagonal) are economical for low to mid-rise. Eccentrically braced frames introduce a short beam link that dissipates seismic energy through ductile yielding. Special moment-resisting frames permit architectural openness at the cost of larger members and careful connection detailing after the lessons of Northridge (1994). Buckling-restrained braces provide symmetric tension-compression yielding without lateral-torsional buckling.

Chapter 4: Wood and Mass Timber

4.1 Light-Frame Construction

The 2x4 and 2x6 platform frame of North American residential construction is the workhorse of low-rise buildings. Repetitive members at 400 or 600 mm on centre carry gravity loads to continuous bottom plates; plywood or OSB sheathing provides diaphragm and shear wall action for lateral loads. Cost is low, skilled labour is widely available, and fire-rated assemblies are codified for up to six storeys in most jurisdictions.

4.2 Heavy Timber and Glulam

Traditional heavy timber uses solid sawn or glue-laminated members of large cross section. Char forms on the surface of wood in a fire, insulating the core; calculable char rates (about 0.7 mm/min for softwoods) enable fire-rated heavy timber without additional protection. Glulam arches and portal frames span 30 m and more.

4.3 Mass Timber

Cross-laminated timber (CLT), laminated veneer lumber (LVL), and dowel-laminated timber panels allow multi-storey wood construction at densities and spans previously reserved for concrete. Canadian codes permit encapsulated mass timber construction up to 12 storeys; taller buildings are being built under alternative compliance paths. Embodied carbon is dramatically lower than concrete or steel if the forest source is sustainably managed.

Chapter 5: Masonry

5.1 Unreinforced Masonry

Unreinforced brick, concrete block, and stone masonry resist only compression and small tension from bed-joint bond. In seismic regions, unreinforced masonry is prohibited for new construction because its brittle failure under lateral load has killed tens of thousands across the twentieth century.

5.2 Reinforced Masonry

Reinforced masonry places steel in vertical cells and horizontal bond beams, grouting the cells solid. Behaviour becomes similar to reinforced concrete: the masonry carries compression and shear, the steel carries tension. Modern reinforced masonry walls can carry seismic shear comparable to concrete shear walls.

Chapter 6: Long-Span Systems

6.1 Shells and Domes

Thin concrete shells (Candela, Isler, Dischinger) carry load primarily in membrane action, keeping bending negligible. Form follows force: funicular shells under their self-weight produce pure compression. Stress through a spherical dome of radius \(R\) under self weight \(w\) per unit surface area was derived in Chapter 2 of AE 101; the hoop tension below \(\theta \approx 51.8^\circ\) is the origin of cracking in masonry domes.

6.2 Cable-Stayed and Suspension

Cables carry load in pure tension, the most efficient structural action. A parabolic cable under uniform horizontal load \(w\) per unit horizontal distance with span \(L\) and sag \(d\) has maximum tension

\[ T_{max} = \frac{wL^2}{8d}\sqrt{1 + (4d/L)^2}. \]

Suspension bridges and cable-stayed roofs exploit this; the enemy is not cable strength but the deflection and aeroelastic behaviour of the flexible structure.

6.3 Tensile Membranes and Pneumatic Structures

Fabric roofs (teflon-coated fibreglass, ethylene tetrafluoroethylene foil) and pneumatic structures (air-supported domes) achieve very large spans with minimal material. The shape is an equilibrium of pretension or internal pressure and must satisfy a principal-curvature condition (minimal surface or anticlastic surface). Form-finding is a nonlinear geometric problem, not a linear analysis.

6.4 Space Frames and Grids

Three-dimensional space frames triangulate in both plan and section, achieving long span with modular fabrication. Proprietary systems (MERO, Triodetic) standardize the node-to-strut connection, lowering labour cost. Grids can be flat, cylindrical (barrel vault), or spherical (geodesic).

Chapter 7: Tall Building Systems

7.1 Rigid Frame to Tube

For buildings below about 20 storeys, a rigid moment frame suffices. Between 20 and 40 storeys, frame-shear wall interaction or diagonally braced frames become efficient. Above 40 storeys, framed tubes treat the perimeter as a punched hollow cantilever, greatly reducing steel weight per unit floor area. Bundled tubes (Willis Tower) and trussed tubes (John Hancock Center) extend this further. Diagrid systems replace orthogonal perimeter columns with diagonals that carry both gravity and lateral loads, visible externally as a structural expression.

7.2 Outriggers and Belt Trusses

Outrigger systems engage perimeter columns through truss arms at mechanical floors, converting core bending into axial forces in the perimeter columns. Belt trusses transfer loads around the perimeter to equalize column forces. Outrigger systems are now standard for 300 m and taller towers.

7.3 Damping and Wind

Above 200 m, wind-induced acceleration can exceed human comfort thresholds even when strength is satisfied. Tuned mass dampers (Taipei 101’s 730 tonne pendulum), viscous dampers, and aerodynamic shaping (twisting, tapering, porosity) reduce dynamic response. The governing equation for a damped oscillator gives peak response near resonance; detuning the building from dominant wind frequencies is cheaper than brute force.

Chapter 8: Selection in Practice

8.1 Economy

Cost per square metre of structure varies with system choice by factors of two. Light-frame wood is least expensive where permitted; steel is competitive for medium spans and fast erection; concrete suits repetitive floor plates and fire-rated housing; mass timber is gaining where embodied carbon counts. Local labour skill and material availability dominate; a system cheap in one country may be impractical in another.

8.2 Sustainability

Life-cycle carbon combines embodied (material manufacture and construction) and operational (energy in use) emissions. A 60-year-life building’s operational carbon historically dominated, but as operational energy fell with tighter envelopes and cleaner grids, embodied carbon grew relatively more important. The choice of structural system is the biggest single embodied-carbon lever on most projects: mass timber, low-carbon concrete (high supplementary cementitious materials content, limestone calcined clay cement), and high-scrap-content steel can each halve the embodied emissions of the conventional alternative.

8.3 Climate and Geography

Seismic regions favour systems with proven ductility: special moment frames, properly detailed shear walls, base isolation, and well-anchored light-frame wood. Hurricane-prone coasts favour closed-cell envelopes, uplift-resistant roof-to-wall connections, and impact-resistant glazing. Cold climates impose thermal-bridge-free connections between structure and enclosure. Hot-humid climates require corrosion-resistant detailing and moisture tolerance. The integration of structural selection with climate is where architectural engineering lives.