Structural Mechanics & Case Studies
Force, stress and the bending beam — and what happens when they are misjudged.
Under every structural system lies the same mechanics: forces in equilibrium, stress and strain in the material, and the shear and bending that a beam must survive. This unit covers those fundamentals — and then learns from real structures that failed, and ones that triumphed.
Learning objectives
By the end of this lesson, you will be able to — mapped to the course outcomes for Concept of Building Structures:
Resolve a force into components and define stress and strain.
Compute axial stress, strain and elongation from load and section.
Tell how the support condition changes a beam's bending and shear.
Draw the right lesson from a real structural failure or success.
Force, stress & strain
A force resolves into components and balances in equilibrium. Push or pull on a member and it develops stress (σ = P/A) and strain (ε = δ/L); in the elastic range they are proportional — σ = Eε (Hooke's law).[1, 4]
Stress, strain & elongation
Set the load, section, length and material and watch the stress, strain and elongation — δ = PL/AE. Keep the stress well below steel's ~250 MPa yield.
Axial stress, strain & elongation
σ = P/A, ε = σ/E, δ = PL/AE. Steel E ≈ 200 GPa.
0.0 MPa
Stress σ
0.000
Strain ε (×10⁻³)
0.000 mm
Elongation δ
Mild steel yields near 250 MPa — keep σ well below that.
Shear, bending & supports
Every loaded beam carries a shear force and a bending moment, mapped along it as the SFD and BMD. The support condition changes everything — a simply-supported beam sags (wL²/8), a cantilever hogs (wL²/2 at the fixed end).[1]
| Aspect | Simply supported | Cantilever |
|---|---|---|
| Support | Simply supported | Cantilever |
| Held by | a pin + a roller at the ends | fully fixed at one end only |
| Max bending moment (UDL w, span L) | wL²/8 at midspan (sagging) | wL²/2 at the fixed end (hogging) |
| Deflection (UDL) | 5wL⁴/384EI at midspan | wL⁴/8EI at the free end |
| Feel | bends down in the middle | droops at the free tip |
Case studies — failure & success
Tacoma Narrows Bridge (1940)
A slender deck oscillated and tore apart in a moderate wind — aeroelastic flutter. Lesson: dynamic and aerodynamic behaviour matters, not just static strength.[3]
Ronan Point, London (1968)
A small gas explosion blew out a load-bearing precast panel and a corner of the tower collapsed progressively. Lesson: structures need alternative load paths and robustness against disproportionate collapse.[2, 3]
Hyatt Regency walkway, Kansas City (1981)
A connection re-detailing doubled the load on a rod hanger and the walkways fell. Lesson: the connection is as critical as the member; check every change.[3]
The Eiffel Tower (1889)
A wrought-iron lattice shaped by the wind-moment diagram — light, stiff and stable. Lesson: when form follows the force diagram, structure becomes architecture.[4]
Study task
Pick one failure from above and, in a short paragraph, explain the structural cause and the single lesson an architect should carry from it into practice.
Self-assessment
1. Axial stress in a member is —
2. For a cantilever of span L with a uniform load w, the maximum bending moment is —
3. The Tacoma Narrows Bridge failed mainly because of —
Recap
References & further reading
- [1]R.K. Bansal, A Textbook of Strength of Materials. New Delhi: Laxmi Publications.
- [2]Matthys Levy & Mario Salvadori, Why Buildings Fall Down. New York: W.W. Norton.
- [3]Henry Petroski, To Engineer is Human: The Role of Failure in Successful Design. Vintage.
- [4]Mario Salvadori, Why Buildings Stand Up. New York: W.W. Norton.
- [5]S. Ramamrutham, Strength of Materials. Dhanpat Rai & Sons.
Further reading
- Mario Salvadori, Why Buildings Stand Up & (with Levy) Why Buildings Fall Down.
- Henry Petroski, To Engineer is Human.
- R.K. Bansal, A Textbook of Strength of Materials.
Sources gathered and fact-checked June 2026. Published values vary by source, sample and method — treat as indicative and confirm against the cited standard before structural use.