Types of loads and stresses

Define each of the five basic stresses (tension, compression, bending, torsion and shear) in one sentence and give an example of an everyday element subject primarily to each one.

The figure shows five members of a structure subjected to different stresses; four are labelled and the fifth is covered. Indicate which stress the member marked with a question mark supports, and justify your answer based on how the forces act.

Explain the difference between a dead load (or permanent load) and a live load (or variable load) on a structure, and classify these loads on a footbridge: the weight of the deck itself, people walking across, accumulated snow and the handrail.

Distinguish between a point load and a distributed load using examples on a beam: a person standing at its centre versus a row of books resting along its entire length. How is each represented in calculation diagrams?

Distinguish between a static load and a dynamic load (impact or repeated load): why a swing that supports a person sitting still might break if someone drops down onto the seat, and how safety factors account for this in design calculations.

Explain in your own words what bending moment is in a beam and why it is maximum at the centre of a simply supported beam loaded in the middle (and zero at the supports). Relate this to where a ruler breaks if you bend it while resting it on two books.

Compare a simply supported beam with the same cantilever beam (fixed at one end) under the same load applied at the centre or at the free end: which deflects more, where the maximum moment is located in each case, and why balconies are calculated as cantilevers.

Explain what buckling is: why a long, slender rod bows laterally under compression long before squashing, and which two geometric characteristics (length and cross-sectional shape) most influence the buckling load.

To shore a floor slab located at a height of $4,0\ \text{m}$, a contractor proposes to splice end-to-end two $2,0\ \text{m}$ steel telescopic props (identical hollow tubular section), claiming that "since the resisting cross-section and the yield strength of the steel are the same, the double prop of $4,0\ \text{m}$ will withstand exactly the same compressive load before failing".

1. a) Quantitatively refute the contractor's claim using Euler's critical buckling load formula ($P_k = \frac{\pi^2 E I}{L_k^2}$): calculate by what factor the maximum allowable load of the $4,0\ \text{m}$ prop is reduced compared to the $2,0\ \text{m}$ one, assuming pinned-end boundary conditions at both ends.
2. b) Explain the physical mechanism of buckling and why it is a failure due to geometric instability rather than an exhaustion of the material's simple compressive strength.
3. c) Design a modification to the jobsite setup that would allow the $4,0\ \text{m}$ props to be used while achieving the same load capacity as the $2,0\ \text{m}$ ones, without changing the metal profile of the prop or increasing the tube thickness.

Explain how a stone arch works: into what stress it converts vertical loads, why masonry/stone materials (which have low tensile strength) are suitable for arches, and what role the lateral abutments play.

In a suspension bridge, the main cables and vertical hangers work almost exclusively in tension. Explain why it is advantageous for the main structural elements to work in tension (they utilise the entire cross-section and do not suffer from buckling) and which elements of the bridge do work in compression (towers, deck).

A novice designer sizes the steel profiles of a grandstand for an outdoor music festival and concludes: "The yield strength of the structural steel is $f_y = 275\ \text{MPa}$. After adding the self-weight and the average weight of the seated attendees, the maximum calculated stress in the beams is $260\ \text{MPa}$. Since $260 < 275$, the structure is completely safe, will not yield, and we also avoid the waste of over-dimensioning with arbitrary safety factors".

1. a) Technically refute the designer's argument by identifying and justifying four real sources of uncertainty (two associated with actions or loads and two associated with material resistance and assembly) that make designing with a $5\ \%$ margin almost certainly lead to disaster.
2. b) In modern building codes (such as the CTE or Eurocodes), a single global safety factor is not used; instead, partial safety factors are applied: actions amplification ($\gamma_F > 1$) and material resistance reduction ($\gamma_M > 1$). Justify what technical advantage is provided by disaggregating safety into independent factors for permanent actions, variable actions, and materials.
3. c) Argue why the required safety factor and Ultimate Limit State verification criteria are much stricter for this spectator grandstand than for an auxiliary structure without permanent human occupancy (such as a tool shed), evaluating the consequences of collapse and the sudden or progressive nature of structural failure.