Forces, loads and stresses

Explain in your own words the difference between a dead load (static load) and a live load (variable load), and classify these loads on a bridge: the weight of the deck itself, passing cars, the weight of the fixed streetlights, winter snow, and storm winds.

The self-weight of a roof is a load that is always present, but snow only appears a few days a year. Explain why these two types of loads are treated differently when designing, and reason what would happen if a roof were designed considering only its dead weight, without accounting for snow.

The figure shows five members subjected to the five basic stresses, labelled with the letters a to e, with arrows representing the forces.

Match each letter with its stress — tension, compression, bending, torsion, or shear — and justify your answer by looking at the direction of the arrows: whether they stretch, squash, bend, twist, or shear the member.

Match each component with the stress it mainly withstands: (a) a zip line cable, (b) a porch pillar, (c) the shaft of a screwdriver when tightening, (d) a bookshelf full of books, and (e) a sheet of paper when cut with scissors. Explain your choice in two of the five cases.

Scissors cut paper because their two blades push very close together in opposite directions, one upwards and the other downwards. Explain what stress the paper experiences at that point and why scissors cut much better near the pivot screw than at the tip (think about the force applied by your hand).

When you stretch elastic bands with your hands, the band stretches and returns to its original shape. Explain what stress the rubber band undergoes while you pull it, what happens if you stretch it too much, and why rubber bands are used for that exact purpose (think about what material you would choose for a zip line cable).

A coat hanger carrying a heavy coat seems simple, but its parts work differently: the wire hook is stretched and the horizontal bar bends slightly. Analyse what stress each part of the hanger withstands and explain why the same plastic hanger holds the coat but breaks if you also hang a school bag from the bar.

On a table, the legs withstand the weight of everything on top without bending, but the tabletop sags if something very heavy is placed in the centre. Explain what stress each part experiences and why the shape of each element (a vertical leg versus a horizontal tabletop) makes one resist its stress better than the other.

A shelf loaded with books gradually sags in the middle. Explain what stress it is experiencing, why it sags downwards in the middle and not at the ends, and what two simple changes you would make so that it sags less (without emptying the shelf).

When wringing out a mop or cloth, you twist it with both hands rotating in opposite directions. State what stress you are applying, describe precisely how the forces act, and name two objects or components in your home that usually work under that same stress.

The figure shows a bridge with three components labelled with the letters a, b, and c: a pillar, one of the cables supporting the deck, and the deck itself where a lorry travels.

State which stress each labelled component mainly withstands (tension, compression, or bending), reasoning what the loads do to each one: which is stretched, which is squashed, and which is bent.

A team of students is building a load-bearing structure using rolled steel I-beams (with an "I"-shaped cross-section). When resting one of the beams on two pillars, a group member proposes placing it on its side (with a wide "H"-shaped cross-section instead of a vertical "I"), arguing that "by having a wider bearing surface at the base, it will support more vertical load without deforming."

1. a) Explain in detail what mechanical stresses (tension and compression) develop on the top face, on the bottom face, and along the centerline (neutral axis) of a beam when it supports a centered vertical load.
2. b) Refute the student's proposal: prove in which of the two positions (vertical "I" or lying flat "H") the beam offers greater resistance to bending, justifying it based on the distance of the material relative to the centerline.
3. c) If the structure had to simultaneously withstand heavy vertical loads and strong lateral wind gusts, predict what limitation the I-beam presents compared to a hollow square tube of the same weight.