What is a force and what is stress?
A force is a push, pull or twist, measured in newtons (N). When a force acts on a material, the material pushes back from inside. This inside effect is stress.
Stress = force ÷ area, σ = F ÷ A. A thin wire and a thick rod carrying the same load: the thin wire has more stress because the force is shared by less area. Units: N/m² (pascal, Pa) or N/mm² (1 N/mm² = 1 MPa).
Too much stress and the material either changes shape for good or breaks. Designers choose materials and shapes so the stress stays well below that limit (a safety factor).
Tension and compression
Tension: forces pull the ends apart. The part gets slightly longer and thinner. Examples: a rope in a tug of war, lift cables, guitar strings, the cables of a suspension bridge.
Compression: forces push the ends together. The part gets slightly shorter and fatter. Examples: pillars, chair legs, the bricks of a wall. Long thin parts under compression can suddenly bow sideways (buckling), so columns are made thicker or braced.
Some materials are good in one and poor in the other: concrete is strong in compression but weak in tension, so steel bars are cast inside it (reinforced concrete).
Bending
When a load presses on a beam held at its ends (or a shelf fixed at one end), the beam bends. The inner (top) face is in compression and the outer (bottom) face is in tension. The middle line, the neutral axis, is neither stretched nor squashed.
That is why putting material far from the middle (top and bottom flanges of an I-beam) resists bending best, and why a ruler is easy to bend flat but hard to bend on its edge.
Torsion and shear
Torsion is a twisting force: one end is turned while the other is held or turned the other way. Examples: a screwdriver shaft, a car drive shaft, turning a key, a towel being wrung out. Round tubes resist torsion well.
Shear happens when two forces act across a part in opposite directions but not in line, so one layer tries to slide over the next. Examples: scissors and a paper guillotine, a hole punch, a bolt or rivet joining two plates that are pulled sideways.
Reinforcing and stiffening materials
To make a product stronger or stiffer without much extra weight, designers change the shape or combine materials:
- Folding and bending: a folded edge on sheet metal or card (a flange) stops it flopping.
- Ribs and webs: thin walls moulded inside plastic cases and on the back of chairs.
- Corrugation: wavy layers, as in cardboard and roof sheets.
- Sections: I-beams, box sections, angles and tubes put material where the stress is.
- Triangulation: triangles cannot change shape without changing a side length, so frames like bridges, cranes and bike frames use them.
- Lamination: gluing thin layers with grains or fibres crossing, as in plywood and laminated beams.
- Textiles: interfacing stiffens collars; webbing tape strengthens bag straps.
- Composites: glass or carbon fibre in resin; steel bars in concrete.
Try it: paper bridge test
Lay one sheet of A4 paper flat between two books 15 cm apart and add coins in the middle until it sags to the table. Count the coins. Now fold the same sheet into a zig-zag (corrugated) strip, or roll it into a tube, and test again. Predict first, then count. You are seeing step 6 of the 3D in real life: same material, new shape, many more coins.
Key formulas and definitions
- Stress σ = F ÷ A
- F in newtons (N), A in m² or mm²
- 1 Pa = 1 N/m²; 1 N/mm² = 1 MPa = 1 000 000 Pa
- Tension → longer and thinner; compression → shorter and fatter
- Bending: one face compression, other face tension, neutral axis in the middle
Worked examples
1. Name the force: a climbing rope holding a climber.
The rope is pulled at both ends, so it is in tension.
2. Name the force: a hole punch going through paper.
Two edges slide past each other across the paper, so it is shear.
3. A steel rod of cross-section 50 mm² carries a pull of 4000 N. Find the stress.
σ = F ÷ A = 4000 ÷ 50 = 80 N/mm² = 80 MPa.
4. A wooden post 100 mm × 100 mm supports 20 kN. Find the stress in N/mm².
A = 100 × 100 = 10 000 mm². F = 20 000 N. σ = 20 000 ÷ 10 000 = 2 N/mm² (compression).
5. Two wires carry the same 600 N load. Wire A has area 2 mm², wire B 6 mm². Which is more stressed and by how much?
A: 600 ÷ 2 = 300 N/mm². B: 600 ÷ 6 = 100 N/mm². Wire A has 3 times the stress, because the area is one third.
6. Why is a corrugated cardboard box much stiffer than a box of the same weight made of flat card?
The wavy middle layer holds the two flat faces apart. Material far from the middle resists bending, just like the flanges of an I-beam, so the box bends far less under the same load.
Common mistakes
- Thinking a beam under bending is in only one kind of stress. The top is in compression and the bottom in tension at the same time.
- Mixing up torsion (twisting about the length) with bending (bowing across the length).
- Forgetting to convert kN to N or cm² to mm² before working out stress.
- Thinking reinforcing always means adding more material. Changing the shape (folds, ribs, triangles) often works better and is lighter.