How this instrument works
Stress answers a question that force alone cannot: how hard is this material working? Ten kilonewtons destroys one bicycle spoke and barely registers inside bridge piers, because what fails is never load itself but intensity — newtons carried by each square millimetre of section. Augustin-Louis Cauchy gave that intensity its mathematical form in an 1822 memoir read to the Paris Academy, proving that loading at any point needs nine components rather than one. William Rankine, writing for British engineers through the 1850s, fixed the vocabulary still in use: stress for what you apply, strain for what results.
Typical magnitudes repay memorising. Mild steel yields near 250 MPa and grade S355 near 355; 6061-T6 aluminium gives way around 276; ordinary structural concrete crushes between 20 and 50 MPa and is barely trusted in tension at all. Carbon fibre tows run past 3500 MPa, spider dragline silk near 1100, and a tuned nylon guitar string sits under roughly 40. Designers work nowhere near those ceilings — an allowable 100 to 160 MPa in steelwork leaves margin for corrosion, fatigue, and whatever a load estimate quietly missed.
This division holds only where load is genuinely axial and spread evenly over a plain section. Saint-Venant's principle warns that uniformity takes roughly one member width to establish, so figures computed beside bolt holes, welds or the gripped jaws of a testing machine mean very little. Geometry that interrupts force flow makes matters worse: a small round hole through a wide plate triples stress at its edge, a result Ernst Kirsch published in 1898 and one reason fatigue cracks begin at fastener holes. During a tensile test the section shrinks as it stretches, so dividing by original area yields engineering stress, which appears to fall once necking starts while true stress — same force, actual shrunken area — climbs until fracture.
- Enter your load into Applied force — newtons by default, with kilonewtons and pounds-force waiting on its unit menu.
- Put the resisting section into Cross-sectional area, picking mm², cm², m² or in². Subtract bolt holes and slots that eat into it.
- Read Stress in pascals, or switch that field to MPa for materials work, or to psi and ksi when your allowables come from a US code.
- Compare against yield or allowable strength for your material, never against ultimate strength, and keep whatever safety factor your code demands.
Worked example — 10 kN through a 100 mm² bar
A mezzanine walkway hangs on square steel bars, 10 mm by 10 mm, each taking 10 kN — near enough the weight of a small car. Enter 10000 into Applied force and 0.0001 m² into Cross-sectional area, which is that 100 mm² section written in SI. Stress returns 100000000 Pa, since 10000 ⁄ 0.0001 = 1 × 10⁸: a round 100 MPa.
Such a figure is deliberately unremarkable. Against S275 steel, yielding at 275 MPa, it leaves a factor of 2.75 — ordinary territory for a static hanger. Yet 100 MPa is equally 14500 psi, and roughly what seawater presses with near the floor of the Mariana Trench. Quiet grey steel holds trench-bottom intensity inside every square millimetre and betrays no outward sign of doing so.
Questions
Should I enter the original cross-section or the necked one?
Original, unless you specifically want true stress. Dividing by undeformed area A₀ gives engineering stress, which is what every design code and material datasheet quotes. True stress divides by instantaneous area, shrinking once necking begins, so both curves separate badly past ultimate tensile strength: engineering stress appears to drop while true stress rises until fracture. For design, stay with original section — that is exactly what published allowables assume.
Why do structural drawings quote MPa instead of pascals?
Because one megapascal is precisely one newton per square millimetre. Sections get measured in millimetres and loads in newtons, so MPa removes every power-of-ten conversion from bench arithmetic — a 100 mm² bar at 10 kN is plainly 100 N/mm². Pascals run far too small for solids; steel yield would read 275000000, which nobody wants inked on a drawing. American codes prefer ksi, thousands of pounds per square inch, where 1 ksi is about 6.895 MPa.
Does a hole or a notch change the answer?
Sharply, and no calculator will warn you. Dividing by net area returns an average, yet stress crowds around any interruption: a small round hole in a wide plate raises edge intensity threefold, and a sharp notch or square internal corner can multiply it much further. Handbooks tabulate that ratio as stress concentration factor Kt. Static ductile metal absorbs a peak by yielding locally; fatigue does not, which is why cracks start at holes, keyways and weld toes.
What is the difference between stress and strain?
Stress is force per unit area, read in pascals; strain is fractional change in length that follows, carrying no units whatever. Steel at 100 MPa stretches about 0.05 percent — half a millimetre over a metre. Young's modulus ties them together, E = σ ⁄ ε, near 200 GPa for steel, provided loading stays elastic. Stress is what you apply to a member; strain is what a gauge bonded to its surface can actually see.
What if force acts along the cut rather than across it?
Then it produces shear stress, written τ, not normal stress σ. Same division of force by area, wholly different failure physics and different allowables — shear yield for structural steel runs around 0.577 of tensile yield under a von Mises criterion. Resolve any inclined load into perpendicular and parallel parts first, feed only the perpendicular part here, then handle what remains separately. Mohr's circle exists because both parts shift as you rotate whichever plane you cut on.
Why is tension positive here when compression is positive for pressure?
Convention, and two fields settled on opposite ones. Solid mechanics counts tension positive because tension opens cracks and governs most metal design. Fluid mechanics counts compression positive because a resting fluid can only push. A block under 1 MPa of hydrostatic pressure therefore carries −1 MPa of normal stress on every face. This sheet returns magnitude; you attach the sign yourself, from whether your load pulls or squeezes.