Structural Engineering & Statics
where the load goes
Concept

Impact — where it appears

A load delivered as a velocity change over a very short time, so the force depends on a contact stiffness nobody knows and the impulse does not. What is calculable is momentum, which is why an impact is analysed as a velocity change shared between two masses rather than as a force.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

How fast the strain arrived, which no strength on this site records. The dynamic increase factor on strength against strain rate, over eight decades. Steel follows Cowper and Symonds' fit, whose constant D = 40.4 s⁻¹ is not an arbitrary parameter — it is the rate at which the material is exactly twice as strong. Concrete in tension follows the model code's two-branch curve and is steeper. The four marked regimes are the argument: a testing machine works at about 10⁻⁴ per second, an earthquake at 5 × 10⁻³, a vehicle impact at a half, a blast at a hundred, and the enhancement across them runs 1.00, 1.08, 1.32, 2.04. So this is a correction that is either negligible or decisive with very little in between, which is why no seismic code carries it and every blast code does. What does not rise is the modulus, which is a lattice property, and the ultimate strength rises only a third as much — so the ultimate-to-yield ratio closes from 1.56 to 1.23 and the material has less warning left in it than it started with.

The steel that is stronger in a millisecond

Every strength quoted anywhere in this collection was measured at about a ten-thousandth of a strain per second, because that is what a testing machine does, and nothing on a drawing says so. Load the same steel a million times faster and its yield stress rises by a third.

materials · strain rate Buildings that sway alike need almost no gap between them. The separation two adjacent buildings need, against the ratio of their periods. The obvious answer is the sum of what each can do — 340 mm — and it is wrong, because the two peaks do not occur at the same instant. The right combination is the one modal responses use, √(u₁² + u₂² − 2ρu₁u₂), with ρ the cross-correlation coefficient of the two responses. ρ depends on the period ratio and behaves the opposite way to intuition: at a ratio of one the two buildings sway together, ρ = 1, and the gap collapses to the difference of the two, 100 mm. At the 0.57 drawn ρ is 0.029 and the gap is 248 mm — 27 per cent less than the sum, and 99 per cent of the square root of the sum of squares.

The gap between two buildings

Two towers side by side in an earthquake need a gap. The obvious answer is the sum of what each can move, and it is wrong — because the two peaks do not happen at the same instant. What decides the answer is the ratio of the two periods, and buildings that sway alike need almost no gap at all.

dynamics · pounding

Named alongside it

The objects these essays reach for when they reach for this one.

BlastCapacity designCollapse loadCowper symondsDampingDuctilityDynamic increase factorElastic modulusFatigueFractureLoad pathModal combination

All concepts