Mechanics of Materials · Factored loads
Trust, quantified
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Trust, quantified

Strength design does not add loads up and hope. It weighs each one by how well we know it: U=1.2D+1.6LU = 1.2D + 1.6L — read aloud, U equals one point two D plus one point six L. DD is the dead load: self weight, slab, permanent finishes — things you can weigh on a drawing. LL is the live load: occupancy, stored goods, people — things you can only estimate. UU is the factored load, the demand the strength check is made against. All three are forces, in the same unit.

The gap between 1.2 and 1.6 is the entire idea, expressed as arithmetic: the load we know least about carries the bigger factor. Applying one average factor to both, or swapping them, is not a rounding error — it is a statement about trust that the code did not make.

Concrete brings its own correlation to the same page: Ec=kfcE_c = k\sqrt{f'_c}, where fcf'_c is the cylinder compressive strength in MPa, EcE_c the elastic modulus, and kk the code coefficient — a user input, always, because ACI, CSA and Eurocode fit different lines through different test populations and their coefficients are not interchangeable. kk is also unit-bound: in its MPa form it is around 4500 to 4700, and the familiar 57 000 of the psi form would be catastrophically wrong in the same slot. Fed MPa, the formula returns MPa, so the trip to the GPa that engineers actually quote is a ÷1000 at the very end — and the answer should land near 25 to 35 GPa or something upstream is wrong.