Structural Engineering & Statics
where the load goes
Generator

The fibre-stress generator

Rendered here at the parameters it defaults to, with every essay that calls it — which is the same list as the blast radius of changing it.
A rectangle at 90% of its plastic momentThe same rectangle drawn three ways: the shape, the strain across its depth, and the stress that strain produces in mild steel. The strain diagram is a straight line, because plane sections stay plane whatever the material is doing. The stress diagram is not: 45% of the area has yielded, working inward from both faces, and the neutral axis sits at 100.0 mm against a centroid at 100.0 mm. The compression resultant is 299.5 kN and the tension resultant 299.5 kN, on a lever arm of 123.9 mm, which multiplies back to the 37.1 kNm the section is carrying.neutral axisrectanglestrainalways a straight linestressthe material's own curve, sidewaysC = 299.5 kN · T = 299.5 kN · lever arm 124 mm · M = 37.1 kNm45% of the area has yielded — 45 mm from the top, 45 mm from the bottom · Mp = 41.2 kNm · shape factor 1.50

8 essays call fibre-stress. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about.

Where it is called

Changing this generator changes every one of these figures.

00.5%1%2%2%0100200300400500600strainstress, N/mm²the 0.2% proof stress: 460 N/mm²mild steelhigh-strength steelaluminium Materials

The stress at which nothing in particular happens

One material in six has a yield point that a specimen actually does something at. For all the others the yield stress is a construction — a line drawn at an arbitrary offset — and every calculation on this site depends on it.

 00.5%1%2%2%050100150200250300350strainstress, N/mm²mild steelcast iron Materials

The property that appears in none of the equations

Ductility is in no design formula on this site. Every method on this site depends on it — and a brittle structure does not merely fail early, it makes the analysis wrong.

 024681000.511.5curvature ÷ curvature at first yieldmoment ÷ moment at first yieldrectangle: 1.50× the yield moment, at 4.1× the yield curvatureI-section: 1.09× the yield moment, at 1.1× the yield curvature Materials

The section that yields from the outside in

A rectangle has half again as much moment in reserve past first yield as its elastic capacity suggests, and an I-section has a seventh. Read as a ranking that gets it backwards — the reserve is bought with curvature, and the rectangle pays four times as much of it.

 neutral axisI-sectionstrainalways a straight linestressthe material's own curve, sidewaysC = 322.5 kN · T = 322.5 kN · lever arm 180 mm · M = 58.1 kNm0% of the area has yielded — 0 mm from the top, 0 mm from the bottom · Mp = 72.6 kNm · shape factor 1.09 Materials

The stress that was there before the load

A rolled steel section leaves the mill carrying eighty N/mm² of stress with nothing applied to it, in a pattern that sums to no force and no moment. It is invisible to every calculation and it is the knee in every column curve.

 00.20.40.60.8100.20.40.60.81moment ÷ plastic momentaxial force ÷ squash loadrectangle: 25.0% of Mp outside the lineI-section: 6.0% of Mp outside the linethe straight-line rule Materials

Two ways to fail, and the curve between them

A column carrying both compression and bending has two capacities and a rule for sharing them out. The rule is a straight line, the truth is a curve, and for a rectangle the straight line gives away a quarter of the plastic moment at half the squash load.

 flange outstandk = 0.4318.6 at 23515.2 at 35513.3 at 460quoted: 14ε1.33× the quoted limit, at every gradeweb, in bendingk = 456.8 at 23546.2 at 35540.6 at 460quoted: 42ε1.35× the quoted limit, at every grade0102030405060width ÷ thickness Materials

The section that cannot reach its own strength

A section classification looks like a table of arbitrary numbers. Set a plate's buckling stress equal to the yield stress and the numbers fall out of a formula written three phases ago — larger than the quoted ones by a constant factor, at every grade.

 -0.6%-0.4%-0.2%0.2%0.4%0.6%-300-200-100100200300strainstress, N/mm²0.469% of the strain never came back Materials

What is left when the load comes off

Unload a section that has yielded and it does not return to nothing. It returns to a self-equilibrating stress field it did not have before, a permanent set, and an elastic range wider than the one it started with.

 pulled at 100 N/mm², left and right300-100 — compressionhoop stress, tinted3.0× at the edgewithin 5% by 3.5 radiithe applied stressdistance from the centre, in hole radii12345 Materials

The hole that multiplies the stress by three

The stress at the side of a hole is three times the applied stress whatever the hole's size, and at the top and bottom of the same hole it is minus one times it — compression in a plate that nothing is pushing.

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