Structural Engineering & Statics
where the load goes
Concept

Ductility — where it appears

6 essays name this object, across one field. What follows is each of them, and the objects they name alongside it.
00.5%1%2%2%0100200300400500600strainstress, N/mm²the 0.2% proof stress: 460 N/mm²mild steelhigh-strength steelaluminium

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.

materials · proof stress 00.5%1%2%2%050100150200250300350strainstress, N/mm²mild steelcast iron

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.

materials · ductility 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

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.

materials · moment curvature 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

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.

materials · section classification 501001502000100200300400500600crack length, mmstress at failure, N/mm²275 N/mm² crosses at 33.5 mm460 N/mm² crosses at 12.0 mmfracture: the crack decides

The flaw that sets the strength

A member with a crack twenty millimetres long fails at its yield stress. Make the steel stronger and the crack that does it gets shorter, so the same flaw that was harmless in the weaker grade decides the stronger one.

materials · fracture 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

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.

materials · stress concentration

Named alongside it

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

Rotation capacityBrittle fractureFractureMoment curvatureStress concentrationStress strainConstitutive lawCritical crackEffective widthElastic modulusElasticityFatigue

All concepts