Concept

Flexural rigidity — where it appears

A member's modulus times its second moment of area, the single quantity that converts a bending moment into a curvature.

Named by 4 essays across 3 fields — each of them below, with the objects they name alongside it.

00.0050.010.0150.020.0250.030.0350.040.0450.05050100150200rotation, radiansmoment, kN·mrigid abovepinned belowweb cleats — pinnedflush end plate — semi-rigidextended end plate — semi-rigid

Neither pinned nor rigid, which is every real connection

Frame analysis offers two options for a joint and reality supplies a continuum between them. Worse, the boundaries are not properties of the connection at all — the same end plate is rigid on a short stiff beam and semi-rigid on a long slender one.

connections · joint stiffness
10centroid at 2.00 mM/EIarea = 180.00 · first moment = 720.00by double integration: 720.00

The area of a diagram is a rotation

A deflection is the double integral of a bending moment, and the two constants of integration are the whole difficulty. Mohr's theorems replace them with two pictures — an area, and where that area's centre of gravity sits.

deflection · moment area
1234403020100-10-20-30-40stage in the beam's lifeshape (mm, sag positive)against noneagainst wetagainst deadagainst total

Built to the wrong shape on purpose

A cambered beam is fabricated curved upward so that load bends it down to something like straight. Nothing in the analysis changes, no stress anywhere is altered, and almost every mistake made with it is a bookkeeping mistake about which loads count.

deflection · camber
a half sine9.870 EI/L²exactits own sag shape9.882 EI/L²0.13% higha mid-span sag10.000 EI/L²1.32% higha parabola12.000 EI/L²21.59% highreference9.8696 EI/L²ten Ritz terms,as an eigenvalue problemevery guess is anupper boundP

Guessing the shape, and getting the load anyway

A column's buckling load can be had from a shape that is wrong everywhere, because the energy criterion is stationary at the true mode. The error in the load is the square of the error in the shape, and it is always high.

stability · stability energy

Named alongside it

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

DeflectionStiffnessSuperpositionBuckled mode shapeCentroidClassificationComposite actionConnectionConservation of energyConstruction sequenceCreepCritical load

All concepts