Structural Engineering & Statics
where the load goes
Concept

Unit load method — where it appears

2 essays name this object, across one field. What follows is each of them, and the objects they name alongside it.
real Mpeak 32.0a unit load, here and nowhere elseunit mM × marea ÷ EI = 213.33the unit load is the only place the question 'deflection where?' is asked

One deflection, without solving everything

To find how far one point of a structure moves, put an imaginary force of one unit there, multiply two moment diagrams together, and integrate. The answer arrives without ever solving for the deflected shape.

deflection · virtual work δ = 631.06 read here10 kN at every top node — each member drawn at the width of its own sharetop chord (four members)47.2%bottom chord (six members)28.5%diagonal (six members)22.3%vertical (five members)2.0%the members that moved the roof, ranked — a symmetric pair is two members and appears twicetop chord, at mid-span14.80%F -52.9 × f -1.765top chord, at mid-span14.80%F -52.9 × f -1.765bottom chord, at mid-span8.77%F 47.1 × f 1.176top chord, near the left support8.77%F -47.1 × f -1.176bottom chord, at mid-span8.77%F 47.1 × f 1.176top chord, near the right support8.77%F -47.1 × f -1.176diagonal, near the left support6.20%F -38.6 × f -0.772diagonal, near the right support6.20%F -38.6 × f -0.772virtual work and a stiffness solution agree to 3.6e-15 — two methods sharing no arithmetic

Which member moved the roof

A beam sags because it curves. A truss has no curvature anywhere — it comes down because every one of its members changes length, and the sum of those changes, weighted member by member, is a ranking that names which ones are worth stiffening. Usually not the ones a designer worries about.

deflection · truss deflection

Named alongside it

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

StiffnessVirtual workChord forceCompatibilityDeflectionForce methodLoad pathMethod of jointsMoment diagramProduct integralZero force member

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