Structural Engineering & Statics
where the load goes
Generator

The truss-deflection 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.
Every member's share of the movement, and they are not the members expectedA Pratt truss of six panels at a depth of 0.85, carrying 10 kN at each top node, with the movement of the bottom chord at mid-span attributed member by member. The unit-load sum δ = ΣF·f·L/EA gives 631.06 at EA = 1: 47.2% from four top chords, 28.5% from six bottom chords, 22.3% from six diagonals, 2.0% from five verticals. The single worst member is a top chord at mid-span at 14.8% of the whole. Each member is drawn at the width of its own share. The same deflection from a stiffness solution that shares none of this arithmetic is 631.06, a relative residual of 3.6e-15.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

Every member's share of the movement, and they are not the members expected. A Pratt truss of six panels at a depth of 0.85, carrying 10 kN at each top node, with the movement of the bottom chord at mid-span attributed member by member. The unit-load sum δ = ΣF·f·L/EA gives 631.06 at EA = 1: 47.2% from four top chords, 28.5% from six bottom chords, 22.3% from six diagonals, 2.0% from five verticals. The single worst member is a top chord at mid-span at 14.8% of the whole. Each member is drawn at the width of its own share. The same deflection from a stiffness solution that shares none of this arithmetic is 631.06, a relative residual of 3.6e-15.

2 essays call truss-deflection. 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.

100 kNthe gap is the shear: 16.3% of the totalbending alone, and what the beam really doesthe shear part alone, magnified 3 times furthertwo straight lines meeting under the loadshearγ = V/GAs is a slope the section is racked through, not a curvature —so this diagram is integrated once, where the moment diagram above it is integrated twice Deflection

The deflection that is not bending

Every deflection on this site so far has been the second integral of a moment, and that calculation silently drops a term. The beam also shears, and the shear deflection is not a correction to the curve — it is a different shape, and for a deep member it is most of the answer.

 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 Deflection

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.

The library, page 5 of 5 — where truss-deflection sits