Truss structures FEA-simulated with linear elements

It is emphasised that these are still "practice simulations"; not being burdened by trying to make a "family" of comparable simulations.

Warren Truss

A Warren Truss under known loading can have the forces in its members readily obtained by graphical vector-addition; and exactly solved by trigonometric resolution of forces.

In the centrally-loaded case shown first, this calculation has been done, with the FEA model concurring with the mathematical result to better than 1-in-1000th-part.

The model now has the point loading off the bridge centre...

Vierendeel Truss

This is the first "large" simulation where there is no ready "on-paper" exact mathematical solution to compare the simulation against. Having seen a succession of simulations where there are "exact on-paper arithmetic" solutions and the outcome of the simulation has concurred with the arithmetic answer, I've "graduated" onwards :-)

The common case is that a structure or component cannot have its stresses analysed by any simple exact "on-paper" arithmetic / mathematical expression.

Vierendeel Trusses are rarely applied in the form of
[Wikipedia link - Vierendeel Truss bridge]
a bridge.
Outside of Belgium... Where there was national pride in finding a mathematical way of analysing stresses sufficiently well to design a bridge in such a form.

It remains however overwhelmingly true to say that a Vierendeel Truss has no simple "on-paper arithmetic" or "vector-graphical" solution.

Final note before showing Vierendeel Truss model and results: these results cannot be quantitatively compared with the Warren Truss because the sections are not identical (Warren Truss - 100mm square-section solid bar; Vierendeel Truss - 200mm square 5mm wall-thickness hollow section).
The length is identical, as is the applied central point load (of 100,000N).

The bending moments and resultant curving bending deflections of the individual structural members, not present in the Warren Truss, are very obvious in these simulations, in the exaggerated elastic deformation results presented in the images.

(R. Smith, 25May2016, 02June2016)