# 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)