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FEA an aid in - the short story -

Find out how the load is transmitted, from application to reaction.

Are there stiff paths and soft paths ?

Are the cross sections appropriate to the loads, Bending ? Compression ? Tension ? Torsion ?

Are there strong and weak paths (take large loads before breaking ?)

Is tress concertation significant, what can be done to reduce it ?

This stepped bar in torsion is an opportunity to investigate means of controlling stress concentration.

Given that the steps are there to meet a number of different requirements.

And, that the stress concentration ratio, as determined by FEA, can be compared and confirmed against well validated values

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The variations that can be made to the outline of a component to reduce stress concentration, can in principal be similar to that applied to flat 2 dimensional components, as can for cylindrical parts, but they are not quite the same.

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A change in the shape of a component carrying a load, will have the effect of increasing the stress, nearly always at a concave corner.

The degree of concentration will depend on the proportions of the change in shape and on the type of load.

Here the effect of tension and bending is shown. In all, it is important to be aware that there are 3 different stress concentration relationships, for tension, bending and torsion.

These graphs and data come from R L Norton. Peterson has the most comprehensive collection of such graphs and formulae.

Draw a bending moment diagram

Note that there is low stress between the top and the bottom fibres of a rectangular beam in bending

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l1

l2

l2l1

A force F is shown applied to an edge of the ‘angle’ L section at right, and reproduced in plan view below

The applied force is somehow divided between the two legs of the L section - l1 & l2 .

What resistance does that force meet ? The aligned leg - l1 has to bend about the neutral axis shown, it has a relatively large second moment of area I1, hence it will be stiff. Leg l2 has a small I2 hence will be relatively flexible.

F

The bolts should be placed as close as possible to the most heavily loaded weld, which is at the end of the web.

One can pile on a multitude of webs and hold down bolt holes, but some are more effective than others, the designer has to arrive at a balance in the cost of the webs, the post and the base.

Tube of max practical diameter bar or any section I beam tube or barrel (max dia)

Axial torque axial tension bending moment axial compression

Appropriate sections, shown as elements of equal cross-section

The load type:

Buckling loads vary basically as –

P ~ E I /L ²

Hence thin struts are seldom used in compression

As mentioned brackets are usually reinforced with the same material as the basic bracket is made from.

To make a reasonable analysis of these components one has to do a buckling test of them