On Howe Trusses Work [again]

Consideration of some additional forms

In my last post I described the ‘deeper magic’ that underlies Howe Trusses by describing the counter intuitive logic, at least to modern engineers, which underlies them. We also referred to a textbook diagram, which included various different families of truss. On that occasion we only looked at those trusses that were necessary to explain the Howe truss. 

In this post I thought it would be useful to revisit the text book diagram, which is reproduced below, and explain some of the remaining trusses.

 

When a truss is particularly deep, perhaps because the span is large, the gap between bays can become large and the top chord of the truss, which is more heavily loaded than the internal chords, becomes vulnerable to vertical buckling [1]. To prevent this from happening the top chord needs to become thick and heavy. In these circumstances it can make sense to shorten its effective length instead by introducing secondary triangulation [g]. 

Today such trusses are not used much because the additional joints make the structure statically indeterminate, which can result in unwanted secondary stresses, if there are minor defects or errors in the jointing.

The k-truss [h] can be a good alternative when a truss needs to be deep and the verticals are prone to buckle. The jointing remains relatively simple, but the k-shape shortens the effective length of the vertical members allowing them to take up a more slender form.

A further efficiency can be made to the design of long span trusses by taking up the form of the overall bending forces to which they are subject [i]. If the truss bridges a single span it is self evident that the maximum force is in the centre of the span reducing to zero at the supports located at either end. A truss which is deep in the middle and shallow at the ends will therefore use materials more efficiently.

That said there is a disadvantage to this form of truss. As the profile of the truss changes along its length the angle of the internal chords must also change. Near the ends of the truss their angle of inclination becomes quite acute and it is there difficult to form the joint and the member is rather inefficient.

A sensible compromise is therefore to add a web-post at either end. This brings the benefit of matching the overall bending forces while making the internal chords at either end of the truss more practical [j].

There are of course many other permutations of truss design, but between this and my prior post we have outlined some of the key principles that underly many of the most common forms.

[1] we have not yet talked about out of plane buckling. This will be the subject of a further post on the subject of trusses.