On Howe Trusses Work

A search for deeper magic

‘"It means," said Aslan, "that though the Witch knew the Deep Magic, there is a magic deeper still which she did not know. Her knowledge goes back only to the dawn of time. But if she could have looked a little further back, into the stillness and the darkness before Time dawned, she would have read there a different incantation”‘ [1]

Trusses are a great way of spanning a long distance; without a web plate they are much lighter than an equivalent beam or girder. Nonetheless not all trusses are equal. There are many different ways that truss chords can be arranged making some more efficient than others. Most arrangements will fall within a family of trusses that share a standard arrangement of chords. Normally structural analysis text books will contain a diagram showing each family stating their names underneath. An example is shown below.

 

For many years there was something that bugged me about this type of diagram. It wasn’t the diagram per se that bugged me, but rather a particular family known as the Howe truss. This truss bugged me, because it didn’t make sense. I couldn’t work out why on earth Mr Howe, whoever he was, had come up with the design that he did. It is just so inefficient, or so it seemed. It turns out, however, that Mr Howe was right and I was wrong. It turns out that he knew deeper magic than I did. In this metaphor that made me the Witch, which I didn’t like very much!

This post is therefore about truss design and about Howe I learned some ‘deeper magic’.

Before we get to my mistake we need to learn something about how trusses work, which will help you understand why I made a mistake in the first place. It will also help you appreciate the existence of deeper magic and how clever Mr Howe was.

In the beginning iron and steel bridges were quite complex, but progressed to simpler arrangements over time. The progression has an intuitive feel to it. At the outset engineers were perhaps thinking about how to lighten the web of a beam or girder and decided to do so by creating a trellis arrangement [a]. For this type of truss there would have been great expense making all the joints and it would have no doubt taken a long time to fabricate. It would also have been clear that being highly redundant it could not be designed by normal static methods.

Engineers would soon have been realised that more economic trusses could be made if the number of internal chords could be reduced. This would make them lighter; they would require fewer joints; and they would be simpler to analyse.

The Bollman truss [b] was designed with pairs of diagonal members extending from the supports at either end to intermediate points on the span. It has an interesting aesthetic, but has several drawbacks. Firstly, if load is applied at a node point only the pair of diagonals connected to that node is mobilised to carry the load; all the others become redundant. A more economic structure would utilise all the chords simultaneously. A second disadvantage is that, except for the middle set, pairs of diagonals are necessarily inclined at different angles. This means that they must carry different magnitudes of load and consequently rather unhelpful secondary stresses are induced. It turns out that diagonals are better suited to being set at a regular angle of inclination, perhaps somewhere between 45 and 60 degrees.

The Warren truss [c] is a good example of this. It has a simple arrangement of diagonals arranged in the shape of equilateral triangles. It minimises the number of members and joints, and what is more, all members are the same length. It is an efficient truss that is simple to fabricate and is statically determinate [easy to analyse]. What is not to like?

Nevertheless, for all its advantages the Warren Truss does have a disadvantage and we can therefore improve on its design. That disadvantage comes from a consideration of the type and distribution of forces its chords must carry. 

If we imagine for a moment that we are dealing with a beam and not a truss a useful analogy can be made. As the truss takes up load and starts to bend the top chord shortens and the bottom one lengthens. There is therefore compression at the top and tension at the bottom.

The internal chords, which must transfer load between the upper and lower chords behave differently. Those which point towards the supports shorten and are in compression; those which point towards the centre of the span lengthen and are in tension.

There is of course a difference between tension and compression forces. Members that are in compression are prone to buckle in the middle while tension members are not. Since the buckling capacity of compression members is proportional to the square of their length there is a distinct advantage to being shorter. 

This brings us nicely to the Pratt truss [d], whose compression members are arranged vertically. Since the verticals are necessarily shorter than the tensioned diagonals this is a highly efficient form of truss, which recognises the type of loads each member carries.

Observant readers will no doubt have foreseen what comes next. The Howe truss [e] is a complete reversal of the Pratt truss. The tension members are now arranged vertically and the compression members diagonally i.e. the longest members are in compression. If you think this doesn’t make sense you are just like I was and don’t appreciate the deeper magic involved. 

There are of course some other truss families in our diagram, but we are going to leave those for another time so that we can concentrate on the mysterious Howe Truss. In order to get to the bottom of the conundrum we need, like Aslan, to go back in time.

Perhaps the first trusses were timber roof trusses. Unlike trusses of iron and steel they would have started simple and became more complex over time. A pitched roof would have been an advantage to early builders, as it is today, because it encourages water to flow away from the building; it is less likely to develop a leak. 

It is self-evident that inclined rafters are required to create the pitch. This in turn implies rafters, which lean against each other and therefore tend to spread at their bases. The associated spreading force is rather unhelpful to the supporting walls. A horizontal thrust applied at their head will of course make them unstable and push them over. To stop this from happening a horizontal tie is added forming the most basic form of triangular truss.

With the success of this form it stands to reason that the designer will soon want to bridge a bigger span. This would have brought a new effect to the designers attention. With increased span the tie beam would begin to sag under its own self weight. To prevent this from happening the solution would be to suspend the middle of the tie beam from the rafters using a new tie member called a King Post. If the spans increased again the rafters would surely begin to sag too. It therefore becomes necessary to prop them with struts supported on the tie beam. To prevent the tie beam from being bent the struts would be joined at the same point the king post is connected, thereby transferring the propping load back into the rafters in tension.

The next development would be to minimise the length of our new struts to stop them from buckling. This can be done by making them perpendicular to the rafters. The trouble with this arrangement is that they now bear on the bottom ties at a distance from the King Post and thus bending is reintroduced to the system. For obvious reasons this is undesirable. The solution is to replace the King post with two tension ties, which join the struts to the apex of the rafters, thus eliminating tension. 

We have nearly reached the end of our detour into timber roof trusses and are almost ready to return to the Howe Truss. Before we get there we must learn one more thing about timber roof trusses. When timber members are in compression they are squashed together and load is conveyed at the joint in bearing. This allows relatively high loads to be transferred. Conversely, when two members are in tension they require timber pegs inserted between them to hold them together. In this case all of the load is transferred through the pegs alone, which are much smaller than the overall member size and are not terribly strong. For this reason tension joints are the weak link in the system.

To overcome this problem engineers began to use wrought iron straps to transfer loads at tension joints. It could not have been long before it was realised that the tension members themselves could take the form of wrought iron rods. The advantage being that they could be inserted through the timber chords and clamped tight with large washer plates.

This results in a hybrid structure, which is very efficient, because in a time when iron was expensive and difficult to produce, it uses relatively cheap timber to carry compressive loads and iron to form the tension members and joints.

This is the key to unlocking the mysterious Howe Truss. The thing which structural analysis, text books never tell you is that the vertical members are wrought iron or steel and the diagonals are in timber. They also don’t tell you that the verticals are tightened at the fixings until they carry a pre-stress, which keeps them permanently in tension. By doing so the compression members are clamped tightly together. The timber members are stocky compared to the slender ties and are therefore not vulnerable to buckling.

This is where that deeper magic begins. The logic which governs the design of modern steel trusses does not apply to older trusses made of timber, due to the limited capacity of timber joints in tension and the cost of making iron.

That said there is something else that you need to know. William Howe was an American engineer who invented his eponymous truss for use in the construction of railroad bridges. In the vast spaces of the United States it stands to reason that it would have been more efficient to cut timbers from trees near to the site of a planned bridge rather than having to transport all the iron members from a fabrication yard.

It all makes sense now, Mr Howe was in fact a rather clever man.

Before I finish this post there is one further thing that I need to explain. Most archive images of Howe trusses have diagonal members in two directions rather than one, they don’t actually look like those found in structural analysis text books. This tells me that their authors are only familiar with the theoretical form of the truss and not how they were made or what they were used for.

The reason for the additional chords is also related to the construction of railroad bridges. Howe realised that as a heavy steam locomotive passed over one of his bridges it would experience uneven loading and this could potentially cause load reversal in some of the chords. The additional members were used to ensure that there were always members acting in compression. 

[1] chapter 15, ‘The Lion the Witch and the Wardrobe’ by C S Lewis.