On Hennebique

Understanding an early patent system

In 1892 Francois Hennebique patented his eponymous ferro-cement system, which is today recognised as one of the earliest forms of reinforced concrete. It was used under licence in many countries, including the UK, where Mouchel was the local partner. The Hennebique system was conceived before the era of codified design, so its worth trying to understand its structural load-paths. 

To do this we must think of Hennebique’s creation, not as a beam, but as a truss made of composite materials. This may seem like an odd thing to do, but it is necessary to explain how stresses are distributed throughout the section. This approach also, as we shall see, highlights several weaknesses in Hennebique beams.

To make sense of this analogy we need to remember that concrete is strong in compression, but weak in tension. Conversely, wrought iron is equally strong in both. It follows that the key to visualising the load-path is see tension where there is iron and compression where it is absent. 

That said, before we look at the Hennebique system itself it is useful to remind ourselves of the alternatives that were available at the time.

The picture below shows a brick jack arch floor, which was conceived as a fire proof system, although given the exposure of the iron flange on the soffit it is more correctly described as non-combustible. The load paths for a jack arch floor are straightforward. The brick arch spans laterally and is supported on iron beams spanning into the page. There are tie rods evident so that arch spreading is contained and only vertical load is transferred by the brickwork.

 An improvement on this design was to replace the brickwork by fully encasing the iron beams with concrete. In principle this would certainly improve the fire resistance of the floor and make it more durable. At least it would have if the concrete didn’t include breeze, which sometimes contained unburnt coke, and sulphates, which could form a mild acid in the presence of water.

This form of construction is known as filler joist construction. It was very common, particularly in the early twentieth century, and many examples remain today. The load path is essentially the same as for the jack arch, except the arch form must be imagined within the body of the concrete, because it would have been much simpler to create a flat soffit than a curve.

The filler joist floor therefore remains a rudimentary structure; there is no composite behaviour between the iron and concrete.

This relationship was changed when it was realised that an inverted T-shape would be more efficient because the concrete fill could resist the compressive stress to which the top iron flange had been subject. The bottom flange was still required to resist tension and the web transferred load between the two by resisting shear.

 

This was an important breakthrough, because the floor was now a composite system, which shared load between concrete and iron. At that time wrought iron was exceedingly expensive and therefore this was much more than an analytical curiosity.

Hennebique’s genius was to make two further steps; or perhaps two and half. Firstly, he replaced the bottom flange of the beam with round iron bars. These were easier to make than a T-beam and had a greater surface area than a single flange with which to bond with the concrete.

 

Secondly, he did away with the iron web, which transferred load between the top and bottom of the beam. To understand the way in which he did this it is helpful to look at other systems that were common at the time.

The next image shows a trussed girders taken from a carpentry manual written in the 1860’s. I have previously written a longer post about this topic, however the key issue in this instance is the way in which timber at the top of the section is used in compression and iron rods are used in tension. Short compression stools are used to transfer load between the two.

  

As can be seen in the following image Hennebique uses exactly the same load path for his concrete system. It is reasonably straightforward to see the tension elements, highlighted in red, however the compression parts, highlighted in blue, must be imagined within the body of the concrete, much as the compression arch is imagined within the filler joist system. I do not mean imagined in the sense that the load path does not really exist. Imagined only in the sense that not all of the concrete in the beam is contributing to the load path.

When Hennebique tested his system he found that though it was successful it did not work as well as it ought; diagonal cracks formed with increasing frequency towards the end of the beam. Such cracks are related to the interaction of shear and bending forces. From Hennebique’s writing I am not entirely sure that he fully understood this mechanism, though nevertheless he found an effective solution. That may be because he found it difficult to describe or I have found it difficult to follow his writing.

 

I think Hennibque believed that there were longitudinal shear forces parallel to the length of the beam, which were causing the failure he had observed in testing. He thought that by intercepting these longitudinal stresses with vertical stirrups of bent iron he could improve the strength of his beam. While such stresses do exist there are also vertical shear stresses, which means that Hennebique’s thinking, if this was what he thought, is incomplete.

Nevertheless, Hennebique’s solution did work and cracking was avoided, though perhaps not wholly for the reasons he thought. We can understand why by referring to the next image, which shows a modern understanding of shear transfer; again red represents tension and blue compression.

We can see in this example that the load path is a fully formed truss with the stirrups and iron bars resisting tension and the top chord and diagonals resisting compression. This modern understanding highlights one reason, beyond a lack of clarity in Hennebique’s writing, that I think Hennebique did not wholly understand the load path.

The case we have thus far examined has a single span with tension at the bottom and compression at the top, however if we were to add additional spans the relationship we have established reverses at the support, with tension at the top and compression at the bottom. In such circumstances we encounter a problem with Hennebique’s stirrups. At mid span they are hooked around the tension bars, but at the support they are open at the top and can be pulled clear. Thus, for multi-span beams the Hennebique system is less efficient than single spans. Had he fully grasped the load-path I am sure Hennebique would have corrected this. Perhaps, as shown above, his tests were all conducted on single spans.

Another shortfall of the Hennebique system is with the tension bars themselves. It will not have escaped the notice of readers with a keen eye that Hennebique’s tension bars have hooks at the end. These were, I am sure, intended to improve the transfer of load between the iron bars and the concrete. At face value this was a sensible measure, because at failure the bars were simply pulled through the concrete. This meant a premature bond failure before the iron had reached yield. This happened because, unlike modern bars, which are deformed to improve the bond, Hennebique’s bars had a smooth surface.

While seemingly a good idea the noted hooks did not really work, though we can forgive Hennebique for this, because the reason why is really rather complicated. In simple terms the bond on the bars must fail before the hooks can be mobilised. Why this happens is perhaps a subject for a different post.

Notwithstanding these shortfalls, which are made with the benefit of hindsight, Hennebique’s system was ultimately very successful and marks him out as a significant figure in the pantheon of structural engineering.

While it is true that Hennebique was not the only person to develop a patent system for reinforced concrete; his was perhaps the most successful. This was probably due to the licensing system he operated marking him out as a great businessman as well as a great engineer. 

On Canaletto & Bridges

Tangent & Radial Trussing

The eighteenth century painter Canaletto was well known for his Venetian paintings, many of which were commissioned by British Patrons. This gave him a reason to move to the UK when war broke out.

One of his commissions, painted during his stay in the UK, is ‘A View of Walton Bridge’. The painting is interesting, not because of Canaletto’s skill in depicting the British weather, nor is it because Canaletto doctored the scene by omitting the masonry viaducts leading up to the bridge. Rather it is the nature of the bridge itself. 

At first sight Walton Bridge appears to be a traditional arch structure, however it is in fact a fine example of the tangent and radial truss. The main span was reported to be 130 feet with two side arches of 44 feet. Sadly, the bridge is no longer in existence, due to timber decay.

Tangent and radial trusses are special, because they take up the form of an arch using only straight members. A simpler example, known as the “Mathematical Bridge’, still exists at the University of Cambridge. 

As the name suggests the primary structural members are arranged at tangents to an imaginary circle, thus giving the appearance of an arch. The radial members are aligned perpendicular to the imaginary circle and would, if extended, meet at its centre.

The form is also interesting because the tangential members, which spring from the abutments, are predominantly compression members, while the the radial members predominantly resist tension. Most articles written about ‘Mathematical Bridge’, or at least the ones I have seen, note that this pattern of tension and compression are an elegant visual representation of the forces within an arch. It seems to me that while oft repeated this observation is not strictly true.

A true arch is a pure compression structure where the line of thrust is contained within its depth. Many arches, including most classical and medieval examples, are not actually true arches, they are in fact spandrel arches. Spandrel arches are characterised by an infill [spandrel] structure located above the true arch. If the infill is of sufficiently depth then the line of thrust can move outside the true arch and load can be conveyed within the spandrel. At a certain point the stresses in the spandrel become more akin to those found in a beam and the arch becomes nothing more than an ornamental soffit to the spandrel. Something like this phenomenon is demonstrated in an earlier post titled ‘On Accidental Bridges’.

It follows that tangent and radial trusses are a better depiction of the forces in a spandrel arch than they are a true arch. The tangential members join with the top chord to convey compressive stress, while the radial members combine with the bottom chord to convey tension. Based on this the arrangement would be more efficient if the radial members were in fact not radial, but were instead arranged perpendicular to the tangential members i.e. if their angle of inclination were defined by the stress pattern rather than the centre of an imaginary circle.

Perhaps the reason for using radial members was to avoid a structure with more complex geometry and more awkward jointing, however there are also several other considerations. 

Firstly the radials must provide restraint to the top chord of the truss so that it does not buckle. They do this by generating u-shape action in combination with members below the bridge deck[1]. Secondly, they form a useful part of the balustrade, which would be less effective were they located at a steeper angle.

Before we finish it is also worth noting that tangent and radial trusses were commonly used as centring [temporary support] for masonry arch bridges while they were being built.

One such example was Westminster Bridge in London. We know tangent and radial trusses were used, because the original drawings have been preserved. That little detail didn’t bother Canaletto, who once again used artistic licence when framing a view of London in his painting ‘London: Seen through an Arch of Westminster Bridge’. The timber centring is clearly not formed of tangent and radial trusses. Perhaps Canaletto judged that the elegant structural form would detract from the view he wanted to paint and therefore substituted something more prosaic. At least that’s what I like to think. 

[1] An earlier post titled ‘On Howe Trusses Work [yet again]’ describes u-frame action in more detail.

On Trussed Girders

A curious case of small changes

Several years ago when conserving an important university building I came across some interesting timber floor structures, which I quickly recognised as ‘trussed girders’. I had seen depictions in many conservation text books, one of which is shown below, and was familiar with the form.....or so I thought. It wasn’t until I studied some actual examples that I realised that something wasn’t quite right. 

You can see in the image above that trussed girders are formed from two timber beams, each of which had a groove cut into one side. Into that groove was inserted wrought iron, plate or sometimes hard wood, which was clamped to the timbers with large bolts aligned vertically. The two timbers were also joined by horizontal bolts, which passed through their cross section.

The problem was I couldn’t decipher how such a beam would work, even after reading accounts of how they were supposed to work. Most of the accounts agreed that designers at the time thought they were improving the capacity of the original timber beams, but modern understanding had demonstrated that their only effect was to instil  an upward pre-camber, which helped to control deflection.

My initial reaction had been that the beam was, from an analytical perspective, upside down. If it were inverted I could see that the timber at the top would be in compression and the iron plate at the bottom would be in tension. There wasn’t a particularly good mechanism for transferring tension into the iron plate, but I figured the large bolts at either end would be capable of something. This would be a sort of composite timber and iron truss, which would at least be a nod to the name ‘trussed girder’.

The trouble was the beam wasn’t upside down and inverting the logic really doesn’t work. The iron plates would need to behave as compression struts, which would tend to push outwards and the timber would need to behave in tension. There was literally no observable evidence for how tension would be generated in the timber. Not only that this would invert everything we know about how Victorian engineers thought about timber trusses. Timber was always in compression and the tension joints were always reinforced with wrought iron.

I also thought about what the conservation books had said. I could certainly agree that the arrangement didn’t appear to convey any additional strength, but I also could not work out by what mechanism the arrangement would apply an upward camber.

The only form of adjustment that I could see was the potential for tightening the nuts on the vertical bolts, but I could not imagine how this action would lead to an upward camber.

The answer to my conundrum was only discovered when I consulted a Victorian carpentry manual. The image below is what I found. 

This was interesting for two reasons. Firstly, there were in fact two examples of my inverted logic, but in both cases an iron shoe is visible at the end of each beam, which is clearly capable of transferring thrust into the tension rods, which project through and below the timber beams.

Secondly, the various other examples of the trussed girder all had an iron plate on the soffit of the timber which formed a tie and complete the internal truss. This is also clearly shown in the details at the bottom of the picture.

The most interesting example was the one third from top, again for two reasons. Firstly, the iron struts are torpedo shaped. This has been done because the designer new full well that thin plates placed in compression will buckle at the centre. He has elected a torpedo shape to specifically place material in the middle of the cross-section so that the tendency to buckle is more ably resisted. 

Secondly, there appears to be a pair of joints in the bottom tie member; one either side of the vertical bolts. If these joints were used to tighten the tie, causing it to shorten, this would pull the ends of the struts together and would unquestionably cause the center of the beam to rise i.e. there was a perfectly rational explanation for how camber could be imparted.

Satisfied that I had solved the puzzle of the ‘trussed girder’ my mind turned to why it had been a puzzle in the first place. Did the authors of those conservation books not know what they were doing? Possibly, but I am not entirely sure that is the whole story.

Maybe, just like me, the authors were familiar with the form, because they had also seen it in prior text books, but hadn’t had reason to stop and think about it more deeply. If so this would be a lesson for all aspiring engineers that even textbooks are not always right.

There is however a more intriguing possibility, perhaps the authors had in fact worked on various historic examples that lacked a bottom tension chord. After all this is what I had found; I would not otherwise have started on this journey.

In this case maybe the authors simply concluded the concept was flawed and moved on, after all some of the illustrations reproduced in text books do look quite old. Maybe, because the authors hadn’t seen a tied variant, they figured the original designers simply hadn’t worked it out right.

My suspicion is that trussed girders were rather well understood by the originators of the concept, however structural design was not codified at this time and people often learned by copying. It is entirely possible the someone had tried to copy an original trussed girder based on arrangements they had witnessed. Perhaps they had misremembered what they had seen or had not appreciated the purpose of the tie. Others may then have seen the amended design and copied it too. Before long it is not hard to conceive of illustrations being draw showing the faulty design.

The lesson would therefore be, when borrowing a design concept be sure that you have properly understood it.

On Howe Trusses Work [yet again]

The benefit of u-frame action

In previous posts we have looked at different forms of truss and how they work. We started with an intrigue about the underlying logic of the Howe Truss and moved on to look at the intricacies of various other forms. Something that may not have been obvious, perhaps until part way through the post immediately prior to this one, is that we have thus far existed in a 2D world, we have not yet looked in the third dimension and considered what happens to trusses out of plane.

The place where this is most obviously important is the top chord. We have discovered already that the top chord is in compression and that failure by compressive buckling is proportional to the square of a member’s length. In the plane of a truss its effective length is relatively short due to the position of the internal chords connected along its length.

Out of plane there is of course no restraint from and therefore the effective length of the top chord is the full length of the truss. The top chord is almost certainly going to buckle. This is a pretty big issue to have overlooked. Fortunately there are several solutions available to solve this particular problem.

In almost all cases trusses come in pairs, for example one either side of a bridge deck. Our first option is therefore to take benefit from the bridge deck, which can be attached to the top chord of both. Since the deck is relatively stiff in plane, sometimes it may even be braced, it will have the capacity to prevent the top truss chords from displacing laterally. They are therefore unable to buckle.

The trouble with this solution is that it is rarely viable in practise. If, for example, our bridge were to span over a motorway, and the deck were located on the truss top chords, one of two scenarios would occur. Either the bottom of the truss would project down into the road below or the whole truss would need to be lifted up into the air meaning that much larger ramps would be needed to get traffic up unto the bridge.

For this reason a better solution is to place the bridge deck on the bottom chords. This, however, reintroduces the problem of top chord buckling. If the trusses are tall enough the possibility exists to introduce a horizontal truss between the two top chords. The purpose of this truss is to resist the out-of-plane loading that results from top chord buckling. It does so by the same means that the vertical trusses resist the loads to which they are subject.The two vertical and one horizontal truss exist in a symbiotic relationship, because the vertical ones can equally resist buckling action in the horizontal truss.

It is also worth noting that if our hypothetical bridge structure is outside it will also be subjected to the full force of the wind and our horizontal truss can, in combination with the bridge deck, be used to resist the wind.

A problem arises when the vertical trusses are not tall enough to permit passage below the horizontal truss. You would not wish to duck as you passed along the bridge. It would of course be possible to increase their height, but this seems an inelegant solution and a waste of material if the trusses need not be so tall. A different approach is needed.

This is the perfect opportunity for u-frame action. U-frame action requires continuity between the vertical chords in the two bridge trusses. This is achieved with horizontal members that connect them beneath the bridge deck. If the connections are stiff enough to resist bending forces then a series of rigid u-shaped structures are formed along the length of the bridge. If the top truss chords then try to move laterally and buckle their vertical chords are able to provide resistance by cantilevering from the horizontal member below the bridge deck. This is known as u-frame action. In this way the bridge trusses remain stable without the need for a horizontal truss. It is a neat solution, which is not obvious to the casual observer, and makes for an elegant bridge with unobstructed views.

 

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. 

 

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.