On Samson & Goliath

Samson and Goliath are a pair of gantry cranes at the Harland and Wolff shipyard in Belfast. They were built by the German engineering firm Krupp. Harland and Wolff was of course the firm made famous by their design and construction of the passenger liner RMS Titanic. That being said, Goliath was completed in 1969 and Samson in 1974, both long after the Titanic was lost at sea. 

The cranes are named after two characters found in the Bible. Goliath was a fearsome Giant, reported to be 9.5 feet tall and Samson was a man of enormous strength. Both names are surely appropriate, because of the cranes’ enormous size and great lifting power, however perhaps Samson is the more appropriate of the two. 

The Old Testament book of Judges tells us that there was a secret to Samson’s great strength. A secret that he had kept from Delilah; at least to begin with. This suggests to me that contrary to the popular image of Samson portrayed in artwork, he must have been a slight man. For if he were a large powerful man surely no one would have thought there was a secret to his great strength.

When observing both cranes one cannot help but notice the oddness of their form and wonder whether there is also a secret to their great strength. They are supported on one side be two slender tubular columns, which are attached to the large box girder that forms the gantry with a small connection. On the other side there is a large box column with a substantial connection to the gantry box girder. The question arises, why is this so?

The secret of Samson and Goliath is subtle. It relies on understanding a simple, yet at the same time complex, structural load path. If you are unfamiliar with engineering terminology then a couple terms need to be explained to understand what is going on.

When two structural members are joined together, but can rotate relative to each other a ‘pinned joint’ is formed. For example, the two parts of a pair of scissors are held together by a pin joint. If the same connection is formed, but the joints are instead held rigidly so that there can be no rotation, a ‘fixed joint’ is formed. This would make a hopeless pair of scissors. It also important to know that pin joints relieve bending forces by rotating instead of offering resistance while fixed joints attract them.

It is clear that one side of the crane gantry is connected to the supporting column with a rigid joint and the other side is connected with a pinned joint. Understanding the effect these joints have on the structure is the key to understanding the structure’s secret. 

Perhaps the best way to do this is to consider what would happen if the connections were jointed differently. Let us consider in the first instance the gantry box girder being fixed to the columns with pin joints, one at either side. 

If the columns on both sides of the crane could rotate relative to the gantry box girder then a mechanism would be formed and a horizontal load applied to the side of the crane would cause the columns to rotate thus allowing the gantry box girder to slide sideways. The crane is unstable and would topple.

Conversely the gantry could be supported by fixed joints, one at either side. In this instance the columns cannot rotate, because they are fixed rigidly to the gantry box girder. The structure is apparently stable, except that it isn’t.

Since the fixed joints do not allow rotation they attract bending forces out of the gantry girder and transfer them into the columns. This is a perfectly satisfactory situation where the supporting column is large, however the two slender tubes will simply buckle again causing the crane to topple.

The obvious solution to this problem is to use a large stiff column on both sides, so that the structure behaves like the portal frames found in a large supermarket or warehouse. There is of course a good reason why this has not been done. 

One of the immutable characteristics of bending forces is that they are always accompanied by shear forces. One cannot exist without the other. In the case of our imagined postalised frame bending forces at the connection between the columns and girder will necessarily co-exist with horizontal shear forces at the column heads and vertical shear forces at either end of the girder.

Horizontal shear forces at the column heads are a problem. The reason they are a problem is that equilibrium demands an equal and opposite shear force at the base of the columns. The two column bases are on wheels, which allow the crane to run back and forth along a set of rails. Horizontal shear forces at the base of the columns are therefore most unwelcome, because they will tend to press the wheels into the side of the rails causing either the rails to buckle or the wheels to jam or both.

It is now time to return to the actual cranes Samson and Goliath, which have one pin joint and one fixed connection at the column heads. It is of course very tempting to assume that when the crane is lifting the pinned connection is free from bending forces and the fixed connection attracts bending from the girder span. It follows that no bending forces are transferred into the slender tubular columns, which makes sense, and some bending forces are transferred into the box column. These after all are the rules and therefore, some engineers will make this assumption. Of course in this case they would be wrong.

Those who make these assumptions have forgotten about equilibrium. A bending force at the head of a column must, as we know, be accompanied by a horizontal shear force. The horizontal shear must in turn have an equal and opposite partner to maintain overall equilibrium, except in this case there can’t be an equal and opposite partner, because the opposite column has a pin joint i.e. if a shear is present the pin joint must carry a bending force which it cannot do.

The solution to this riddle is of course that the fixed connection does not carry any bending forces and behaves as if it was a pinned connection. How is this possible; as that is not the rule? This is the subtle part of the solution that is often missed. 

Since the large column is not infinitely stiff it will, when loaded, start to deflect ever so slightly due to the bending force its fixed joint would like to impart. This deflection is just sufficient to rotate the head of the column, but without changing the angle between the column and the girder i.e. rotation occurs in the column rather than at the joint, which causes the structure to behave as if there were a pinned connection. Only a very small movement is required for this effect to occur.

Now, since there are no bending forces at the head of either column there are no horizontal shears in the column heads and therefore equilibrium demands no shears at the base of the columns either. This means the cranes are free to travel up and down their rails without becoming stuck.

Conversely, if a horizontal load is applied, say the wind, the box column is sufficiently stiff, in combination with the fixed joint, to deflect only a small amount before resisting the horizontal load and keeping the crane stable. This is the reason for having a large box column on one side only. It is the secret of the Samson and Goliath Cranes.

Incidentally, the reason there are two rather than one slender column is to ensure that the cranes are stable out of plane. The keen observer will notice that the tubular columns rake in opposite directions to provide the required stable platform.

On Cladding Garden Sheds

Sometimes interesting structural load paths present themselves in unexpected places. The photograph below is such an example. It shows a cross section of timber cladding boards at the door threshold on my parent’s shed, which is located at the bottom of their garden behind the garage. You can see the end of the garage through the glass panels in the door. 

What is interesting is trying to understand why the timber cladding board in the centre of the picture has started to cup, which has in turn caused the tongue and groove’s cut into the board’s long edges to begin separating from adjacent boards

This requires us to know something about how trees are converted into boards and why this affects the way that they move and warp. It also requires us to understand how this affects the way cladding boards should be detailed.

There are three methods of converting a log into boards. The most common is known as plain / flat-sawn, which essentially involves slicing the log into vertical strips. It is the most common choice because it minimises the amount of timber wastage and maximises the number of boards. It is therefore cheap.

The second most common method is known as quarter-sawn. As the name suggests this involves cutting the log into quarters and then flat-sawing each quarter. This produces a little more waste than conventional, flat-sawn timber and is therefore more expensive.

Rift-sawn boards are reasonably uncommon, because there is high waste and therefore they are expensive. In this case the boards are sawn in a radial pattern.

The reason that various methods of forming boards exist is because they each intersect a tree’s growth rings in different way. Flat-sawn boards are cut tangential to the growth rings; rift-sawn boards are cut radially and quarter-sawn somewhere in between. The benefit this brings will shortly become clear. 

When a tree is felled its moisture content could well be 100%. As it starts to dry out free water will evaporate from its cells until it reaches somewhere between 25 and 35%. Beyond this point water is lost from the cell walls of the timber fibres themselves. This causes the timber to shrink. Since shrinkage tangential to the growth rings is roughly twice that in the radial direction the method used to form the boards becomes really important.

Flat-sawn boards will distort out of plane causing the middle of the boards to move towards what would have been the heart of the tree. Quarter-sawn boards will tend to warp in plane. In contrast to both other forms of cut rift-sawn boards tend to be dimensional stable.

Knowing what we now do we can return to the garden shed cladding. 

If we look closely at the board edges we can detect from the pattern of growth rings that the boards were flat-sawn. They were always going to vulnerable to distortion. If we look even more carefully we can also see that the growth rings in the middle board are orientated in the opposite direction to the boards either side. This has had the effect of causing the middle board to pull the edges of the two adjacent boards outwards.

This has of course been exacerbated, because the builder did not understand how to fix the boards so as to minimise the effect of shrinkage. The photo above shows that the boards have tongue and groove edges that are meant to interlock while being allowed to slip past each other. 

To minimise the effect of shrinkage this arrangement is supposed to be nailed through the upper shoulder of each board with the lower edge being free to move while being restrained by the tongue and groove joint at the bottom of the board.

Of course you can see in the photo below that the clown that built this structure has double nailed the centre portion of each board forcing the shrinkage movements to the outer edges. 

That clown was of course a teenager who later became an engineer and decided to write an engineering blog.

On Balloons, Chains & Arches

At first inspection the image above is not terribly interesting. It’s a picture of some helium balloons attached to a piece of string, which is tied to an advertising board at either end. Helium is of course lighter than air and therefore the balloons have risen until they are restrained by the string. The resulting shape is recognisable as an arch.

On closer inspection the image is possibly more interesting than you might think and that’s why I took the photograph. To understand why it's interesting you would need to know something about arches.

Everyone is familiar with the form of an arch and have likely seen many examples. Perhaps the most obvious examples would be arched bridges, which were traditionally built of masonry. More modern examples are built of iron and steel.

From antiquity arch bridges had been designed by trial and error with rules of proportion being gradually developed from the classical period onwards. This worked reasonably well, however engineers were never quite sure how far an arch design could be pushed before it became unstable. A reliable design theory was required, which did not rely on having to build lots of examples to see what happened. In fact how to determine the minimum thickness of an arch remained a major challenge until the mid nineteenth century.

Notwithstanding the desire to avoid trial and error it was an important challenge for several other reasons. Thin arches were generally viewed as being more elegant than thick ones. Thin arches are also cheaper because they are constructed of fewer raw materials and because they are lighter. Lighter arches could have smaller abutments and the timber supports (centring), used to support the arch while it was being constructed, could be less substantial. 

One of the first people to make progress on the structural behaviour of arches was none other than Robert Hooke; one of the foremost thinkers of his day and a contemporary of Issac Newton. 

Hooke of course new what is intuitive to almost everyone. Arches are compression structures that convey loads to the ground by squashing together the masonry blocks from which they are constructed. He would also have known that, much like building a house of cards, the two sides of an arch will tend to spread, and will eventually collapse, unless retrained by abutments.

Hooke's genius was to figure out the most efficient shape for an arch to be. He expressed his insight as “Ut contiuum flexile, sic stabit contiguum rigidum inversum”. [It was the 17th century so everything smart was written in Latin].  A rough English translation would be “as hangs the flexible line, so inverted will stand the rigid arch”.

In other words hook had realised that the best form for an arch with a given span and a given rise is that formed by inverting the shape of a chain suspended between the arch supports.

Self evidently the hanging chain is a tension structure, which modern engineers would call a catenary. Its shape conveys visually the idealised load-path. We recognise catenary cables in the form of a suspension bridge or as shown below in a rudimentary barrier.

Hooke also realised that the compressive thrust in an arch is the inverse of the tension in a hanging chain, which would allow restraints to be designed more efficiently.

Building on Hooke’s insight later engineers showed mathematically that providing an arch’s load path is contained within its thickness the arch would remain stable.

So why does this make my balloon photograph interesting; why did I take that picture? The reason, if you are not ahead of me already, is simple. As we have said already arches are solid structures that convey compression forces while catenaries are flexible structures that convey tension. Both their shapes and the forces they carry are opposite.

The balloon structure I photographed is interesting, because it is a tension structure that has taken the form of an arch. In actual fact it is an inverted catenary and not an arch at all. It has effectively inverted Hooke’s inversion.