On Century Tower

Ductility and seismic design

Century tower is an interesting building with a striking facade. The question is whether it has been designed this way for aesthetic reasons or whether there are any engineering reasons for its appearance? 

The building is located in Tokyo and this fact provides us with several clues. The external structure is redolent of Japanese calligraphy and that is surely not accidental. We also know that Tokyo is in region of seismic activity and it turns out this is also important.

For minor events buildings designed to resist earthquakes are expected to survive without damage, however for an earthquake of moderate size some damage to the cladding and fittings is considered acceptable. The real design challenge is what happens when a major event takes place. In these circumstances permanent deformation is expected to principal structural members. Not only is this expected it is actually required; it is part of the design strategy and this is why buildings with seismic resistance look and feel different to those which do not.

That said, one of the reasons Century Tower is interesting is because it does not look like a traditional seismic design. To understand why this is we need to take a couple of steps backwards.

Ordinary buildings tend to be kept stable by triangulated bracing, however this is not a good solution for earthquake resistance, because of the potential failure mechanisms if the design load were to be exceeded. Fracture of a tension brace or buckling of a compression brace would be catastrophic for a building’s stability.

A better way to survive an earthquake is to ensure that deformation occurs instead. This has the advantage of being a non-catastrophic failure mode and is also a useful way of absorbing seismic energy.

As we saw in my last post ‘On Ductility’ steel is a ductile material, which permits plastic strains [deformation] to develop without failure occurring. The art is to make the deformations take place where you want them to and avoid those locations where you don’t.

The first step in this process is to give the structure a vierendeel frame rather than a braced one. We have met the vierendeel frame before in earlier blog posts. Its primary characteristic is rigid joints which permit no rotation at the junctions between beams and columns. This forces deformations to occur within the members themselves due to bending. If sufficient bending stresses are developed then plastic hinges will form and these happen to be rather effective at absorbing energy.

Conventional wisdom is to adopt a tight structural grid so as to maximise the number of opportunities for plastic hinges to form and also to avoid overly large members. The down side to this approach is that modern open plan floor plates and open facades, which let in light, are difficult to achieve.

The next step is to ensure that plastic hinges occur in the beams rather than the columns. This is achieved by making the latter much stiffer than the former; the so called strong column-weak beam approach. The reason for this is self-evident, plastic hinges in the columns will render them incapable of supporting the weight of the building and will cause it to topple. Conversely, plastic hinges in the beams will lead to deformation, but not collapse.

Century Tower is interesting because it retains the strong column-weak beam approach, however it does so while adopting an open two storey structure. This is achieved with an eccentrically braced frame [EBF] en lieu of a vierendeel frame. EBF’s are essentially a modified system of K bracing. Each bay consists of two rigid braces, which are sized to avoid yielding, connected to a ductile beam, which is intended to develop plastic hinges where the braces apply their thrusts.

Thus, although the EBF is not strictly a vierendeel it effectively behaves in the same way. Rigid braces lock the beam-column junction and thereby force plastic hinges to develop in the gap between them. Providing hinges form before the braces are able to yield they cannot fail catastrophically, as they would in a orthodox frame.

It is a rather clever system, although it requires a more careful analysis than a conventional vierendeel, because there are fewer locations for plastic hinges to form i.e. the structure needs to behave as intended and must successfully mobilise each bay. This is not an easy thing to work out, as the precise nature of a given earthquake is difficult to predict.

Now, returning to the question with which we started, has this rather striking facade been designed for aesthetic reasons or is it for engineering reasons?

I think it would be fair to say that there are strong architectural reasons for the design. Firstly, the ability to have a modern open plan building with large windows and perhaps secondly to hint at Japanese culture. It is however quite clear that the structural form also plays a rather important role in resisting seismic forces.

The answer to the question is therefore that the facade has been designed with both aesthetic and engineering requirements in mind. It is a good example of the symbiotic relationship that exists between architect and engineer. 

I rather suspect that the design went through many iterations before the final solution was settled upon and that both parties had a significant role in its development. 

On Ductility

The benefit of elastoplastic materials

One of the most useful structural properties a material can have is ductility. In order to understand why this is so it is first necessary to explain some related concepts. We will start with stress and strain.

Stress is a measure of load intensity; more precisely it is the ratio of force divided by area. This concept can be visualised by considering how it is that someone can lie down on a bed of nails without being harmed, yet if the same person were to tread on a single nail it would pierce their foot. The reason a bed of nails causes no harm is because the person’s weight is spread over the cumulative area of many nails whereas a single nail concentrates a person’s weight over a very small area i.e. the bed of nails applies low stress, while the single nail applies high stress.

When a structural member is exposed to stress it will change in length. If the stress is tensile it will become longer and if it is compressive the reverse is true. If the material is uniform then the elongation or shortening is spread evenly along the length of the member. For example, a member that is half as long will change in length by half as much. The ratio of elongation or shortening per unit length is defined as strain.

Stress and strain are of course related; higher stress will cause higher strain. A useful way of expressing this relationship is to plot a stress-strain graph. The convention is to measure stress on the vertical axis and strain on the horizontal axis.

If a material is ductile, like steel, the relation of stress to strain will be directly proportional resulting in a straight line on our graph [1]. The inclination of the straight line is know as the elastic modulus, for reasons we will see shortly.

There will, however, come a point where strain will increase more quickly than stress and the graph is no longer a straight line. The proportional limit of the material has thus been breached. Soon after this point the graph will become horizontal, which means that strain will increase without a corresponding increase in stress. This threshold is known as the yield stress.

Beyond yield the internal structure of the material will begin to change at an atomic level. This process is known as strain hardening and it results in additional strength, and therefore higher stress, in return for further strains.

Eventually the stress-strain curve will again flatten leading to increased strains, but this time with decreasing stress. The point where this occurs is know as the ultimate stress.

Increased strain accompanied by decreasing stress is a rather curious effect. Why would increasing strain result from a reduced stress? There is of course a rational answer to this question. 

When any material is stretched there is a corresponding narrowing to facilitate the stretch. Generally this is too small to notice, however beyond the point at which the stress-strain curve flattens the effect becomes more pronounced and ‘necking’ occurs.

If we were to calculate true stress, based on a necked [reduced] cross-section, rather than continuing with a nominal stress, based on the original cross-section, then the stress-strain plot would in fact continue to grow. After a period of necking fracture will eventually occur.

Returning to the beginning of our stress-strain plot we can modify our approach. This time instead of continually increasing the stress applied to our test member we can load it to a known stress and then unload it again. We can then increase the stress to a slightly higher value and then unload again. This sequence of loading and unloading may be repeated.

When we do this we find that as long as we remain below the proportional limit the unloaded member will fully recover its original shape and will follow the straight line portion of the stress-strain graph. Beyond the proportional limit a full recovery will not be made; there will be some residual strain left behind.

When the member fully recovers its shape it is said to be elastic. The point at which it loses its elasticity is known as the elastic limit. Beyond the elastic limit materials are considered to be plastic. For many materials, like steel. The proportional limit, yield stress and elastic limit are relatively closer together and are in practise treated as if they were the same. For some materials, such as rubber, the elastic limit lies well beyond the proportional limit.

When large permanent strains start to occur within the plastic zone the term plastic flow is adopted. 

There are several reasons why ductility, incorporating both elastic and plastic behaviour, is important. We shall discuss one of them below and save another for the next post.

Supposing we wished to design a series of floor beams for a new building. The owners would not be terribly happy if they were to permanently deform and sag while the building was in use. For this reason we would want them to remain within the elastic range. We would therefore perform our design based on limiting stresses in the beams to the yield stress of the material.

This would satisfy the requirements for every day use of the building, however supposing an unforeseen or extreme event occurred, which caused the floor to become overloaded. In such circumstances you would not wish the floor beams to fail suddenly and without warning, for this would inevitably lead to a loss of life. 

Self-evidently it would be preferable for there to be a visible warning that something was wrong so that the occupants could vacate the floor safely and remedial action could be taken. This opportunity is provided by plastic behaviour in the floor beams. Although permanent deformation will occur within the plastic range the floor will at least remain stable and safe.

It is fairly obvious how this principle will work if the floor beams are made of steel, but perhaps less so for concrete. After all concrete is not a ductile material. It is weak in tension and fails explosively in compression.

The first problem is solved by casting steel reinforcement into the concrete in zones where the concrete is in tension. The reinforcing bars, rather than the concrete, resist the applied tensile stresses.

The addition of steel reinforcing bars also provides the means to deal with concrete’s lack of ductility. The reinforcement is deliberately designed to have a smaller capacity in tension than the concrete has in compression. This way as the reinforced concrete bends the reinforcing bars in the tension zones will reach their elastic limit before the concrete reaches its brittle limit in the compression zones. This principle is known as under-reinforcement and it is key to all reinforced concrete design. 

Thus reinforced concrete becomes a ductile material.

[1] In this example we are of course assuming the application of tensile stress

On Compressive Membranes

System behaviour in fire

Something that isn’t often appreciated is that when a building is designed to achieve a 90 minute fire rating it doesn’t mean the building is designed to remain standing for 90 minutes. This might seem odd, however if we were to pose the question what size of fire is to be resisted for 90 minutes, it is immediately obvious that there is complexity involved. 

In reality a 90 minute fire rating means that the fire resisting components in the building have been tested in a furnace against a standardised fire lasting for 90 minutes. This allows the relative behaviour of different materials to be tested, however it tells us absolutely nothing about how long a real building will survive subject to a real fire. 

This is in part because fire tests treat standardised components individually, however real components are not a standard size and they act as part of a system not as individual elements. If we are being really picky we might also argue that real fires are different to standardised furnace tests.

It follows that if the structural behaviour of a system subjected to fire can be understood then this can be harnesses en lieu of the rather crude prescriptive approach, which is normally applied.

The floors of many modern buildings are constructed by casting a thin slab of concrete on a corrugated metal deck. The concrete is reinforced using a light steel mesh and the metal deck spans between down-stand steel beams. Often metal studs are welded to the top of the steel beams and are embedded in the concrete. This is known as composite construction, because the steel and concrete act together.

To protect the steel from fire the prescriptive approach is to coat it with a fire resting coating, normally intumescent paint. Intumescent paint swells when it gets hot forming an insulating layer, which prevents the steel from over-heating. Without this insulation layer steel looses significant strength and stiffness at approximately 500 degrees.

If, however, the structural system is taken into account many of the beams may not require intumescent paint. This is beneficial because intumescent paint is expensive. 

In the example shown there are primary beams joining the columns together to form a series of identical bays with two secondary beams in each bay. If we were to suppose that the secondaries are unprotected then we can begin to think about the load-path in a hypothetical fire.

As the fire becomes increasingly hot the secondaries will also become hot and will start to loose strength and stiffness. Eventually they will have little residual capacity. When this happens the floor will begin to sag and instead of supporting the concrete floor the beams will hang from it due to the embedded studs. This process is likely to be accelerated by thermal expansion which causes the beams to buckle as they push against their supports.

Conversely the primary beams, located on the column lines, are protected and will remain unaffected by the ensuing fire. They continue to form a rigid frame around each structural bay. As the floor sags it begins to tug on the primary frame simultaneously pulling each side of the bay towards the middle. Much of this work is being done by the light reinforcing mesh embedded in the floor.

This effect causes a compressive ring to be set up in the concrete at the perimeter of each bay. This ring starts to resist the floor’s tugging and allows a point of equilibrium to be reached where the weight of the hanging floor is balanced by the compressive force in the concrete ring. Although the floor has displaced significantly it has not collapsed and has therefore maintained its integrity. The fact that it has displaced significantly is not materially important, as the sole aim is survival. After a major fire a building would not expect to survive completely unaffected.

This load-path means that some of the primary beams must carry additional load, which was previously supported by the unprotected secondaries. This is acceptable, because in the fire case it is permissible for the additional load to be absorbed by the their factor of safety.

It is also worth noting that the required load assumed for most buildings is in fact much greater than the load the floors will ever see. This means the actual factor of safety is normally higher than is assumed in the cold design.

This form of system behaviour is known as a compressive membrane and I have used it successfully to assess the fire resistance of buildings on several occasions. It is a more rational approach to fire safety than the rather arbitrary prescriptive approach, which has been used historically.

On Resistance & Reaction

Surprising qualities of timber in fire

The photograph below is relatively grainy, but is reasonably well known in the field of structural fire engineering. I first came across it at University, however I haven’t been able to determine its original source. I understand that it dates to 1906 and was taken in San Francisco, which could imply that it was linked to the large and devastating earthquake of that year. 

That said, as the sub-title for this post suggests this is not a post about earthquakes. Any relevance to the San Francisco earthquake would be due to the widespread fires that it caused.

That is because the image above pictures a fire damaged roof with steel beams sagging over a supporting timber, which has, by contrast, retained its structural integrity. This is rather interesting, because it defies the common sense view that steel is a superior material to timber in a fire. Self-evidently something else is going on.

For a number of years the timber industry has been promoting timber’s credentials as a green material, however recently I have noticed that it has become rather more active in promoting timber as a good fire resisting material. It has almost become a cliche that timber is better in fire than steel. The photograph above would certainly appear to support this claim. 

I suspect that this new found advocacy for timber’s fire resisting qualities is a response to a number of recent fires; tragically some with significant loss of life.

Yet somehow the facts don’t quite seem to fit do they. Steel buildings don’t burn down and you don’t throw steel onto your campfire to make it burn. It is perhaps a good time to recycle the analogy I deployed in my post titled ‘On Howe Trusses Work’, for this is another case of there being several layers of understanding i.e. a deeper magic.

We should probably start by trying to define what we mean by fire resistance. This is not as easy as you might think. There are normally three attributes that constitute fire resistance. The first is load capacity. This is the ability of a structure to retain its strength and stability in a fire. The second is integrity. This is the ability of a structure to contain a fire and prevent the passage of hot gases through splits, gaps and fissures. The final attribute is insulation. This is the ability of a structure to prevent the transfer of heat from the face of structure exposed to fire to the unexposed face.

The photograph above demonstrates that in respect of load-bearing capacity an adequately sized timber will retain its integrity longer than steel. It is also reasonably clear that timber is a good insulator while steel is a good conductor. Placing your hand on the back of a steel plate placed in front of a fire would hurt more than a sheet of timber, at least to begin with.

Integrity is perhaps harder to judge. Timber will eventually burn through, however steel is more likely to open a gap by distorting. I shall declare this category a draw, as the inference one draws depends largely on the boundaries that are set.

Based on this rather crude assessment we reach the surprising conclusion that timber is indeed more resistant to fire than steel by a score of 2.5 to 0.5. The trouble is that this isn’t the whole story, because ‘fire resistance’ is not the same as ‘reaction to fire’.

Reaction to fire means how easily a material can be ignited and how much it contributes to the growth of a fire. On this measure timber unquestionably fairs worse than steel. Steel is of course classified as a non-combustible material.

It follows that when we talk about fire resistance in engineering we are not actually talking about the common meaning.

Using engineering definitions it may be concluded that during the ignition and growth phase of a fire ‘reaction to fire’ is the more significant material property, however once a fire is fully developed ‘resistance to fire’ becomes more important. Thus, whether steel or timber is considered better depends on timing.

That said, if we must decide then I would choose reaction to fire as more important, because resistance becomes moot if a fire doesn’t start in the first place. That is not to say that resistance isn’t important, because a steel building doesn’t stop someone from leaving a pile of combustible material in the lobby, which could catch fire. 

Another consideration would be the continued existence of historic buildings. It would not be a good idea to simply demolish those which are made of timber, because of the perceived fire risk. We need tools to understand how they will behave when subjected to fire so that mitigation can be established.

There are of course many other examples that could be considered, however these are sufficient to demonstrate that structural fire engineering is a complex business that requires a proper examination of all the relevant factors in a given circumstance.

Incidentally the reason why timber has good resistance to fire is related to its insulating properties. When timber burns it starts to char at a predictable rate. As the charring layer forms it insulates the timber beneath helping to prevent ignition at depth. For this reason steel fixings in timber can be problematic, because they conduct heat into the core of a section.

Since the rate of charring is known an engineer can calculate, for a given duration, a sacrificial thickness of timber that will be charred, while leaving a residual section of timber capable of supporting the required load.

Rates of charring do vary between timber species; the predominant factor being density. Broadly speaking the denser a wood the slower its rate of combustibility and its associated charring rate. 

This knowledge, while sounding modern, is not new. Jarrah, a hardwood [1] was commonly used for railway sleepers in tunnels and on bridges, because of its slow charring response to hot tinders falling from steam engines.

It is worth noting, however, that the relationship between density and fire resistance is not universal. Some woods have chemical contents that make them more likely to burn, however even in such cases density does tend to be the more dominant factor.

[1] it is a common misconception that hardwoods, as the name would suggest, are by definition harder and denser than softwoods. This is a useful general rule, but is not strictly true. Balsa, which is used for model aeroplanes, is a hard wood, while the rather strong pitch pine is a softwood.

 

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.