Choice of Deck Cross Section.
The previous item of ‘more detailed information’, entitled “Background on choice of design for First Road Crossing”, describes the circumstances which led to the catastrophic collapse of the Tacoma Narrows Bridge in the USA in 1940. Initial work on the Severn Bridge started shortly after that and there can be no doubt that its designers were well aware of the potential consequences of neglecting the lessons learned.
In the late 1950s, using an anemometer mounted on a mast 110 feet (33 m) high (the height of the proposed Severn Bridge deck) and an array of instruments mounted on the then existing Severn Railway Bridge, some 3 miles (5 km) upstream, a spectrum of data on local wind speed, direction and inclination, was established over a width of about 300 feet (90 m). This information would be put to good use when the 1/100-scale model options for the Severn Bridge deck were tested in a wind tunnel at Bedford. At that stage, it was assumed that the deck design would follow American practice with a stiffening girder, about 33 feet (10 m) deep and of open-lattice truss construction, as had been proposed in the 1930s.
However, in the late 1950s, the Government stipulated that the new Forth Road Bridge would take priority over the Severn. The Forth Bridge would, not surprisingly, be designed on the same principles as those being developed for the Severn Bridge, although the main span across the Forth would be slightly longer, at 3300 feet (1008 m). Mott Hay and Anderson were appointed in association with Freeman Fox and Partners to design the Forth crossing using a conventional design for the stiffening girder, consisting of a horizontal concrete slab, above a latticed steel-work construction (a truss) that supports it.
There was a new development on the Forth Bridge in that the road deck was made of stiffened steel panels resting on cross girders at the top chords of the trusses. These panels were light in themselves and the overall dead weight was also kept to a minimum by specifying a thin layer (c 1 ½ inch or 40 mm) of mastic asphalt as the running surface. Nevertheless, the total dead weight of the Forth deck was some 18,000 tons which required the towers, main cables and anchorages to be designed to cope with this load plus the weight of the traffic on the deck. Construction on the Forth proceeded about two years ahead of the Severn.
This delay allowed different deck cross-section to be considered for the Severn Bridge, 4 of which are illustrated below.
At an early stage in the design process for the deck, it was necessary to test the 1/100 scale models of the various options being considered for this crucial item, using a wind tunnel to check the strength of the deck, when exposed to the strongest side winds that might occur. It was also necessary to ensure that the deck would not start oscillating during a less powerful but steadier wind flow. However, very early in the first part of this procedure, the model fixings in the wind tunnel failed and the model was completely destroyed. During the delay that followed, the Consultants, Freeman Fox and Partners, were moved by inspiration to develop an unprecedented design for the deck section, quite different from anything that had been tried before. It was based on the technology developed to design aircraft wings.
A problem. The box girder would clearly have no difficulty in coping with anticipated lateral wind forces but during the later stages of the tests, a slight movement had been seen from the model while it was being subjected to a less powerful but steady wind. This led to concerns, and then to doubts about the box girder’s ability to resist oscillations. The presence of this small amount of movement was worrying, given the absence of any obvious source of damping. The wind-flow over the welded box girder was so smooth and undisturbed that there was very little chance that the deck cross-section itself would be able to provide a worth-while contribution to any damping.
So the search was on for a fresh energy-absorbing element that could be relied upon to eliminate any embryonic oscillation that might occur. The Consultants were seeking an independent source of energy which, when transferred to the deck, would be capable of denying embryonic oscillations the opportunity of becoming uncontrolled and divergent.
The introduction of Inclined Hangers
The choice of the welded box girder for the bridge deck, was widely welcomed, although it would not have been accepted, if there had been any real doubt about finding a reliable source of energy which could be transferred into the deck to ensure that there would be sufficient dampening of all the oscillations that might seek to establish a foothold. In a second major innovative move, the Consultants decided that all the hangers used to suspend the deck from the main cables, would be hung in an inclined pattern, as shown on the following diagram. The purpose of this move was to increase the structure’s ability to prevent the deck from oscillating.
The pattern for inclined hangers.
The introduction of inclined hangers gave the Consultants a game-changing opportunity to prevent any embryonic oscillation that might form in the deck from developing into an uncontrollable and divergent oscillation. Engineers have long known that certain elements of a suspension bridge act in a very similar manner to the equivalent items on a washing line. They have been aware that, if an additional garment is hung on a washing line, away from the centre, the point on which it hangs, will sag and, more importantly, it will move a short distance towards the nearest point on the washing line that is held fast by a fixed support.
Similarly, when a vehicle travels over a suspension bridge, the deck will not only dip down a little at the moving point of the load, the whole deck will move a short distance longitudinally towards the nearest tower, whether the vehicle is travelling towards, or away from, that tower. The bridge deck is often called the stiffening girder because it spreads out the tensions among the hangers, in order to avoid excessive local sag under an exceptional load.
The purpose of employing inclined hangers is to take advantage of the opportunity to generate more frequent switching of the tensions between each pair of hangers that is connected directly to any of the cable clamps. As a result, the tensions in each of the hangers, and the bridge deck, will be in an almost-continual state of change. These changes will be related to the lengths of the hangers involved, and the angle between each pair, in each case. This means that the longer hangers on each side of the towers are effectively only subject to a change in vertical load from passing vehicles. Those near the centre of the main span and those towards the ends of the side spans suffer, not only the changing vehicle loads, but the much more significant reversals in tension due to the relative longitudinal movement of the deck in relation to the cable clamps to which they are attached.
Preparations. The deck of the bridge is freely suspended from the two catenary cables, using 172 hangers on each cable. And because the cables hang in catenary in the vertical plane, the two lines of lower anchorages, one on each side of the deck, that are attached to the surface of the deck to receive the hangers, are also in the same vertical plane. The next step was to wrap clamps around the cables at locations set at positions along the cables equivalent to 60ft apart horizontally. Each clamp was provided with a double eye to secure the top ends of the two hangers in each pair together, before they are allowed to diverge from each other as they go down to meet the deck. The lower ends of the hangers have to be moved 30 ft longitudinally, but in opposite directions, in order to be fastened into the two double deck anchorage eyes that had been fixed to the surface of the deck to receive them, and to provide the hangers with their relevant inclinations. The other halves of both these deck anchorages will be occupied by hangers from the cable clamps that are their nearest neighbours on either side
Both sides of the deck were treated as described in the above paragraph and, as a result, there is a single line of double sockets at 60ft centres on each side of the bridge deck. These lines are parallel to each other and identical in other respects. In every case, the cable clamp is located, horizontally, at the mid-point between each pair of sockets from one of the lines on the bridge deck.
Lateral restraints and vertical rockers have been provided at each tower and anchorage, to restrain the horizontal and vertical movement of the ends of the deck but permit longitudinal movements of the deck, unhindered. So the deck is restrained laterally and vertically, at both sides of the towers, but permitted the move with traffic loading and thermal expansion. The ends of the side spans are restrained vertically, laterally and longitudinally at the anchorages.
What actually happens? To cover the various activities that ensue, it is worth starting from a period of shutdown, when the deck will be lying in its position of equilibrium and before the traffic arrives, any two hangers involved will each carry half of the total tension that goes up through the cable clamp to the main catenary cable above. The total tensions carried by both of the cable clamps will remain similar at all times because the dead loads they carry are constant and virtually identical.
The process of additional damping will start with the build-up of vehicles running across the bridge in each direction. Each time that happens, the bridge deck will dip slightly and make a small longitudinal movement towards the nearest tower, similar to the garment on the washing line. The displacement will be proportional to the weight of the vehicle. The first tranche of vehicles will add to the tensions in the hangers, and provide many small longitudinal movements of the deck, which will soon coalesce into a distinct movement in one direction. The actual distances moved by the deck would be more correctly described as being the algebraic sum of the movements in a particular direction. Quite quickly, the deck will have moved a significant amount longitudinally, one way or the other, and this will enable the system to click, autonomously, into a higher gear. (Remember that the direction of these additional movements is governed by its location in relation to the positions of the towers, not by the direction in which the vehicle was travelling).
Now consider what will happen when the deck has made a fairly short movement in a particular direction. The system will react to a longitudinal movement of the deck, destroying the parity between the tensions in the two adjacent hangers. The system will move from point A to point B, in the time that the deck took to move to its new location, just like when an extra garment is added to a washing line, the difference between them may not appear to be very significant but it must be remembered that the crucial triangle at the centre of the issue is wholly comprised of steel which can be very demanding in such circumstances, a fact that is borne out by the contents of the next paragraph. And it must be remembered that the effect of the movement will probably impinge upon every pair of hangers that serves the deck – the whole caboodle. Think about it!
There has however been an important down-side to the use of inclined hangers. Depending upon their length and position on the deck, some of the shorter hangers are subject to increased fatigue damage, due to the frequency of the switching of the tensile stresses within each pair of hangers that shares a common cable clamp on one of the main cables. This is a sure sign that there has been ample switching of tension within the pairs involved. The shorter hangers might need to be replaced after a fairly short time in service. No traffic restrictions are needed, while the hangers are being replaced but the additional maintenance charges are significant.
The previous paragraphs illustrate how the idea of suspending the deck of the Severn Bridge using hangers erected in an inclined pattern, had made it possible for large tensile stresses to be redistributed within each pair of hangers that share an upper cable clamp. It was exactly the kind of new energy source that the consultants had been seeking to combat the possibility of an oscillation developing within the completed structure, similar to the one that destroyed the Tacoma Narrows bridge in 1940. It is particularly intriguing that the actual source of that additional energy should be the ‘live load’ that crosses the bridge. However, the consultants concluded that the most sensible approach would be to avoid situations that could lead to a hanger becoming slack, or otherwise overstretched under extreme live loading conditions, and they were supported in that decision by the government Department for Transport.
Manufacture of the hangers. The above demonstration of the ability of the inclined hangers to provide a new source of energy that must be generated from the live load of traffic, raises questions about the construction of individual hangers. The dead load of the bridge deck is extremely uniform throughout its length and so all cable clamps (at 60 ft centres) would carry basically the same share of that weight. At the same time, the average daily live load borne by each cable clamp would be virtually identical. It was also clear, at that stage, that more than 50% of all the hangers would be long enough to be treated in exactly the same manner as if they had been hung vertically. This all suggested that the current practice of the day, based on a multi-strand configuration, would probably be adequate. At the same time, there was strong support for developing a strand that would further strengthen the structure against the possibility of oscillations by maximising the amount of hysteresis in the hangers (this work was undertaken but very little has been said about it since). These deliberations resulted in a strand that contained a total of 178 separate wires, made up from the following three sizes, 0.118 ins, 0.133 ins and 0.339 ins with a lay of 7.5 d. The resulting strand would provide a maximum working load of 100 tons and a breaking load of 225 tons. At this stage the way forward was clear for the suspending of all the longer hangers from cable clamps and making the necessary connections to the sockets that would be fixed to the deck to receive them. But before that work started the possible need for a modification to the system outlined above, in order to cope properly with all the shorter hangers, was undertaken.
The initial system for supporting the bridge deck that was used to suspend all the longer hangers is described in the above with a section of main cable on one side of the deck, with the two hangers in one pair, coming together directly underneath the main cable to which they are both fixed using a special connection attached to the base of the cable clamp. Lower down, on the top of the deck, a line of sockets had been fixed to the deck at 60 ft centres, to secure the lower ends of the hangers. Each cable clamp was positioned directly over the mid-point between two sockets. An initial examination confirmed that that this arrangement, in the form described above, would not be able to cope with the shortest hangers. This meant that a modification was required together with a decision concerning the point at which the modification would need to be introduced.
The Included angle. It soon became clear that the critical item when dealing with shorter hangers is the angle ‘included’ between the two hangers at the point where they come together under the cable clamp to which they are both fixed.. This angle will be quite small In the case of the longer hangers but consider what would happen if it reached the 60 degrees shown on the diagram above (note, an angle of 60 degrees has been chosen just to simplify the mathematics). The triangle that includes both of the hangers and the line of the deck beneath them, approximates to an isosceles triangle. This means that these hangers are inclined at an angle of 30 degrees to the vertical. Because of that, only 86% of the tensions in the hangers (i.e., the sum of the vertical components of these tensions) would be used to support the weight of the bridge deck, together with the live load of traffic on it. The other 14%, the horizontal components of the tensions in the two hangers, would cancel each other out, being dissipated into the bridge deck. And at the mid point of the span where the main cable drops lower, approaching the centre of the bridge, the included angle between the two hangers would need to be larger still in order to conform with the model.
The chosen modification involved a simple change to the rules that are implied in the model that is described above. Having reached the point chosen to make the change, the consultants extracted the included angle at that point and decreed that it should apply to all subsequent operations that would otherwise have adopted a wider angle between hangers.
Changes in hanger tensions due to longitudinal movements of the deck
This diagram shows an elevation of a short length of the support mechanism developed for connecting the bridge deck to the main catenary cable when viewed from one side. The cable clamps, that transfer the loads from the hangers to the main cable, are positioned along the cable at 60 ft intervals, horizontally, and they each have to secure two hangers, one from either side. The eyes that are used to fix the hangers to the deck are located mid-way, horizontally, between the cable clamps to either side. They are fitted along a line just off the flat area on top of the deck, where an additional section of box girder has been welded on to the main box girder, to provide the short cantilever that carries the footpath and cycle track at the side of the deck. (see Deck Section Diagram in Main Elements).
Once decisions were taken on the dimensions of the spans and the towers, together with the shape of the main cable and the horizontal space between the cable clamps, there will be no scope for adjusting hanger lengths. They will simply be a matter for calculation
The purpose behind the introduction of inclined hangers is to produce a situation in which the energy stored in the hangers will increase and decrease much more rapidly and by larger amounts than would be the case with vertical hangers. This should provide the structure with much greater potential for dampening embryonic oscillations of the type that destroyed the bridge at Tacoma Narrows. The Severn Bridge has already given good service for more than 50 years and, with adequate maintenance, should continue to do so for the full 120 years of its design life, and beyond.
Unfortunately, there is a downside to the introduction of inclined hangers. It is extremely important that components of the structure that are active in suspending the deck, should remain in service for long periods. And when necessary, they must be capable of being removed and replaced, without requiring traffic restrictions. The rapid fluctuations in traffic loading associated with inclined hangers, and the additional loads that are imposed, make these hangers especially vulnerable to fatigue failure. This is particularly true of the shorter hangers located in the central area of the bridge. The situation is manageable but it requires significantly more maintenance than was originally planned.
It has been shown that the level of stress for hangers in an inclined pattern could rise to at least twice the maximum level experienced in a pattern of vertical hangers, especially where the hangers are short and near the centre of the main span. And it has been established that the relative fatigue life of an individual hanger on that bridge can be expressed, mathematically, as being inversely proportional to the fourth power of the range of stress involved. When this formula is used to explore the effect of doubling the range of stress in a hanger, as in the present circumstances on Severn Bridge, it confirms that we should expect the fatigue life of some of these hangers to be reduced to one sixteenth of the life that would apply if the hangers had been in a vertical pattern (the fourth power of 2 being 2 x 2 x 2 x 2, which equals 16).
It should have been no surprise, therefore, to find fatigue failures of wires within hangers on the Severn Bridge after only six to ten years service. After a period during which individual hangers that had failed, were replaced ad hoc, a wholesale strengthening programme for the bridge put in hand. All hangers were replaced using stronger and less fatigue-prone strand construction, and new designs of socket were installed.
Mott Hay and Anderson continued in their role to design and supervise the construction of the crossing, but now jointly with Freeman Fox and Partners. Motts led overall and designed all the foundations. Freeman Fox were responsible for the steel superstructures. The superstructure of the main suspension bridge was a major technical advance on all previous long-span road bridge designs.
A total of three suspension bridges were built with inclined hangers, between 1965 and 1980, all with Freeman Fox and Partners as main consultants. It is interesting to note that the inclined hangers on the Humber Bridge have proved less prone to such problems, possible because of a less severe traffic loading pattern. On the other hand, those of the first Bosphorus Bridge have been so fatigue prone, probably because of a traffic loading pattern even more extreme than on Severn, that they were all recently replaced by new vertical ones. Suffice to say that, to date, no other major suspension bridge has been fitted with a system of inclined hangers.
At the time, the Severn Bridge was hailed not only for its majestic appearance but also for its technical excellence. The all-up weight of steel in the Severn Bridge, 3,240 feet (988 m) span, was 19,000 tons for the deck, cable suspension system and towers compared with 39,000 tons for the earlier Forth Bridge which had a main span only 60 feet (20 m) longer.
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