5.8 Design problems
Table 7 summarises the many design problems of the piers uncovered by Mr Law and his team. We have already seen the numerous fractured lugs in the remains of the bridge, shown in Figure 29. Was the weakness of the lugs somehow associated with their shape?
Table 7 Tay Bridge defects: design defects
|Design defects||Number||Where found||Reference|
|1||lugs of low strength||all lugs||–||14,193|
|2||bolt holes with conical sections, so bolts act only against a short length of the hole||all bolt holes||–||12,619|
|3||1.125 inch bolts for tie bars fitted to 1.25 inch bolt hole in lugs, flanges||all joints||–||12,580|
|4||strut not abutting column wall||all struts||–||14,669 12,608|
|5||strut bolts difficult to tighten||all struts||–||14,553|
|6||no spigot on column ends, so columns can move laterally||some columns||P1, T1/2, C3/4||14,718|
|7||L girders not continuous across pier head||all||–||12,655|
|8||pier base too small||all||–||12,712|
|9||batter on 18 inch columns too low||all||–||12,717|
|10||girders resting only on piers||most||P1, 2, 4–6, 8–10, 12||12,665|
|11||girder not centred on piers; deviation at joint between high and low girders||1||P28||12,703|
One feature that attracted attention was the conical form of the lugs, a shape cast into the metal during manufacture at the Wormit foundry. The reason may have been to aid withdrawal of cores or to help the metal crystallise correctly, but it meant bolts under tension from the bars would act against only a small area of the hole rather than the load being uniformly distributed. The slack in the fitment of bolts was mentioned above, but the problem extended to the struts as well.
The ends of the two U-channel struts were not flush with the column surface, so that any compression would load the two bolts, and not be shared with the column at all. This problem can be seen at the top joint in the centre of Figure 28 for example. The bolts were themselves difficult to tighten correctly. Some columns were provided with a spigot or projection, which enabled positive location between columns. One such example can be seen to the left of centre in Figure 23. Yet other column flanges were not so designed (see Figure 26), so columns could move laterally when strained owing to the slack in the bolt holes and poor tightening.
A potentially serious problem that could affect structural stability arose with the L girders at the pier heads. The two girders were not laterally connected at all, so if asymmetric loads occurred, the two sets of three columns were less strongly connected.
The pier foundations were too small for the great height of the columns, most of which were vertical. Only the outer 18 inch columns leaned inwards with a small batter – in building terminology, it is a designed slope on a structure.
The high girders themselves were not attached at all to most of the piers, simply resting on roller bearings, which allowed longitudinal movement of expansion and contraction (Figure 37). At only three points were the girders strongly fixed to the piers, as shown in Figure 10. Lateral movement of the girders was therefore only restrained by friction of wrought against cast iron.
Assess the effect of the various kind of defects identified by Mr Law and his team during the enquiry on the lateral stability of the high girders. Perform your analysis systematically by considering in order:
Be careful to consider the extent or numbers of each defect in relation to the stability of the whole structure, and include any direct evidence from the BoT set of photographs.
The various casting flaws alleged by Law appear from the transcript of the BoT enquiry to be of limited extent according to the data of Table 5. No specific examples of cold shuts or burnt-in lugs were given in evidence, although there were probably exhibits of unknown provenance. They have now disappeared with the passage of time. The same comment applies to slag inclusions and the allegations of ‘sluggish’ metal during casting.
None of the BoT photographs show the alleged defects, although the ones shown in this unit represent only a small sample of what would have been seen by Henry Law and team. Cold shuts or burnt-in lugs could have affected the form of fracture, but all the ones shown here exhibit similar fracture surfaces. If highly localised and rare, they would have been of limited effect on lateral stability, and it would be difficult to explain how the whole of the high girder section fell when only piers 4 and 5 were loaded by the train at the time of the collapse.
The effect of blow holes, with or without beaumont's egg, would depend on their exact position in relation to critical loads on the structure. The simple collapse theory of Question 6 suggests the wind braces are the critical parts of the structure under lateral loading, so holes at lugs would be detrimental. However, there is no evidence from the photographs to show their presence here, although at least one specific example was given in oral evidence – pier 28, the south standing pier.
It is difficult to see how variations of wall thickness of the columns could have seriously threatened the structure because the columns would have been in compression until collapse was initiated. Isolated examples of cracked columns were reinforced, so it is unlikely that casting defects or isolated cracks could account for the fall of all of the high girders when strained by wind loading and the passing train.
It is also difficult to understand how many of the fitment defects could have seriously affected the integrity of the high girders. From the evidence presented at the enquiry, they were generally of restricted extent, with some notable exceptions.
They concern the bolt holes that may have been enlarged somewhat, although the surviving or visible evidence is limited. The other defect is that of the gib and cotter joint. Both features occur in critical loading situations during lateral displacement of the high girders, so by allowing extra movement in tie bars or struts, produced considerable extra movement of the structure as a whole. They were also very extensive, so could well have affected the stability under side loading.
The most serious design flaws in the highest part of the bridge were those associated with the critical wind bracing tie bars. The integral single lugs at the column bases seem to have been weak, judging by the number of broken lugs visible in the photographs (see Figures 28, 29, 30 and 31). A substantial proportion of lugs on the wind braces were fractured, especially those facing east, in which direction the bridge fell. They possessed conical bolt holes, which will have concentrated tensile stress at the lugs over and above what would be normally be produced by a round hole. So if the piers were strained to the east, it is these parts that represent the weakest link in the load path.
Most of the connections of tie bars and struts also showed some flexibility owing to the loose fit of bolts to holes, although if some holes needed further widening during construction, the effect must have been variable. Spigots are a secondary feature that might affect column stability, but only if the flanges were poorly attached, for which there is little direct evidence.
The lack of lateral continuity across the head of all the piers (Figure 34) is more serious because the two sets of three columns are not tied together, so if wind braces break, the two sets become separate, hence less able to withstand lateral collapse. The high girders were mainly just resting on the pier heads, so they only held the two sets of columns together by friction. The totally collapsed piers 4 and 5 showed only columns from the west side, which seems to suggest separation did indeed occur at some stage during the disaster. Toppling of the piers would have been more likely with vertical columns despite the presence of a small batter on the outer members.
In his report presented to the enquiry, Mr Law examined the problem of the stability of the bridge using conventional static analysis, that is, he estimated the moments acting on the high girders and train under ‘worst conditions’.
This approach can be used for examining the stability of a ladder leaning against a wall. The outcome of this type of analysis is the idea that the ladder will slip catastrophically at a specific angle of repose against the wall, and the key variable that emerges from analysis is the coefficient of friction of the ladder feet acting against the floor on which they are resting.
Law's results and calculations were included in a lengthy appendix – as was normal then and is still the accepted practice in the courts.
One significant uncertainty lay in the mechanical strength of the many reinforcing components used to stabilise the space frame structure of the piers, such as the diagonal bracing bars. In view of the numerous failures of the diagonal bars in the centres faces of the piers, it was important to measure the strength of the individual components.