Wind Theory

The ‘blown down by the wind’ scenario

T Martin,  I A MacLeod

Tay Rail Bridge during the storm of 28th Jan 2002.

This was the only time trains were stopped from crossing the bridge due to the wind force. Wind speeds of 80 M/Hr (force 12 on the Beaufort scale) are required for the trains to be stopped. During the storm a gust of 105M/Hr was recorded.

Introduction

 This is an account of how the Tay Rail Bridge disaster may have occurred based on investigations using software to model the behaviour of the structure under wind loading.

The context

It is just after  7.00 pm on 28th December 1879.  The 4.15 train from Edinburgh leaves Wormit station on the south side of the Firth of Tay to cross the first Tay Rail Bridge heading for Dundee on the north side.  It never arrives in Dundee.  While the train was on the navigation spans of the bridge they collapsed into the Firth taking 75 people to their deaths.  In terms of loss of life this was the worst disaster due to structural collapse recorded in the UK (other than due to war actions).

Some structural concepts

Take a chair which sits on a carpet (so that the legs do not slip on the floor) and push it horizontally away from you at the top.  The legs on the side from which the chair is pushed will rise off the floor,  To prevent this happening one could fix the legs of the chair to the floor.  Then when you push it, the legs which previously lifted up would be in tension.  That is - the forces on them would be trying to pull the ends apart.  The forces in the other legs are acting in the opposite direction, trying to push the ends of the legs together.  These are compression forces.

The effect of the wind on a pier of the Tay Bridge is similar that of pushing a chair horizontally.  The columns of the pier on the windward side (i.e. the direction from which the wind is blowing) are in tension tending to lift up from the foundation; the columns on the leeward side (i.e. the side away from the wind, the ‘sheltered’ side) are in compression.

Figure 1

What were the circumstances of the collapse

The bridge had 72 of  spans of the order of 44 metres length and 13 navigation spans of the order of  74 metres length.   For the 44 metre spans the spanning girders of the bridge were below the level of the track (deck spans - Fig. 1) the 74 metre spans had ‘through girders’ i.e. in order to increase the clearance below the bridge the girders were situated mainly above the track such that the train ran in a ‘tunnel’ of girders.  These came to be know as the ‘High Girders’ and are referred to by that name here.

Figure 2

The girders were supported by piers consisting of 6 columns set out as in the plan diagram (Fig. 2). The columns were connected together by bracing members of which the most important in stiffening the piers were the diagonal ties(Fig. 3). The maximum height of the piers was 26.8 m above high water.  The piers were supported by caisson foundations i.e. large concrete cylinders sitting on the bed of the estuary.  Between the bases of the columns of the pier and the top of the caissons was two courses of stone masonry.

Figure 3

At the time of the collapse there was a very strong, gusty wind blowing - estimated to be Force 10/11 on the Beaufort Scale.  It blew from the west at right angles to the line of the bridge.  A observer foolish enough to be on a pier at the time of the collapse would have noticed that, on the windward end of the piers, during a wind gust the masonry into which the column bolts were anchored would lift up by a small amount - The diagram, on the right, shows how this type of movement was amplified in the final collapse.  This was because the bolts to hold the columns in place were only anchored into the top two courses of masonry 

The observer might see some of the diagonal ties snapping and the bridge shaking violently.  Then the train comes on to the high girders.  The lifting of the windward bolts causes extra force to be taken by the ties i.e. if the bolts had been anchored to the foundation below the masonry, the forces in the ties would have been less.  The critical tie - the tie which would be expected to fail first - was the inner tension tie in the second level above the base.  This is the tie that slopes upwards from left to right in the diagram. (Note that the other tie in each panel which slopes in the opposite direction is a compression tie for this direction of loading and because of the shape of its cross section it is ineffective in taking such loading.).  When it fails, more load is thrown into the inner tie at the next level up. It fails and failure of the inner ties zips up to the top of the pier (Fig. 4).

  Figure 4

The piers now no longer act as a set of six columns braced together but as two sets of 3 braced columns resulting in the lateral stiffness of the assembly being about 1/3 of that when all the bracing is intact.  The bridge is now what is called in Scots ‘shooogly’.  It is very flexible and sways violently in the gusts.  The train is thrown from side to side swaying in a arc about the base of the piers.   As the train  enters the fourth high girder an extra strong gust causes a leeward column to fail in compression probably at the second level (Fig 5).  Now the sway of the train and the girders is no longer circular about the base and side to side but unidirectional downwind.  The trajectory of the girders and train starts to dip downwards.  The columns on the upwind side fail in tension and all the columns break into pieces. 

Figure 5

The systems continues to rotate but cannot fall outwards to the full height of the pier because the leeward columns have failed in compression.  The wreckage falls into the water with distances from the edge of the caissons to the underside of the girder varying between 16 feet and 44 feet (Fig. 6).

Figure 6

This failure then develops horizontally as the effect of the falling girders exacerbate the effect of the failed ties.  All 13 navigation spans collapse but the failure does not propagate into the other spans because they are shorter, lower in elevation and hence significantly more able to resist damage.

All the people on the train would be killed in the impact of a little later by drowning.These events - windward columns lifting thus increasing the load in the ties, ties failing due to only wind action in Beaufort Force 10/11 conditions, tie failure starting at the second level of bracing -  are consistent with an analysis that we have carried out on a pier structure.

What was wrong with the design of the bridge?

The designer of the bridge, Sir Thomas Bouch, took advice about the intensity of wind pressure to be used in the design of the bridge.  The lowest value recommended to him was 10 pounds per square foot and he used that.   He assessed that a wind load of this intensity would not cause uplift on the bolts securing the bases of the columns and that the forces in the ties would be negligibly low.  But at that time French and American engineers were using 40 to 50 pounds per square foot for wind loading.  Modern UK codes of practice would require the Tay Bridge to be designed for over 50 pounds per square foot wind loading.  Technology for design of structures for wind was in its infancy in Bouch’s time but when there is uncertainty in a situation it is better to play safe.  He did not.

Secondly, the columns were made from cast iron with the lugs( projections from the columns for fixings) cast with the columns.  The holes in the lugs were cast using a tapered insert (for easy removal) such that these holes were parallel sided but tapered when they came out of the moulds.  The normal procedure is then to drill out material from the lugs to create parallel sided holes.  This was not done and caused the lugs to be unnecessarily weak. The tie system failed mainly at the lugs.  However the ties were not strong enough and had the lugs had adequate strength, the ties themselves could have failed in the prevailing conditions of  28 December 1879. Tests on tie assemblages (including the lugs) taken from the wreckage gave average strength for the ties as 24.1 Tons whereas Bouch believed that the ties would take 32.5 tons.

In structural design the safe approach is to overestimate the loading and to underestimate the strength.  Bouch got it wrong in both directions.  He underestimated the loading and overestimated the strength.

Why did Bouch get it wrong?

Bouch had earlier used 30 pounds per square foot for wind loading for a preliminary design of a the Forth Rail Bridge and in an early design for the Tay Bridge 20 pounds per square foot was used.   Both of these values are too low but use of either would have meant that special provisions would have had to be made for wind loading such that the bridge might (just) have survived the storm. Bouch also knew that he was wrong not to specify that the holes in the lugs should be drilled out.  He admitted this at the Court of Inquiry.

Why did he make these manifest errors?  We know that he was under pressure from his clients to get the bridge in service quickly and to keep the cost down.  He was renowned for producing bridges at moderate cost.  He wanted to maintain this reputation.  But his clients could afford to spend more on the construction of the bridge.  After the collapse funds were quickly found to rebuild to and adequate specification. 

Bouch had bad health problems at the time of the design of the Tay Bridge and his actions appear as a man who has lost the place.  His correct action should have been to tell his clients that unless they were prepared to spend adequate sums to build a safe bridge he would hold them responsible for the consequences.  But of course it was his responsibility to build a safe bridge and if his clients would not let him do this he should have resigned from his commission from them.  Not an easy, but a sometimes necessary, course of action. Bouch’s situation has resonances for modern construction.  Clients still try to pressure consultants to cut costs and hence reduce safety.  The professional engineer must not buckle to such pressure.

Summary

We do not claim that the sequence of events described in this account is what actually happened.  What we do claim is that there is good evidence to suggest that it could  have happened in this way.  The train could have been derailed before the piers collapsed, there was evidence of bad construction and poor maintenance and there could have been a contribution from fatigue.  But these features are not necessary to explain the collapse.  The bridge was doomed due to bad design.  If the wind on 28th December 1879 had not caused the collapse a later stronger wind would have done the job.