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Carrying the Loads
The specification that was included in the Sydney Harbour Bridger contract provided to potential contractors included the weights that the Bridge was required to support. The four railway tracks, mentioned elsewhere, required for the proposed electric railway network were, of course, prominent together with the roadway between the pairs of tracks.
The list of different types of load followed customary engineering practice and the items are easily recognisable in modern structural design methods. The two main categories are “dead load” due to the weight of the supporting structure itself and that of the various types of traffic and other applied loads: “live load”. On a calm evening at average temperature, the Bridge is under only dead load at the time of the New Year’s Eve fireworks – barring the weight of the fireworks.
Please see Chapter 8 in AREMA website
Dead Load
The specification required that the overall weight of the structure be allowed for, with a further two per cent for contingencies.
This introduces an important dilemma for the structural designer. How can the dead load be found for designing the structure when the strength calculations have yet to be made that include the live loads AND the dead load?
What this means is that, in many cases, a trial-and-error calculation system has to be adopted. A first estimate of the dead load - based on an initial sketch design - is used and the entire calculation is repeated a number of time, converging on the eventually correct answers.
It is quite clear that the experience of the designers plays an important part in this phase. Also, over many years approximate formulas have evolved for starting guidance in the case of simpler structures.
The experience factor becomes even more important in the cases of structures at or beyond the size limit of practice at the time.
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Dead Load
110. Weight of Materials
In estimating the weight of the structure, for the Purpose of computing the stresses therein, the following unit weights shall be used:
| Asphalt |
150lb per cubic foot (2403 kg/cu m) |
| Concrete, stone |
150lb per cubic foot (2403 kg/cu m) |
| Concrete, coke, including floating |
84lb per cubic foot (1345 kg/cu m) |
| Granite |
170lb per cubic foot (2723 kg/cu m) |
| Steel, rolled |
490lb per cubic foot (7849 kg/cu m) |
| Steel, cast |
485lb per cubic foot (7769 kg/cu m) |
| Wrought-iron |
480lb per cubic foot (7689 kg/cu m) |
| Cast-iron |
450lb per cubic foot (7208 kg/cu m) |
| Timber, Ironbark or Grey Gum |
75lb per cubic foot (1201 kg/cu m) |
| Rails and fastenings |
35lb per lin. Foot (561 kg/cu m) |
| Guard rails and fastenings |
32lb per lin. Foot (513 kg/cu m) |
111. Dead Load
The dead load shall consist of the entire weight of steel-and other materials in the structure, computed in accordance with the above unit weights, with a per cent. addition to the calculated weight of steel for over-run'
Live Loads
Roadway
Two loading conditions were stated for the Bridge: a local loading for cross-girders and stringers and a general requirement for the deck overall. In the first case a motor commercial vehicle was considered to be acting on an area of 330 square feet (30 sq. m). Outside such relatively concentrated loads, a general area load of “one hundred pounds per square foot” (4.8 kPa) was the requirement.
Railway
Although Bradfield, in his reports, had been clearly interested in multiple-unit electric railway coaches for the Sydney suburban system, the type of railway design load required by the specification consisted of two heavy electric locomotives followed by a long, uniform load of much lower intensity. This is recognisable as echoing the load system – “Cooper E”– used on North American railways then and now (http://www.tpub.com/content/armytransportation/TI-850-02/TI-850-020112.htm ), where two large steam locomotives haul a continuous load of much lower intensity per unit length. (Whilst steam locomotives now have much less presence, their occasional use must be allowed for.)
The railway loading was applied to all four tracks: two on each side of the roadway. The modern term for this level of loading is “heavy rail” as distinct from the smaller wheel loads such as found in the trams that took over the eastern pair of tracks, and now motor vehicles.
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Live Loads
112. General
All live loading or any combination thereof to be arranged to produce maxima stresses.
113. Deck System Definition
The deck system is to include the flooring plates, transverse rolled steel joists, stringers, the cross girders and the ends of cross girders cantilevered beyond the main trusses; also any sub-members and connections of the main system which may be more heavily stressed-by the loading specified for the deck system than by the loading specified for the main system.
114. Main System Definition
The main system is to include all members of the cantilevers, girders of suspended span, arches, and girders of approach spans, other than those specified under deck system'
115. Footway Loading Deck System
To be designed for the stresses produced by a uniform load of 100lb per square foot (4.8 kPa) over the footway.
116. Deck System - Roadway Loading
The flooring plates, transverse rolled steel joists and stringers.to be designed for the stresses produced by a conventional motor lorry, wheel base 12 ft. x 6 ft (3.6 x 1.8 m).; overall length 24 feet (7.3 m), overall width 8 feet (2.4 m), space occupied 30 ft. x 12 ft (9 x 3.6 m). weight front axle 18,000 1b. (8.2 tonne), back axle 36,000 lb (16.4 tonne). The remainder of the roadway to be covered with a live load of 100 lb. per square foot (4.8 kPa). All other members of deck system to be designed for a live load of I00 lb. per square foot (4.8 kPa) of roadway.
117. Railway Loading Deck System
To be designed for the stresses produced by two coupled conventional electric locomotives, each 65 feet (20 m)long overall and weighing 360,000lbs (16.3 tonne), followed by a train 1000 feet long (305 m) weighing 2,200lb.per lineal foot (303 kg/ linear m.), on each of the four tracks.
118. Main System - Railway Roadway and Footway Loading
The cantilevers, girders of suspended span and trusses of main arches to be designed for a uniform live load of 12,000 lbs. per lineal foot (17.9 tonne/ linear m) of Bridge, i.e., 6,000 lbs. per lineal foot (8.95 tonne / lineal m) of each main cantilever, girder of suspended span, or truss of main arch. The maximum loaded length per track to be taken as 1,100 feet (335 m), and the minimum loaded length as 300 feet (91.4 m).
The girders of approach span no.1 to be designed for a uniform live load of 9,000lbs. per lineal foot (13.4 tonne/linear m) of girder.
The girders of other approach span to be designed for a uniform live load. of 10,000lbs. per lineal foot (14.9 tonne/ linear m) of girder.
Deck System Impacts
The hard running surface of train wheels on steel rails results in a low shock-absorbing property – especially when compared with pneumatic tyres on made road surfaces. The impact is particularly noticeable at rail joints and other surface dislocations. Although extensive use of steam locomotives was not envisaged on the passenger lines, an impact factor was selected as 50% additional to static load on stringers, decreasing to 10% on the main bridge trusses. The corresponding values for the roadway were 25% and 10%. Please see Chapter 38.0 Railroad structures in Bureau of Structures website
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119. Impact Deck System
Impact is to be added to the statically computed maximum live load stresses as under:
Railway Loading
| Stringers, railway loading ".. |
50 per cent |
| Floor beams and cantilevered ends of floor beams, railway loading |
40 per cent |
| All other members of deck system as defined in Clause 113, railway loading |
25 per cent |
Roadway Loading
| Stringers, transverse rolled steel joists and flooring plates, roadway loading |
50 per cent |
| Floor beams, roadway loading |
20 per cent |
| All other members of deck system as defined in Clause 113, roadway loading |
10 per cent |
120. Impact Main System
| Members of main system carrying two panel loads, and outer girders of approach spans |
25 per cent |
| Girders of approach spans |
20 per cent |
| All other members of main system |
10 per cent |
121. Impact Footway Loading
No allowance to be added to stresses produced by the live load on footways.
122. Impact General
Impact shall not be added to the stresses produced by wind loads or by longitudinal and centrifugal forces.
Wind Loads
The Tay Bridge collapse in Scotland in 1879 and the enquiry that followed caused engineers worldwide to look more closely at the effects of wind on structures. Much work was done in co-operation with meteorologists, resulting in national codes of practice.
The Australian code (AS 1170.2 – 2011) now contains 101 pages but things were somewhat simpler in the 1920s. It was required by the specification and contract that a “wind load normal to the bridge of 30 pounds per square foot (1.44 kPa) of exposed surface of the two trusses” be allowed for. This works out at slightly more than modern requirements. A similar type of allowance needed to be made for forces from wind blowing longitudinally to the Bridge.
During the enquiry into the Tay Bridge, it was suggested that the lateral force on a train crossing the bridge at the time of the collapse may have contributed to the failure. A reminder of this may be found in the requirement for the Sydney Harbour Bridge that “an exposed surface of a train” would be subject to a wind load of 300 pounds per lineal foot (446 kg per lineal m.).
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Wind Loading
123. Wind Loading To be designed for the stresses produced by-
- A wind load normal to Bridge of 3o lb. per sq. foot (1.44 kPa) of the exposed surface of two trusses and one and a half times the elevation of the floor, 150 lb. per Iineal foot (224 kg/ lineal m) of Bridge on foot-way fence (fixed load) and 30 lb. per sq. foot (1.44 kPa) on travellers and falsework, &c., during erection.
- A wind load parallel with the Bridge of 3o lb. per sq. foot (1.44 kPa) acting on one-half the area assumed for normal wind pressure in paragraph (a).
- A wind load (moving load) of 3oo lb. per lineal foot (447 kg/lineal m)on the exposed surface of a train applied 7 feet (2.133 m) above base of rail. Applied over length corresponding to maximum live load stress in the member. All loads equally divided between main trusses.
Temperature
Thermal expansion of the various components and the differences in expansion between different components and different materials were considered in the specification. A variation range of 67°C in the uniform temperature of the whole structure and of 28°C between the temperature of the steel and of the masonry was to be assumed.
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Temperature
123. Wind Loading
To be designed for the stresses produced by-
- A variation of.120 degrees Fahrenheight.(49° C) in the uniform temperature of the whole structure, normal temperature being taken as 60 degrees Fahrenheight (15.5° C).
- A difference of 50 degrees Fahrenheight. (10° C) between the temperature of steel and masonry.
- deleted
- Stresses due to a difference of temperature of. 25 degrees Fahrenheight (- 4° C). between the outer web exposed to the sun and the other webs of compression members.
Coefficient of expansion for steel for 1 degree Fahrenheit= 0.0000061 in (12.6 x 10-6/°C).
Centrifugal and other forces
The northern approach to the Bridge has a horizontal curvature of 362 metres radius and the resulting lateral force exerted by two trains travelling at 80 km/h was to be taken into account.
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Centrifugal, Traction, Brake, Friction and other forces
125 Longitudinal Force
To be computed for a total longitudinal force of 650 lb. per lineal foot (969 kg/ lineal m) of live load corresponding to the maximum live load stress in member, the force considered as a total for two loaded tracks in the same direction. Longitudinal force applied to main arch trusses to be considered in horizontal directions.
126 Brake Force
deleted
127 Torsion Stresses
deleted
128. Friction
The tangential force produced by the rotation of a pin in its hole shall be assumed as 33 1/3 per cent of the force on the pin. These stresses are secondary stresses
129. Centrifugal Force
The northern approach spans to be designed to provide for the centrifugal force due to a train on each of the two tracks in the same direction, the force to be applied 5 feet (1.5 m) above base of rails. Cantilever Bridge, minimum radius of curve, 8 chains (161 m), speed 25 miles per hour (40 km/h); Arch Bridge, minimum radius of curve, 18 chains (362 m), speed 50 miles per hour (80 km/h).
Provision to be made for the increased load carried by any member of the girders or deck due to the eccentricity of the load and to the effect of the centrifugal force.
130.Elastic Properties of Main Pier
In calculating the stresses of the anchor arm, the main pier is to be assumed both rigid and elastic, in which latter case the pier will be assumed to resist torsion only. Modulus of torsion assumed at 1,200,000 lb. per sq. inch (8274 MPa).
Erection Loads
131. Dead Load
The weight of the loaded travellers, erection plant and materials. If weights are estimated from detail drawings add 2 per cent. for overrun. On all weights based on information from suppliers of machinery and tackle add 10 per cent. for possible overrun.
132. Live Load
The heaviest load for each position of the travellers, &c
133. Impact
For main trusses fifty per cent of the load hanging from the upper blocks of main hoist, for staging, stringers, and floor beams 25 per cent.
134. Wind
A wind load of 30 lb. per sq. foot (1.4 kPa)on the exposed surface of two trusses.
135. Wind and Live load
Considered not to co-exist.
Loading used to determine The Sectional Area of Members
136. Loading to Determine the Sectional Area of Members
All the co-existing loads and stresses and the deformation shall determine the section of the different members with the following restrictions -
Temperature stresses due to (d) shall be considered as secondary stresses. Temperature stresses due to (c) and (d) shall be assumed to co-exist with one third wind loads (a) and (c).
The various parts of the structure shall be proportioned for the maximum stresses produced by
- A combination of dead load, live load, impact, brake force, longitudinal force, centrifugal force, one-third wind loads, Clause 123 (a) and (c) or (b), temperature stresses, Clause 124 (a), (b), Primary unit stresses to be used in proportioning.
- A combination of dead load, three-quarters live load, impact, temperature stresses, Clause 1244 (a)) and (b), centrifugal force, longitudinal force and wind pressure as specified in Clause 123 (a) or (b)" Primary unit stresses to be used in proportioning.
- Any combination of co-existing stresses due to wind loads, longitudinal force, centrifugal force, temperature, with dead load, live load, impact and all secondary stresses. Secondary unit stresses to be used in proportioning.
Earthquake
A modern engineer would notice the omission from the specification of any consideration of seismic forces. The national Australian earthquake code did not appear until 1979.
