6 Response of Bridge to Changes in Loading 6.1 Methodology 6.2 Analytical Study 6.3 Comparison of Various Loading Patterns 6.4 Transverse Behaviour 6.5 Approach Viaducts

6 Response of Bridge to Changes in Loading

6.1 Methodology

Details of the current bridge assessment are not available at this time. Thus, in order to make a comparison between the various options it is necessary to assume a base case against which to make comparisons.

The base case is taken as the results of actions on the structure due to 4 lanes of full BSALL traffic plus footway loading.

6.2 Analytical Study

An analytical model of the bridge has been set up to determine the response to the various load patterns of the alternatives. The model has been calibrated against the original design reported results (see ICE paper) and found to be reasonably in agreement.

At present, the study has been limited to the effects of changes in vertical load only. Lateral load effects have not changed significantly since construction. Live loads have assumed to be symmetrical - the effect of possible torsional components is discussed below.

6.2.1 Effect of Torsion

The original bridge was designed to carry traffic, footway and cycle loading in accordance with BS153. The analytical decomposition of this load to the main bridge girders is described in the ICE report and summarised in Fig 2.33 on p.376. (reproduced in 3.2 above).

From this diagram it can be seen that for case (i), the total distributed load per feet length of the bridge can be characterised by a vertical load of 3.43 W lb/ft accompanied by a torque of 22.7 W ft-lb/ft. W is the distributed lane load in lb/ft. The load amplification in the more heavily loaded girder is given by the ratio [(3.43/2) + (22.7/78)]/[(3.43/2) = 1.17 i.e. 17%. This represents a conservative upper bound estimate of moment amplification in the girder system as it ignores torsional resistance of the girder and the beneficial effect of the global suspension system. As both the rail loading and the live loading (BSALL reduced) are generally symmetrical load systems, when applied for maximum bending, the effect is likely to be of a small order. However, although likely to be insignificant, this effect should be included in ongoing studies.

6.2.2 Effect of Design Method

The design methodology at the time of construction (1964) was based on the working stress method. This implies an approximate equivalent load factor with respect to minimum yield in steel in the order of 1.60 - 1.70 (approximately confirmed by the allowable working stresses in the ICE report). This is similar to the load factor on live load in BS5400 = 1.1 x 1.5 = 1.65. However BS5400 uses characteristic yield. The minimum value can be assumed to be around 5% lower. Thus, the combined safety factor is 1.65 x 1.05 = 1.73. Clearly, this simple comparison does not hold good for all load cases and load effects - but may be useful in attempting to calibrate the study.

6.3 Comparison of Various Loading Patterns

6.3.1 Comparison with ICE report (ref 1)

The following results have been tabulated for comparison:

1) Original 1964 loading results as reported in the ICE paper.

2) Original 1964 loading results as derived from the current analysis model.

These results are useful for two reasons:

a) They help confirm the validity of the analysis model.

b) They give a useful indication of the original design intent.

6.3.2 Live Load Patterns Considered

For the purpose of this report, the study has been limited to cases in which either one or two rail tracks are provided with footway loading and with or without reduced highway applied to one lane in each direction. This selection is judged sufficient, within the present study, to justify whether or not a multi modal scheme for the bridge is feasible or not.

Option

BSALL
All inclusive

BSALL
Restricted

Light Rail
(50 m or 100 m trains)

0

4 lanes

n/a

n/a

1

n/a

n/a

2 tracks

2

n/a

2 lanes *

1 track

3, 4, 5, 6

n/a

2 lanes *

2 tracks

* Note: 4 lanes of loading may be applicable to single lane carriageways when applied as notional lanes in accordance with BS5400. This aspect should be reviewed in subsequent studies.

Results are presented for both 50 and 100 m loaded lengths for the train loading (as defined in 3.7.4 above).

6.3.3 Analytical Results Compared

The following analytical results have been extracted for comparison:

1) Bending moments in the main span stiffening truss at the 1/8th points

2) Maximum deflection of the trusses in main and side spans

3) Maximum vertical slope changes at the tower and side span joints

4) Maximum combined vertical slope change across the tower joints.

In addition, the effect of additional dead load and dead load plus live load, on the main suspension cable tension has been reported.

(a) Comparison between ICE report and Current analysis

Maximum bending in mainspan stiffening truss (kNm)

Location
along
main
span

BS153
1964
ICE
Report

BS5153
1964
Current
Analysis

1/8 span

133770

123111

1/4 span

121932

114107

1/2 span

117880

103490

Maximum truss deflection (m)

Location

BS153
1964
ICE
Report

BS153
1964
Current
Analysis

Main span

3.29

3.09

Side span

2.38

2.48

Maximum vertical change of slope and direction (radians) due to live load bending

Location

BS153
1964
ICE
Report

BS153
1964
Current
Analysis

Main span at towers

0.019

0.019

Side span main tower

-0.020

-0.022

Side span side tower

0.020

0.019

Maximum main cable tensions (kN)

Condition

BS153
1964
ICE
Report

BS153
1964
Current
Analysis

DL

121100

116300

DL+LL

135350

129450

(b) Results for 50 m train loading cases

Maximum live load bending in mainspan stiffening truss (kNm)

Option

0
(Base Case)

1

2

3

4

5

6

BSALL
4 lanes
Unrestricted
(Base Case)

No
traffic
+
2 LRT

BSALL
2 lanes
Reduced +
1 LRT

BSALL
2 lanes
Reduced +
2 LRT

BSALL
2 lanes
Reduced +
2 LRT

BSALL
2 lanes
Reduced +
2 LRT

BSALL
2 lanes
Reduced +
2 LRT

1/8 span

110570

60810

82770

112370

= 3

= 3

= 3
     

(+2%)

      

1/4 span

106430

59050

80040

108532

= 3

= 3

= 3
     

(+2%)

      

1/2 span

97880

56210

74700

101779

= 3

= 3

= 3
     

(+4%)

      

Maximum dead and live load tension in main cable (kN)

Option

0
(Base Case)

1

2

3

4

5

6

BSALL
4 lanes
Unrestricted
(Base Case)

No
traffic
+
2 LRT

BSALL
2 lanes
Reduced +
1 LRT

BSALL
2 lanes
Reduced +
2 LRT

BSALL
2 lanes
Reduced +
2 LRT

BSALL
2 lanes
Reduced +
2 LRT

BSALL
2 lanes
Reduced +
2 LRT

DL

116300

115488

118533

121375

119040

117214

125435
   

(+2%)

(+4%)

(+2%)

(+1%)

(+8%)

DL+LL

135050

117538

128130

131925

129590

127764

135985
           

(+1%)

Maximum live load truss deflection (m)

Option

0
(Base Case)

1

2

3

4

5

6

BSALL
4 lanes
Unrestricted
(Base Case)

No
traffic
+
2 LRT

BSALL
2 lanes
Reduced +
1 LRT

BSALL
2 lanes
Reduced +
2 LRT

BSALL
2 lanes
Reduced +
2 LRT

BSALL
2 lanes
Reduced +
2 LRT

BSALL
2 lanes
Reduced +
2 LRT

Main Span

3.64

1.70

2.18

2.57

= 3

= 3

= 3

Side Span

2.31

0.77

1.51

1.84

= 3

= 3

= 3

50 m train cases (continued)

Maximum live load change of slope (rads)

Option

0
(Base Case)

1

2

3

4

5

6

BSALL
4 lanes
Unrestricted
(Base Case)

No
traffic
+
2 LRT

BSALL
2 lanes
Reduced +
1 LRT

BSALL
2 lanes
Reduced +
2 LRT

BSALL
2 lanes
Reduced +
2 LRT

BSALL
2 lanes
Reduced +
2 LRT

BSALL
2 lanes
Reduced +
2 LRT

Main span at towers

0.018

0.008

0.013

0.016

= 3

= 3

= 3

Side span main tower

-0.023

-0.009

-0.016

-0.018

= 3

= 3

= 3

Side span side tower

0.020

0.006

0.013

0.015

= 3

= 3

= 3

Maximum live load total change of slope ('crank angle') (rads)

Option

0
(Base Case)

1

2

3

4

5

6

BSALL
4 lanes
Unrestricted
(Base Case)

No
traffic
+
2 LRT

BSALL
2 lanes
Reduced +
1 LRT

BSALL
2 lanes
Reduced +
2 LRT

BSALL
2 lanes
Reduced +
2 LRT

BSALL
2 lanes
Reduced +
2 LRT

BSALL
2 lanes
Reduced +
2 LRT

Main span at towers

0.029

0.013

0.021

0.025

= 3

= 3

= 3

(c) Results for 100 m train loading cases

Maximum live load bending in mainspan stiffening truss (kNm)

Option

0
(Base Case)

1

2

3

4

5

6

BSALL
4 lanes
Unrestricted
(Base Case)

No
traffic
+
2 LRT

BSALL
2 lanes
Reduced +
1 LRT

BSALL
2 lanes
Reduced +
2 LRT

BSALL
2 lanes
Reduced +
2 LRT

BSALL
2 lanes
Reduced +
2 LRT

BSALL
2 lanes
Reduced +
2 LRT

1/8 span

110570

87870

96170

138870

= 3

= 3

= 3
     

(+26%)

      

1/4 span

106430

84710

92690

133430

= 3

= 3

= 3
     

(+25%)

      

1/2 span

97880

79970

86400

124680

= 3

= 3

= 3
     

(+27%)

      

Maximum dead and live load tension in main cable (kN)

Option

0
(Base Case)

1

2

3

4

5

6

BSALL
4 lanes
Unrestricted
(Base Case)

No
traffic
+
2 LRT

BSALL
2 lanes
Reduced +
1 LRT

BSALL
2 lanes
Reduced +
2 LRT

BSALL
2 lanes
Reduced +
2 LRT

BSALL
2 lanes
Reduced +
2 LRT

BSALL
2 lanes
Reduced +
2 LRT

DL

116300

115488

118533

121375

119040

117214

125435
   

(+2%)

(+4%)

(+2%)

(+1%)

(+8%)

DL+LL

135050

118990

128833

133435

131100

129274

137495
           

(2%)

Maximum live load truss deflection (m)

Option

0
(Base Case)

1

2

3

4

5

6

BSALL
4 lanes
Unrestricted
(Base Case)

No
traffic
+
2 LRT

BSALL
2 lanes
Reduced +
1 LRT

BSALL
2 lanes
Reduced +
2 LRT

BSALL
2 lanes
Reduced +
2 LRT

BSALL
2 lanes
Reduced +
2 LRT

BSALL
2 lanes
Reduced +
2 LRT

Main Span

3.64

1.48

2.46

3.12

= 3

= 3

= 3

Side Span

2.31

1.18

1.74

2.31

= 3

= 3

= 3

100 m train cases (continued)

Maximum live load change of slope (rads)

Option

0
(Base Case)

1

2

3

4

5

6

BSALL
4 lanes
Unrestricted
(Base Case)

No
traffic
+
2 LRT

BSALL
2 lanes
Reduced +
1 LRT

BSALL
2 lanes
Reduced +
2 LRT

BSALL
2 lanes
Reduced +
2 LRT

BSALL
2 lanes
Reduced +
2 LRT

BSALL
2 lanes
Reduced +
2 LRT

Main span at towers

0.018

0.012

0.015

0.019

= 3

= 3

= 3
     

(+5%)

      

Side span main tower

-0.023

-0.013

-0.018

-0.020

= 3

= 3

= 3

Side span side tower

0.020

0.009

0.015

0.018

= 3

= 3

= 3

Maximum live load total change of slope ('crank angle') (rads)

Option

0
(Base Case)

1

2

3

4

5

6

BSALL
4 lanes
Unrestricted
(Base Case)

No
traffic
+
2 LRT

BSALL
2 lanes
Reduced +
1 LRT

BSALL
2 lanes
Reduced +
2 LRT

BSALL
2 lanes
Reduced +
2 LRT

BSALL
2 lanes
Reduced +
2 LRT

BSALL
2 lanes
Reduced +
2 LRT

Main span at towers

0.029

0.019

0.024

0.030

= 3

= 3

= 3
     

(+3%)

      

6.3.4 Review and Conclusions

(a) Bending in the girder

The single track schemes show decreased live load girder moments for 50 m and 100 m trains. For the twin track schemes with traffic 50 m long trains show only nominal increased moments, but 100 m trains show noticeable increased moments - the significance of which requires review in ongoing studies.

Based on bending in the girder, single track options appear to be viable whilst twin track options may also be considered if the train length is limited to 50 m as proposed.

(b) Deflection

All schemes show a reduction in deflection relative to the BSALL base design.

Based on deflections, all options could be studied further.

(c) Rotations

All options show rotations that are similar or less than the BSALL results.

Based on rotations, all options could be studied further.

(d) Cable tension

All schemes, excluding Option 6, show a decrease in cable tension under combined dead load plus live load. In the case of Option 6, the increase is only 2% and 1%, respectively, for the 100 m and 50 m length train conditions.

Based on the cables tension, all options could be studied further.

6.4 Transverse Behaviour

It is understood (ICE Report - ref 1) that the bridge was designed to carry 45 units of HB loading in combination with HA loading. The HB vehicle weights 1800 kN and a single HB axle load carries 450 kN. This is significantly higher than the axle loads associated with a light rail or tram system.

In order to make a qualitative comparison between the various options, the bending moment effects on a typical transverse frame have been determined for the original HB loading. These are plotted in the figure 'Case 0' following. Given that it is believed that the plate thicknesses do not vary along the length, it is reasonable to assume that the capacity of the top transverse beam will not be less than the peak value as shown.

Three other cases, Options 2, 3 and 1 are compared for reference. In all cases, four lanes of restricted BSALL traffic loading have been modelled to reflect the possibility of a local break down (for instance). The rail loads have also been increased using a Dynamic Amplification Factor of 1.20.

It can be seen that there is a reasonable certainty that the transverse beams (assuming that they still have a similar level of integrity as originally intended) are capable of carrying the LRT loads proposed.

Combination 1: Reference Design: DL + HB45 units + HA (to BS153- 1964)

Combination 1: Reference Design: DL + HB45 units + HA (to BS153- 1964)

Maximum Bending Moments (kNm)

Combination 2: Single Track LRT & 2x6m Carriageways: DL + LRT+BSALL 4L (max 2axles)

Combination 2: Single Track LRT & 2x6m Carriageways: DL + LRT+BSALL 4L (max 2axles)

Maximum Bending Moments (kNm)

Combination 3: Twin Track LRT & 2x5.2m Carriageways: DL +2LRT+BSALL 4L (max 2axles)

Combination 3: Twin Track LRT & 2x5.2m Carriageways: DL +2LRT+BSALL 4L (max 2axles)

Maximum Bending Moments (kNm)

Combination 3: Twin Track LRT & 2x5.2m Carriageways: DL +2LRT+BSALL 4L (max 2axles)

Maximum Bending Moments (kNm)

6.5 Approach Viaducts

The spans of the approach viaducts vary between 34 and 54 m in length. Details of the construction are sketchy. However, we can compare for each option the change in dead load due to the reconfiguration combined with the live load as an indicator of the likely effect.

The smallest loaded length of the adjusted BSALL available at present is for 100 m. This should give a fair comparison of the maximum sagging and minimum hogging demands on the girders compared to the base loading case (4 lanes of BSALL all inclusive + footpath). The comparison considers two lanes of the reduced BSALL UDL plus footpath loading in association with one or two tracks of railway UDL. The KEL's have been excluded for simplicity.

Option

BSALL
All inclusive

BSALL
Restricted

Light Rail

Change in Dead Load
(kN/m)

Live Load
(kN/m)

Relative Total
(kN/m)

0

4 lanes

n/a

n/a

0.0

47.3

47.3
(base)

1

n/a

n/a

2 track

-1.2

40.0

38.8
(82%)

2

n/a

2 lanes

1 track

-2.3

37.7

35.4
(75%)

3

n/a

2 lanes

2 tracks

+3.6

57.7

61.3
(130%)

4

n/a

2 lanes

2 tracks

+3.3

57.7

61.0
(129%)

5

n/a

2 lanes

2 tracks

+2.7

57.7

60.4
(128%)

6

n/a

2 lanes

2 tracks

+0.9

57.7

58.6
(123%)

The % ratio in the last column is a fair indication of the relative load effects before and after based on the current assessment loading. Note: It does not factor in the initial dead load which is not known at present. If we assume, for instance that the original dead load is in the order of 300 kN/m (250 kg/sq.m of steel work, 0.25 concrete deck plus, say, 50 kN/m for the superimposed load) then the total increase for option 3 is (300 + 61.3) / (300 + 47.3) = 4%

Thus: for the worst case, the total increase in load is less than 5%.

This simple comparison indicates that, at worst, some minor strengthening and modification of the viaduct structures for live load effects may be required for the twin track options with highway loading, but this would need to be confirmed against a more detailed assessment when the details of the as-built construction are established. Single track options, or those without traffic should not require strengthening.