The Consolidation of Steel Bridges - Superstructures by pre-stressing

The Consolidation of Steel Bridges - Superstructures by pre-stressing

Summary

As a result of overloading as regards the bearing capacity as a result of the working load increase, the consolidation of the steel decks of bridges by increasing the girder section attaching new elements is mostly inefficient (using great amount of steel the increase of the bearing capacities is low; see the work: The Consolidation of Steel Bridges Superstructures).

More the allowable stress of the steel is consumed by permanent load, more inefficient is this consolidation.

Better solutions of consolidation are obtained when an initial stress state is introduced to act contrary to the stress state produced by the loads.

The following consolidation solutions have been taken into consideration

1. The consolidation by enhancing the base of the girder section with chord plates applied directly on the base of pre-flexion girder
2. The consolidation with pre-stressed rigid steel tension rod

KEYWORDS: steel bridge floor, consolidation, consolidation chord plates, pre-flexion, pre-stressed rigid steel tension rod.

Notation:

;: the distance from the section centroid of the unconsolidated girder section to the top fibre/bottom fibre;

; : the distance from the section centroid of the consolidated girder section to the top fibre/bottom fibre;

: the section centroid of the unconsolidated girder section;

: the section centroid of the consolidated girder section;

: the thickness of the consolidation chord plates applied on the base of the girder section;

: the length of the consolidation tension rod;

: the distance from the section centroid of the consolidation steel tension rod to the inferior base of the girder;

;: the moment of inertia (second moment of area) of the unconsolidated net/rough girder section;

: the moment of inertia (second moment of area) of the consolidated net girder section;

; : the area of the unconsolidated net/rough girder section;

: the area of the consolidation pre-tension rod;

: the girder pre-flexion force;

: the self-tension axial stress from the consolidation tension rod;

: the pre-tension axial stress from the consolidation tension rod;

: the maximum bending moment given by the weight of the unconsolidated structure;

: the maximum bending moment given by the weight of the consolidation elements;

: the bending moment given by the pre-flexion;

: the maximum bending moment given by the traffic loads;

: the weighted average value of the bending moment on the tension rod consolidation length, given by the traffic and permanent loads;

: the bending moment in the girder given by X₁

: the bending moment in the girder given by X₂

;: the normal unit stress produced by M_gn on the unconsolidated girder section at the top fibre/bottom fibre;

;: the normal unit stress produced by M_g on the unconsolidated girder section at the top fibre/bottom fibre;

;: the normal unit stress produced by M_p on the unconsolidated girder section at the top fibre/bottom fibre;

;;: the normal unit stress produced by M_p on the consolidated girder section at the top fibre/bottom fibre(in the points 1 and 2);

;;: the normal unit stress produced by M_u on the consolidated girder section at the top fibre/bottom fibre(in the points 1 and 2);

;;(;): the total normal unit stress produced on the consolidated girder section at the top fibre/bottom fibre(in the points 1 and 2);

;: the normal unit stress produced by X₂ on the consolidated girder section at the top fibre/bottom fibre;

;: the normal unit stress produced by exploitation load and X₁ at the top fibre/bottom fibre;

: allowable normal stress of the steel from the unconsolidated girder;

allowable normal stress of the steel from the consolidation elements;

allowable normal stress of the steel from the consolidation pre-tension rod;

Introduction

Bellow are presented two consolidation solutions by pre-stressing, for the main simple web girders of a bridge superstructure with an exceeded bearing capacity and a case study in which the methods used are being explained.

The consolidation of the steel decks of bridges can be made using two categories of methods:

Methods in which the girder section is increased attaching new elements.

It is known that the steel superstructures of bridges have a long lasting operating time by comparison with concrete superstructures (especially those from pre-stressed concrete); they can easily exceed 100 years.

The maintenance of a steel superstructure during the operating time must be carried out accordingly (mainly the painting of the superstructure according to the maintenance schedule), so that the superstructure will not be affected by the damages. The difference of traffic loads between the initial design values and the real value at a given moment can lead to the exceeding of the bearing capacity. As a result a series of consolidation works are required in order to ensure the further use of the superstructure in safe conditions.

For instance, the superstructure of railroad bridges over the Danube at Felesti and Cernavoda, which were designed in 1889, was calculated for a convoy with a 13,00t per axle for locomotives and a distributed load of 4,5t per metre for carriages.

In the 1960s, after almost 65 years of operation, as a result of the increase of the traffic loads (an increase by almost 100%) in some stay rods of the Cernavoda bridge, were developed normal unit stress exceeding yield stress. Consequently the consolidation of the bridge floor was begun and the consolidation works were carried out as following:

the enhancement of the inferior base of the main girders by introducing a third unprestressed web plate;

the enhancement of the diagonal bars section by adding pre-stressed or unpre-stressed fabricated elements;

the installation of new longitudinal girders;

the consolidation of the cross-bars with an unpre-stressed railway switchgear system;

the consolidation of the superior base of the two main girders by introducing a third pre-stressed steel plate;

Below are presented three consolidation solutions for the main simple web girders of a bridge superstructure with an exceeded bearing capacity and a case study in which the methods used are being explained.

The three consolidation methods have in common the following:

the consolidation involves the enhancement of the inferior base of the girder, the access to the superior base is not possible in the case of a top-road bridge due to the bridge floor;

adding new elements is done without introducing initial stress in the structure (pre-flexion, pre-tension, etc.);

the consolidated bridge floor is assembled through riveting and the new introduced elements are attached also through riveting;

CONSOLIDATION METHODS

The consolidation by enhancing the base of the girder section with chord plates applied directly on the base of pre-flexion girder

From a technological point of view the working stages are as follows:

scaffoldings are placed under the girders which are stressed (the pre-flexion) using presses applied on the scaffoldings;

the rivet heads from the inferior base of the girder are cut (without taking   out the cut rivets) on the area on which new steel plates are to be attached;

the new steel plates are placed in the correct position, regarding the position of the existing rivets;

the cut rivets are taken out one by one and are replaced with the new ones, which are installed in the rectified holes;

As regards the calculation, it results the following stress states, which when combined give the final girder stress state:

a) On the unconsolidated section of the girders develops a stress state produced by the bending moment given by the weight of the unconsolidated structure and of the new introduced elements and the bending moment given by pre-flexion(the initial stress state) (Figure 1);

FIGURE 1 (1)

b) After the chord plates fastening on the pre-stressed structure, the presses are removed which is equivalent to load the girders with the pre-flexion forces R; the consolidated girder section takes over the bending moment given by R forces (Figure 2).

FIGURE 2 (2)

(2)

c) The consolidated structure is put in use - the consolidated girder section takes over the bending moment given by traffic loads. (Figure 3).

d) The final stress state on the consolidated section (Figure 4)

FIGURE 4

The strength condition for the consolidated structure is:

(4)

2.2. The consolidation with pre-stressed rigid steel tension rod

One or several rigid steel pre-tension rod which will introduce an advantageous initial stress state for the structure, will be attached to the unconsolidated main girders.

In the most simple solution, a rectilinear rigid steel tension rod(rods) is introduced under the inferior base of the main girders.

The area of the consolidation pre-tension rod A_t is chosen and then the self-tension axial stress from the consolidation tension rod X₁ is determined

This method involves the installation of a rigid steel tension rod under the inferior base of the main girders, the rod is fixed at the ends of the girder. Inside the rigid steel tension rod applied is developed a tensile force, produced by the traffic loads (self-tensile force), which is determined on the girder-tension rod structure once statically indeterminate.

The stress states from the structure are the following:

a) On the unconsolidated section of the girders is developed a stress state produced by the bending moment given by permanent loads (Figure 5). The weight of the tension rod has not been taken into consideration;

FIGURE 5

(5)

b) On the consolidated section with the tension rod positioned at distance e towards the inferior base of the girder is developed a stress state produced by the bending moment given by traffic loads and the tensile force (self-tensile force) from the tension rod (Figure 6);

FIGURE 6

  (6)

c) The final stress state in the girder results when the two states presented are combined.

  (7)

The tension rod section is also checked out:

(8)

The necessary value of force X, so that the strength of the consolidated girder is ensured, is determined from the relations (7) and two values for X are resulted. The highest one is used to determine the necessary area of the consolidation tension rod from the relation:

  9)

The relation (9) results from the solving of the undetermined static system from Figure 7.

(FIGURE 7)

The relation (9) will be used for any position of the traffic load on the structure if for the bending moment produced by them on the tension rod consolidation length of the girder is considered a weighted average value M_um, in these conditions the free term Δ_1p of the static balance equation:

with an invariable form.

From relation (9) results:

(10)

It is made up the tension rod section with the area   , it is recalculated X with relation (9) and it is checked the consolidated girder section with relation (7) and the tension rod section with relation (8).

2.2. The consolidation by enhancing the base of the girder section with chord plates applied directly on the base of the girder by cancelling out the permanent loads stress

The solution is applied if the permanent loads have a high value and consume an important part of the main girders bearing capacity.

The working stages are those mentioned at point 2.1., only that previously must be installed scaffolds under the main girders, thus any stress being eliminated. After adding new steel plates and disassembling the scaffolds, the consolidated section takes over all the loads permanent loads and traffic loads.

The stress state is shown in Figure 4.

FIGURE 4

The strength condition for the consolidated structure is:

(4)

2.3. The consolidation with unprestressed rigid steel tension rod applied under the inferior base of the main girders

This method involves the installation of a rigid steel tension rod under the inferior base of the main girders, the rod is fixed at the ends of the girder. Inside the rigid steel tension rod applied is developed a tensile force, produced by the traffic loads (self-tensile force), which is determined on the girder-tension rod structure once statically indeterminate.

The stress states from the structure are the following:

d) On the unconsolidated section of the girders is developed a stress state produced by the bending moment given by permanent loads (Figure 5). The weight of the tension rod has not been taken into consideration;

FIGURE 5

  (5)

e) On the consolidated section with the tension rod positioned at distance e towards the inferior base of the girder is developed a stress state produced by the bending moment given by traffic loads and the tensile force (self-tensile force) from the tension rod (Figure 6);

FIGURE 6

  (6)

f) The final stress state in the girder results when the two states presented are combined.

  (7)

The tension rod section is also checked out:

(8)

The necessary value of force X, so that the strength of the consolidated girder is ensured, is determined from the relations (7) and two values for X are resulted. The highest one is used to determine the necessary area of the consolidation tension rod from the relation:

  9)

The relation (9) results from the solving of the undetermined static system from Figure 7.

(FIGURE 7)

The relation (9) will be used for any position of the traffic load on the structure if for the bending moment produced by them on the tension rod consolidation length of the girder is considered a weighted average value M_um, in these conditions the free term Δ_1p of the static balance equation:

with an invariable form.

From relation (9) results:

(10)

It is made up the tension rod section with the area  , it is recalculated X with relation (9) and it is checked the consolidated girder section with relation (7) and the tension rod section with relation (8).

CASE STUDY

The three consolidation methods are applied for main girder of a bridge with the following characteristics (Figure 8):

FIGURE 8

The maximum unit stress of the girder produced by the bending moment given by the permanent and traffic loads is up to 160,8 N/mm².

3.1. The consolidation by enhancing the base of the girder section with chord plates applied directly on the base of the girder without cancelling out the permanent loads stress

The inferior base of the girder is consolidated with three 35010 mm steel plates (Figure 9) from OL 37.2 (σ_ac=145 N/mm²) steel.

FIGURE 9

It can be observed that the usage degree of the consolidation steel plates is:

so an uneconomical usage of the steel plates.

The steel consumption for the consolidation is:

if the consolidation is made on the central area of the main girders with a 12 m length.

3.2. The consolidation by enhancing the base of the girder section with chord plates applied directly on the base of the girder by cancelling out the permanent loads stress

The inferior base of the girder is consolidated with two 30010 mm steel plates (Figure 10) from OL 37.2 (σ_ac=145 N/mm²) steel.

FIGURE 10

It can be observed that the usage degree of the consolidation steel plates is:

so an efficient usage of the steel plates.

The steel consumption for the consolidation is:

3.3 The consolidation with unprestressed rigid steel tension rod applied under the inferior base of the main girders

The inferior base of the girder is consolidated with unprestressed rigid steel tension rod consisting of two L-shaped bars from OL 37.2 (σ_ac=145 N/mm²) steel , located under the girder base at a distance of e = 300 mm (Figure 11).

FIGURE 11

The length on which the girder is consolidated (the length of the consolidation tension rod) is l_t = 12.00 m.

On the unconsolidated section of the girder results the stress state given by the permanent loads illustrated by relation (5).

By applying condition (7) for the total unit stress of the consolidated girder, in which σ_uc^s and σ_ucⁱ are given by relation (6), results the axial tension force needed in the tension rod (two values are obtained, from which the highest value is taken into consideration).

X =

By replacing the value of X, as it is mentioned previously, in relation (10) results the necessary rough area of the tension rod:

For the tension rod section are selected two L-shaped bars 2L 10010012 for which:

X is recalculated with relation (9):

The unit stress of the consolidated girder is verified with relations (7) in which are introduced relations (5) and (6), resulting:

The tension rod is checked at the tensile axial force (the net section of the tension rod has been taken into account) with relation (8):

The usage degree of the tension rod is:

The steel consumption for the consolidation is:

If the tension rod is placed at a distance of e = 50 cm results an axial force of X = 217880 N, and the tension rod section will consist of two L-shaped bars 2L 808010 with A

CONCLUSIONS

If the results obtained through the consolidation methods discussed are analysed the following conclusions can be drawn:

The consolidation through these three methods does not use initial stress states obtained through different means like pre-bending the structure before consolidation, using some pre-stressed consolidation elements;

The consolidation solution presented at 2.2 offers more advantages than the one presented at 2.1 as a result of cancelling out the permanent loads during the consolidation, the steel consumption needed for the consolidation being lower.

The tension rod consolidation is the most advantageous because the steel consumption needed for the consolidation is the lowest; the disadvantage is that the bridge building height increases, and the bridge outlet decreases.

Acknowledgements

Notation:

the distance from the section centroid of the unconsolidated girder section to the top fibre/bottom fibre;

the distance from the section centroid of the consolidated girder section to the top fibre/bottom fibre;

the section centroid of the unconsolidated girder section;

the section centroid of the consolidated girder section;

the thickness of the consolidation chord plates applied on the base of the girder section;

the length of the consolidation tension rod;

the distance from the section centroid of the consolidation steel tension rod to the inferior base of the girder;

the moment of inertia (second moment of area) of the unconsolidated net/rough girder section;

the moment of inertia (second moment of area) of the consolidated net girder section;

the area of the unconsolidated net/rough girder section;

the net/rough area of the consolidation tension rod;

the maximum bending moment given by the weight of the unconsolidated structure;

the maximum bending moment given by the weight of the consolidation elements;

the maximum bending moment given by the traffic loads;

the weighted average value of the bending moment M_u on the tension rod consolidation length;

the axial stress from the consolidation tension rod;

the girder bending moment given by the axial stress X;

the normal unit stress produced by M_gn on the unconsolidated girder section at the top fibre/bottom fibre;

the normal unit stress produced by M_g on the unconsolidated girder section at the top fibre/bottom fibre;

the normal unit stress produced by M_u on the consolidated girder section at the top fibre/bottom fibre (in the points 1 and 2);

the total unit stress at the top fibre/bottom fibre (in the points 1 and 2) of the consolidated girder;

the unit stress in the consolidation tension rod;

allowable normal stress of the steel form the unconsolidated girder;

allowable normal stress of the steel form the consolidation elements;

allowable normal stress of the steel form the consolidation tension rod;

References

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