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The Consolidation of Steel Bridges  Superstructures by prestressing
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
KEYWORDS: steel bridge floor, consolidation, consolidation chord plates, preflexion, prestressed 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 pretension rod;
_{}: the girder preflexion force;
_{}: the selftension axial stress from the consolidation tension rod;
_{}: the pretension 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 preflexion;
_{} : 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 X_{1}
_{}: the bending moment in the girder given by X_{2}
_{};_{}: 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 X_{2} on the consolidated girder section at the top fibre/bottom fibre;
_{};_{}: the normal unit stress produced by exploitation load and X_{1} 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 pretension rod;
Introduction
Bellow are presented two consolidation solutions by prestressing, 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 prestressed 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
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 prestressed or unprestressed fabricated elements;
the installation of new longitudinal girders;
the consolidation of the crossbars with an unprestressed “railway switchgear” system;
the consolidation of the superior base of the two main girders by introducing a third prestressed 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 toproad bridge due to the bridge floor;
adding new elements is done without introducing initial stress in the structure (preflexion, pretension, 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 preflexion girder
From a technological point of view the working stages are as follows:
scaffoldings are placed under the girders which are stressed (the preflexion) 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 preflexion(the initial stress state) (Figure 1);
FIGURE 1 (1)
_{} _{}
_{} _{}
b) After the chord plates fastening on the prestressed structure, the presses are removed which is equivalent to load the girders with the preflexion 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 prestressed rigid steel tension rod
One or several rigid steel pretension 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 pretension rod A_{t} is chosen and then the selftension axial stress from the consolidation tension rod X_{1} 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 (selftensile force), which is determined on the girdertension 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 (selftensile 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 (selftensile force), which is determined on the girdertension 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 (selftensile 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/mm^{2}.
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 350×10 mm steel plates (Figure 9) from OL 37.2 (σ_{ac}=145 N/mm^{2}) 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
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 300×10 mm steel plates (Figure 10) from OL 37.2 (σ_{ac}=145 N/mm^{2}) 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 Lshaped bars from OL 37.2 (σ_{ac}=145
N/mm^{2}) steel , located under the girder base at a distance of e =
FIGURE 11
The length on which the girder is consolidated (the length of the
consolidation tension rod) is l_{t} =
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_{uc}^{i} 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 Lshaped bars 2L 100×100×12 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 =
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 prebending the structure before consolidation, using some prestressed 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
Jantea, C., Varlam, F., Poduri metalice. Alcatuire si calcul. , Editura Venus, Iasi, 1996.
Műhlbacher, R., Preumont, A., Poduri metalice. Probleme special., Editura I.P. Iasi, 1981.
Serbescu, C., Műhlbacher, R., Amariei, C., Pescaru, V., Probleme special in constructii metalice,
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