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
 The consolidation by enhancing the base
of the girder section with chord plates applied directly on the base of preflexion girder
 The consolidation with prestressed
rigid steel tension rod
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;
1. 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 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 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;
2. CONSOLIDATION METHODS
2.1.
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)
_{} _{}
(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).
3. 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 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 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 = 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_{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 = 50 cm results an axial force
of X = 217880 N, and the tension rod section will consist of two Lshaped bars
2L 80×80×10 with A…………
4. CONCLUSIONS
If the results obtained through the consolidation methods discussed are
analysed the following conclusions can be drawn:
1.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;
2.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.
3.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
1.
Jantea, C., Varlam, F., Poduri metalice. Alcatuire si calcul. ,
Editura Venus, Iasi, 1996.
2. 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,