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Lecture 16.4: Traditional Residual Life

Assessment for Bridges

OBJECTIVE/SCOPE

To demonstrate the means by which existing bridges may be assessed and, where necessary, strengthened.

PRE-REQUISITES

None.

RELATED LECTURES

Lecture 15B.2 Actions on Bridges

SUMMARY

A majority of existing steel bridges for road and rail are riveted structures built in the last century.

Many of these old bridges have been repaired or strengthened several times following damage in the World Wars or due to changes of service requirements. The safety of these bridges for modern traffic loads throughout their remaining service life needs to be assessed.

A classical method for the assessment of the remaining fatigue safety of existing railway bridges is given. This method is based on the procedure given in the Standards of the German Railways. It is noted that the S-N lines referred to in this method do not comply with the S-N lines given in Eurocode 3. Also the safety assumptions used in this method are different to those specified in Eurocode 3. The method may, however, be easily transferred into the Eurocode system. The method is illustrated by a numerical example. Similar principles apply to highway bridges.

General methods for strengthening bridges are outlined and a case study is presented.

1. INTRODUCTION

The nature of bridge behaviour is such that the structure should be subject to regular inspection and maintenance. Old steel bridges that are subjected to growing traffic density and traffic loads may need a general safety check to evaluate them to determine their residual safety and remaining service life. This may include:

• experimental determination of the stresses
• assessment of condition
• strengthening of elements
• replacement of elements
• speed reduction
• traffic reduction
• partial or total closing of the line or highway.

Methods for evaluating the remaining service life of existing structures are becoming increasingly important as the number of structures exceeding their design life is growing exponentially. This growth is related to the bridge construction boom which began over one hundred years ago. Few structures need to be replaced when they reach their design life, because the design life was not defined scientifically in the past. Most structures are able to endure fatigue loading well beyond their original design life.

The design life is that period for which a bridge is required to perform safely with an acceptable probability that it will not require repair.

Generally, little is known of previous loading, structural modifications or possible crack location in an existing bridge. Starting with simple conservative assumptions and proceedings in steps, an acceptable decision can be taken regarding the safety of the structure.

In the following a classical method for the assessment of the remaining fatigue safety of existing railway bridges is given. This method is based on the procedure given in the Standards of the German Railways.

It is noted that the S-N lines referred to in this method do not comply with the S-N lines given in Eurocode 3. Also, the safety assumptions used in this method are different to those specified in Eurocode 3. The method may, however, be easily transferred into the Eurocode system in due course.

2. GENERAL ELEMENTS

2.1 The Wöhler Curves

A first step in evaluating the remaining service life of an existing steel railway bridge is to assess their fatigue life with Wöhler curves.

Fatigue failure occurs in elements subjected to variable loads at values significantly below those that would cause failure under static conditions. The first systematic studies on fatigue were carried out by Wöhler. The expression linking the number of cycles N and the stress range Ds = smax-s_min (the algebraic difference between the two extremes of a stress cycle) can be plotted on a logarithmic scale as a straight line. The line is known as the Wöhler curve (or the S-N curve). The fatigue strength is defined by a series of Wöhler curves, each applying to a typical detail category (the designation given to a particular welded or bolted detail). These curves are obtained experimentally from a great number of tests. Generally the linear part of the Wöhler curve is defined by:

N_i = (Ds_R /Ds_i)^k . N_R (1)

or N_i = C Ds_i^k

where:

C = N_R Ds_R^k (2)

or log N_i = log (N_R Ds_R^k) - k log Ds_i (3)

where:

Ds₁, Ds₂ are individual stress ranges in a design spectrum

n_i are the number of applied repetitions of damaging stress ranges Ds_i

N_i are the number of stress range repetitions Ds₁, Ds₂.... bringing about failure, corresponding to n₁, n₂ .... repetitions of applied stress cycles.

N_R = 2 ´ 10⁶ cycles

Ds_R = fatigue strength at N_R cycles

k is the slope of the curve.

There are different forms of Wöhler curves that may be used for damage calculations:

• with unique slope (Figure 1); even low stress ranges contribute to fatigue of the material.
• with unique slope and cut-off limit (Figure 2); low stress ranges below the break point make no contribution to material fatigue.
• with two slopes (Figure 3); small stress ranges below the break point have a smaller but finite effect.

The following points should be noted:

1. The Wöhler curves are established statistically; a small number of experimental tests cannot be used to modify them.
2. For riveted structures the value of the slope is k = 5,0; for welded elements k has the value 3,75.

2.2 The Palmgren - Langer - Miner Rule

The cumulative damage induced by different loading patterns acting on a structure is given by:

S = (4)

Equation (4) can be transformed (Figure 4)

(5)

From Equation (1) for a linear part of the S-N curve

N_i = N_R Ds_R^k / Ds_i^k = C / Ds_i^k (6)

N_e = N_R Ds_R^k / Ds_e^k = C / Ds_e^k (7)

(e = equivalent)

where C is a constant value defined by N = 2 ´ 10⁶

Substituting Equations (6) and (7) into Equation (5) gives:

(8)

and finally:

S n_i Ds_i^k = n_e Ds_e^k (9)

Stress ranges can be related to the value

Ds_UIC = (max s_UIC - min s_UIC)

where s_UIC are the stresses resulting from the standard UIC loading, with appropriate allowance for dynamic effects, as discussed below.

If l = Ds_i /Ds_UIC then

S n_i Dl_i^k = n_e . l_e^k (10)

Mathematically the relation expresses the equivalence between the different areas in Figure 4.

2.3 Dynamic Coefficients for Actual Trains

The dynamic effect of a moving train is generally expressed as a percentage of the static live load. For instance the International Union of Railways (UIC) and the German Standard DS 805 [2] gives the following expression for the dynamic coefficient:

1 + r (11)

where r = a₁ r¢ + a₂ r²  r < 1 (12)

r¢ refers to an intact rail

r² takes into account the imperfections of the rail

The values a₁ and a₂ are:

The German Standard [2] gives the following definitions for the rail quality:

Quality 3 - Imperfections of 2 mm depth on 1000 mm length; usually before 1930, or when the speed v < 80 km/h

Quality 2 - Imperfections of 1 mm depth on 1000 mm length of the rail; for speed 80 < v < 140 km/h

Quality 1 - without rail imperfections; for v > 140 km/h

The values of r¢ and r² are given in Tables 1 and 2.

2.4 Dynamic Coefficient for the UIC Loading

The UIC 71 loading represents the static effect of normal rail traffic on the track, as shown in Figure 5.

Taking into account the dynamic effects resulting from the movement of vehicles at speed, the equivalent load can be calculated from the static loads, multiplied by a dynamic factor as follows:

 The values of the characteristic length L_f can be taken from Table 3.

3. MAIN STEPS FOR THE ASSESSMENT OF THE FATIGUE SAFETY OF EXISTING RAILWAY BRIDGES

According to DS 805 [2] the definition of an existing structure is one which is more than 10 years old. The main steps in evaluating the safety of existing bridges are as follows:

• The cumulative damage induced by different trains is given by the Palmgren-Langer-Miner rule of summation:

S = where (14)

• The Wöhler curve for calculating N_i has the form:

N_i = (15)

where Ds_R is the design stress range value for N_R = 2 ´ 10⁶ cycles, obtained by applying a safety coefficient

Ds_R = D /g_R (g_R = 1,65)

D is the f = 50% fatigue strength at N_R = 2 ´ 10⁶ cycles

Ds_i is the stress range value for N_i cycles

• The stress ranges are related to the value Ds_uic (maximum stress range) produced by the UIC 71 loading pattern:

Ds_uic = max s_uic - min s_uic

and  Ds_i / Ds_uic = l_i;  D / Ds_uic = l_R (16)

The following points should be noted:

1. The introduction of these values enables the ratio l_i to be tabulated:

l_i = Ds_i / Ds_uic =  [(1 + r)/f].(DM_i / DM_uic)            (17)

2. For a simply supported girder in Table 3 (Case 5) the bending moments produced by the UIC 71 loading pattern are given in Table 4.

• The Wöhler curves become:

N_i =  [l_R/l_i]^k N_R(18)

• Using the above expression and the PLM rule, the cumulative damage is:

S_p = S_i [(n_il_i^k)/(N_Rl_R^k)] = [1/N_Rl_R^k].S_i n_il_i^k  (19)

• The expression S n_i l_i^k refers to all trains which have crossed the bridge; to calculate the total damage to the structure up to the present time S_p, the stress ratio l_i is split in a sum (l_Tj is produced by the trains "j"). If N_j is the number of trains type "j" crossing the bridge in one day and T_n is the period in years throughout which these trains have crossed the bridge, the total number of trains crossing during this period is:

Z_Tm = 365 T_n S_j N_j (20)

For the evaluation of the fatigue safety of the structure it is necessary to reconsider the traffic in the past. This a difficult problem; analysing all the traffic for a certain period it is possible to typify the trains. Such train types of fatigue according to the DS 805, are given in Table 5; the corresponding values for the related damage l_Tj for each train are shown in Table 6.

• The total damage for the above mentioned period is:

S_Tm = 365/(N_Rl_R^k) . T_n S_j N_jnl_Tj^k                                     (21)

• Summing this throughout the life of the structure (T_n, with n = 1,2 ..m)

S_p =  365/(N_Rl_R^k) . S^m_n=1 T_n S_j N_jn(l_Tjn)^k                          (22)

• Clearly if S < 1 the structure or the element has sufficient safety against fatigue failure.
• The fatigue safety for the cumulative damage is given by:

g_t,p = [1/S_p]^1/k ³ 1                (23)

• The above formula has a simple explanation; the transformation can be followed in Figure 6:

[1/S_p]^1/k = [N_R l_R^k/Sn_i l_i^k]^1/k

[1/S_p]^1/k = l_R[N_R /S n_i l_i^k]^1/k

With S n_i l_i^k = N_R l_p^k

gives 1/l_p^k= N_R /S n_i l_i^k

and finally [1/S_p]^1/k = l_R/l_p ³ 1

The ratio of the two values depends on the adopted safety concept; the smaller l_p is in comparison to l_R, the greater the safety.

• Finally the main practical possibilities are:

1. Structures or elements, for which the condition

g_t^k . S_p £ 1 (24)

is satisfied and there are no cracks. These may be regarded as sufficiently safe against fatigue failure.

In the relation above g_t is a split coefficient depending on the age of the structure at the moment of calculation:

g_t = g_R,t . g_S,t (25)

g_R,t =

g_S,t = 1,15

t_g - age of the structure.

2. If:

1,0 £ g_t^k . S_p < 1,1 (26)

and no cracks are found which need immediate action, then at the next inspection special attention must be paid to these elements.

3. If:

1,1 £ g_t^k . S_p < 1,2 (27)

immediate special inspection must be ordered and repeated after 3 years; special attention must be paid to the cracks and their rate of growth.

4. When:

g_t^k . S_p ³ 1,2 (28)

immediate special inspection must be ordered and repeated every year. Other maintenance measures must be taken; special attention must be paid to the cracks.

This process is illustrated in the example on page 24.

It should be noted that it is not possible to prevent all failures, but if major collapses are to be prevented, the lessons from previous failures must be learned. Figure 7 shows a fatigue crack which appeared in a stringer of a bridge build in 1911 with a span of 75 m. This failure was caused by an imperfect rail joint.

4. STRENGTHENING OF STEEL BRIDGES

4.1 General Considerations

During service, bridges are subject to wear; in addition, the initial volume of traffic has increased, particularly over the last 50 years. Many bridges therefore require strengthening.

It is first necessary to assess the condition of the bridge, and then, if necessary, to have a scheme for strengthening. The inspection should consider:

(a) the age of the bridge and any repairs;

(b) the extent and location of any defects: cracks, local deformations, corrosion, etc.

(c) in situ data on steel grade, stress and strain at different points, etc.

The assessment should include a feasibility study to demonstrate the cost-benefit of strengthening. It must be emphasised that strengthening may extend the life of a bridge by about 20-40 years. It does not create a new bridge, and hence is only a realistic proposition if the cost is less than 40% of a replacement bridge.

4.2 Methods of Strengthening

4.2.1 Direct Strengthening

This is used to overcome local defects and involves fitting additional elements. There are two possibilities:

• Existing flush surfaces to which new elements are fitted directly (Figure 8a).
• Surfaces which require some initial preparation, e.g. by removing the heads of rivets (Figure 8b) to provide a flush face to which new elements can be fitted.

4.2.2 Indirect strengthening

In this case independent elements are inserted within the structure. There are many types. Some may allow initial prestressing forces, thereby increasing the efficiency of the reinforcement.

The principal methods of providing indirect strengthening are:

The tendons can be a simple bar or a built-up section placed at the level of tension chord; it may be prestressed and is typically used to strengthen bridges of lattice girder or truss construction (Figure 9 and Figure 10).

Prestressed cables can be used in a similar way, fitted alongside or within existing tension elements.

For the example shown in Figure 11, three cables were introduced at the centre of the lower tension chord; as a result of the prestressing force in the cables this chord became almost completely unstressed under dead load. To increase the load carrying resistance of the complete trusses, the upper chord and the lateral diagonals were also reinforced but using direct strengthening measures.

Deck bridges can be strengthened by adding a third main girder connected to the existing structure in order to increases its load carrying resistance (Figure 12).

Reinforcement by a new chord connected to that existing by a triangulated arrangement of members, effectively increasing the height of the main truss (Figure 13).

The concrete slab replaces the sleepers; this maintains the original constructional depth. The concrete slab will act as an integral part of the compression flanges of the stringers and floor beams, Figure 14.

For semi - through trusses and through trusses where the wind-bracing has been removed during electrification of the line, it may be necessary to increase the rigidity of the transverse frame. For this purpose a tendon is introduced into the cross-section (Figure 15).

4.2 The Reinforcement of the "Angel Saligny" Bridge Over the Danube

The bridge over the Danube at Cernavoda (Figure 16) was built in 1895. Since then, especially after World War II, traffic and hence live load have grown in the structure to a level which endangered its safety. As a result major strengthening was necessary. This work had to be completed without interrupting the traffic.

Many of the methods outline above were used (Figure 17).

The bottom chords were strengthened by adding a third web connected by riveted diaphragms. The stringers were replaced.

For strengthening the cross girders, a pretensioned girder was used.

For the compression diagonals direct strengthening was achieved by fitting additional plates. The tension diagonals were strengthened with tendons.

The most difficult problem was strengthening of the upper chord. It was finally decided to introduce a third chord located between the existing ones (Figure 18). In order to relieve the existing chords of the stresses produced by dead load, the third chord, representing 45% of the existing sections, was prestressed.

A total of 4.000 tonnes of steel was used. Strengthening was completed in 1967. After 25 years of subsequent use the bridge has presented no special maintenance problems.

5. CONCLUDING SUMMARY

• Bridges should be subject to regular inspection and assessment.
• Classical methods can be used to provide an indication of safety levels with regard to fatigue failure.
• If strengthening is required, a variety of techniques can be used.
• Strengthening measures may increase the service life of a bridge by 20 to 40 years. The relative cost and benefit of strengthening compared with replacing the structure by a new bridge should be carefully considered.

6. REFERENCES

[1] "Bestehende Eisenbahnbrücken. Bewertung der Tragsicherheit und konstruktive Hinweise" DS 805, Deutsche Bundesbahn Mai 1991.

7. ADDITIONAL READING

1. "Vorschrift für Eisenbahnbrücken und sonstige Ingenieurbauwerke" DS 804, Deutsche Bundesbahn, Januar 1983.
2. "Steel, Concrete and Composite Bridges" British Standard BS 5400, Part 10, 1980.
3. Smith, I.F.C., "Fatigue Design Concepts" IABSE Periodica 4/1984.
4. Eurocode 3: "Design of Steel Structures: ENV 1993-1-1: Part 1, General Rules and Rules for Buildings, CEN, 1992.

From Section 2.4, the dynamic amplification factor is given by:

 + 0,82 = 1,53

From Table 4, maximum bending moment = 537,7 kN.m

s_uic = (1,53 × 537,7 × 10⁶) / (2 × 2890 × 10³)  = 14,23 kN/cm²

Ds_R = 100 N/mm²        l_R = 1,65 × 100/142,3  = 1,16

Ds_uic = 142,3 N/mm²

The calculation of the total damage S is shown in Table 7.

S_p = {365 /(2.10⁶ × 1,16⁵)}  ´ 747 = 649 . 10^-4

g_R,t = = 1,40

g_t = 1,40 ´ 1,15 = 1,61

1,61⁵ ´ 649 ´ 10^-4 = 0,70 £ 1

Þ Safety (first case)

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