REVIEW OF FATIGUE PROVISIONS OF BS:5400 FOR
DESIGN OF RAILWAY BRIDGES
R.K. Gupta* & R.K. Goel**
ABSTRACT
bl ys[k esa Hkkjrh; jsy ds ekud bLikr iqy lafgrk rFkk ch-,l-&5400]
Hkkx&10 esa] jsyos iqyksa ds JkafUr vfHkdYi (QSfVx fMtk+bZu) gsrq]
fn;s x;s izko/kkuksa ds v/;;u dks izLrqr fd;k x;k gSA Hkkjrh; jsy ds
ekud bLikr iqy lafgrk dh dfe;ks dk mYys[k djrs gq,s ch-,l-&5400]
Hkkx&10 ds izko/kkuksa dks le>us dk iz;kl fd;k x;k gSA ;s izko/kku ,l,u- doZ (S-N curve) ij vk/kkfjr gSa rFkk yksfMaxl ds izdkj, fLFkfr;ksa, :V
th-,e-Vh- (GMT), tksM+kas (Connections) ds izdkj vkfn dks /;ku esa j[krs
gq, cuk,s x;s gSaA jsyos iqyksa ls lEcfU/kr izko/kkuksa dks bl ys[k
esa dzeokj rjhds ls izLrqr fd;k x;k gSA bu izko/kkuksa dks Hkkjrh;
jsyos ds iqyksa ds fM+tkbZu esa ykxw djus esa vkus okyh dfBukb;ksa
dh ppkZ djrs gq,s] vuqlU/kku dh vko’;drkvksa dk fu/kkZj.k fd;k x;k gSA
The paper presents a thorough study of existing provisions of
IRS Steel Bridge Code and the BS-5400, Part-10 in respect of fatigue
design of Railway Bridges.
The short comings of Indian Railway
Standard Steel Bridge Code have been highlighted and the concepts
of fatigue design have been discussed. Provisions of BS-5400, Part10 which are based on S-N curve approach are found quite elaborate,
covering different aspects like loadings, loading situations, route
GMT, class of connection etc.
The design provisions for Railway
Bridges have been discussed in this paper in a systematic manner.
1
* Executive Director/Bridges & Structures Directorate/RDSO/Lucknow,
The limitations of the study are discussed and the areas of future
research have been identified.
2
1.0
INTRODUCTION
1.1
The Code of Indian Railway Standards for Steel Bridge recommends
method to allow for the effect of fatigue in design of parts of steel bridges,
which are subjected to repeated fluctuations of stress. These fluctuations
may cause fatigue failure of members or connections at lower stresses than
those at which they would fail under static load. Such failures are primarily
due to stress concentrations introduced by the constructional details. Thus,
all the details are designed to avoid as far as possible the stress
concentrations likely to result in excessive reductions of the fatigue strength
of members or connections. Care is also taken to avoid a sudden reduction
of the section of a member or part of a member, especially where bending
occurs.
1.2
Concept of EUDL (Equivalent Uniformly Distributed Load) is used to
determine the maximum bending moment and maximum shear force for the
type of IRS loading.
The EUDL for maximum bending moment and
maximum shear force depends upon the span and the dynamic augment
increases with speed. The EUDL for maximum bending moment for different
spans, including the dynamic augment for a maximum speed of 160Kmph
are given in tabular form for IRS-MBG loading.
1.3
To allow for the effect of fatigue the allowable working stress is
determined from the Appendix ‘G’ of IRS Steel Bridge Code for wide range
of constructional details.
The code covers mild and high tensile steel
3
fabricated or connected by welding, riveting or bolting. The allowable stress
‘P’ depends on the ratio of minimum stress fmin to maximum stress fmax,
number of repetitions of stress cycle ‘N’, the method of fabrication and the
type of connection.
In determining the ratio fmin/ fmax gross area is
considered. The code classifies the constructional details into seven classes
i.e. Class A to Class G according to type of steel, type of fabrication and
connection. All the details are designed such that the stress induced under
design loads are within the allowable limits.
1.4
The allowable stresses are the principal stress at the point under
consideration.
Thus in the design of girder the combined effect of both
bending and co-existent shear stress is considered and the bridge members
are generally designed for 10 million cycles of stresses produced under the
design load.
2.0
SHORT COMINGS OF IRS APPROACH
2.1
There is no rational basis for adopting counts of 10 million number of
cycle to determine the allowable stress levels.
2.2
Fatigue is a cumulative phenomenon; this is not reflected in the above
procedure.
2.3
Stress-ratio procedure does not take into account the effect of all
stress ranges experienced by a member.
4
2.4
Material S-N curve forms the basis of all fatigue analysis and design
which is not the case with the present procedure.
3.0
PROVISIONS OF BS-5400
In order to overcome the above shortcomings of IRS approach, the
provisions of BS-5400 were scrutinized. Its provisions are based on the
concept of cumulative fatigue damage. The code concerns with the fatigue
design methodology for highway and railway bridges and takes into
consideration the various drawbacks of IRS approach. The methods of
fatigue assessment provided in the code are based on Palmgren-Miner’s
damage summation model. Fatigue life assessment is based on the S-N
curve approach wherein the number of cycles to failure is dependent only on
stress range and not on maximum stress values. For fatigue assessment of
Railway bridges the provisions and design methodology have been
described in a systematic manner. The important provisions concerned with
design of railway bridges are discussed below.
3.1
STRESS RANGE CALCULATION, σRmax
3.1.1 Cl. 6.1.1 For Welded Details
σRmax is taken as the greatest algebraic difference between principal
stresses not more than 45 degree apart in any one stress cycle. i.e. If
σmax is 9.4 kg/mm2 & σmin is (-) 2.0 kg/mm2, then σRmax would be 11.
4 kg/mm2.
5
3.1.2 Cl. 6.1.3 For Non-Welded Details
(i)
In case, stress range is entirely on compression side i.e. when
there is no stress reversal taking place, the effect of fatigue
loading may be ignored.
(ii)
In case of stress reversal
The effective stress range to be used in the fatigue
assessment
σRmax =
60% of range from zero stress to maximum compressive
stress + 100 % of range from zero stress to maximum
tensile stress
i.e. when σmax
is
(+) 9.4 kg/mm2 & σmin is (-) 2 kg/mm2 then
σRmax would be equal to 7.64 kg/mm2 (=0.6 x 9.4 + 2).
It is evident that for the same values of maximum and minimum
principal stresses, the stress range taken for fatigue analysis in
welded details is much higher as compared to corresponding values
for non-welded details.
It therefore, implies that under the same
loading conditions the welded details are more susceptible to fatigue
failure then the non-welded.
6
3.1.3 Clause 7.3.1 For Non-Consideration of Dead Load Stress in
Welded Members
In welded members the dead load stress need not be considered
whereas for non-welded members, the dead load stresses will have to be
considered in determining the effective stress range when compression
stresses occur.
3.2
Standard Live Loads Considered
3.2.1 Type RU Loading : This loading allows for all combination of vehicles
currently running or projected to run on railways in Europe including United
Kingdom and is to be adopted for the design of bridges carrying main line
railways of 1.4m gauge and above. RU loading consists of four 250 kN
concentrated loads preceded and followed by a uniformly distributed load of
80 kN/m. The arrangement of this loading is as shown in Fig.1.
80 KN/m
250
0.8m
250
1.6m
250
1.6m
250
1.6m
80 KN/m
0.8m
No limitation
No limitation
Fig.1
Type RU Loading
3.2.2 Type RL Loading : Nominal type RL loading consists of a single 200
kN concentrated load coupled with a uniformly distributed load of 50
kN/m for loaded length up to 100m. For loaded lengths in excess of
100m the distributed a nominal load shall be 50 kN/m for the first
100m and shall be reduced to 25 kN/m for lengths in excess of 100m,
7
as shown in Fig.2. Alternatively two concentrated nominal loads, one
of 300 kN and the other of 150 kN, spaced at 2.4m intervals along the
track, shall be used on deck elements where this gives a more severe
condition. These two concentrated loads shall be deemed to include
dynamic effects. RL loading is a reduced loading for use only on
passenger rapid transit for use only on passenger rapid transit railway
systems on lines where main line locomotives and rolling stock do not
operate.
200 kN
50 kN/m
25 kN/m
25 kN/m
100m
No limitation
No limitation
Fig.2
4.0
Type RL Loading
CALCULATION OF VARIOUS FACTORS
(i)
Design Life Factor, k1 = 1.0 for standard design life of 120
years for standard load spectra for a permanent railway bridge
standard loading as given in Table 2 for RU loading and Table
3 for RL loading. (It is for assumed traffic volume of 18 - 27
GMT)
8
Table 2* : Standard load spectra for RU loading
Group
number
Load proportion, kw
Range
Length,
L(m)
2
3
4
5
7
10
15
20
30
50
Heavy Traffic
1
2
3
4
5
6
7
8
Medium Traffic
1
2
3
4
5
6
7
8
Light Traffic
1
2
3
4
5
6
7
8
0.75
0.55
0.45
0.35
0.25
0.15
0.05
0.75
0.55
0.45
0.35
0.25
0.15
0.05
0.75
0.65
0.55
0.45
0.35
0.25
0.15
0.05
0.5
to
0.6
0.4
to
0.5
0.3
to
0.4
0.2
to
0.3
0.1
to
0.2
0
to
0.1
0.7
t0
0.8
0.6
to
0.7
0.5
to
0.6
0.4
to
0.5
0.3
to
0.4
0.2
to
0.3
0.1
to
0.2
0
to
0.1
217
95
27
2
7
10
6
5
0
2
5
132
53
42
44
69
24
7
10
8
0.65
0.65
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.7
0.6
t0
to
to
to
to
to
to
to
t0
to
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.8
0.7
Total number of live load cycles (nR x 106) for various loading groups and types
58
23
0
0
0
0
0
0
0
0
0
23
13
3
3.5
3
1
1
2
3
65
26
12
18
11
10
3
3
1
0
0
0
46
20
9
3
9
4
4
0
0
0
0
5
6
8
8
5
0
4
71
40
1.5
18
19
0
2
4
0
0
0
82
71
34
34
22
1.5
6
4
0
0
0
28
43
62
40
74
99
79
60
41
0
0
0
0
0
0
0
0
0
18
40
4
4
0.3
0.3
0.6
0.3
0.5
1.7
14
3
18
3
11
6
3
4
4
0
0
8
27
22
4
0.3
3
0
0
3
130
65
0
8
1
4
0
0
0
0
16
87
33
3
18
43
0.3
3
0
0
0
0
32
47
35
17
40
30
0
0
0
5
81
116
52
40
13
54
138
134
1
0
0
0
0
0
0
0
0
0
4
2
2
2
0.1
0.1
0.1
0.1
0.2
0.3
17
0.2
1
0.1
1
0.5
0.5
0.5
0.5
0
45
3
3
2
2
0.3
0.3
0.3
0.3
1
0
45
89
30
30
3
51
46
2
0
0
2
111
202
60
60
3
27
174
136
* Table No. corresponds to the one given in code.
NOTE 1- L is the base length of the point load influence line (see figure 12). For intermediate values of L, permissible stress ranges may be derived from the spectra for
the two adjacent lengths shown in the table and the value interpolated. nR values apply to one track.
NOTE 2 – The values are based on a traffic volume of 27 x 10 6 tonnes per annum.
9
Table 3* : Standard load spectra for RL loading
Group number
Load proportion, Kw
Range
Length, L(m)
2
3
4
5
7
10
15
20
30
50
1
2
3
4
5
6
0.55
0.45
0.35
0.25
0.15
0.05
0.5
0.4
0.3
0.2
0.1
0
to
to
to
to
to
to
0.6
0.5
0.4
0.3
0.2
0.1
Total number of live load cycles (nR x 106) for
various loading groups and types
9
120
189
42
0
0
1
112
68
10
170
0
0
29
75
3
74
180
0
6
110
0
2
75
0
38
65
0
0
77
1
10
56
37
0
77
1
13
0
49
30
15
1
13
0
0
50
80
0
8
6
0
0
265
1
13
0
0
0
80
* Table No. corresponds to the one given in code.
Note 1 – L is the base length of the point load influence line. For intermediate
value of L, permissible stress ranges may be derived from the spectra for the two
adjacent lengths. Shown in the table and the values interpolated. nR values apply
to one track.
Note 2 – The values are based on a traffic volume of 27 x 106 tonnes per
annum.
If design life is other than 120 years, then the value of k1 is to
be taken as lesser of the following –
1
(a)

m
120

k1 = 
 Design life in yrs. 
1

 m2
120

= 
 Design life in yrs 
10
When m = inverse slope of σr – N curve appropriate to detailed
class to be obtained from Table-8.
Table 8* : σr – N relationships and constant amplitude nonpropagation stress range values
Detail class
m
K2
σ0 (N/mm2)
W
G
F2
F
E
D
C
B
S
3.0
3.0
3.0
3.0
3.0
3.0
3.5
4.0
8.0
0.16 X 1012
0.25 X 1012
0.43 X 1012
0.63 X 1012
1.04 X 1012
1.51 X 1012
4.23 X 1013
1.01 X 1015
2.08 X 1022
25
29
35
40
47
53
78
100
82
* Table No. corresponds to the one given in code.
Note –
Values applicable to non-standard criteria may be obtained from
Appendix A.
Multiple cycle factor, k2 is to be applied when there are more
than one cycle of stress induced by the loading event.
1
=
  σ R2  m  σ R3  m  σ R4  m
m






1







 


σ 
σ 
 R1 
 R1 
  σ R1 

m = inverse slope of σr – N curve (Table-8)
σR1, σR2, σR3 -------- are stress ranges in decreasing order of
magnitude.
11
(ii)
RU loading factor, k3 depends upon the detailed class of
connection & Base length of the point load influence line.
The
relevant value are to be taken from table-4
Table 4* : Value of k3 for RU loading of Railway bridges
Detail stress
Length, L(m)
< 3.4
3.4 to 4.0
4.0 to 4.6
4.6 to 7.0
7.0 to 10.0
10.0 to 14.0
14.0 to 28.0
> 28.0
Heavy traffic
D
C
E
F
F2
G
W
Values of k3
1.00
1.00
1.09
1.09
1.23
1.22
1.37
1.36
1.53
1.56
1.71
1.75
1.92
1.95
2.19
1.95
B
S
1.01
1.13
1.30
1.46
1.62
1.62
2.03
2.03
1.14
1.28
1.46
1.65
1.65
165
1.83
1.83
Medium traffic
D
C
E
F
F2
G
W
1.09
1.23
1.37
1.53
1.71
1.92
2.19
2.46
1.09
1.22
1.36
1.56
1.75
1.95
2.18
2.18
B
S
1.13
1.30
1.46
1.62
1.81
2.03
2.03
2.03
1.28
1.46
1.46
1.65
1.83
1.83
1.83
1.83
Light traffic
D
C
E
F
F2
G
W
1.37
1.53
1.71
1.92
2.19
2.46
2.74
3.06
1.60
1.79
1.79
2.05
2.31
2.31
2.56
2.87
Note – L is the base length of the point load influence line (see Figure 12)
* Table No. corresponds to the one given in code.
(iii)
GMT factor, k4 = 1 for GMT of 18 to 27 which is the GMT assumed
in standard RU/RL load spectra. For GMT other than 18 to 27 the
values to be taken from Table – 5. It is evident that the factor
reduces with increase in GMT.
Table 5* : Values of k4 for railway bridges
Annual traffic tonnage on one track (million of tones)
42 to 27
27 to 18
18 to 12
12 to 7
7 to 5
<5
0.89
1.0
1.13
1.27
1.42
1.6
* Table No. corresponds to the one given in code.
12
B
S
1.60
1.80
1.80
2.00
2.34
2.50
2.50
2.50
1.71
1.71
1.95
2.20
2.20
2.20
2.20
(iv)
Lane factor, k5 takes into consideration the stress induced at a
detail due to two tracks. The relevant values are to be taken from
Table – 6.
(v)
RL loading factor, k6 is just as the RU loading factor k3 and the
relevant value are to be taken from Table -7. This loading factor is
to be considered in place of RU loading factor.
As already
discussed, this type of loading is not matching with any of IRS type
loading.
Table 6* : Values of k5 for railway bridges
Ratio
P1
Ratio
k5
P2
0.5
0.6
1.42
to
0.6 to
75
1.27
0.75 to
0.9
1.125
P1
P1  P2 P1
0.9
1.0
1.0
to
+
0.0 to 0.7
0.7 to 1.0
1.0
0.89
* Table No. corresponds to the one given in code.
Table 7* : Values of k6 for RL loading of railway bridges
Detail Class
Length, L(m)
<3.0
3.0 to 3.4
3.4 to 4.0
4.0 to 10.0
10.0 to 15.0
15.0 to 20.0
> 20.0
D
C
E
F
F2
G
W
Values of k6
1.23 1.28
1.34 1.37
1.43 1.49
1.57 1.62
1.77 1.79
1.98 1.99
2.08 2.05
B
S
1.35
1.45
1.55
1.68
1.90
2.00
2.09
1.65
1.71
1.80
1.91
2.10
2.10
2.10
* Table No. corresponds to the one given in code.
13
P2 Ratio
p2
P1
5.0
Discussion on k3 & k6
It is apparent that the values of k3 are ranging from 1.0 to 2.19 and
similarly
values of k6 are ranging from 1.23 to 2.08 for detailed class of
connection ‘D’ which is the appropriate classification for the type of connections
adopted on Indian Railway bridges. Both these factors increases with L which is
the base length of the point load Influence line. The standard refers to Fig. 12 to
elaborate it and makes a further reference to Fig. 9. As understood, for the road
bridges the length is to be taken from lane stress history for the road bridges as
the base length of the loop containing the largest ordinate (+ve or –ve). For an
element of the highway bridge loaded by more than one lane, L is to be
determined from the Influence line for the lane producing the largest value of
stress ordinate.
As the σT, the limiting stress range is obtained by multiplication of these
factors k1, k2, k3,….. with σ0, the fatigue strength of connection gets improved
with any increase in the values of these multiplying factors. Now, the problem is
how to determine ‘L’ values for railway bridges. For simply supported spans we
may assume ‘L’ as equal to the effective span of the bridge as the maximum
stress ordinate would be developed on full base length. This may be workable
for design of stringers and simply supported plate girder bridges, however, for
truss girder bridges where axial stress are the prime stresses, choosing
appropriate value of ‘L’ would be difficult. For IRS loading, these factors might be
quite different. However, this much is easily understood that the limiting stress
14
range or the limiting fatigue strength increases if the base length ‘L’ is more. For
simplicity, ‘L’ may be taken as the appropriate base length of the influence line
diagram for the member under consideration.
6.0
DESIGN σr- N RELATIONSHIP
6.1
Clause 11.2 of BS : 5400 The number of repetitions to failure ‘N’ of any
one stress range σr is obtained form the equation
N x r
or
m
 k2
Log 10 N  log 10 k 2  m log 10 σ r
Clause k2 & m are as given in Table – 8.
The values given in Table-8 are based on two standard deviations below
the mean line with a probability of failure of 2.3%. The probabilities of failure
associated with various numbers of standard deviations below the mean line are
given in Clause A.1 of Appendix-A of BS-5400 part-10.
6.2
Clause 11.2–Computation of no. of cycles to failures The number of
repetitions to failure ‘N’ of any one stress range σr is obtained from the equation
N  r  K2
m
or
Log10N = Log10k2 – mlog10σr
Values of k2 & m are as given in Table – 8.
6.3
Clause 11.3– Treatment of low stress cycles Number of repetitions of
each stress range σr less than σ0 should be reduced in the proportion (σr/σ0)2.
15
Where σ0 = Stress range given by equation in Clause 11.2
N = 107
i.e. 10 million cycles
6.3.1 It is further given for easy calculations that
nσ r
n

N
k2
m
n
 7
10
m 2
n n σr

N k 2 σ02

 σr

 σ0
n
10 7
m

 when σ r  σ 0

m 2
when σ r  σ 0
7.0
CALCULATION OF LIMITING STRESS RANGE, σT
7.1
First find σ0 constant amplitude non-propagating stress range for the
constructional detail, as chosen appropriately on the basis of Table – 17, this
value is to be taken from Table -8.
e.g. for Detail Class ‘D’ for riveted type of connections,
m = 3.0
k2 = 1.52 x 1012
σ0 = 53 N/mm2
7.2
The limiting stress range σT can now be calculated in accordance with
Clause 9.2.2.1 (d)
σT = k1, k2, k3, k4, k5, σ0
= k1, k2, k4, k5, k6, σ0
for RU loading
for RL loading
16
8.0
CHECK FOR DESIGN ADEQUACY:
The design adequacy of the given detail may now be checked as per
Clause 9.2.2.2 and Clause 9.2.2.3
8.1
Where σRmax (Maximum Stress Range) does not exceed σT, i.e σRmax  σT,
the detail may be considered to have a fatigue life in excess of the specified
design life.
8.2
Where σRmax is more than σT, we have following two options:
(i)
The detail may be assessed by more precise procedure given in
Clause 9.3.
(iii)
The detail may be strengthened so as to reduce σRmax or it should
be designed to a higher class.
9.0
MORE PRECISE PROCEDURE OF DAMAGE CALCULATION
9.1
General
This method involves a calculation of Miner’s summation and may be used
for any details for which the σr -N relationship is known and for any known load
for stress spectra.
9.2
Design Spectrum for Standard Loading
9.2.1
The design spectrum can be determined by the use of either table 2 for
RU loading or table 3 of RL loading (amended where appropriate in accordance
with 7.3.3). These tables indicate, for simply supported members, the equivalent
frequency of occurrence of stress ranges of varying magnitudes resulting from
17
the passage of the individual trains forming various standard traffic types, where
the stress ranges are expressed as proportions of the maximum stress range and
the load proportion, kw is the ratio of actual to standard gross weights of vehicles,
bogies or axles in a load spectrum.
Now in order to draw the standard load spectra for a particular type of
loading one has to determine the maximum stress range due to that loading and
then the histogram of number of cycles verses stress ranges of varying
magnitudes can be plotted with the help of Table 2 or Table 3 of the code for the
appropriate base length(L). This method of drawing standard load spectra is
based on the understanding of the provision given in Clause 7.3. and Appendix-E
of the code. The annual traffic tonnage for standard traffic types and the
composition of standard traffic mix are given in Table 15 and Table 16 of the
code.
Table 15*
Traffic
type
Heavy
Train
type
7
8
9
Medium
5
7
8
1
Light
1
2
3
4
5
6
Train weight, No. of trains Total
annual
tones
per annum
tonnes x 106
1120
4821
5.40
1120
7232
8.10
852
15845
13.50
Total
27.00
600
22500
13.50
1120
2411
2.70
1120
6027
6.75
1794
2257
4.05
Total
27.00
1794
752
1.35
372
14516
5.40
344
23546
8.10
172
47093
8.10
600
4500
2.70
572
2360
1.35
Total
27.00
18
tonnage,
Table 16*
Train
Type
1
2
3
4
5
6
Train weight,
tonnes
246
253
380
203
209
231
Number of trains Total annual tonnage,
per annum
tonnes x 106
11545
2.84
54032
13.67
9786
2.74
6453
1.31
26986
5.64
3463
0.80
Total
27.00
9.2.2 In the case of loading from more than one track, account should be taken
of the possibility of stress fluctuations arising from the passage of trains on not
more than two track, both separately and in combination. As an approximation,
the effects of two track loading may be obtained by dividing σR max (see 9.3.2.1)
by the coefficient k5 which can be obtained from table 6.
9.2.3 Where the approach, passage and departure of a unit uniformly distributed
load procedures more than one cycle of stress, as for instance in multi-span
longitudinal or cross members or in continuous deck slabs, all the cycles should
be taken into account.
The appropriate standard trains composing the load
spectra should be traversed across the relevant point load influence lines and the
resulting stress histories should be analyzed by the reservoir method, given in
appendix B, to derive the respective stress spectra. These should then be
combined with the appropriate annual occurrences obtained from table 15 to 16,
proportioned for the required traffic volume and multiplied by the specified design
life to produce the overall design spectrum. As an approximation, the effect of
19
the additional cycles may be obtained by dividing either σR max (see 9.3.2.1) or
σR max/k5 (see 9.3.2.2) by the coefficient k2 which should be obtained from 9.2.4.
9.3
Design Spectrum for Non-Standard Loading
9.3.1 Where the loading does not comply with 7.3.1 the appropriate train should
be traversed across the relevant point load influence lines and the resulting
stress histories should be analyzed by the rainflow method to derive the
respective stress spectra. These should then be combined with the appropriate
total occurrences in the design life of the bridge to compile the overall design
spectrum. For non-welded details the stress range should be modified as given
in clause 6.1.3.
9.3.2 In assessing an existing structure, a design spectrum may be compiled
from strain readings or traffic records obtained from continuous monitoring.
9.4
Simplification of Spectrum
Where a non-standard loading is used in accordance with 7.1 or the stress
ranges are obtained from strain gauge readings, the design spectrum should be
divided into at least 10 equal intervals of stress. All the stress ranges in any one
interval should be treated as the mean range in that interval and low stress
ranges should be treated in accordance with clause 11.3.
20
9.5
Calculation of Damage
Using the design spectrum the value of Miner’s summation n/N should be
calculated in accordance with clause 11 and it should not exceed 1.0 for the
fatigue life of the detail to be acceptable.
10.0
CONCLUSION:
The British Code (BS-5400, Part 10) addresses the problem of fatigue
design exhaustively and if provisions are based on rational.
It takes into
consideration the design parameters such as traffic density, number of lanes,
loading type, design life, multiple cycles of stress produced by loading event and
suggest a simplified approach for assessing the fatigue life of the component
being designed.
Fatigue life of the component depends on the type of
connection adopted which is also taken into consideration by choosing different
values of parameters describing the shape of the characteristic S-N curve of the
fabrication material.
11.0
LIMITATIONS AND AREA OF FURTHER RESEARCH
11.1
The simplified procedure given in the code is applicable for standard type
of loadings applicable to European conditions. For IRS type of loading the values
of loading parameters and various coefficient needs to be developed for which
further study and research is required.
11.2
For using detailed assessment procedure a standard load spectra
applicable to types of trains and traffic density found on Indian Railways needs to
be developed.
21
11.3
The characteristic S-N curves for the steel and the types of connections
adopted for design of bridges in Indian Railways needs to be developed for
proper assessment of the fatigue strength of bridge members.
12.0
ACKNOWLEDGEMENT
The author gratefully acknowledges the support provided by Executive
Director (B&S), RDSO for undertaking this study. The assistance provided by
Shri R.K. Sharma, Section Engineer,. and Smt. Suman Verma, P.A. of B&S Dte
is also thankfully acknowledged.
13.0
REFERENCES
13.1
British Standards BS 5400 : Steel, Concrete and Composite Bridges, Part
10. Code of Practice for Fatigue, British Standards Institution, 1980.
13.2
British Standards BS 5400 : Steel, Concrete and Composition Bridges,
Part 2. Specification for Loads, British Standards Institution, 1978.
13.3 IRS Code of Practice for the Design of Steel/Wrought Iron Bridges (Steel
Bridge code) Revised 1962, (with all the amendments).
13.4
IRS Bridge Rules – Revised 1964 Incorporating Correction Slip 1 to 15,
Reprinted 1986.
13.5
Loads to be considered in Railway Bridge Design, UIC Code, Leaflet No.
776-1 R 4th Edition, 1-7-94.
13.6
Statistical distribution of axle loads and stresses in railway bridges Report
No. ORE D 128/RP5, RP6 & RP7.
22