ASSESSMENT OF RESIDUAL LIFE OF GIRDERS OF BRIDGE No

Ni = Theoretical number of stress cycles corresponding to
observed stress ranges from S-N curve.
i = 1,2,3 …. Upto n stress ranges
When the damage ( D) become equal to 1, the specimen fails and so the failure
occurs when D= ∑ ni/Ni. = 1
Many researchers have not been able to find good credence to this hypothesis.
The main reason is that a stress cycles causes different extent of damage
depending on its application on the material during its life. Research carried out
by ORE, under question D-128, has suggested that under assumption of normal
distribution of fatigue test data, the probability of failure by fatigue is considerably
low when the life is evaluated at two Standard deviations below 50 % probability
curve. To achieve this, the cumulative damage factor in the above equation is
taken as 0.3, where N is taken from mean S-N curve. Therefore, in our study
the criterion for fatigue failure is taken as D= ∑ ni / Ni = 0.3
4.2.2 S.N. Curve: The relationship between constant amplitude stress range
(Sre) applied to the specimen and number of cycles upto its failure (N) is called
SN Curve. Generally it is plotted on log-log scale with number of cycles in
millions on abscissa and stress range in N/mm 2 on ordinates. The slopping line
represents the finite fatigue life of the material. Mathematically SN curves are
defined in log-log form by the following equations:
Log N = Log a –M.Log Sre
Where, log a is the intercept on x-axis and M is the reciprocal of the slope of
the finite life portion of the SN curve. In normal form N is represented by the
following equation:
N = a / (Sre) m
4.2.3 Fatigue testing: Instead of using the S-N curve from the code for class
‘D’, Twelve numbers of specimen ( Six numbers each from top and web plate ) taken for
fatigue testing from the abandoned bridge No 73 girders for getting the actual fatigue
behavior of the material. The result of the fatigue testing can be used for bridge No. 75 as
the bridges are made up of similar material and are in operation on the similar times with
similar traffic. The specimens were tested for fatigue life in RDSO laboratory. The
specimen without holes were fabricated by welding end plates on either side of the
specimen as shown in fig.1. and subjected to fatigue test as per program of loading as
shown in table -2. The number of cycles at which the samples tested/failed is also shown
in the table. Sample designated as W-1 and B-1 were tested up to 10 million
cycles at the stress range 40 N/mm2 and did not fail even after completing 10
million cycles. Other samples were tested up to 2 million cycles due to some
higher load ranges and some of them failed before reaching 2 million cycles. The
higher values of load ranges are selected, so that the values of stress ranges
cover almost all the parts of the anticipated SN curve. The minimum load for
fatigue testing is taken as 30 KN for all the samples. It has been observed that
generally fatigue crack appears near the welding of end plates and propagates
8