analysis of existing bridge for fatigue life · the following classes of live loads as per irc are:...

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International Journal of Civil Engineering and Technology (IJCIET)

Volume 8, Issue 12, December 2017, pp. 1056–1076, Article ID: IJCIET_08_12_114

Available online at http://http://www.iaeme.com/ijciet/issues.asp?JType=IJCIET&VType=8&IType=12

ISSN Print: 0976-6308 and ISSN Online: 0976-6316

© IAEME Publication Scopus Indexed

ANALYSIS OF EXISTING BRIDGE FOR

FATIGUE LIFE

Vijayashree M

Assistant Professor, Department of Civil Engineering,

Sri Venkateshwara College of Engineering, Bengaluru, India

Shwetha Shetty M R



Anil Kumar M S



Santhosh N


Sambhram Institute of Technology, Karnataka, India

ABSTRACT

Indian road congress (IRC) recommends a design procedure, prescribed in IRC 21

for design of bridges for flexure. The procedure takes a “Hypothetical vehicles” to be

considered across the bridge for analysis. However in real situation, the vehicles

which move on the bridge are quite different from the hypothetical vehicle considered

in IRC. Hence, this procedure does not reflect the realistic scenario. It is felt that the

effect of movement of real vehicles has to be examined. The bridge when designed

only for flexure may be subjected to premature failure as the concept of fatigue is not

accounted which is an important parameter to be analysed for estimating life of

structure. Considering “Real vehicles” for analysis purpose makes more sense.

“Moving load analysis” conducted to determine the design bending moment will yield

more realistic and reliable data. Hence fatigue analysis is carried out by considering

real vehicles obtained from traffic survey and its implicit factor was found.

Therefore in this work one of the existing bridges have been evaluated for fatigue

life using finite element package as per Indian standard codes.

Key words: cyclic loading, C Program, fatigue, Indian road congress, implicit factor,

load cycles, moving load analysis, rain flow counting, SAP 2000, stress range.

Cite this Article: Vijayashree M, Shwetha Shetty M R, Anil Kumar M S and

Santhosh N, Analysis of Existing Bridge for Fatigue Life. International Journal of

Civil Engineering and Technology, 8(12), 2017, pp. 1056-1076.

http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=8&IType=12

Analysis of Existing Bridge for Fatigue Life


1. INTRODUCTION

Bridge symbolizes the ideas and aspirations of humanity. They are designed differ in the way

they support loads. These loads include the weight of the bridges themselves, the weight of

the material used to build the bridges, and the weight and stresses of the vehicles crossing

them. In flexural analysis for short span bridges or culverts, main loads to be considered are

dead load, live load and impact effect of live loads. For design purpose hypothetical vehicles

as prescribed by IRC is used.

The following classes of live loads as per IRC are:

IRC class AA loading

IRC class A loading

IRC class B loading

1.1. Fatigue

The word „fatigue‟ originated from the Latin expression „fatigue‟ which means „to tire‟. The

phenomenon of fatigue refers to the behaviour of structures under the action of repeated

application of loads. It is a progressive, internal and permanent structural change in the

material. At the beginning of the loading the propagation of the microcracks is rather slow

and as loading continues the micro-cracks will proceed, propagate and lead to macro-cracks,

which may grow further. The macro-cracks determine the remaining fatigue life caused by

stress until failure occurs.

1.2. Different Approaches to Fatigue Analysis

According to the definition of the fatigue life, the approaches for fatigue analysis can be

classified into

The crack propagation method or Fracture Mechanics approach.

The strain-life method and

The stress-life method or S-N curve approach:

The Stress Life, S-N method was the first approach used in attempt to understand and

quantify fatigue. It was the standard fatigue design method for almost 100 years. The S-N

approach is still widely used in design applications.

In order to obtain the curve, each of the tested specimens is exposed to a cyclic loading

with constant amplitude. Then the number of cycles until failure in the specimen is observed.

The logarithm of the number of load cycles to failure, N, at a specific maximum stress level,

σmax is plotted in a diagram. One such curve is valid for a constant ratio between maximum

and minimum stress. To obtain statistically reasonable information for each curve, it is

necessary to test several specimens at each different numbers of cycles to failure.

During the propagation portion of fatigue, damage can be related to crack length. Methods

have been developed which can relate loading sequence to crack extension. The important

point is that during propagation, damage can be related to an observable and measurable

phenomenon. This has been used for a great advantage in the aerospace industry, where

regular inspections are incorporated into the design of damage tolerant structures.

From IRC-58 2011

Vijayashree M, Shwetha Shetty M R, Anil Kumar M S and Santhosh N


Where SR is stress ratio, N = number of cycles to failure.

1.2.1. Linear damage rule

The linear damage rule was first proposed by Palmgren in 1924 and was further developed by

Miner in 1945.Today,this method is commonly known as Miner‟s Rule. The following

terminology will be used in the discussion

cycle ratio =n/N

Where n is number of cycles at stress level S

N is the fatigue life in cycle at stress level S

The damage fraction D is defined as the fraction of life used up by an event or a series of

events failure in any of the cumulative damage theories is assumed to occur when the

summation of damage fractions equals 1 or ∑Di ≥1

The linear damage rule states that the damage fraction Di, at stress level Si is equal to the

cycle ratio

. For example, the damage fraction D, due to one cycle of loading is

. In

other words, the application of one cycle of loading consumes

of the fatigue life. The

failure criterion for variable amplitude loading can now be stated as ∑

≥ 1

n =

Here Sr-stress level

m – Empirical constant assumed as 3 for concrete.

1.2.2. Load Cycles

A load cycle is a closed loop in “load space”. For harmonic loading, the load cycles starts

from a certain load magnitude, moves through a max-value and a min-value back to the start

magnitude (or the other way around).The load cycle is then completely defined by the

amplitude and mid value.

Figure 1 Harmonic cycle Figure 2 Non harmonic cycle

0

1

2

3

0 20 40 60

stre

ss in

Mp

a

position of load head in meters



The problem in identifying a load cycle comes when we are not dealing with harmonic

loadpaths. Since the stress variations obtained is of variable amplitudes and the effect of this

is important in fatigue analysis we adopt rainflow counting method.

1.2.3. Cycle Counting

It is necessary to reduce the complex history into a number of events which can be compared

which can be compared to the available constant amplitude test data. This process of reducing

a complex load history into a number of constant amplitude events involves what is termed as

cycle counting.

Counting methods have initially been developed for the study of fatigue damage generated

in aeronautical structures. Since different results have been obtained from different methods,

errors could be taken in the calculations for some of them. Level crossing counting, peak

counting, simple range counting and rain flow counting are the methods which are using

stress or deformation ranges. One of the preferred methods is the rain flow counting method.

The origin of the name of rain flow counting method which is called „Pagoda Roof

Method‟ can be explained as that the time axis is vertical and the random stress S(t) represents

a series of roofs on which waterfalls.

1.2.4. Rain flow Counting

The first step in implementing this procedure is to draw the strain-time history so that the time

is oriented vertically, with increasing time downward. One could now imagine that the strain

history forms a number of “Pogada roofs”. Cycles are then defined by the manner in which

rain is allowed to “drip” or “fall” down the roofs (This is previously mentioned analogy used

by Matsuishi and Endo, from which the rainflow method of cycle counting received its name).

A number of rules are imposed on the dripping rain so as to identify closed hysteresis loops.

The rules specifying the manner in which rain falls are as follows:

To eliminate the counting of half cycles, the strain time history is drawn so as to begin and

end at the strain value of greatest magnitude.

A flow of rain begun at each strain reversal in the history and is allowed to continue to flow

unless:

o The rain began at a local maximum point (peak) and falls opposite a local maximum

point greater than that from which it came.

o The rain began at a local minimum point (valley) and falls opposite to local minimum

point greater (in magnitude) than that from which it came.

o It encounters a previous rainflow.

Figure 3 Example to show rainflow counting



As shown in the “Fig 3”, the given strain –time history begins and ends at the strain value

of greatest magnitude (pointA). Rainflow is now initiated at each reversal in the strain history.

A. Rainflow from point A over points B and D and continues to the end of the history since

none of the conditions for stopping rainflow are satisfied.

B. Rainflow from point B over point C and stops opposite point D, since both B and D are

local maximums and the magnitude of D is greater than B(rule 2a)

C. Rainflow from point C and must stop upon meeting the rainflow from point A (rule 2c)

D. Rainflows from point D over points E and G, continues to the end of the history since none

of the conditions for stopping rainflow are satisfied.

E. Rainflows from point E over point F and stops opposite point G, since both E and G are

local minimums and the magnitude of G is greater than E(rule2b)

F. Rainflows from point F and must stops upon meeting the flow from point D(rule2c)

G. Rainflows from point G over point H and stops opposite point A, since both G and A are

local minimums and the magnitude of A is greater than G(rule2b)

H. Rainflows from point H and must stop upon meeting the rainflow from point D(rule2c)

Having completed the above, we are now able to combine events to form completed

cycles. In these example events A-D and D-A are combined to form a full cycle. Event B-C

combines with event C-B (of strain range C-D) to form an additional cycle. Similarly, cycles

are formed at E-F and G-H.

2. CASE STUDY ON A BRIDGE ON NH 169-A ACROSS SWARNA

RIVER IN SHIVAPURA

A Bridge on NH 169-A across Swarna River in Shivapura - Thirthahalli Malpe section and

for the chosen bridge fatigue behavior is studied using S-N approach and life to failure is

determined.

2.1. Objectives

To obtain the maximum bending moment and stresses that bridge would suffer from the

moving load analysis for different composition of traffic using SAP2000.

To find out the fatigue life of the existing reinforced concrete bridge under moving load.

To find out the uncertainty of the bridges by comparing the fatigue life.

To develop C Program to determine the maximum bending moment and stresses that bridge

would suffer from the moving load analysis for different composition of traffic.

To compare variations of the stresses found from C-program and from SAP2000.

To find out the implicit factors by comparing the bending moment at mid span for real

vehicles and hypothetic vehicles as prescribed in IRC for different spans.



2.2. Data Collection

2.2.1. Bridge Data Collection

BRIDGE LOCATION SHIVAPURA ACROSS SWARNA RIVER ON NH-169A

THIRTHAHALLI MALPE SECTION

TYPE OF BRIDGE RC T-BEAM GIRDER

SPAN OF BRIDGE 100m

DISTANCE BETWEEN PIERS 20m

Figure 4 Plan of bridge location

Figure 5 Cross section of deck slab

Geometric properties of the cross-section are;

Moment of inertia (Ixx) = 2.293×1012

mm4

Section modulus (Z) = 2.00 ×109 mm

3

2.2.2. Traffic Data Collection

A definite knowledge of the volume and composition of traffic is essential for fatigue

analysis. The information can be obtained by periodic traffic census and sample surveys,

which are required to be judiciously conducted at periodic trends on many roads.

Traffic census was obtained from Ministry of Surface Transport, Government of India

from 22-07-2016 to 28-07-2016 for 24 hours between Theerthahalli–Udupi on National

Highway 169 A. Following is the list of vehicles that had been observed during traffic

counting.



Table 1 List of Vehicles That Had Been Observed During the Traffic Counting

SL NO VEHICLE TYPE NUMBER(PCU)

1 Cars/ Jeeps/ Taxies Van/ Three Wheelers (Auto Rickshaw) 4170

2 Two Wheeler (motor Cycle / Scooter Etc...) 2120

3 LCV (Light Commercial vehicles eg. Mini Truck) 1419

4 Bus 1590

5 Two Axle Trax/Tanker 1197

6 Multi Axle Truck/Truck Trailer/Tanker 652.5

7 Agricultural Tractor / with Trailer 49.5

8 Cycle/Cycle Rickshaw/Other Human Powered 45

9 Bullock Cart / Horse Cart/Other Animal Powered 0

10 Others (Specify) 0

TOTAL 11243

As per IRC: SP: 72 – 2007, The large number of cars, two wheelers and light commercial

vehicles are of little consequence and only the motorized commercial vehicles of gross laden

weight of 3 tones and above (i.e. BS, 2AT and MAT) are to be considered for computation of

design traffic. The details of the vehicles considered along with its specification are tabulated

in “Table 2”.

Table 2 Real Vehicles Considered For the Case Study

Vehicle type BUS (BS) 2AT MAT

vehicle name LPO 1618 LPK 1613 LPK 2518

Wheel base 6.3 m 3.58 m 3.88 m & 4.88 m

Total length of vehicle 12 m 6.365 m 7.08 m

Width of vehicle 2.6 m 2.115 m 2.44 m

Front axle load-FAW (unloaded) 14.4 kN 16 kN 16 kN

Rear axle load-RAW (unloaded) 34 kN 32.1 kN 41.8 kN

Max permissible FAW 54 kN 60 kN 60 kN

Max permissible RAW 108 kN 102 kN 190 kN

Figure 6 LPO 1618 Figure 7 LPK 2518 Figure 8 LPK 1613

2.3. Moving Load Analysis for the Collected Data

In practical situations, live loads such as vehicular loads act on bridges. “The loads whose

position changes with respect to time are called moving load”. By virtue of its motion, such

loads generally induce a dynamic response in the structure. The loads due to the self-weight

of the bridge act at specified points while rolling loads on an account of vehicle passing over

the bridge act at critical points, producing maximum effects.

In the moving loads, when a system of loading crosses a beam, the Shear Force (negative

as well as positive) and Bending Moments at any section of the beam varies as the system of

loads move from one end of the beam to the other end.



2.3.1. Assumption for Analysis

Critical section is mid span section. The mid span section is assumed to suffer maximum BM

which is usually true.

The slab is simply supported.

Concrete suffers fatigue failure prior to steel.

For the traffic data obtained, following assumptions are made;

The position of the vehicle in lateral direction is not considered.

The load train moving on one lane will exactly occur on the other lane at the same time.

Impact factor = 25 %

The train of loads moves from left to right.

High Speed- 50 Kmph; Low Speed- 25 Kmph

2.3.2. Vehicle Combinations Considered

L - LOADED

UL - UNLOADED

MAT - MULTIAXLED TRUCKS

2AT – TWO AXLED TRUCKS

BS – BUS

Table 3 Vehicles combinations Considered For the Case Study

Vehicle combination high low Vehicle combination high low

LBS+ULBS Case1 Case2 LMAT+ULMAT Case11 Case12

L2AT+UL2AT Case3 Case4 LBS+ULMAT Case13 Case14

LBS+UL2AT Case5 Case6 LMAT+UL2AT Case15 Case16

ULBS+L2AT Case7 Case8 ULBS+LMAT Case17 Case18

L2AT+LBS Case9 Case10 L2AT+ULMAT Case19 Case20

“Table3” shows vehicle combinations and are further considered for two types of

movements:

Scenario 1 high – Fast moving vehicles – 50Kmph vehicle speed (Clear spacing between

vehicles is 2.5 m).

Scenario 2 low– Slow moving vehicles - 25Kmph vehicle speed (Clear spacing between

vehicles is 1.5m)

2.3.3. Vehicle Combinations with Loading Pattern

CASE 1: LBS+ULBS (high) CASE 2: LBS+ULBS (low)



CASE 3: L2AT+UL2AT (high) CASE 4: L2AT+UL2AT (low)

CASE 5: LBS+UL2AT (high) CASE 6: LBS+UL2AT (low)

CASE 7: ULBS+L2AT (high) CASE 8: ULBS+L2AT (low)

CASE 9: L2AT+LBS (high) CASE 10: L2AT+LBS (low)

CASE 11: LMAT+ULMAT (high) CASE 12: LMAT+ULMAT (low)

CASE 13: LBS+ULMAT (high) CASE 14: LBS+ULMAT (low)



CASE 15: LMAT+UL2AT (high) CASE 16: LMAT+UL2AT (low)

CASE 17: ULBS+LMAT (high) CASE 18: ULBS+LMAT (low)

CASE 19: L2AT+ULMAT (high) CASE 20: L2AT+ULMAT (low)

2.4. Moving Load Analysis using SAP 2000

Bridge superstructure was modelled in SAP 2000 v-14 which is shown in the “figure 9”. It

consists of three interior girders and two exterior girders. The total width of bridge is 12900

mm which includes crash barrier and foot path. The bridge is provided with two lanes of 3.5

m each.

Figure 9 Bridge Superstructure

2.4.1. Results of Moving Load Analysis

The vehicle combination is defined here on bridge is LBS+ULBS with speed 50 Kmph. This

combination is defined to study Bending Moment and Stress distribution variation on the

entire bridge section. In the moving load analysis, we know that Bending Moment and the

stresses are higher under the load. In the “figure10” the bending moment variation along the



bridge section which are obtained from SAP-2000 are shown. From those figures, we can

conclude that SAP-2000 is valid software and can be used for present study.

Moving load analysis is thus done for two types of vehicle movements (fast moving

vehicles and slow moving vehicles). From the obtained bending moment stresses are found

from bending moment equation and are represented graphically in below.

Following are the bending moment diagrams obtained from moving load analysis for the

Case1: LBS+ULBS

Figure 10 Bending moment diagrams obtained from moving load analysis for the Case1: LBS+ULBS

Above graphs provide the details of stress (MPa) vs position of wheel from left support

(m).



Above graphs provide the details of stress (MPa) v/s position of wheel from left support

(m).

Above graphs provide the details of stress (MPa) vs position of wheel from left support

(m).



All the graphs provide the details of stress (MPa) vs position of wheel from left support

(m).Stress values for different vehicle combination which are taken from the graph are shown

in “table 4”.Since the graph follows harmonic loading, cycle is counted as 1.

Table 4 Maximum stress and Cycle obtained for different vehicle combination

Case Vehicle Combinations Speed Cycle Sr Max Mpa

Case 1 LBS+ULBS high 1 0.205

Case 2 LBS+ULBS low 1 0.204

Case 3 L2AT+UL2AT high 1 0.269

Case 4 L2AT+UL2AT low 1 0.266

Case 5 LBS+UL2AT high 1 0.176

Case 6 LBS+UL2AT low 1 0.206

Case 7 ULBS+L2AT high 1 0.21

Case 8 ULBS+L2AT low 1 0.2488

Case 9 L2AT+LBS high 1 0.281

Case 10 L2AT+LBS low 1 0.3125

Case 11 LMAT+ULMAT high 1 0.533

Case 12 LMAT+ULMAT low 1 0.5475

Case 13 LBS+ULMAT high 1 0.186

Case 14 LBS+ULMAT low 1 0.2174

Case 15 LMAT+UL2AT high 1 0.603

Case 16 LMAT+UL2AT low 1 0.524

Case 17 ULBS+LMAT high 1 0.625

Case 18 ULBS+LMAT low 1 0.627

Case19 L2AT+ULMAT high 1 0.2475

Case 20 L2AT+ULMAT low 1 0.2568

2.4.2. Fatigue life calculations (as per the procedure given in the IRC 58)-“equation1”

Considering no growth in traffic:

Let us consider loading case 1: LBS+ULBS

The maximum stress obtained from table; for case 1 is 0.205MPa.

The minimum stress obtained from table; for case 1 is 0 MPa.

= 1 + ∑[SrSr

maxmin

]m

Here, Sr- Stress level; m - Empirical constant assumed as 3 for concrete.

Therefore,

n =1 + [0.2050]3

n= 1.00 cycles

n /year = n*365

= 365 cycles

From IRC: 58 - 2011



N=unlimited for SR <0.45

N =[

4.4 577

]3.268 When 0.45<=SR<=0.55

SR−0.43

Log10 N =

0.9718−SR

For SR >0.55

0.0828

Where, SR is stress ratio, Nf = Number of cycles to failure.

Here SR =stress caused at maximum load

modulus of rupture of concerte= 0.7*√fck (Assuming fck= 30 MPa) = 3.83 MPa

S R= 0.205/ 3.83= 0.053

Since SR<0.45 therefore assume Nf =2×106

Cumulative damage= ∑ Nfn

Cumulative damage = [20×365

2X10^6] = 0.00365

Life to failure= 273.9726 years.

Similar calculations are carried out for other cases and tabulated as shown in “table5”

Table 5 Two Vehicle Combinations without Traffic Growth

Case Vehicle

Combinations Speed

Cycl

e

Sr

Max

Mpa

n

n/year

(cycles

)

SR

Cum.

Dama

ge

Life

to

failu

re

Case 1 LBS+ULBS high 1 0.205 1 365 0.053

0.0036

5

274

Case 2 LBS+ULBS low 1 0.204 1 365 0.0532

Case 3 L2AT+UL2AT high 1 0.269 1 365 0.07

Case 4 L2AT+UL2AT low 1 0.266 1 365 0.069

Case 5 LBS+UL2AT high 1 0.176 1 365 0.046

Case 6 LBS+UL2AT low 1 0.206 1 365 0.054

Case 7 ULBS+L2AT high 1 0.21 1 365 0.055

Case 8 ULBS+L2AT low 1 0.2488 1 365 0.065

Case 9 L2AT+LBS high 1 0.281 1 365 0.073

Case 10 L2AT+LBS low 1 0.3125 1 365 0.082

Case 11 LMAT+ULMAT high 1 0.533 1 365 0.139

Case 12 LMAT+ULMAT low 1 0.5475 1 365 0.143

Case 13 LBS+ULMAT high 1 0.186 1 365 0.049

Case 14 LBS+ULMAT low 1 0.2174 1 365 0.057

Case 15 LMAT+UL2AT high 1 0.603 1 365 0.157

Case 16 LMAT+UL2AT low 1 0.524 1 365 0.137

Case 17 ULBS+LMAT high 1 0.625 1 365 0.163

Case 18 ULBS+LMAT low 1 0.627 1 365 0.164

Case19 L2AT+ULMAT high 1 0.2475 1 365 0.065

Case 20 L2AT+ULMAT low 1 0.2568 1 365 0.067



Table 6 Two Vehicle Combinations with 25 years of traffic Growth

Case Vehicle Combinations Speed Cycle Sr Max

Mpa n

n/year

(cycles) SR

Cum.

Damage

Life

to

failur

e

Case 1 LBS+ULBS high 13.5 0.205 1 4927.5 0.053

0.0092 109

Case 2 LBS+ULBS low 32.2 0.204 1 11763.9 0.053

Case 3 L2AT+UL2AT high 8.55 0.269 1 3122.5 0.07

Case 4 L2AT+UL2AT low 20.4 0.266 1 7456.03 0.069

Case 5 LBS+UL2AT high 22 0.176 1 8048.3 0.046

Case 6 LBS+UL2AT low 52.6 0.206 1 19216.3 0.054

Case 7 ULBS+L2AT high 22 0.21 1 8048.25 0.055

Case 8 ULBS+L2AT low 52.6 0.2488 1 19216.3 0.065

Case 9 L2AT+LBS high 22 0.281 1 8048.3 0.073

Case 10 L2AT+LBS low 52.3 0.3125 1 19246.3 0.082

Case 11 LMAT+ULMAT high 3.37 0.533 1 1230.96 0.139

Case 12 LMAT+ULMAT low 8.05 0.5475 1 2940.9 0.143

Case 13 LBS+ULMAT high 6.8 0.186 1 6157.3 0.049

Case 14 LBS+ULMAT low 40.2 0.2174 1 14702.2 0.057

Case 15 LMAT+UL2AT high 11.9 0.603 1 4354.5 0.157

Case 16 LMAT+UL2AT low 28.4 0.524 1 10397 0.137

Case 17 ULBS+LMAT high 16.8 0.625 1 6157.6 0.163

Case 18 ULBS+LMAT low 40.28 0.627 1 14702.2 0.164

Case19 L2AT+ULMAT high 11.93 0.2475 1 4354.5 0.065



Case Vehicle

Combinations Speed Cycle

Sr

Max

Mpa

n n/year

(cycles) SR

Cum.

Damage

Life

to

failur

e


0.03883

26

Case 2 LBS+ULBS low 196.5 0.204 1 71722.5 0.0532


Case 4 L2AT+UL2AT low 124.6 0.266 1 45468.96 0.069

Case 5 LBS+UL2AT high 134.5 0.176 1 49080.64 0.046

Case 6 LBS+UL2AT low 3.21 0.206 1 1171.65 0.054

Case 7 ULBS+L2AT high 134.46 0.21 1 49080.64 0.055

Case 8 ULBS+L2AT low 3.21 0.2488 1 1171.65 0.065

Case 9 L2AT+LBS high 134.46 0.281 1 49080.64 0.073

Case 10 L2AT+LBS low 3.21 0.3125 1 1171.65 0.082






Case 16 LMAT+UL2AT low 173.7 0.524 1 63397.76 0.137




Case 20 L2AT+ULMAT low 173.7 0.2568 1 63397.76 0.067

2.5. Moving load analysis using C Program

Program to carryout moving load analysis is shown below:

#include<stdio.h>

#include<conio.h>

Void main ()

{

int n,i;



float p[10],l,c,a,x[10],m[10],t=0,y;

printf("enter the span\n");

scanf("%f",&l);

printf("enter number of loads\n");

scanf("%d",&n);

for(i=0;i<n;i++)

{

printf("enter the weights of the loads %d \n",i+1); scanf("%f",&p[i]);

printf("enter the distance of load %d \n",i+1);

scanf("%f",&x[i]);

}

c=l/2;

printf("enter the increment length \n");

scanf("%f",&a);

x[0]=x[0]-a;

for(i=0;i<n;i++)

{

x[i]=x[0]-x[i];

}

y=x[n-1];

while(y<=l)

{

for(i=0;i<n;i++)

{

if(x[i]>=0 && x[i]<=c)

{

m[i]=t+((p[i]*x[i]*(l-c))/l);

t=m[i];

//printf("t 1st condition is %f\n",t);

}

else if(x[i]>c && x[i]<=l)

{

m[i]=t+((p[i]*(l-x[i])*c)/l);

t=m[i];

//printf("t 2nd condition is %f\n",t);

}

else

{

m[i]=0;

//printf("t 3rd condition is %f\n",t);

}



}

printf("bending moment at this iteration is %f\n",t);

t=0;

y=y+a;

for(i=0;i<n;i++)

{

x[i]=x[i]+a;

}

}

getch();

}

2.5.1. Fatigue Life Calculations

Considering no growth in traffic:

Let us consider loading case 1: LBS+ULBS

The maximum stress obtained from table 3.7; for case 1 is 0.396 MPa.

The minimum stress obtained from table 3.7; for case 1 is 0 MPa.

Using the same “equation 1” we get Life to failure= 273.9726 years.

Similar calculations are carried out for other cases and tabulated as shown in “table 8”

Table 8 Maximum stress and Cycle obtained for different vehicle combination from C program

Case Vehicle Combinations Speed Cycle Sr Max Mpa

Case 1 LBS+ULBS high 1 0.396

Case 2 LBS+ULBS low 1 0.369

Case 3 L2AT+UL2AT high 1 0.438

Case 4 L2AT+UL2AT low 1 0.451

Case 5 LBS+UL2AT high 1 0.391

Case 6 LBS+UL2AT low 1 0.391

Case 7 ULBS+L2AT high 1 0.396

Case 8 ULBS+L2AT low 1 0.435

Case 9 L2AT+LBS high 1 0.506

Case 10 L2AT+LBS low 1 0.556

Case 11 LMAT+ULMAT high 1 1.039

Case 12 LMAT+ULMAT low 1 1.034

Case 13 LBS+ULMAT high 1 0.364

Case 14 LBS+ULMAT low 1 0.381

Case 15 LMAT+UL2AT high 1 1.042

Case 16 LMAT+UL2AT low 1 1.036

Case 17 ULBS+LMAT high 1 1.039

Case 18 ULBS+LMAT low 1 1.044

Case19 L2AT+ULMAT high 1 0.448

Case 20 L2AT+ULMAT low 1 0.474



Table 9 Two Vehicle Combinations without Traffic Growth

Case Vehicle


Sr Max

Mpa n

n/year

(cycles) SR

Cum.

Damage

Life

to

failur

e

Case 1 LBS+ULBS high 1 0.396 1 365 0.1034

0.00365 274

Case 2 LBS+ULBS low 1 0.369 1 365 0.0963

Case 3 L2AT+UL2AT high 1 0.438 1 365 0.1144

Case 4 L2AT+UL2AT low 1 0.451 1 365 0.1178

Case 5 LBS+UL2AT high 1 0.391 1 365 0.1021

Case 6 LBS+UL2AT low 1 0.391 1 365 0.1021

Case 7 ULBS+L2AT high 1 0.396 1 365 0.1034

Case 8 ULBS+L2AT low 1 0.435 1 365 0.1136

Case 9 L2AT+LBS high 1 0.506 1 365 0.1321

Case 10 L2AT+LBS low 1 0.556 1 365 0.1452

Case 11 LMAT+ULMAT high 1 1.039 1 365 0.2713

Case 12 LMAT+ULMAT low 1 1.034 1 365 0.27

Case 13 LBS+ULMAT high 1 0.364 1 365 0.095

Case 14 LBS+ULMAT low 1 0.381 1 365 0.0995

Case 15 LMAT+UL2AT high 1 1.042 1 365 0.2721

Case 16 LMAT+UL2AT low 1 1.036 1 365 0.2705

Case 17 ULBS+LMAT high 1 1.039 1 365 0.2713

Case 18 ULBS+LMAT low 1 1.044 1 365 0.2726

Case19 L2AT+ULMAT high 1 0.448 1 365 0.117



Case Vehicle


Sr Max

Mpa

n n/year

(cycles)

SR Cum.

Damag

e

Life

to

failur

e


0.0092

109

Case 2 LBS+ULBS low 32.2 0.204 1 11763.9 0.0963


Case 4 L2AT+UL2AT low 20.4 0.266 1 7456.03 0.1178

Case 5 LBS+UL2AT high 22 0.176 1 8048.3 0.1021

Case 6 LBS+UL2AT low 52.6 0.206 1 19216.3 0.1021

Case 7 ULBS+L2AT high 22 0.21 1 8048.25 0.1034

Case 8 ULBS+L2AT low 52.6 0.2488 1 19216.3 0.1136

Case 9 L2AT+LBS high 22 0.281 1 8048.3 0.1321

Case 10 L2AT+LBS low 52.3 0.3125 1 19246.3 0.1452






Case 16 LMAT+UL2AT low 28.4 0.524 1 10397 0.2705








Case Vehicle


Sr

Max

Mpa

n n/year

(cycles) SR

Cum.

Damage

Life

to

failur

e


0.03884

26

Case 2 LBS+ULBS low 196.5 0.204 1 71722.5 0.096


Case 4 L2AT+UL2AT low 124.6 0.266 1 45468.96 0.118

Case 5 LBS+UL2AT high 134.5 0.176 1 49080.64 0.102

Case 6 LBS+UL2AT low 3.21 0.206 1 1171.65 0.102

Case 7 ULBS+L2AT high 134.46 0.21 1 49080.64 0.103

Case 8 ULBS+L2AT low 3.21 0.2488 1 1171.65 0.114

Case 9 L2AT+LBS high 134.46 0.281 1 49080.64 0.132

Case 10 L2AT+LBS low 3.21 0.3125 1 1171.65 0.145






Case 16 LMAT+UL2AT low 173.7 0.524 1 63397.76 0.27




Case 20 L2AT+ULMAT low 173.7 0.2568 1 63397.76 0.124

Figure 11 C Program Input and Output



3. RESULTS AND DISCUSSIONS

The results for the case study on the Bridge on NH 169-A across Swarna River in Shivapura -

Thirthahalli Malpe section and for the chosen bridge fatigue behavior is studied using S-N

approach and life to failure is determined and also the results are compared and validated by

using SAP 2000 Software and C –program.

3.1. Fatigue Life Comparison

Table 12 Fatigue Life Comparison for no traffic growth.25years and 50years traffic growth

Fatigue life without traffic

growth

Fatigue life for 25 years traffic

growth

Fatigue life for 50 years traffic

growth

274 109 26

Figure 12 Comparison of Stress determined from SAP-2000 and C- Program

3.2. Discussions

From the “figure 12” it can be seen that the stress values determined from C-Program is more

than the stress values determined from SAP-2000

C-Program does not consider Material Properties, Section properties and other factors that

affect fatigue analysis, since SAP-2000 considers factors affecting fatigue; the stress values

determined from SAP analysis can be seen more reliable than the analysis carried out using C

program.

The maximum bending moment due to hypothetical vehicle – class AA as given in IRC 6 is

1880 KN-m and by considering real vehicle for 20 m span bridge is 1270 KN-m.

Therefore, implicit factor of safety with respect to bending moment is 1.48

4. CONCLUSIONS

Many of the bridges constructed in south interior region are not been designed for earthquake

forces and fatigue life. Therefore in this work one of the existing bridges are been evaluated

for fatigue life using finite element package as per Indian standard codes.

Bridge is selected, modelled and analysed using SAP-2000 and bending moment values has

been obtained for ten vehicle combinations.

Life to failure for bridge has been determined for present, 25 years traffic growth and 50 years

of traffic growth as 274 years, 109 years and 26 years.



The reasons for reduction in life to failure towards increase in traffic growth are mainly due to

increase in cyclic loading.

C program has been developed to carryout moving load analysis for case study and respective

stress values are determined for different vehicular combinations and obtained results is found

almost twice that of stress values determined from SAP.

The reason for variation in stress in two methods of analysis is mainly due to factors that

affect fatigue life such as material property, stress ratio, cycle to failure, section property etc.

Implicit factor of safety for case study with respect to bending moment is 1.48

REFERENCES

[1] Mohammad Reza Saberi, Bridge Fatigue Service-Life Estimation Using Operational

Strain Measurement, 10.1061/(ASCE)BE.1943-5592.0000860-2016

[2] HabeebaA, Sabeena M.V, Anjusha R, Fatigue Evaluation of Reinforced Concrete

Highway Bridge, Vol. 4, Issue 4- April 2015

[3] Dr. Raquib Ahsan ,Fatigue in Concrete Structures (2013)

[4] Patrick Fehlmannand Thomas, Experimental Investigations on the Fatigue

[5] Behavior of Concrete Bridges, IABSE Reports, Vol. 96- 2009

[6] W. Derkowski, Fatigue life of reinforced concrete beams under bending strengthened with

composite materials, Vol. 6-2006

[7] R Ranganathan, Reliability analysis and design of structures

[8] Indian Road Congress (IRC) 6:2010, Standard Specifications and Code of Practice for

Road Bridges

[9] Indian Road Congress (IRC) (2002) IRC 58, Guidelines for design of rigid pavements,

Indian Road Congress, New Delhi, India

[10] Indian Road Congress (IRC) 21-2000, Standard Specifications and Code of Practice for

Road Bridges

[11] Indian Road Congress (IRC) 9-1972 Traffic census on non-urban roads, Indian Road

Congress, New Delhi, India

[12] Satyam Kumar, Dr. Uday Krishna Ravella , Atul Kuma r Shrivastava, Dr.Midathoda Anil

and Dr. S. K. Kumar Swamy A Review on Human Cervical Fatigue Measurement

Technologies and Data Analysis Methods. International Journal of Mechanical

Engineering and Technology, 8(7), 2017, pp. 1474–1484.

[13] D. Rajesh, V. Balaji, A. Devaraj and D. Yogaraj. An Investigation on Effects of Fatigue

Load on Vibration Characteristics of Woven Fabric Glass/Carbon Hybrid Composite

Beam under Fixed-Free End Condition using Finite Element Method. International

Journal of Mechanical Engineering and Technology, 8(7), 2017, pp. 85–91

analysis of existing bridge for fatigue life · the following classes of live loads as per irc are:...

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