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//Strength Of Material By G.H.Ryder
//Chapter 19
//Example 1
//To Find Maximum stress at the Fatigue limit for repeated stress conditions, according to Gerber's law and Goodman's Law
clc();
//Initialization of Variables
SigmaU=600; //Ultimate tension strength, Unit in N/mm^2
El=180;//Endurance limit under reversed stress, Unit in N/mm^2
//Computations
// Under Reversed Stress
M=0; //B.M for reversed stress=0, Unit in K
Sigma=El; //Unit in Unit in N/mm^2
R=2*Sigma; //Stress Range, N/mm^2
n=SigmaU/R; //By Gerber's Formula
//Under Repeated stress
//R=Sigma
//M=Sigma/2
//Sigma=(SigmaU/n)*(1-M^2/SigmaU^2)
//From Gerber's Law
//Solving for quadatic in Sigma
a=1, b=4*SigmaU*n,c=-4*SigmaU^2;
Sigma=(-b+sqrt(b^2-4*c*a))/(2*a); //The answer vary due to round off error
//Result1
printf("The maximum stress at fatigue limit for repeated stress condition is :\n\t")
printf("%.0f N/mm^2 According to Gerbers Law\n\t",Sigma) //The answer vary due to round off error
//According to Goodman's Law
Sigma=(SigmaU/n)/(1+1/(2*n)); //The answer vary due to round off error
//Result2
printf("%.0f N/mm^2 According to Goodmans Law",Sigma)
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