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//Strength Of Material By G.H.Ryder
//Chapter 1
//Example 10
//(a) To Calculate exiting stress in steel
//(b)To Calculate final stress in steel in steel if additional end trust is applied
clc();
//Initialization of variables
Ds=18; //Diameter of steel rod, Unit in mm
Dc=39; //Outside diameter of copper sleeve, Unit i mm
dc=24;//Inside diameter of copper sleeve, Unit in mm
EsbyEc=2;//Ratio of Young's modulus of steel to young's of copper
d=1.5//depth of copper removed, Unit in mm
//Computations
SigmaS1=10;//Tension stress set up in steel, Unit in N/mm^2
As=(%pi/4)*Ds^2; //Cross section Area of steel rod, Unit in mm^2
Ac=(%pi/4)*(Dc^2-dc^2); //Cross section Area of copper sleeve, Unit in mm^2
Acr=(%pi/4)*((Dc-2*d)^2-dc^2); //Area of reduce sectoin of copper, Unit in mm^2
SigmaC1=(As/Ac)*SigmaS1; //Stress set up in copper tube, Unit in N/mm^2
//(a)When tube reduced in area for half it's length
//Let SigmaC2 be stress in reduced secton in copper & SigmaCdash in the reminder
//Let SigmaS2 be stress in rod
//Equilibrium equation: Load on tube=Load on Rod
//SigmaC2*Acr=SigmaC2dash*Ac=SigmaS2*As
//SigmaC2=(As/Acr)*SigmaS2......(i)
//SigmaC2dash=(As/Ac)*SigmaC2.....(ii)
//Compatibility Equation: Reduction in lenght of rod=Reduction in length of tube
//(SigmaS1-SigmaS2)*l/Es=(SigmaC2-SigmaC1)*l/(2*Ec) + (SigmaC3dash-SigmaC1)*l/(2*Ec)
//Solving Equilibrium Equations and compatibility equation
SigmaS2=(SigmaS1+EsbyEc*SigmaC1)/(1+As*EsbyEc/(2*Acr)+As*EsbyEc/(2*Ac)); //Unit in N/mm^2 The answer vary due to round off error
//Result (a)
printf("The exiting stress in steel, SigmaS2= %.1fN/mm^2\n",SigmaS2)
//(b)An additonal end thrust of 5000N is applied
P=5000;//Additonal end thrust, Unit in N
//Let SigmaS3 And SigmaC3 be stresses in reduce section of steel and copper respectively
//Let SigmaC3dash be stress in remainder section of copper
//Equlibrium Equation:
//P=SigmaC3*Acr-SigmaS3*As
//SigmaC3=P/Acr+(As/Acr)*SigmaS3............(iii)
//SigmaC3dash=P/Ac+(As/Ac)*SigmaS3............(iv)
SigmaS3=(SigmaS1+EsbyEc*SigmaC1-(EsbyEc/2)*(P/Acr+P/Ac))/(1+EsbyEc*As/(2*Acr)+EsbyEc*As/(2*Ac)); //Unit in N/mm^2, The answer vary due to round off error
//Result (b)
printf("Final Stress in Steel,SigmaS3=%.1f N/mm^2",SigmaS3)
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