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+

+

+//example 8.14

+//check stability

+//calculate stresses at  toe and heel

+clc;funcprot(0);

+//given

+c=1;

+H=10;             //heigth of dam

+hw=10;            //heigth of water in reservior

+wb=8.25;          //bottom width

+Bt=1;             //top width

+Hs1=0.1;          //slope on upstream side

+gamma_w=9.81;     //unit weigth of water

+gamma_m=22.4;     //unit weigth of masonary

+f=1400;           //permissible shear stress at joint

+miu=0.75;         //coefficient of friction

+fi=atan(0.625);

+theta=atan(0.1);

+

+W1=Bt*H*gamma_m;

+W2=H*H*Hs1*gamma_m/2;

+W3=H*6.25*gamma_m/2;

+W4=hw*gamma_w*H*Hs1/2;

+P=gamma_w*hw^2/2;

+U=wb*gamma_w*hw*c/2;

+SumV=W1+W2+W3+W4-U;

+L3=2*(wb-(Hs1*H)-Bt)/3;

+L1=(wb-(Hs1*H)-Bt)+Bt/2;

+L2=(wb-(Hs1*H)-Bt)+Bt+(Hs1*H/3);

+L4=(wb-(Hs1*H)-Bt)+Bt+(2*Hs1*H/3);

+L5=2*wb/3;L6=hw/3;

+M1=W1*L1;M2=W2*L2;M3=W3*L3;M4=W4*L4;

+M5=U*L5;M6=P*L6;

+SumM=M1+M2+M3+M4-M5-M6;

+Mplus=M1+M2+M3+M4;

+Mminus=M5+M6;

+FOS=miu*SumV/P;

+SFF=(miu*SumV+wb*1400)/P;

+FOO=Mplus/Mminus;

+FOS=round(FOS*100)/100;

+SFF=round(SFF*10)/10;

+FOO=round(FOO*100)/100;

+mprintf("Factor of safety against sliding=%f. >1 ",FOS);

+mprintf("\nShear friction factor=%f.",SFF);

+mprintf("\nFactor of safety against overturning=%f. <1.5",FOO);

+mprintf("\nDam is unsafe against overturning");

+

+x=SumM/SumV;

+e=wb/2-x;

+p=hw*gamma_w;

+pnt=(SumV/wb)*(1+(6*e/wb));      //calculation is done wrong in book;value of b is not taken correctly

+pnh=(SumV/wb)*(1-(6*e/wb));

+sigmat=pnt*sec(fi)^2;

+sigmah=pnh*sec(theta)^2-p*tan(theta)^2;

+taut=pnt*tan(fi);

+tauh=-(pnh-p)*tan(theta);

+pnt=round(pnt*10)/10;

+pnh=round(pnh*10)/10;

+sigmat=round(sigmat*10)/10;

+sigmah=round(sigmah*10)/10;

+taut=round(taut*10)/10;

+tauh=round(tauh*10)/10;

+mprintf("\n\nNormal stress at toe=%f kN/square.m.",pnt);

+mprintf("\nNormal stress at heel=%f kN/square.m.",pnh);

+mprintf("\nPrincipal stress at toe=%f kN/square.m.",sigmat);

+mprintf("\nPrincipal stress at heel=%f kN/square.m.",sigmah);

+mprintf("\nShear stress at toe=%f kN/square.m.",taut);

+mprintf("\nShear stress at heel=%f kN/square.m.",tauh);