{
"cells": [
 {
		   "cell_type": "markdown",
	   "metadata": {},
	   "source": [
       "# Chapter 8: GRAVITY DAMS"
	   ]
	},
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.10: EX8_10.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"\n",
"\n",
"//example 8.10\n",
"//calculate width of base if no tension is to develop\n",
"//check the stability\n",
"clc;funcprot(0);\n",
"//given\n",
"c=1;\n",
"hw=6;              //heigth of water in reservior\n",
"Bt=1.5;            //width of top of dam\n",
"H=6;              //heigth of the dam\n",
"gamma_m=20;       //unit weigth of masonary \n",
"gamma_w=9.81;    //weigth density of water\n",
"f=1800;          //compressive strength\n",
"miu=0.6;         //coefficient of friction\n",
"\n",
"//to develop no tension e=b/6;x=b/3.\n",
"//hence on solving the relations we get\n",
"\n",
"P=poly([-39.074 2.944 1],'b','c');    //equation is written wrong in book\n",
"wb=roots(P);                          //sign of coefficient is 2.944 is not taken correctly in book\n",
"\n",
"\n",
"//roots are 4.94 and -7.89\n",
"//since negative value cannot be taken\n",
"\n",
"wb=4.94;\n",
"mprintf('Neglecting the negative value.\nWidth of base is=4.94 m.');\n",
"W1=Bt*gamma_m*H;\n",
"W2=gamma_m*H*(wb-Bt)/2;\n",
"L1=(wb-Bt)+(Bt/2);\n",
"L2=(2*(wb-Bt))/3;\n",
"M1=W1*L1,\n",
"M2=W2*L2;\n",
"U=gamma_w*H*c*wb/2;\n",
"L4=2*wb/3;\n",
"M4=U*L4;\n",
"W3=gamma_w*H^2/2;\n",
"L3=hw/3;\n",
"M3=W3*L3;\n",
"SumW=W1+W2-U;\n",
"SumM=M1+M2-M4-M3;\n",
"pn=2*SumW/wb;\n",
"pn=round(pn*10)/10;\n",
"mprintf('\nMaximum stress=%f kN/square.m.',pn);\n",
"mprintf('\nDam is safe against compression');\n",
"FOS=miu*SumW/W3;\n",
"FOS=round(FOS*100)/100;\n",
"mprintf('\nFactor of safety against sliding=%f. <1',FOS);\n",
"mprintf('\nDam is unsafe against sliding.');\n",
""
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.11: EX8_11.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"\n",
"\n",
"//example 8.11\n",
"//calculate width of base if no tension is to develop\n",
"//check the stability if uplift is neglected\n",
"clc;funcprot(0);\n",
"//given\n",
"c=1;\n",
"hw=6;              //heigth of water in reservior\n",
"Bt=1.5;            //width of top of dam\n",
"H=6;              //heigth of the dam\n",
"gamma_m=20;       //unit weigth of masonary \n",
"gamma_w=9.81;    //weigth density of water\n",
"f=1800;          //compressive strength\n",
"miu=0.6;         //coefficient of friction\n",
"\n",
"//to develop no tension e=b/6;x=b/3.\n",
"//hence on solving the relations we get\n",
"\n",
"P=poly([-19.908 1.5 1],'b','c')\n",
"wb=roots(P);\n",
"\n",
"//roots are 3.774 and -5.27\n",
"//since negative value cannot be taken\n",
"\n",
"wb=3.77;\n",
"mprintf('Neglecting the negative value.\nWidth of base is=3.77 m.');\n",
"\n",
"W1=Bt*gamma_m*H;\n",
"W2=gamma_m*H*(wb-Bt)/2;\n",
"L1=(wb-Bt)+(Bt/2);\n",
"L2=(2*(wb-Bt))/3;\n",
"M1=W1*L1,\n",
"M2=W2*L2;\n",
"W3=gamma_w*H^2/2;\n",
"L3=hw/3;\n",
"M3=W3*L3;\n",
"SumW=W1+W2;\n",
"SumM=M1+M2-M3;\n",
"pn=2*SumW/wb;\n",
"pn=round(pn*10)/10;\n",
"mprintf('\nMaximum stress=%f kN/square.m.',pn);\n",
"mprintf('\nDam is safe against compression');\n",
"\n",
"FOS=miu*SumW/W3;\n",
"FOS=round(FOS*1000)/1000;\n",
"mprintf('\nFactor of safety against sliding=%f. > 1',FOS);\n",
"mprintf('\nDam is safe against sliding.');"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.12: EX8_12.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"\n",
"\n",
"//example8.12\n",
"// calculate maximum permissible heigth of shutter so that no tension develops\n",
"clc;funcprot(0);\n",
"//given\n",
"Bt=3;            //width of top of dam\n",
"H=12;           //heigth of the dam\n",
"wb=9;           //width of base of dam\n",
"gamma_m=21;           //unit weigth of masonary\n",
"gamma_w=9.81;    //weigth density of water\n",
"\n",
"W1=Bt*gamma_m*H;\n",
"W2=gamma_m*H*(wb-Bt)/2;\n",
"\n",
"//taking moment about a point on base at 3m from toe\n",
"L1=3+Bt/2;\n",
"L2=(2*(wb-Bt)/3)-3;\n",
"M1=W1*L1,\n",
"M2=W2*L2;\n",
"M=M1+M2;\n",
"\n",
"//net moment about this point should be zero for equilibrium\n",
"s=(M*6/gamma_w)^(1/3)-12;\n",
"s=round(s*100)/100;\n",
"mprintf('maximum permissible heigth of shutter=%f m.',s);\n",
""
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.13: EX8_13.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"\n",
"\n",
"//example 8.13\n",
"//calculate hydrodynamic earthquake pressure\n",
"//moment at 50m below water surface\n",
"clc;funcprot(0);\n",
"//given\n",
"c=1;\n",
"H=100;           //heigth of dam\n",
"hw=100;          //heigth of water in reservior\n",
"FB=1;            //free board\n",
"s=0.15;          //slope of upstream face\n",
"gamma_w=9.81;    //unit weigth of water\n",
"alphah=0.1;\n",
"\n",
"theta=atan(s);\n",
"y=50;\n",
"Cm=0.735*(1-(theta*2/%pi));\n",
"Cy=(Cm/2)*((y*(2-y/hw)/hw)+(y*(2-y/hw)/hw)^0.5);\n",
"pe=Cy*alphah*gamma_w*hw;\n",
"F=0.726*pe*y;\n",
"M=0.299*pe*y^2;\n",
"pe=round(pe*1000)/1000;\n",
"F=round(F*10)/10;\n",
"M=round(M*10)/10;\n",
"mprintf('hydrodynamic earthquake pressure=%f kN/square.m\nshear=%f kN/m.\nMoment=%f kN-m/m.',pe,F,M);\n",
""
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.14: EX8_14.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"\n",
"\n",
"//example 8.14\n",
"//check stability\n",
"//calculate stresses at  toe and heel\n",
"clc;funcprot(0);\n",
"//given\n",
"c=1;\n",
"H=10;             //heigth of dam\n",
"hw=10;            //heigth of water in reservior\n",
"wb=8.25;          //bottom width\n",
"Bt=1;             //top width\n",
"Hs1=0.1;          //slope on upstream side\n",
"gamma_w=9.81;     //unit weigth of water\n",
"gamma_m=22.4;     //unit weigth of masonary\n",
"f=1400;           //permissible shear stress at joint\n",
"miu=0.75;         //coefficient of friction\n",
"fi=atan(0.625);\n",
"theta=atan(0.1);\n",
"\n",
"W1=Bt*H*gamma_m;\n",
"W2=H*H*Hs1*gamma_m/2;\n",
"W3=H*6.25*gamma_m/2;\n",
"W4=hw*gamma_w*H*Hs1/2;\n",
"P=gamma_w*hw^2/2;\n",
"U=wb*gamma_w*hw*c/2;\n",
"SumV=W1+W2+W3+W4-U;\n",
"L3=2*(wb-(Hs1*H)-Bt)/3;\n",
"L1=(wb-(Hs1*H)-Bt)+Bt/2;\n",
"L2=(wb-(Hs1*H)-Bt)+Bt+(Hs1*H/3);\n",
"L4=(wb-(Hs1*H)-Bt)+Bt+(2*Hs1*H/3);\n",
"L5=2*wb/3;L6=hw/3;\n",
"M1=W1*L1;M2=W2*L2;M3=W3*L3;M4=W4*L4;\n",
"M5=U*L5;M6=P*L6;\n",
"SumM=M1+M2+M3+M4-M5-M6;\n",
"Mplus=M1+M2+M3+M4;\n",
"Mminus=M5+M6;\n",
"FOS=miu*SumV/P;\n",
"SFF=(miu*SumV+wb*1400)/P;\n",
"FOO=Mplus/Mminus;\n",
"FOS=round(FOS*100)/100;\n",
"SFF=round(SFF*10)/10;\n",
"FOO=round(FOO*100)/100;\n",
"mprintf('Factor of safety against sliding=%f. >1 ',FOS);\n",
"mprintf('\nShear friction factor=%f.',SFF);\n",
"mprintf('\nFactor of safety against overturning=%f. <1.5',FOO);\n",
"mprintf('\nDam is unsafe against overturning');\n",
"\n",
"x=SumM/SumV;\n",
"e=wb/2-x;\n",
"p=hw*gamma_w;\n",
"pnt=(SumV/wb)*(1+(6*e/wb));      //calculation is done wrong in book;value of b is not taken correctly\n",
"pnh=(SumV/wb)*(1-(6*e/wb));\n",
"sigmat=pnt*sec(fi)^2;\n",
"sigmah=pnh*sec(theta)^2-p*tan(theta)^2;\n",
"taut=pnt*tan(fi);\n",
"tauh=-(pnh-p)*tan(theta);\n",
"pnt=round(pnt*10)/10;\n",
"pnh=round(pnh*10)/10;\n",
"sigmat=round(sigmat*10)/10;\n",
"sigmah=round(sigmah*10)/10;\n",
"taut=round(taut*10)/10;\n",
"tauh=round(tauh*10)/10;\n",
"mprintf('\n\nNormal stress at toe=%f kN/square.m.',pnt);\n",
"mprintf('\nNormal stress at heel=%f kN/square.m.',pnh);\n",
"mprintf('\nPrincipal stress at toe=%f kN/square.m.',sigmat);\n",
"mprintf('\nPrincipal stress at heel=%f kN/square.m.',sigmah);\n",
"mprintf('\nShear stress at toe=%f kN/square.m.',taut);\n",
"mprintf('\nShear stress at heel=%f kN/square.m.',tauh);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.15: EX8_15.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"\n",
"\n",
"//example 8.15\n",
"//Check the stability and determine sliding factor and shear factor\n",
"clc; funcprot(0);\n",
"//Given\n",
"c=1;\n",
"miu=0.75;          //coefficient of friction\n",
"H=90;              //heigth of dam\n",
"wb=73.1;           //width of base\n",
"Bt=7;              //width of top of dam\n",
"hw=89;             //heigth of water in reservior\n",
"Hs1=28;            //heigth of slope on upstream side\n",
"Hs2=83;            //heigth of slope on downstream side\n",
"Cm=0.735;\n",
"alphah=0.1;\n",
"gamma_m=23.5;        //unit weigth of concrete\n",
"gamma_w=9.81;        //unit weigth of water\n",
"theta=atan(8/28);\n",
"fi=atan(0.7);\n",
"//self weigth of dam\n",
"W1=(Hs1*8*gamma_m)/2,\n",
"W2=(Bt*H*gamma_m),\n",
"W3=(Hs2^2*0.7*gamma_m)/2,\n",
"//weigth of superimposed water\n",
"W4=(Hs1*8*gamma_w)/2,\n",
"W5=(hw-Hs1)*8*gamma_w,\n",
"U=hw*wb*2*gamma_w/6;                  //uplift force\n",
"wp=hw^2*gamma_w/2;                   //water pressure\n",
"hp=0.726*Cm*alphah*gamma_w*hw^2;     //hydrodynamic pressure\n",
"Mhp=0.299*Cm*alphah*gamma_w*hw^3;    //moment due to hydrodynamic pressure\n",
"//inertial load due to horizontal acceleration\n",
"I1=W2/10;\n",
"I2=W3/10;\n",
"I3=W1/10;\n",
"SumV=W1+W2+W3+W4+W5-U;\n",
"SumH=wp+hp+I1+I2+I3;\n",
"L1=(wb-8)+8/3,\n",
"L2=(0.7*Hs2)+(Bt/2),\n",
"L3=(2*Hs2*0.7)/3,\n",
"L4=(wb-8)+(2*8)/3,\n",
"L5=(wb-8)+(8/2),\n",
"L6=hw/3;\n",
"L7=2*wb/3;\n",
"M1=W1*L1,M2=W2*L2,M3=W3*L3,M4=W4*L4;\n",
"M5=W5*L5;\n",
"M6=wp*L6;\n",
"M7=U*L7;\n",
"M8=I1*45;\n",
"M9=I2*83/3;\n",
"M10=I3*28/3;\n",
"Mplus=M1+M2+M3+M4+M5;\n",
"Mminus=M6+M7+M8+M9+M10+Mhp;\n",
"SumM=Mplus-Mminus;\n",
"x=SumM/SumV;\n",
"e=wb/2-x;\n",
"pnt=(SumV/wb)*(1+(6*e/wb));\n",
"pnh=(SumV/wb)*(1-(6*e/wb));\n",
"sigmat=pnt*sec(fi)^2;\n",
"p=hw*gamma_w;\n",
"pe=Cm*alphah*gamma_w*hw;\n",
"sigmah=pnh*sec(theta)^2-(p+pe)*tan(theta)^2;\n",
"taut=pnt*tan(fi);\n",
"tauh=-(-pnh-(p+pe))*tan(theta);\n",
"mprintf('Normal stress at toe=%i kN/square.m.',pnt);\n",
"mprintf('\nNormal stress at heel=%i kN/square.m.',pnh);\n",
"mprintf('\nPrincipal stress at toe=%i kN/square.m.',sigmat);\n",
"mprintf('\nPrincipal stress at heel=%i kN/square.m.',sigmah);\n",
"mprintf('\nShear stress at toe=%i kN/square.m.',taut);\n",
"mprintf('\nShear stress at heel=%i kN/square.m.',tauh);\n",
"\n",
"FOS=miu*SumV/SumH;\n",
"SFF=(miu*SumV+wb*1400)/SumH;\n",
"FOO=Mplus/Mminus;\n",
"Ffi=1.2;Fc=2.4;\n",
"F=(miu*SumV/Ffi+1400*wb/Fc)/SumH;\n",
"FOS=round(FOS*100)/100;\n",
"F=round(F*100)/100;\n",
"SFF=round(SFF*100)/100;\n",
"FOO=round(FOO*100)/100;\n",
"mprintf('\n\nFactor of safety against sliding as per IS:6512-1972=%f. <1.5',FOS);\n",
"mprintf('\nFactor of safety against sliding as per IS:6512-1984=%f. >1',F);\n",
"mprintf('\nShear friction factor=%f. <6',SFF);\n",
"mprintf('\nFactor of safety against overturning=%f. <1.5',FOO);\n",
"mprintf('\n\nDam is unsafe for given loading conditions');"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.16: EX8_16.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"\n",
"\n",
"//example 8.16\n",
"//Check the stability and determine principal and shear stress at toe and heel\n",
"clc; funcprot(0);\n",
"//Given\n",
"c=1;\n",
"miu=0.7;          //coefficient of friction\n",
"H=70;              //heigth of dam\n",
"ht=0;              //heigth of tail water\n",
"Lf=6.5;           //location of foundation gallery from heel\n",
"wb=52.5;           //width of base\n",
"Bt=7;              //width of top of dam\n",
"hw=70;             //heigth of water in reservior\n",
"Hs1=35;            //heigth of slope on upstream side\n",
"Hs2=60;            //heigth of slope on downstream side\n",
"gamma_m=24;        //unit weigth of concrete\n",
"gamma_w=9.81;        //unit weigth of water\n",
"theta=atan(0.1);\n",
"fi=atan(0.7);\n",
"//self weigth of dam\n",
"W1=(Hs1*3.5*gamma_m)/2,\n",
"W2=(Bt*H*gamma_m),\n",
"W3=(Hs2^2*0.7*gamma_m)/2,\n",
"//weigth of superimposed water\n",
"W4=(Hs1*3.5*gamma_w)/2,\n",
"W5=(hw-Hs1)*3.5*gamma_w,\n",
"wp=hw^2*gamma_w/2;                   //water pressure\n",
"Pt=gamma_w*ht,\n",
"Ph=gamma_w*hw,\n",
"Pg=(ht+(hw-ht)/3)*gamma_w,\n",
"U=(Pt*(wb-Lf))+(Pg*Lf)+((Ph-Pg)*Lf/2)+((Pg-Pt)*(wb-Lf)/2)*c,\n",
"l1=(wb-Lf)/2,l2=(2*(wb-Lf))/3,l3=(wb-Lf)+(Lf/2),l4=(wb-Lf)+((2*Lf)/3),\n",
"L7=(((Pt*(wb-Lf))*l1)+((Pg-Pt)*(wb-Lf)*l2/2)+((Pg*Lf)*l3)+((Ph-Pg)*Lf*l4/2))/U,\n",
"L1=(wb-3.5)+3.5/3,\n",
"L2=(0.7*Hs2)+(Bt/2),\n",
"L3=(2*Hs2*0.7)/3,\n",
"L4=(wb-3.5)+(2*3.5)/3,\n",
"L5=(wb-3.5)+(3.5/2),\n",
"L6=hw/3;\n",
"M1=W1*L1,M2=W2*L2,M3=W3*L3,M4=W4*L4;\n",
"M5=W5*L5;\n",
"M6=wp*L6;\n",
"M7=U*L7;\n",
"SumV1=W1+W2+W3;\n",
"SumM1=M1+M2+M3;\n",
"SumV2=SumV1+W4+W5;\n",
"SumM2=SumM1+M4+M5-M6;\n",
"SumV3=SumV2-U;\n",
"SumM3=SumM2-M7;\n",
"Mplus=1547377;\n",
"Mminus=870421;\n",
"SumH=wp;\n",
"\n",
"//case 1. Reservior empty\n",
"x=SumM1/SumV1;\n",
"e=wb/2-x;\n",
"pnt=(SumV1/wb)*(1+(6*e/wb));\n",
"pnh=(SumV1/wb)*(1-(6*e/wb));\n",
"sigmat=pnt*sec(fi)^2;\n",
"sigmah=pnh*sec(theta)^2;\n",
"taut=pnt*tan(fi);\n",
"tauh=pnh*tan(theta);\n",
"pnt=round(pnt*10)/10;\n",
"pnh=round(pnh*10)/10;\n",
"sigmat=round(sigmat*10)/10;\n",
"sigmah=round(sigmah*10)/10;\n",
"taut=round(taut*10)/10;\n",
"tauh=round(tauh*10)/10;\n",
"mprintf('case 1. Reservior empty:');\n",
"mprintf('\nNormal stress at toe=%f kN/square.m.',pnt);\n",
"mprintf('\nNormal stress at heel=%f kN/square.m.',pnh);\n",
"mprintf('\nPrincipal stress at toe=%f kN/square.m.',sigmat);\n",
"mprintf('\nPrincipal stress at heel=%f kN/square.m.',sigmah);\n",
"mprintf('\nShear stress at toe=%f kN/square.m.',taut);\n",
"mprintf('\nShear stress at heel=%f kN/square.m.',tauh);\n",
"\n",
"//case2. reservior full without uplift\n",
"x=SumM2/SumV2;\n",
"e=wb/2-x;\n",
"p=hw*gamma_w;\n",
"pnt=(SumV2/wb)*(1+(6*e/wb));\n",
"pnh=(SumV2/wb)*(1-(6*e/wb));\n",
"sigmat=pnt*sec(fi)^2;\n",
"sigmah=pnh*sec(theta)^2-p*tan(theta)^2;\n",
"taut=pnt*tan(fi);\n",
"tauh=-(pnh-p)*tan(theta);\n",
"pnt=round(pnt*10)/10;\n",
"pnh=round(pnh*10)/10;\n",
"sigmat=round(sigmat*10)/10;\n",
"sigmah=round(sigmah*10)/10;\n",
"taut=round(taut*10)/10;\n",
"tauh=round(tauh*10)/10;\n",
"mprintf('\n\ncase 2. reservior full without uplift:');\n",
"mprintf('\nNormal stress at toe=%f kN/square.m.',pnt);\n",
"mprintf('\nNormal stress at heel=%f kN/square.m.',pnh);\n",
"mprintf('\nPrincipal stress at toe=%f kN/square.m.',sigmat);\n",
"mprintf('\nPrincipal stress at heel=%f kN/square.m.',sigmah);\n",
"mprintf('\nShear stress at toe=%f kN/square.m.',taut);\n",
"mprintf('\nShear stress at heel=%f kN/square.m.',tauh);\n",
"\n",
"//case3. reservior full with uplift\n",
"x=SumM3/SumV3;\n",
"e=wb/2-x;\n",
"p=hw*gamma_w;\n",
"pnt=(SumV3/wb)*(1+(6*e/wb));\n",
"pnh=(SumV3/wb)*(1-(6*e/wb));\n",
"sigmat=pnt*sec(fi)^2;\n",
"sigmah=pnh*sec(theta)^2-p*tan(theta)^2;\n",
"taut=pnt*tan(fi);\n",
"tauh=-(pnh-p)*tan(theta);\n",
"pnt=round(pnt);\n",
"pnh=round(pnh);\n",
"sigmat=round(sigmat);\n",
"sigmah=round(sigmah);\n",
"taut=round(taut);\n",
"tauh=round(tauh);\n",
"mprintf('\n\ncase 3. reservior full with uplift:');\n",
"mprintf('\nNormal stress at toe=%f kN/square.m.',pnt);\n",
"mprintf('\nNormal stress at heel=%f kN/square.m.',pnh);\n",
"mprintf('\nPrincipal stress at toe=%f kN/square.m.',sigmat);\n",
"mprintf('\nPrincipal stress at heel=%f kN/square.m.',sigmah);\n",
"mprintf('\nShear stress at toe=%f kN/square.m.',taut);\n",
"mprintf('\nShear stress at heel=%f kN/square.m.',tauh);\n",
"\n",
"FOS=miu*SumV3/SumH;\n",
"SFF=(miu*SumV3+wb*1400)/SumH;\n",
"FOO=Mplus/Mminus;\n",
"Ffi=1.5;Fc=3.6;\n",
"F=(miu*SumV3/Ffi+1400*wb/Fc)/SumH;\n",
"FOS=round(FOS*1000)/1000;\n",
"SFF=round(SFF*100)/100;\n",
"FOO=round(FOO*100)/100;\n",
"F=round(F*1000)/1000;\n",
"mprintf('\n\nFactor of safety against sliding=%f.',FOS);\n",
"mprintf('\nShear friction factor=%f.',SFF);\n",
"mprintf('\nFactor of safety against overturning=%f.',FOO);\n",
"mprintf('\nFactor of safety for load combination B=%f. > 1',F);\n",
"mprintf('\nDam is safe ');\n",
"\n",
"//Case4.considering seismic forces\n",
"Cm=0.712;\n",
"alphah=0.1;\n",
"alphav=0.08;\n",
"hp=0.726*Cm*alphah*gamma_w*hw^2;     //hydrodynamic pressure\n",
"Mhp=0.299*Cm*alphah*gamma_w*hw^3;    //moment due to hydrodynamic pressure\n",
"//inertial load due to horizontal acceleration\n",
"I1=W2/10;\n",
"I2=W3/10;\n",
"I3=W1/10;\n",
"v=SumV1*alphav;\n",
"Mv=116444;\n",
"SumV4=SumV3-v;\n",
"SumH1=SumH+I1+I2+I3+hp;\n",
"M8=I1*35;\n",
"M9=I2*20;\n",
"M10=I3*35/3;\n",
"Mminus1=1161849;\n",
"SumM4=SumM3-M8-M9-M10-Mhp-Mv;\n",
"\n",
"x=SumM4/SumV4;\n",
"e=wb/2-x;\n",
"p=hw*gamma_w;\n",
"pe=Cm*alphah*gamma_w*hw;\n",
"pnt=(SumV4/wb)*(1+(6*e/wb));\n",
"pnh=(SumV4/wb)*(1-(6*e/wb));\n",
"sigmat=pnt*sec(fi)^2;\n",
"sigmah=pnh*sec(theta)^2-(p+pe)*tan(theta)^2;\n",
"taut=pnt*tan(fi);\n",
"tauh=(-pnh+(p+pe))*tan(theta);\n",
"pnt=round(pnt);\n",
"pnh=round(pnh);\n",
"sigmat=round(sigmat);\n",
"sigmah=round(sigmah);\n",
"taut=round(taut);\n",
"tauh=round(tauh);\n",
"mprintf('\n\ncase 4.considering seismic forces');\n",
"mprintf('\nNormal stress at toe=%f kN/square.m.',pnt);\n",
"mprintf('\nNormal stress at heel=%f kN/square.m.',pnh);\n",
"mprintf('\nPrincipal stress at toe=%f kN/square.m.',sigmat);\n",
"mprintf('\nPrincipal stress at heel=%f kN/square.m.',sigmah);\n",
"mprintf('\nShear stress at toe=%f kN/square.m.',taut);\n",
"mprintf('\nShear stress at heel=%f kN/square.m.',tauh);   //answer is wrong in book\n",
"\n",
"FOS=miu*SumV4/SumH1;\n",
"SFF=(miu*SumV4+wb*1400)/SumH1;\n",
"FOO=Mplus/Mminus1;\n",
"Ffi=1.2;Fc=2.7;\n",
"F=(miu*SumV4/Ffi+1400*wb/Fc)/SumH1;\n",
"FOS=round(FOS*1000)/1000;\n",
"SFF=round(SFF*100)/100;\n",
"FOO=round(FOO*100)/100;\n",
"F=round(F*100)/100;\n",
"mprintf('\n\nFactor of safety against sliding=%f.',FOS);\n",
"mprintf('\nShear friction factor=%f.',SFF);\n",
"mprintf('\nFactor of safety against overturning=%f.',FOO);\n",
"mprintf('\nFactor of safety for load combination E=%f. > 1',F);\n",
"mprintf('\nDam is safe ');"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.17: EX8_17.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"\n",
"\n",
"//example 8.17\n",
"//design practical profile of gravity dam\n",
"clc;funcprot(0);\n",
"//given\n",
"c=1;\n",
"rlb=1450;          //R.L of base of dam\n",
"rlw=1480.5;        //R.L of water level\n",
"Sg=2.4;            //specific gravity of masonary\n",
"gamma_w=9.81;      //unit weigth of water\n",
"w=1;               //heigth of waves\n",
"f=1200;            //safe compressive stress for masonary\n",
"FB=1.5*w;\n",
"rlt=FB+rlw;        //R.L of top of dam\n",
"H=rlt-rlb;         //heigth of dam\n",
"LH=f/(gamma_w*(Sg+1))\n",
"LH=round(LH*100)/100;\n",
"mprintf('Heigth of dam=%f m.',H);\n",
"mprintf('\nlimiting heigth of dam=%f m.',LH);\n",
"mprintf('\nDam is low gravity dam');\n",
"hw=rlw-rlb;\n",
"//keep top width,a=4.5.\n",
"a=4.5;\n",
"P=hw/(Sg^0.5);\n",
"P=round(P*10)/10;\n",
"mprintf('\nBase width of elementary profile=%f m.',P);\n",
"uo=a/16;\n",
"wb=uo+P;\n",
"wb=round(wb);\n",
"mprintf('\nBase width=%f m.',wb);\n",
"D=2*a*(Sg^0.5);\n",
"D=round(D);\n",
"mprintf('\nDistance upto which u/s slope is vertical from water level=%f m.',D);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.18: EX8_18.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"\n",
"\n",
"//example 8.18\n",
"//determine if dam is safe against sliding\n",
"clc;funcprot(0);\n",
"//given\n",
"hw=97;           //heigth of water in reservior\n",
"Bt=7;            //width of top of dam\n",
"H=100;           //heigth of the dam\n",
"Hs2=90;          //heigth of slope on downstream side\n",
"wb=75;           //width of base of dam\n",
"miu=0.75;        //coefficient of friction\n",
"gamma_d=2.4;     //weigth density of concrete\n",
"gamma_w=1000;    //weigth density of water\n",
"\n",
"P=gamma_w*hw^2/(2*1000);\n",
"W1=Bt*gamma_d*H;\n",
"W2=(wb-Bt)*Hs2*gamma_d/2;\n",
"W=W1+W2;\n",
"FOS=miu*W/P;\n",
"FOS=round(FOS*1000)/1000;\n",
"mprintf('Factor of safety against sliding=%f.',FOS);\n",
"mprintf('\nDam is safe against sliding');"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.19: EX8_19.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"\n",
"\n",
"//example 8.19\n",
"//calculate \n",
"//Factor of safety against overturning\n",
"//Factor of safety against sliding\n",
"//Shear friction factor\n",
"clc;funcprot(0);\n",
"//given\n",
"c=1;\n",
"H=10;             //heigth of dam\n",
"hw=10;            //heigth of water in reservior\n",
"wb=8.25;          //bottom width\n",
"Bt=1;             //top width\n",
"Hs1=0.1;          //slope on upstream side\n",
"gamma_w=9.81;     //unit weigth of water\n",
"gamma_m=22.4;     //unit weigth of masonary\n",
"f=1400;           //permissible shear stress at joint\n",
"miu=0.75;         //coefficient of friction\n",
"fi=atan(0.625);\n",
"theta=atan(0.1);\n",
"\n",
"W1=Bt*H*gamma_m;\n",
"W2=H*H*Hs1*gamma_m/2;\n",
"W3=H*6.25*gamma_m/2;\n",
"W4=hw*gamma_w*H*Hs1/2;\n",
"P=gamma_w*hw^2/2;\n",
"U=wb*gamma_w*hw*c/2;\n",
"SumV=W1+W2+W3+W4-U;\n",
"L3=2*(wb-(Hs1*H)-Bt)/3;\n",
"L1=(wb-(Hs1*H)-Bt)+Bt/2;\n",
"L2=(wb-(Hs1*H)-Bt)+Bt+(Hs1*H/3);\n",
"L4=(wb-(Hs1*H)-Bt)+Bt+(2*Hs1*H/3);\n",
"L5=2*wb/3;L6=hw/3;\n",
"M1=W1*L1;M2=W2*L2;M3=W3*L3;M4=W4*L4;\n",
"M5=U*L5;M6=P*L6;\n",
"SumM=M1+M2+M3+M4-M5-M6;\n",
"Mplus=M1+M2+M3+M4;\n",
"Mminus=M5+M6;\n",
"FOS=miu*SumV/P;\n",
"SFF=(miu*SumV+wb*1400)/P;\n",
"FOO=Mplus/Mminus;\n",
"FOS=round(FOS*100)/100;\n",
"SFF=round(SFF*10)/10;\n",
"FOO=round(FOO*100)/100;\n",
"mprintf('Factor of safety against sliding=%f.',FOS);\n",
"mprintf('\nShear friction factor=%f.',SFF);\n",
"mprintf('\nFactor of safety against overturning=%f.',FOO);\n",
"mprintf('\nDam is unsafe against overturning');"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.1: EX8_1.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"\n",
"\n",
"//example 8.1\n",
"//calculate forces induced due to earthquake\n",
"clc;funcprot(0);\n",
"//given\n",
"H=100;              //heigth of dam\n",
"wb=70;              //width of base of dam\n",
"wt=7;               //width of top of dam\n",
"l=1;                //length of dam\n",
"hw=98;              //heigth of water in dam\n",
"hsu=90;             //heigth of slope on downstream side\n",
"s=1/0.7;            //slope on downstream side\n",
"gammad=24;          //unit weigth of dam\n",
"gammaw=9.81;        //unit weigth of water\n",
"E=2.05D7;           //modulus of elasticity\n",
"\n",
"//(a) inertial forces and moments\n",
"alpha0=0.05;        //from table 8.1\n",
"alphah=2*alpha0;\n",
"//at 10m from top\n",
"F10=integrate('25.2-0.25*y','y',0,10);\n",
"M10=integrate('25.2*(1-0.01*y)*(10-y)','y',0,10);\n",
"//at 100m below top\n",
"F100=F10+integrate('0.15*(1-0.01*y)*16.8*y','y',10,100);\n",
"M100=M10+90*F10+integrate('0.15*(1-0.01*y)*16.8*y*(100-y)','y',10,100);\n",
"mprintf('Inertial forces:\nAt 10m from top: F=%f kn;M=%ikn-m\nAt 100m from top: F=%f kn;M=%ikn-m.',F10,M10,F100,M100);\n",
"\n",
"//(b) hydrodynamic pressure and moment\n",
"//at 10m from top\n",
"y=8;\n",
"W10=1680;\n",
"alphah=F10/W10;\n",
"Cm=0.735;\n",
"Cy=(Cm/2)*((y*(2-y/hw)/hw)+(y*(2-y/hw)/hw)^0.5);\n",
"p=Cy*alphah*gammaw*hw;\n",
"P10=0.726*p*y;\n",
"Mp10=0.299*p*y^2;\n",
"P10=round(P10*100)/100;\n",
"Mp10=round(Mp10*100)/100;\n",
"//at 100m from top\n",
"y=98;\n",
"W100=84840;\n",
"alphah=F100/W100;\n",
"Cm=0.735;\n",
"Cy=(Cm/2)*(y*(2-y/hw)/hw+(y*(2-y/hw)/hw)^0.5);\n",
"p=Cy*alphah*gammaw*hw;\n",
"P100=0.726*p*y;\n",
"Mp100=0.299*p*y^2;\n",
"mprintf('\nHydrodynamic forces:\nAt 10m from top: F=%f kn;M=%fkn-m\nAt 100m from top: F=%i kn;M=%ikn-m.',P10,Mp10,P100,Mp100);\n",
"\n",
""
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.20: EX8_20.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"\n",
"\n",
"//example 8.20\n",
"//calculate streeses at heel and toe of dam\n",
"clc;funcprot(0);\n",
"//given\n",
"c=1;\n",
"hw=80;           //heigth of water in reservior\n",
"Bt=6;            //width of top of dam\n",
"H=84;           //heigth of the dam\n",
"Hs2=75;          //heigth of slope on downstream side\n",
"wb=56;           //width of base of dam\n",
"Lf=8;             //distance of foundation gallery from heel\n",
"gamma_d=23.5;     //weigth density of concrete\n",
"gamma_w=9.81;    //weigth density of water\n",
"ht=6;            //heigth of tail water\n",
"\n",
"W1=Bt*gamma_d*H;\n",
"W2=gamma_d*Hs2*(wb-Bt)/2;\n",
"W3=gamma_w*ht*4/2;\n",
"W4=gamma_w*hw^2/2;\n",
"W5=gamma_w*ht^2/2;\n",
"Pt=gamma_w*ht,\n",
"Ph=gamma_w*hw,\n",
"Pg=(ht+(hw-ht)/3)*gamma_w,\n",
"U=(Pt*(wb-Lf))+(Pg*Lf)+((Ph-Pg)*Lf/2)+((Pg-Pt)*(wb-Lf)/2)*c,\n",
"l1=(wb-Lf)/2,l2=(2*(wb-Lf))/3,l3=(wb-Lf)+(Lf/2),l4=(wb-Lf)+((2*Lf)/3),\n",
"L6=(((Pt*(wb-Lf))*l1)+((Pg-Pt)*(wb-Lf)*l2/2)+((Pg*Lf)*l3)+((Ph-Pg)*Lf*l4/2))/U,\n",
"L1=(wb-Bt)+(Bt/2),\n",
"L2=(2*(wb-Bt))/3,\n",
"L3=4/3;\n",
"L4=hw/3;\n",
"L5=ht/3;\n",
"M1=W1*L1,M2=W2*L2,M3=W3*L3,M4=W4*L4,M5=W5*L5,M6=U*L6;\n",
"SumV=W1+W2+W3-U;\n",
"SumH=W4-W5;\n",
"SumM=M1+M2+M3-M4+M5-M6;\n",
"x=SumM/SumV;\n",
"e=wb/2-x;\n",
"pnt=(SumV/wb)*(1+(6*e/wb));\n",
"pnh=(SumV/wb)*(1-(6*e/wb));\n",
"pnt=round(pnt*10)/10;\n",
"pnh=round(pnh*10)/10;\n",
"mprintf('Maximum Normal stress at toe=%f kN/square.m.',pnt);\n",
"mprintf('\nMaximum Normal stress at heel=%f kN/square.m.',pnh);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.2: EX8_2.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"\n",
"\n",
"//example 8.2\n",
"//calculate forces induced due to earthquake by responce spectrum method\n",
"clc;funcprot(0);\n",
"//given\n",
"H=100;              //heigth of dam\n",
"wb=70;              //width of base of dam\n",
"wt=7;               //width of top of dam\n",
"l=1;                //length of dam\n",
"hw=98;              //heigth of water in dam\n",
"hsu=90;             //heigth of slope on downstream side\n",
"s=1/0.7;            //slope on downstream side\n",
"gammad=24;          //unit weigth of dam\n",
"gammaw=9.81;        //unit weigth of water\n",
"E=2.05D7;           //modulus of elasticity\n",
"beta=1;\n",
"I=2;\n",
"Fo=0.25;           //from table 8.2\n",
"                  //t=Sa/g;\n",
"t=0.19;           //from fig. 8.4\n",
"alphah=beta*I*Fo*t;\n",
"T=5.55*H^2/wb*(gammad/(gammaw*E))^0.5;\n",
"//(a) Base shear\n",
"W=l*gammad*(wt*H+((hsu/s)*hsu)/2);\n",
"Fb=0.6*W*alphah;\n",
"mprintf('Base shear=%f KN.',Fb);\n",
"\n",
"//(b) Base moment\n",
"hbar=((wt*H^2/2)+((hsu/s)*hsu^2/6))/((wt*H)+(hsu/s)*hsu/2);\n",
"Mb=0.9*W*hbar*alphah;\n",
"mprintf('\nBase moment=%f KN-m.',Mb);\n",
"\n",
"//(c) shear at 10m from top\n",
"Cv=0.08;\n",
"F10=Cv*Fb;\n",
"F10=round(F10);\n",
"mprintf('\nshear at 10m from top=%f KN.',F10);\n",
"\n",
"//(d) Moment at 10m from top\n",
"Cm=0.02;\n",
"M10=Cm*Mb;\n",
"M10=round(M10);\n",
"mprintf('\nmoment at 10m from top=%f KN.',M10);\n",
"//(e) Hydrodynamic pressure\n",
"//at 10m from top\n",
"y=8;\n",
"W10=1680;\n",
"Cm=0.735;\n",
"Cy=(Cm/2)*((y*(2-y/hw)/hw)+(y*(2-y/hw)/hw)^0.5);\n",
"p=Cy*alphah*gammaw*hw;\n",
"P10=0.726*p*y;\n",
"Mp10=0.299*p*y^2;\n",
"P10=round(P10*100)/100;\n",
"Mp10=round(Mp10*100)/100;\n",
"//at 100m from top\n",
"y=98;\n",
"W100=84840;\n",
"Cm=0.735;\n",
"Cy=(Cm/2)*(y*(2-y/hw)/hw+(y*(2-y/hw)/hw)^0.5);\n",
"p=Cy*alphah*gammaw*hw;\n",
"P100=0.726*p*y;\n",
"Mp100=0.299*p*y^2;\n",
"mprintf('\nHydrodynamic forces:\nAt 10m from top: F=%f kn;M=%fkn-m\nAt 100m from top: F=%i kn;M=%ikn-m.',P10,Mp10,P100,Mp100);\n",
"\n",
""
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.3: EX8_3.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"\n",
"\n",
"//example 8.3\n",
"//calculate forces induced due to earthquake\n",
"clc;funcprot(0);\n",
"//given\n",
"H=100;              //heigth of dam\n",
"wb=70;              //width of base of dam\n",
"wt=7;               //width of top of dam\n",
"l=1;                //length of dam\n",
"hw=98;              //heigth of water in dam\n",
"hsu=90;             //heigth of slope on downstream side\n",
"s=1/0.7;            //slope on downstream side\n",
"gammad=24;          //unit weigth of dam\n",
"gammaw=9.81;        //unit weigth of water\n",
"E=2.05D7;           //modulus of elasticity\n",
"//(a) Seismic coefficient method\n",
"alpha0=0.05;        //from table 8.1\n",
"alphah=2*alpha0;\n",
"alphav=0.75*alphah;\n",
"//at 10m from top\n",
"F10=integrate('alphav*168*(1-0.01*y)','y',0,10);\n",
"//at 100m below top\n",
"F100=F10+integrate('alphav*(1-0.01*y)*16.8*y','y',10,100);\n",
"mprintf('Part(a):\nAt 10m from top: F=%f kn\nAt 100m from top: F=%f kn.',F10,F100);\n",
"\n",
"//(b)Response spectrum method\n",
"beta=1;\n",
"I=2;\n",
"Fo=0.25;           //from table 8.2\n",
"                  //t=Sa/g;\n",
"t=0.19;           //from fig. 8.4\n",
"alphah=beta*I*Fo*t;\n",
"alphav=0.75*alphah;\n",
"//at 10m from top\n",
"F10=integrate('alphav*168*(1-0.01*y)','y',0,10);\n",
"//at 100m below top\n",
"F100=F10+integrate('alphav*(1-0.01*y)*16.8*y','y',10,100);\n",
"F100=round(F100*100)/100;\n",
"mprintf('\nPart(b):\nAt 10m from top: F=%f kn\nAt 100m from top: F=%f kn.',F10,F100);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.4: EX8_4.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"\n",
"\n",
"//example 8.4\n",
"//calculate hydrodynamic pressure on10m,40m and 100m from top\n",
"clc;funcprot(0);\n",
"//given\n",
"H=100;              //heigth of dam\n",
"wb=73;              //width of base of dam\n",
"wt=7;               //width of top of dam\n",
"l=1;                //length of dam\n",
"hw=98;              //heigth of water in dam\n",
"hsu=90;             //heigth of slope on downstream side\n",
"s=1/0.7;            //slope on downstream side\n",
"gammad=24;          //unit weigth of dam\n",
"gammaw=9.81;        //unit weigth of water\n",
"E=2.05D7;           //modulus of elasticity\n",
"\n",
"//at 10m from top\n",
"y=8;\n",
"alphah=0.1;\n",
"Cm=0.72;\n",
"Cy=(Cm/2)*((y*(2-y/hw)/hw)+(y*(2-y/hw)/hw)^0.5);\n",
"p10=Cy*alphah*gammaw*hw;\n",
"F10=0.726*p10*y;\n",
"Mp10=0.299*p10*y^2;\n",
"\n",
"//at 40m from top\n",
"y=38;\n",
"alphah=0.1;\n",
"Cm=0.72;\n",
"Cy=(Cm/2)*((y*(2-y/hw)/hw)+(y*(2-y/hw)/hw)^0.5);\n",
"p40=Cy*alphah*gammaw*hw;\n",
"F40=0.726*p40*y;\n",
"Mp40=0.299*p40*y^2;\n",
"\n",
"//at 100m from top\n",
"y=98;\n",
"alphah=0.1;\n",
"Cm=0.72;\n",
"Cy=(Cm/2)*((y*(2-y/hw)/hw)+(y*(2-y/hw)/hw)^0.5);\n",
"p100=Cy*alphah*gammaw*hw;\n",
"F100=0.726*p100*y;\n",
"Mp100=0.299*p100*y^2;\n",
"p10=round(p10*1000)/1000;\n",
"F10=round(F10*1000)/1000;\n",
"Mp10=round(Mp10*10)/10;\n",
"p40=round(p40*1000)/1000;\n",
"F40=round(F40*1000)/1000;\n",
"Mp40=round(Mp40*10)/10;\n",
"p100=round(p100*100)/100;\n",
"F100=round(F100*1000)/1000;\n",
"Mp100=round(Mp100*10)/10;\n",
"mprintf('\nHydrodynamic Forces:\nAt 10m from top: P=%f KN/square m;F=%f KN;M=%f KN-m.\nAt 40m from top: P=%f KN/square m.;F=%f KN;M=%f KN-m.\nAt 100m from top: P=%f KN/square m;F=%f KN;M=%f KN-m.',p10,F10,Mp10,p40,F40,Mp40,p100,F100,Mp100);\n",
"\n",
"//vertical component of reservior water on horizontal section\n",
"s1=3/60;\n",
"Wh=(F100-F40)*s1;\n",
"Wh=round(Wh*100)/100;\n",
"mprintf('\n\nvertical component of reservior water on horizontal section=%f kN/m.',Wh);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.8: EX8_8.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"\n",
"\n",
"//example 8.8\n",
"//calculate Heigth of dam when\n",
"//no tension is permissible\n",
"//factor of safety against slidingis 1.5\n",
"clc;funcprot(0);\n",
"//given\n",
"\n",
"wb=3;          //width of dam;\n",
"miu=0.5;       //coefficient of friction\n",
"Sg=2.4;        //specific gravity of masonary\n",
"gamma_w=9.81;  //unit weigth of water\n",
"c=1;\n",
"\n",
"//when uplift is considered\n",
"//when no tension is permissible then e=wb/6;\n",
"\n",
"p1=wb*Sg*gamma_w;\n",
"p2=c*wb*gamma_w/2;\n",
"p3=p1-p2;\n",
"p4=p1*wb/2-p2*2;\n",
"p5=gamma_w/6;\n",
"d1=p4/p3; d2=p5/p3;\n",
"d3=1.5-d1;\n",
"H=((0.5-d3)/d2)^0.5;\n",
"H=round(H*100)/100;\n",
"mprintf('when uplift is considered:')\n",
"mprintf('\nHeigth of dam when no tension is permissible=%f m.',H);\n",
"H=p3*0.5/(1.5*p5*3);\n",
"mprintf('\nHeigth of dam when factor of safety against sliding is 1.5=%f m.',H);\n",
"\n",
"//when uplift is not considered\n",
"p1=wb*Sg*gamma_w;\n",
"p4=p1*wb/2;\n",
"p5=gamma_w/6;\n",
"d1=p4/p1;\n",
"d2=p5/p1;\n",
"H=(0.5/d2)^0.5;\n",
"H=round(H*100)/100;\n",
"mprintf('\n\nwhen uplift is not considered:')\n",
"mprintf('\nHeigth of dam when no tension is permissible=%f m.',H);\n",
"H=p1*0.5/(1.5*p5*3);\n",
"mprintf('\nHeigth of dam when factor of safety against sliding is 1.5=%f m.',H);\n",
""
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.9: EX8_9.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"\n",
"\n",
"//example 8.9\n",
"//calculate streeses at heel and toe of dam\n",
"clc;funcprot(0);\n",
"//given\n",
"c=1;\n",
"hw=6;           //heigth of water in reservior\n",
"Bt=1.5;            //width of top of dam\n",
"H=6;           //heigth of the dam\n",
"wb=4.5;           //width of base of dam\n",
"Sg=2.4;           //specific gravity of masonary\n",
"gamma_w=9.81;    //weigth density of water\n",
"\n",
"W1=Bt*gamma_w*Sg*H;\n",
"W2=gamma_w*Sg*H*(wb-Bt)/2;\n",
"L1=(wb-Bt)+(Bt/2);\n",
"L2=(2*(wb-Bt))/3,\n",
"M1=W1*L1,M2=W2*L2,\n",
"\n",
"//Reaervior empty\n",
"SumW=W1+W2;\n",
"SumM=M1+M2;\n",
"x=SumM/SumW;\n",
"e=wb/2-x;\n",
"pnt=(SumW/wb)*(1+(6*e/wb));\n",
"pnh=(SumW/wb)*(1-(6*e/wb));\n",
"pnt=round(pnt*10)/10;\n",
"pnh=round(pnh*10)/10;\n",
"mprintf('Reservior empty:');\n",
"mprintf(' \nNormal stress at toe=%f kN/square.m.',pnt);\n",
"mprintf('\nNormal stress at heel=%f kN/square.m.',pnh);\n",
"\n",
"//Reservior full\n",
"W3=gamma_w*H^2/2;\n",
"U=gamma_w*H*c*wb/2;\n",
"SumV=SumW-U;\n",
"L3=hw/3;\n",
"L4=2*wb/3;             //lever arm\n",
"M3=W3*L3;\n",
"M4=U*L4;               //moment about toe\n",
"SumM1=SumM-M4-M3;\n",
"x=SumM1/SumV;\n",
"e=wb/2-x;\n",
"pnt=(SumV/wb)*(1+(6*e/wb));\n",
"pnh=(SumV/wb)*(1-(6*e/wb));\n",
"pnt=round(pnt*10)/10;\n",
"pnh=round(pnh*10)/10;\n",
"mprintf('\n\nReservior full:');\n",
"mprintf(' \nNormal stress at toe=%f kN/square.m.',pnt);\n",
"mprintf('\nNormal stress at heel=%f kN/square.m.',pnh);\n",
""
   ]
   }
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			{
			 "text": "MetaKernel Magics",
			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
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