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+{
+"cells": [
+ {
+		   "cell_type": "markdown",
+	   "metadata": {},
+	   "source": [
+       "# Chapter 9: COMBINED STRESSES"
+	   ]
+	},
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 9.10: Chapter9_Example_10.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"clc\n",
+"//initialization of variables\n",
+"clear\n",
+"b=2 //cm\n",
+"h=2 //cm\n",
+"T=2000 //kg-cm\n",
+"V=250 //kg\n",
+"M=2000 //kg-cm\n",
+"// calculations\n",
+"Mmax=M*6/(b*h*b)\n",
+"Vmax=3*V/(2*b*h)\n",
+"Zt=0.208*b^2*h\n",
+"Tmax=T/(Zt)\n",
+"\n",
+"sigma=Mmax\n",
+"printf('points A,B,')\n",
+"printf('\n sigma=%d kg/cm^2 (tension)',sigma)\n",
+"printf('\n points C,D,')\n",
+"printf('\n sigma=%d kg/cm^2 (cmpression)',sigma)\n",
+"tau=Vmax+Tmax\n",
+"printf('\n point E')\n",
+"printf('\n tau=%.2f kg/cm^2 shear',tau)\n",
+"tau=Vmax-Tmax\n",
+"printf('\n tau=%.2f kg/cm^2 shear',tau)\n",
+"// at G\n",
+"sigma_x=sigma\n",
+"sigma_y=0\n",
+"tau_xy=Tmax\n",
+"sigma_1=(sigma_x+sigma_y)/2+sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n",
+"sigma_2=(sigma_x+sigma_y)/2-sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n",
+"// results\n",
+"printf('\n at point G')\n",
+"printf('\n sigma_1 = %d kg/cm^2 (tension)',sigma_1)\n",
+"printf('\n sigma_2 = %d kg/cm^2 (compression)',sigma_2)\n",
+"\n",
+"// Question was asked only to find out at A,B,C,D,E,F and G"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 9.11: Chapter9_Example_11.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"clc\n",
+"//initialization of variables\n",
+"clear\n",
+"w=10 //cm\n",
+"s=2.8 //m\n",
+"P=1 //tonne\n",
+"Ft=1.4 //cm\n",
+"Wt=0.8 //cm\n",
+"Ix=13989.5 //cm^4\n",
+"Z=699.5 //cm^3\n",
+"// calculations\n",
+"BM= 2.8 \n",
+"T=P*1000*8.21\n",
+"SF=P*1000\n",
+"BS=BM*10^5/(Z)\n",
+"sigmaXA=BS*18.6/20\n",
+"K=w*Ft*19.3+18.6*Wt*9.3\n",
+"tau_xy_C=SF/(Ix*Wt)*K\n",
+"tau_xy_A=tau_xy_C*(w*Ft*19.3)/K     \n",
+"tau_xy_B=tau_xy_A*0.5*Wt/w\n",
+"sigmaXB=sigmaXA*19.3/20\n",
+"\n",
+"tau_max=3*Ft*8210/(w*Ft^3+37.2*Wt^3)\n",
+"tau_A=3*Wt*8210/(w*Ft^3+37.2*Wt^3)\n",
+"\n",
+"//For point A\n",
+"Shear=tau_xy_A-tau_A\n",
+"sigma_x=sigmaXA\n",
+"sigma_y=0\n",
+"tau_xy=Shear\n",
+"sigma_1=(sigma_x+sigma_y)/2+sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n",
+"sigma_2=(sigma_x+sigma_y)/2-sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n",
+"\n",
+"printf('For point A')\n",
+"printf('\n Total shear= %.1f kg/cm^2 ',Shear)\n",
+"printf('\n Bending stress = %d kg/cm^2 (Compr.)',sigma_x)\n",
+"printf('\n Principal stresses are %d (tension), %d (comp.) kg/cm^2 ',sigma_1,sigma_2)\n",
+"\n",
+"//For point B\n",
+"printf('\n FOr point B')\n",
+"printf('\n Bending shear stress is %.2f k/cm^2',tau_xy_B)\n",
+"sigmaXB=BS*19.3/20\n",
+"sigma_x=sigmaXB\n",
+"sigma_y=0\n",
+"tau_xy=tau_max\n",
+"sigma_1=(sigma_x+sigma_y)/2+sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n",
+"sigma_2=(sigma_x+sigma_y)/2-sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n",
+"printf('\n Principal stresses are %d (tension), %d (comp.) kg/cm^2 ',sigma_1,sigma_2)\n",
+"\n",
+"// Answers in the text are approximations"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 9.12: Chapter9_Example_12.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"clc\n",
+"//initialization of variables\n",
+"clear\n",
+"b=10 //cm\n",
+"h=10 //cm\n",
+"P=5 //tonne\n",
+"e=1 //cm\n",
+"E=12*10^4 //kg/cm^2\n",
+"str=130 // kg/cm^2\n",
+"n=3\n",
+"L=2 //m\n",
+"// calculations\n",
+"L=L*100 //cm\n",
+"Pcr=%pi^2*E*b*h^3/(12*L^2)\n",
+"Pcr=Pcr/1000\n",
+"Smax=-P*1000/(b*h)-(P*1000*1*5*12/10^4)*1/(1-(n*P/Pcr))\n",
+"// results\n",
+"printf('permissible stress = %d kg/cm^2',str)\n",
+"printf('\n develoed stress = %.1f kg/cm^2',Smax)\n",
+"printf('\n Since it is below the permissible stress, the design is safe')\n",
+""
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 9.13: Chapter9_Example_13.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"clc\n",
+"//initializatio of variables\n",
+"clear\n",
+"// linked to 9.13\n",
+"b=10 //cm\n",
+"h=10 //cm\n",
+"P=5 //tonne\n",
+"e=1 //cm\n",
+"E=12*10^4 //kg/cm^2\n",
+"str=130 // kg/cm^2\n",
+"n=3\n",
+"L=2 //m\n",
+"// calculations\n",
+"L=L*100 //cm\n",
+"Pcr=%pi^2*E*b*h^3/(12*L^2)\n",
+"Pcr=Pcr/1000\n",
+"Smax=-P*1000/(b*h)-(P*1000*1*5*12/10^4)*1/(1-(n*P/Pcr))\n",
+"Smax=abs(Smax)\n",
+"\n",
+"rr=b*h^3/(12*100)\n",
+"Smax_se=P*1000/(b*h)*(1+e*5/rr*sec(%pi/2*sqrt(n*P/Pcr)))\n",
+"Perror=(Smax-Smax_se)/Smax\n",
+"Perror=Perror*100\n",
+"Perror=abs(Perror)\n",
+"// results\n",
+"printf('Using secent formula, stress obtained is %d kg/cm^2',Smax_se)\n",
+"printf('\n hence, the percentage error %.2f',Perror)\n",
+"// approximate answees in the text"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 9.14: Chapter9_Example_14.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"clc\n",
+"//initialization of variables\n",
+"clear\n",
+"P=400 //kg/m\n",
+"L=10 //m\n",
+"F=10 //tonne\n",
+"n=3\n",
+"Ixx=5943.1 //cm^4\n",
+"A=52.03 //cm^2\n",
+"rx=10.69 //cm\n",
+"E=2*10^6 //kg/cm^2\n",
+"// calculations\n",
+"Pcr=%pi^2*E*Ixx/((L*100)^2)\n",
+"Pcr=Pcr/1000\n",
+"e=P*L^2/(8*F*1000)\n",
+"g=e*12.5*100/rx^2\n",
+"Smax=F*1000/A*(1+g*1/(1-n*(F/Pcr)))\n",
+"// results\n",
+"printf('The maximum stress developed is %d kg/cm^2',Smax)\n",
+"\n",
+"// approximate calculations involved in the text book"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 9.15: Chapter9_Example_15.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"clc\n",
+"//initialization of variables\n",
+"clear\n",
+"// linked to 9_14\n",
+"// calculations\n",
+"P=400 //kg/m\n",
+"L=10 //m\n",
+"F=10 //tonne\n",
+"n=3\n",
+"Ixx=5943.1 //cm^4\n",
+"A=52.03 //cm^2\n",
+"rx=10.69 //cm\n",
+"E=2*10^6 //kg/cm^2\n",
+"Pcr=%pi^2*E*Ixx/((L*100)^2)\n",
+"Pcr=Pcr/1000\n",
+"e=P*L^2/(8*F*1000)\n",
+"g=e*12.5*100/rx^2\n",
+"Smax=F*1000/A*(1+g*1/(1+n*(F/Pcr)))\n",
+"// results\n",
+"printf('The maximum stress developed is %d kg/cm^2',Smax)\n",
+"\n",
+"// approximate answer in the text"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 9.1: Chapter9_Example_1.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"clc\n",
+"//initialization of variables\n",
+"clear\n",
+"//case (a)\n",
+"A=72.9 //cm^2\n",
+"Iy=633 //cm^4\n",
+"Ix=1199 //cm^4\n",
+"t=24/(5*Ix)+13.5/(5*Iy)\n",
+"r=1/(A*t)\n",
+"printf('case (a) \n r = %.3f cm',r)\n",
+"// case (b)\n",
+"t=24/(5*Ix)-13.5/(5*Iy)\n",
+"r=1/(A*t)\n",
+"printf('\n case (b) \n r = %.1f cm',r)\n",
+"//case (c)\n",
+"t=-24/(5*Ix)+13.5/(5*Iy)\n",
+"r=1/(A*t)\n",
+"printf('\n case (a) \n r = %.1f cm',r)\n",
+"printf('\n So the load is to be placed on the leg OD, at a distance of %.1f cm from O',r )\n",
+""
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 9.3: Chapter9_Example_3.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"clc\n",
+"//initialization of variables\n",
+"clear\n",
+"b=14 //cm\n",
+"d=20 //cm\n",
+"rx=8.46 //cm\n",
+"ry=2.99 //cm\n",
+"// calculations\n",
+"ex=2*rx^2/d\n",
+"ey=2*ry^2/b\n",
+"h=2*ex\n",
+"w=2*ey\n",
+"// results\n",
+"printf('for steel height=%.3f cm and width=%.3f cm',h,w)\n",
+"// ISHB 225\n",
+"b=22.5 //cm\n",
+"d=22.5 //cm\n",
+"rx=9.8 //cm\n",
+"ry=4.96 //cm\n",
+"// calculations\n",
+"ex=2*rx^2/d\n",
+"ey=2*ry^2/b\n",
+"h=2*ex\n",
+"w=2*ey\n",
+"// results\n",
+"printf('\n for an ISHB height=%.3f cm and width=%.3f cm',h,w)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 9.4: Chapter9_Example_4.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"clc\n",
+"//initialization of variables\n",
+"clear\n",
+"t=280 //kg/cm^2\n",
+"c=840 //kg/cm^2\n",
+"xbar=7.5 //cm from AB\n",
+"A=210 //cm^2\n",
+"// calculations\n",
+"e=50+xbar //cm\n",
+"Iyy=7433 //cm^2\n",
+"k=(1/210+e*xbar/Iyy)\n",
+"P=t/k\n",
+"k1=(-1/210+e*(xbar+5)/Iyy)\n",
+"P1=c/k1\n",
+"P_safe=min(P1,P)\n",
+"// results\n",
+"printf('The safe load is %d kg',P_safe)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 9.5: Chapter9_Example_5.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"clc\n",
+"//initialization of the variables\n",
+"clear\n",
+"s=1.6 //m\n",
+"s1=4 //m\n",
+"pi=28 //degrees\n",
+"w=16 //kg/m^2\n",
+"p=100 //kg/m^2\n",
+"pl=20 //cm\n",
+"pb=10 //cm\n",
+"r=500 //kg/m^3\n",
+"// calculations\n",
+"pi=pi*%pi/180 //radians\n",
+"W=w*s+(r*pl*pb/(100*100))\n",
+"P=p*s\n",
+"L=P+W*cos(pi)\n",
+"Mx=L*s1^2*100/8\n",
+"sigma_1=Mx*6/(pb*pl^2)\n",
+"My=W*sin(pi)*s1^2*100/8\n",
+"sigma_2=My*6/(pl*pb^2)\n",
+"sigma=sigma_1+sigma_2\n",
+"// results\n",
+"printf('Due to bending in the noth the planes, D experiences maximum \n compression of %.2f kg/cm^2 and B has maximum tension of %.2f kg/cm^2',sigma,sigma)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 9.6: Chapter9_Example_6.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"clc\n",
+"//initialization of the problems\n",
+"clear\n",
+"s=1.6 //m\n",
+"s1=4 //m\n",
+"pi=28 //degrees\n",
+"w=16 //kg/m^2\n",
+"p=100 //kg/m^2\n",
+"pl=20 //cm\n",
+"pb=10 //cm\n",
+"r=500 //kg/m^3\n",
+"Zx=54.8 //cm^3\n",
+"Zy=3.9 //cm^3\n",
+"// calculations\n",
+"pi=pi*%pi/180 //radians\n",
+"W=w*s+8.1\n",
+"P=p*s\n",
+"L=P+W*cos(pi)\n",
+"Mx=L*s1^2*100/8\n",
+"sigma_1=Mx/Zx\n",
+"My=W*sin(pi)*s1^2*100/8\n",
+"sigma_2=My/Zy\n",
+"sigma=sigma_1+sigma_2\n",
+"// results\n",
+"printf('Maximum stresses are %d kg/cm^2, tension or compression',sigma)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 9.7: Chapter9_Example_7.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"clc\n",
+"//initialization of variables\n",
+"clear\n",
+"s=1.6 //m\n",
+"s1=4 //m\n",
+"pi=28 //degrees\n",
+"w=16 //kg/m^2\n",
+"p=100 //kg/m^2\n",
+"pl=20 //cm\n",
+"pb=10 //cm\n",
+"r=500 //kg/m^3\n",
+"sg=5 //cm\n",
+"E=12*10^4\n",
+"pi=pi*%pi/180 //radians\n",
+"// calculations\n",
+"W=w*s+(r*pl*pb/(100*100))\n",
+"P=p*s\n",
+"L=P+W*cos(pi)\n",
+"Mx=L*s1^2*100/8\n",
+"sigma_1=Mx*6/(pb*pl^2)\n",
+"My=W*sin(pi)*s1^2*100/8\n",
+"sigma_2=My*6/(pl*pb^2)\n",
+"st=sigma_1*sg/10\n",
+"Ts=st-sigma_2\n",
+"ez=Ts/E\n",
+"// results\n",
+"printf('The strain gauge, aligned to the z axis will give compression strain of %.1e',ez)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 9.8: Chapter9_Example_8.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"clc\n",
+"//initialization of variables\n",
+"clear\n",
+"P=3 //tonne/m\n",
+"s=6 //m\n",
+"l=50 //cm\n",
+"b=20 //cm\n",
+"k=0.5 //m\n",
+"//calculations\n",
+"R=P*s/2\n",
+"sf=R-k*P\n",
+"bm=R*k-P*k^2/2\n",
+"tau_xy=1.5*sf*1000/(l*b)\n",
+"tau_max=tau_xy\n",
+"str=bm*s*10^5/(b*l*l)\n",
+"\n",
+"// consider the line a-a\n",
+"\n",
+"sigma_x=str*12.5/25\n",
+"sigma_y=0\n",
+"tau_xy=tau_xy*(1-(12.5/25)^2)\n",
+"\n",
+"sigma_1=(sigma_x+sigma_y)/2+sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n",
+"sigma_2=(sigma_x+sigma_y)/2-sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n",
+"\n",
+"printf('For the line a-a the bending stress and shearing stress are \n respectively %.2f kg/cm^2, %.2f kg/cm^2 ',sigma_x,tau_xy)\n",
+"printf('\n The principal stresses are %.2f kg/cm^2 (tension) %.2f kg/cm^2 (compression) ',sigma_1,sigma_2)\n",
+"\n",
+"//consider the line c-c\n",
+"printf('\n For the line c-c the bending stress and shearing stress are \n respectively %.2f kg/cm^2, %.2f kg/cm^2 ',sigma_x,tau_xy)\n",
+"printf('\n The principal stresses are %.2f kg/cm^2 (compression) %.2f kg/cm^2 (tension) ',sigma_2,sigma_1)\n",
+"\n",
+"//for the line b-b\n",
+"tau_xy=tau_max\n",
+"sigma_x=0\n",
+"sigma_y=0\n",
+"sigma_1=(sigma_x+sigma_y)/2+sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n",
+"sigma_2=(sigma_x+sigma_y)/2-sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n",
+"// results\n",
+"printf('\n For the line b-b the bending stress and shearing stress are \n respectively %.2f kg/cm^2, %.2f kg/cm^2 ',sigma_x,tau_xy)\n",
+"printf('\n The principal stresses are %.2f kg/cm^2 (tension) %.2f kg/cm^2 (compression) ',sigma_1,sigma_2)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 9.9: Chapter9_Example_9.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"clc\n",
+"//initialization of variables\n",
+"clear\n",
+"P=3 //tonne/m\n",
+"s=6 //m\n",
+"l=50 //cm\n",
+"b=20 //cm\n",
+"k=0.5 //m\n",
+"//calculations\n",
+"R=P*s/2\n",
+"sf=R-k*P\n",
+"bm=R*k-P*k^2/2\n",
+"tau_xy=1.5*sf*1000/(l*b)  //max shear stress\n",
+"tau_max=tau_xy  \n",
+"str=bm*s*10^5/(b*l*l)  //max bending stress\n",
+"\n",
+"// consider the line a-a\n",
+"\n",
+"sigma_x=str*12.5/25\n",
+"sigma_y=0\n",
+"tau_xy=tau_xy*(1-(12.5/25)^2)\n",
+"\n",
+"sigma_1=(sigma_x+sigma_y)/2+sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n",
+"sigma_2=(sigma_x+sigma_y)/2-sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n",
+"\n",
+"theta=1/2*atan(2*tau_xy/(sigma_x-sigma_y))\n",
+"sigma_p=sigma_1/cos(theta)\n",
+"P=sigma_p*2*l*b/(3*1000)\n",
+"printf('A prestressing force of %.2f Tonne must be applied to balance the tension at a-a',P)\n",
+"\n",
+"//At bottom point D or C\n",
+"pre_str=P*2*1000/(l*b)\n",
+"net=str-pre_str\n",
+"printf('\n At bottom point D or C')\n",
+"printf('\n Net tension = %.2f kg/cm^2 ',net)\n",
+"\n",
+"//consider the line b-b\n",
+"pre_str=P\n",
+"sigma_x=pre_str\n",
+"sigma_y=0\n",
+"tau_xy=tau_max\n",
+"sigma_1=(sigma_x+sigma_y)/2+sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n",
+"sigma_2=(sigma_x+sigma_y)/2-sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n",
+"printf('\n At section b-b')\n",
+"printf('\n pre-stress=%.2f kg/cm^2',pre_str)\n",
+"printf('\n principal stresses are %.2f, %.2f kg/cm^2 ',sigma_1,sigma_2)\n",
+"\n",
+"//for the line c-c\n",
+"sigma_x=str*12.5/25\n",
+"sigma_y=0\n",
+"tau_xy=tau_xy*(1-(12.5/25)^2)\n",
+"sigma_1=(sigma_x+sigma_y)/2+sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n",
+"sigma_2=(sigma_x+sigma_y)/2-sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n",
+"pre_str=pre_str/2\n",
+"net=sigma_1+pre_str\n",
+"sigma_x=net\n",
+"sigma_y=0\n",
+"sigma_1=(sigma_x+sigma_y)/2+sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n",
+"sigma_2=(sigma_x+sigma_y)/2-sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n",
+"// results\n",
+"printf('\n At section c-c')\n",
+"printf('\n the direct stress is %.2f kg/cm^2',net)\n",
+"printf('\n pre-stress = %.2f kg/cm^2',pre_str)\n",
+"printf('\n principal stresses are %.2f, %.2f kg/cm^2 ',sigma_1,sigma_2)\n",
+"\n",
+"// wrong calculations in the thext for some parts\n",
+""
+   ]
+   }
+],
+"metadata": {
+		  "kernelspec": {
+		   "display_name": "Scilab",
+		   "language": "scilab",
+		   "name": "scilab"
+		  },
+		  "language_info": {
+		   "file_extension": ".sce",
+		   "help_links": [
+			{
+			 "text": "MetaKernel Magics",
+			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+			}
+		   ],
+		   "mimetype": "text/x-octave",
+		   "name": "scilab",
+		   "version": "0.7.1"
+		  }
+		 },
+		 "nbformat": 4,
+		 "nbformat_minor": 0
+}