From 3727ade10dd304eb7a596cac7adb00302953e402 Mon Sep 17 00:00:00 2001 From: Trupti Kini Date: Thu, 24 Nov 2016 23:30:37 +0600 Subject: Added(A)/Deleted(D) following books A Electrical_&_Electronic_Systems_by_Neil_Storey/Chapter11.ipynb A Electrical_&_Electronic_Systems_by_Neil_Storey/Chapter12.ipynb A Electrical_&_Electronic_Systems_by_Neil_Storey/Chapter13.ipynb A Electrical_&_Electronic_Systems_by_Neil_Storey/Chapter14.ipynb A Electrical_&_Electronic_Systems_by_Neil_Storey/Chapter15.ipynb A Electrical_&_Electronic_Systems_by_Neil_Storey/Chapter16.ipynb A Electrical_&_Electronic_Systems_by_Neil_Storey/Chapter18.ipynb A Electrical_&_Electronic_Systems_by_Neil_Storey/Chapter19.ipynb A Electrical_&_Electronic_Systems_by_Neil_Storey/Chapter2.ipynb A Electrical_&_Electronic_Systems_by_Neil_Storey/Chapter20.ipynb A Electrical_&_Electronic_Systems_by_Neil_Storey/Chapter21.ipynb A Electrical_&_Electronic_Systems_by_Neil_Storey/Chapter22.ipynb A Electrical_&_Electronic_Systems_by_Neil_Storey/Chapter23.ipynb A Electrical_&_Electronic_Systems_by_Neil_Storey/Chapter5.ipynb A Electrical_&_Electronic_Systems_by_Neil_Storey/Chapter6.ipynb A Electrical_&_Electronic_Systems_by_Neil_Storey/Chapter8.ipynb A Electrical_&_Electronic_Systems_by_Neil_Storey/Chapter9.ipynb A Electrical_&_Electronic_Systems_by_Neil_Storey/screenshots/pic1.png A Electrical_&_Electronic_Systems_by_Neil_Storey/screenshots/pic2.png A Electrical_&_Electronic_Systems_by_Neil_Storey/screenshots/pic3.png A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter10_67BmtXx.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter10_LGPoR7F.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter10_PDCS2qh.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter10_lNjLAte.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter10_n5s4jXl.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter10_npy5vv0.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter10_pjpRgex.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter11_IE4byFL.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter11_RAQoou9.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter11_VcicGy5.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter11_hoqMFBX.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter11_iBTGbp8.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter11_k1rTVhh.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter11_nGrFEGY.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter11_pfzLlc6.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter1_1FJHa67.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter1_2wryDDQ.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter1_BuZVTIP.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter1_UCsno1y.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter1_Yd7uN6t.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter1_bGP3Wsd.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter1_pFJzyF5.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter2_242icmu.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter2_Rcy1wii.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter2_TvxYpxT.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter2_VU0Vuul.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter2_Xiz19Ms.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter2_rAG8C10.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter2_xUN650b.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter3_0WKL8dM.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter3_BsRbQCe.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter3_IF7BAbT.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter3_Qh2uphO.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter3_WS64jkH.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter3_aM1BqRM.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter3_tEQK8Lr.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter4_0E18xYL.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter4_4P7HQZZ.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter4_8GR2j3i.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter4_KE5ki12.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter4_LmrwpIC.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter4_ZuWrQKN.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter4_wUtoaip.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter5_0Ke5Vhq.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter5_23aeJMe.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter5_4a14Khd.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter5_eftppGy.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter5_jOQv5Ua.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter5_m75AW4e.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter5_mZ9916M.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter6_2OboaPO.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter6_Cf1Ae70.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter6_IZI7GIy.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter6_TRm6El0.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter6_WfVJQIc.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter6_Z5dEk19.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter6_z9FlTqT.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter8_6BR5OK6.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter8_FV7Jgrb.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter8_Q79Sp1O.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter8_Qhj9HPA.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter8_fBoE3j3.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter8_mFOxHz2.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter8_zNY63b3.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter9_039FJN6.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter9_0AhnrOb.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter9_8K1gGKx.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter9_E4M5MRA.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter9_Ivqhz8T.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter9_ZSvbidk.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter9_u7ekl0N.ipynb A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/screenshots/ch1_mHmqCLQ.png A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/screenshots/ch_9_UicjBqW.png A MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/screenshots/ch_xk3ylh6.png A basic_electrical_engineering_by_nagsarkar_and_sukhija/Chapter2_eh02mMg.ipynb A basic_electrical_engineering_by_nagsarkar_and_sukhija/Chapter4_QnODdtI.ipynb A basic_electrical_engineering_by_nagsarkar_and_sukhija/Chapter5_IwMblyq.ipynb A basic_electrical_engineering_by_nagsarkar_and_sukhija/chapter11_nHcyQSN.ipynb A basic_electrical_engineering_by_nagsarkar_and_sukhija/chapter1_ivpTi0v.ipynb A basic_electrical_engineering_by_nagsarkar_and_sukhija/chapter3.ipynb A basic_electrical_engineering_by_nagsarkar_and_sukhija/chapter6_7Vcvq3x.ipynb A basic_electrical_engineering_by_nagsarkar_and_sukhija/chapter7_Iro5ijO.ipynb A basic_electrical_engineering_by_nagsarkar_and_sukhija/chapter8_dRxKPQv.ipynb A basic_electrical_engineering_by_nagsarkar_and_sukhija/chapter9_QP9exWK.ipynb A basic_electrical_engineering_by_nagsarkar_and_sukhija/screenshots/chap1_gG9EuuG.png A basic_electrical_engineering_by_nagsarkar_and_sukhija/screenshots/chapter2_RW9JXUw.png A basic_electrical_engineering_by_nagsarkar_and_sukhija/screenshots/chapter6_kNIRtlM.png --- .../Chapter11_VcicGy5.ipynb | 654 +++++++++++++++++++++ 1 file changed, 654 insertions(+) create mode 100644 MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter11_VcicGy5.ipynb (limited to 'MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter11_VcicGy5.ipynb') diff --git a/MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter11_VcicGy5.ipynb b/MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter11_VcicGy5.ipynb new file mode 100644 index 00000000..06fa6f21 --- /dev/null +++ b/MECHANICS_OF_SOLIDS_by_S.S._Bhavikatti/Chapter11_VcicGy5.ipynb @@ -0,0 +1,654 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter11-PRINCIPAL STRESSES AND STRAINS" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# example 11.2 page number 352" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(a) P= 14726.22 N\n", + "(b) P= -44178.65 N compressive\n", + "Material fails because of maximum shear and not by axial compression.\n", + "P= 24544.0 N\n", + "The plane of qmax is at 45° to the plane of px. \n" + ] + } + ], + "source": [ + "from math import sqrt,pi\n", + "\n", + "#A material has strength in tension, compression and shear as 30N/mm2, 90 N/mm2 and 25 N/mm2, respectively. If a specimen of diameter 25 mm is tested in tension and compression identity the failure surfaces and loads. \n", + "\n", + "#variable declaration\n", + "\n", + "#In tension: Let axial direction be x direction. Since it is uniaxial loading, py = 0, q = 0 and only px exists.when the material is subjected to full tensile stress, px = 30 N/mm^2.\n", + "\n", + "pt=float(30)\n", + "pc=float(90)\n", + "ps=float(25)\n", + "\n", + "d=float(25)\n", + "px=float(30) #N/mm^2\n", + "py=0\n", + "q=0\n", + "p1=(px+py)/2+sqrt(pow(((px-py)/2),2)+pow(q,2))\n", + "\n", + "p2=(px+py)/2-sqrt(pow(((px-py)/2),2)+pow(q,2))\n", + "\n", + "qmax=(px-py)/2\n", + "\n", + "#Hence failure criteria is normal stress p1\n", + "\n", + "A=pi*pow(d,2)/4\n", + "\n", + "#Corresponding load P is obtained by\n", + "p=p1\n", + "P=p1*A\n", + "\n", + "print \"(a) P=\",round(P,2),\"N\"\n", + "\n", + "#In case of compression test,\n", + "\n", + "px=-pc\n", + "py=q=0\n", + "\n", + "P=-px*A\n", + "\n", + "print \"(b) P=\",round((-P),2),\"N compressive\"\n", + "\n", + "#at this stage\n", + "\n", + "qmax=sqrt((pow((px-py)/2,2))+pow(q,2))\n", + "\n", + "print \"Material fails because of maximum shear and not by axial compression.\"\n", + "qmax=25\n", + "px=2*qmax\n", + "\n", + "P=px*A\n", + "print\"P=\",round(P),\"N\"\n", + "print \"The plane of qmax is at 45° to the plane of px. \"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# example 11.3 page number 354" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "pn= 30.0 N/mm^2\n", + "pt= 86.6 N/mm^2\n", + "p= 91.65 N/mm^2\n", + "alpha= 19.1 °\n" + ] + } + ], + "source": [ + "#The direct stresses at a point in the strained material are 120 N/mm2 compressive and 80 N/mm2 tensile. There is no shear stress.\n", + "\n", + "from math import sqrt,cos,sin,atan,pi\n", + "#variable declaration\n", + "\n", + "#The plane AC makes 30° (anticlockwise) to the plane of px (y-axis). Hence theta= 30°. px = 80 N/mm^2 py = – 120 N/mm^2 ,q = 0\n", + "\n", + "px=float(80)\n", + "py=float(-120)\n", + "q=float(0)\n", + "theta=30\n", + "pn=((px+py)/2)+((px-py)/2)*cos(2*theta*pi/180)+q*sin(2*theta*pi/180)\n", + "\n", + "print\"pn=\",round(pn),\"N/mm^2\"\n", + "\n", + "pt=((px-py)/2)*sin(2*theta*pi/180)-q*cos(2*theta*pi/180)\n", + "\n", + "print\"pt=\",round(pt,1),\"N/mm^2\"\n", + "p=sqrt(pow(pn,2)+pow(pt,2))\n", + "\n", + "print\"p=\",round(p,2),\"N/mm^2\"\n", + "\n", + "alpha=atan(pn/pt)*180/pi\n", + "\n", + "print \"alpha=\", round(alpha,1),\"°\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# example 11.4 page number 355" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "theta= 37.98 ° and 127.98 °\n", + "p1= 278.08 N/mm^2\n", + "p2= 71.92 N/mm^2\n", + "qmax= 103.08 N/mm^2\n" + ] + } + ], + "source": [ + "from math import sqrt,cos,sin,atan,pi\n", + "#variable declaration\n", + "#Let the principal plane make anticlockwise angle theta with the plane of px with y-axis. Then\n", + "\n", + "px=float(200) #N/mm^2\n", + "py=float(150) #N/mm^2\n", + "q=float(100) #N/mm^2\n", + "\n", + "theta1=(atan((2*q)/(px-py))*180)/(pi*2) \n", + "theta2=90+theta1\n", + "print\"theta=\",round(theta1,2),\"°\" \" and \",round(theta2,2),\"°\"\n", + "\n", + "p1=(px+py)/2+sqrt(pow(((px-py)/2),2)+pow(q,2))\n", + "\n", + "print \"p1=\",round(p1,2),\"N/mm^2\"\n", + "\n", + "p2=(px+py)/2-sqrt(pow(((px-py)/2),2)+pow(q,2))\n", + "\n", + "print \"p2=\",round(p2,2),\"N/mm^2\"\n", + "\n", + "qmax=sqrt((pow((px-py)/2,2))+pow(q,2))\n", + "\n", + "print\"qmax=\",round(qmax,2),\"N/mm^2\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# example 11.5 page number 356" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "p1= 82.8 N/mm^2\n", + "p2= -62.8 N/mm^2\n", + "qmax= 72.8 N/mm^2\n", + "theta= 7.97 ° and 97.97 °\n", + "theta'= 37.03 ° and= 52.97 °\n", + "answer in book is wrong\n" + ] + } + ], + "source": [ + "\n", + "from math import sqrt,cos,sin,atan,pi\n", + "#variable declaration\n", + "#Let the principal plane make anticlockwise angle theta with the plane of px with y-axis. Then\n", + "\n", + "px=float(80) #N/mm^2\n", + "py=float(-60) #N/mm^2\n", + "q=float(20) #N/mm^2\n", + "\n", + "\n", + "p1=(px+py)/2+sqrt(pow(((px-py)/2),2)+pow(q,2))\n", + "\n", + "print \"p1=\",round(p1,2),\"N/mm^2\"\n", + "\n", + "p2=(px+py)/2-sqrt(pow(((px-py)/2),2)+pow(q,2))\n", + "\n", + "print \"p2=\",round(p2,2),\"N/mm^2\"\n", + "\n", + "qmax=sqrt((pow((px-py)/2,2))+pow(q,2))\n", + "\n", + "print\"qmax=\",round(qmax,2),\"N/mm^2\"\n", + "\n", + "#let theta be the inclination of principal stress to the plane of px.\n", + "\n", + "\n", + "theta1=(atan((2*q)/(px-py))*180)/(pi*2) \n", + "theta2=90+theta1\n", + "print\"theta=\",round(theta1,2),\"°\" \" and \",round(theta2,2),\"°\"\n", + "\n", + "#Planes of maximum shear make 45° to the above planes.\n", + "theta11=45-theta1\n", + "theta22=theta2-45\n", + "print\"theta'=\",round(theta11,2),\"°\",\"and=\",round(theta22,2),\"°\"\n", + "\n", + "print\"answer in book is wrong\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# example 11.6 page number 357" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "p1= -35.96 N/mm^2\n", + "p2= -139.04 N/mm^2\n", + "qmax= 51.54 N/mm^2\n", + "theta= 37.98 ° and 127.98 °\n" + ] + } + ], + "source": [ + "from math import sqrt,cos,sin,atan,pi\n", + "#variable declaration\n", + "#Let the principal plane make anticlockwise angle theta with the plane of px with y-axis. Then\n", + "\n", + "px=float(-100) #N/mm^2\n", + "py=float(-75) #N/mm^2\n", + "q=float(-50) #N/mm^2\n", + "\n", + "\n", + "p1=(px+py)/2+sqrt(pow(((px-py)/2),2)+pow(q,2))\n", + "\n", + "print \"p1=\",round(p1,2),\"N/mm^2\"\n", + "\n", + "p2=(px+py)/2-sqrt(pow(((px-py)/2),2)+pow(q,2))\n", + "\n", + "print \"p2=\",round(p2,2),\"N/mm^2\"\n", + "\n", + "qmax=sqrt((pow((px-py)/2,2))+pow(q,2))\n", + "\n", + "print\"qmax=\",round(qmax,2),\"N/mm^2\"\n", + "\n", + "#let theta be the inclination of principal stress to the plane of px.\n", + "\n", + "\n", + "theta1=(atan((2*q)/(px-py))*180)/(pi*2) \n", + "theta2=90+theta1\n", + "print\"theta=\",round(theta1,2),\"°\" \" and \",round(theta2,2),\"°\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# example 11.7 page number 358" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(i) p1= 131.07 N/mm^2\n", + "p2= -81.07 N/mm^2\n", + "(ii) qmax= 106.07 N/mm^2\n", + "theta= -22.5 ° clockwise\n", + "theta2= 22.5 °\n", + "p= 108.97 N/mm^2\n", + "phi= 13.3 °\n", + "mitake in book answer is wrong\n" + ] + } + ], + "source": [ + "from math import sqrt,cos,sin,atan,pi\n", + "#variable declaration\n", + "#Let the principal plane make anticlockwise angle theta with the plane of px with y-axis. Then\n", + "\n", + "px=float(-50) #N/mm^2\n", + "py=float(100) #N/mm^2\n", + "q=float(75) #N/mm^2\n", + "\n", + "\n", + "p1=(px+py)/2+sqrt(pow(((px-py)/2),2)+pow(q,2))\n", + "\n", + "print \"(i) p1=\",round(p1,2),\"N/mm^2\"\n", + "\n", + "p2=(px+py)/2-sqrt(pow(((px-py)/2),2)+pow(q,2))\n", + "\n", + "print \"p2=\",round(p2,2),\"N/mm^2\"\n", + "\n", + "qmax=sqrt((pow((px-py)/2,2))+pow(q,2))\n", + "\n", + "print\"(ii) qmax=\",round(qmax,2),\"N/mm^2\"\n", + "\n", + "#let theta be the inclination of principal stress to the plane of px.\n", + "\n", + "\n", + "theta1=(atan((2*q)/(px-py))*180)/(pi*2) \n", + "\n", + "print\"theta=\",round(theta1,2),\"°\" \" clockwise\"\n", + "\n", + "#Plane of maximum shear makes 45° to it \n", + "\n", + "theta2=theta1+45\n", + "print\"theta2=\",round(theta2,2),\"°\" \n", + "\n", + "#Normal stress on this plane is given by\n", + "\n", + "pn=((px+py)/2)+((px-py)/2)*cos(2*theta2*pi/180)+q*sin(2*theta2*pi/180)\n", + "\n", + "pt=qmax\n", + "\n", + "#Resultant stress\n", + "p=sqrt(pow(pn,2)+pow(pt,2))\n", + "\n", + "print \"p=\",round(p,2),\"N/mm^2\"\n", + "\n", + "#Let ‘p’ make angle phi to tangential stress (maximum shear stress plane). \n", + "\n", + "phi=atan(pn/pt)*180/pi\n", + "\n", + "print \"phi=\",round(phi,1),\"°\"\n", + "\n", + "#there is mistake in book\n", + "print\"mitake in book answer is wrong\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# example 11.9 page number 361" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " p1= 0.17 N/mm^2\n", + " p2= -84.17 N/mm^2\n" + ] + } + ], + "source": [ + "from math import sqrt\n", + "\n", + "#variable declaration\n", + "\n", + "w=float(100) #wide of rectangular beam,mm\n", + "h=float(200) #height or rectangular beam dude,mm\n", + "\n", + "I=w*pow(h,3)/12\n", + "\n", + "#At point A, which is at 30 mm below top fibre \n", + "y=100-30\n", + "M=float(80*1000000) #sagging moment,KN-m\n", + "\n", + "fx=M*y/I\n", + "\n", + "px=-fx\n", + "F=float(100*1000 ) #shear force,N\n", + "b=float(100)\n", + "A=b*30\n", + "y1=100-15\n", + "\n", + "q=(F*(A*y1))/(b*I) #shearing stress,N/mm^2\n", + "\n", + "py=0\n", + "p1=(px+py)/2+sqrt(pow(((px-py)/2),2)+pow(q,2))\n", + "p2=(px+py)/2-sqrt(pow(((px-py)/2),2)+pow(q,2))\n", + "print \" p1=\",round(p1,2),\"N/mm^2\"\n", + "print \" p2=\",round(p2,2),\"N/mm^2\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# example 11.10 page number 362\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(i) p1= 0.8333 N/mm^2\n", + " p2= -0.8333 N/mm^2\n", + "theta= 45.0 ° and 135.0 °\n", + "(ii) p1= 0.0122 N/mm^2\n", + " p2= -32.4196 N/mm^2\n", + "theta= -1.0 ° and 89.0 °\n", + "mistake in book\n", + "(iii) p1= 0.0 N/mm^2\n", + " p2= -64.8148 N/mm^2\n", + "theta= -0.0 ° and 90.0 °\n" + ] + } + ], + "source": [ + "from math import sqrt,atan\n", + "\n", + "P1=float(20) #vertical loading from A at distance of 1m,KN.\n", + "P2=float(20) #vertical loading from A at distance of 2m,KN.\n", + "P3=float(20) #vertical loading from A at distance of 3m,KN.\n", + "Ra=(P1+P2+P3)/2 #Due to symmetry\n", + "\n", + "Rb=Ra \n", + "#At section 1.5 m from A\n", + "F=(Ra-P1)*1000\n", + "M=float((Ra*1.5-P1*0.5)*1000000)\n", + "b=float(100)\n", + "h=float(180)\n", + "\n", + "I=float((b*pow(h,3))/12)\n", + "\n", + "# Bending stress \n", + "#f=M*y/I\n", + "y11=0\n", + "f1=(-1)*M*y11/I\n", + "y22=45\n", + "f2=(-1)*M*y22/I\n", + "y33=90\n", + "f3=(-1)*M*y33/I\n", + "#Shearing stress at a fibre ‘y’ above N–A is\n", + "#q=(F/(b*I))*(A*y1)\n", + "#at y=0,\n", + "y1=45\n", + "A1=b*90\n", + "q1=(F/(b*I))*(A1*y1)\n", + "#at y=45\n", + "y2=float(90-45/2)\n", + "A2=b*45\n", + "q2=(F/(b*I))*(A2*y2)\n", + "#at y=90\n", + "q3=0\n", + "\n", + "#(a) At neutral axis (y = 0) : The element is under pure shear \n", + "\n", + "py=0\n", + "\n", + "p1=(f1+py)/2+sqrt(pow(((f1-py)/2),2)+pow(q1,2))\n", + "\n", + "p2=(f1+py)/2-sqrt(pow(((f1-py)/2),2)+pow(q1,2))\n", + "print \"(i) p1=\",round(p1,4),\"N/mm^2\"\n", + "print \" p2=\",round(p2,4),\"N/mm^2\"\n", + "\n", + "theta1=45\n", + "theta2=theta1+90\n", + "print\"theta=\",round(theta1),\"°\",\" and \",round(theta2),\"°\"\n", + "\n", + "#(b) At (y = 45)\n", + "py=0 \n", + "\n", + "p1=(f2+py)/2+sqrt(pow(((f2-py)/2),2)+pow(q2,2))\n", + "\n", + "p2=(f2+py)/2-sqrt(pow(((f2-py)/2),2)+pow(q2,2))\n", + "print \"(ii) p1=\",round(p1,4),\"N/mm^2\"\n", + "print \" p2=\",round(p2,4),\"N/mm^2\"\n", + "\n", + "thetab1=(atan((2*q2)/(f2-py))*180)/(pi*2)\n", + "thetab2=thetab1+90\n", + "print\"theta=\",round(thetab1),\"°\",\" and \",round(thetab2),\"°\"\n", + "#mistake in book\n", + "print\"mistake in book\"\n", + "\n", + "#(c) At Y=90\n", + "\n", + "py=0\n", + "\n", + "p1=(f3+py)/2+sqrt(pow(((f3-py)/2),2)+pow(q3,2))\n", + "\n", + "p2=(f3+py)/2-sqrt(pow(((f3-py)/2),2)+pow(q3,2))\n", + "print \"(iii) p1=\",round(p1,4),\"N/mm^2\"\n", + "print \" p2=\",round(p2,4),\"N/mm^2\"\n", + "\n", + "thetac1=(atan((2*q3)/(f3-py))*180)/(pi*2)\n", + "thetac2=thetac1+90\n", + "print\"theta=\",round(thetac1),\"°\",\" and \",round(thetac2),\"°\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# example 11.11 page number 364\n" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " p1= 5.21 N/mm^2\n", + " p2= -107.56 N/mm^2\n", + "qmax= 56.38 N/mm^2\n" + ] + } + ], + "source": [ + "from math import sqrt\n", + "\n", + "#variable declaration\n", + "L=float(6) #m\n", + "w=float(60) #uniformly distributed load,KN/m\n", + "Rs=L*w/2 #Reaction at support,KN\n", + "\n", + "#Moment at 1.5 m from support\n", + "M =float( Rs*1.5-(w*pow(1.5,2)/2))\n", + "#Shear force at 1.5 m from support \n", + "F=Rs-1.5*w\n", + "\n", + "B=float(200) #width of I-beam,mm\n", + "H=float(400) #height or I-beam,mm\n", + "b=float(190)\n", + "h=float(380)\n", + "I= (B*pow(H,3)/12)-(b*pow(h,3)/12)\n", + "\n", + "#Bending stress at 100 mm above N–A\n", + "y=100\n", + "\n", + "f=M*1000000*y/I\n", + "\n", + "#Thus the state of stress on an element at y = 100 mm, as px = f,py=0\n", + "px=-f\n", + "py=0\n", + "A=200*10*195+10*90*145\n", + "q=(F*1000*(A))/(10*I) #shearing stress,N/mm^2\n", + "\n", + "p1=(px+py)/2+sqrt(pow(((px-py)/2),2)+pow(q,2))\n", + "p2=(px+py)/2-sqrt(pow(((px-py)/2),2)+pow(q,2))\n", + "print \" p1=\",round(p1,2),\"N/mm^2\"\n", + "print \" p2=\",round(p2,2),\"N/mm^2\"\n", + "\n", + "\n", + "qmax=sqrt((pow((px-py)/2,2))+pow(q,2))\n", + "\n", + "print\"qmax=\",round(qmax,2),\"N/mm^2\"\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [Root]", + "language": "python", + "name": "Python [Root]" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} -- cgit