// Numbas version: exam_results_page_options
{"name": "Truss: zero force members", "extensions": ["geogebra"], "custom_part_types": [], "resources": [["question-resources/FBD_kZRowVa.png", "/srv/numbas/media/question-resources/FBD_kZRowVa.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Truss: zero force members", "tags": ["Mechanics", "mechanics", "Statics", "statics", "truss", "zero-force"], "metadata": {"description": "Given a loaded truss, identify any zero force members by inspection.", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>{applet()}</p>\n<p></p>\n<p><span data-jme-visible=\"false\">Scripts in part seems to cause breakage of marking algorithm - moved it to advise section.&nbsp;</span></p>\n<div data-jme-visible=\"false\">\n<p><strong>Loads: </strong>down is positive</p>\n<p>{f}</p>\n<p><strong>Loads and reactions:</strong> &nbsp;down is positive &nbsp;&nbsp;</p>\n<p>{loads[0]} = {f[loads[0]]} {loads[1]} = {f[loads[1]]} &nbsp;{supports[0]} = {reactions[0]} &nbsp; {supports[1]} = {reactions[1]} &nbsp; &nbsp;$\\Sigma M_A:$&nbsp;&nbsp;=&nbsp;&nbsp;{13 x[loads[0]]+ 17 x[loads[1]] + reactions[0] * x[supports[0]] &nbsp;&nbsp;+ reactions[1] * x[supports[1]]}</p>\n<p></p>\n<p><strong>Forces in members:</strong> &nbsp;Tension is positive</p>\n<p>{m}</p>\n<p><strong>Joint Equilibrium:</strong></p>\n<p>Joint A: &nbsp;{polar(f[\"A\"], -90) + polar(AB,0) + polar(AG,30)}</p>\n<p>Joint B: &nbsp;&nbsp;{polar(f[\"B\"], -90) + polar(AB,180) + polar(BC,0) &nbsp;+ polar(BG,120) &nbsp;+ polar(BH,60)&nbsp;}</p>\n<p>Joint C: &nbsp; {polar(f[\"C\"], -90) + polar(BC,180) + polar(CD,0) + polar(CH,120) &nbsp;+ polar(CN,60) }</p>\n<p>Joint&nbsp;D: &nbsp; {polar(f[\"D\"], -90)&nbsp;+&nbsp;polar(CD,180) + polar(DE,0) + polar(DO,120)&nbsp;+ polar(DL,60)}</p>\n<p>Joint E: &nbsp; {polar(f[\"E\"], -90) + polar(DE,180) + polar(EF,0) + polar(EL,120) + polar(EM,60)}</p>\n<p>Joint F: &nbsp; {polar(f[\"F\"], -90) + polar(EF,180) + polar(FM,150)}</p>\n<p>Joint G: &nbsp; {polar(f[\"G\"], -90) + polar(GH,30) &nbsp;+ polar(AG,-150) + polar(BG,-60)}</p>\n<p>Joint H: &nbsp;{polar(f[\"H\"], -90) + polar(HN,0) + polar(CH, -60) + polar(BH,-120) + polar(GH, -150) + polar(HI, 30)}</p>\n<p>Joint I: &nbsp; {polar(f[\"I\"], -90) + polar(IJ,30) + polar(NI,-60) + polar(HI,-150)}</p>\n<p>Joint J: &nbsp; {polar(f[\"J\"], -90) + polar(JK,-30) + polar(JO,-60) + polar(JN,-120) + polar(IJ,-150)}</p>\n<p>Joint K: &nbsp; {polar(f[\"K\"], -90) + polar(KL,-30) + polar(KO,-120) + polar(JK,150)}</p>\n<p>Joint L: &nbsp;{polar(f[\"L\"], -90) + polar(LM,-30&nbsp;) + polar(EL, -60) + polar(DL,-120) + polar(LO, 180) + polar(KL, 150)}</p>\n<p>Joint M: &nbsp; {polar(f[\"M\"], -90) + polar(FM,-30) + polar(EM,-120) + polar(LM,150)}</p>\n<p>Joint N: &nbsp;{polar(f[\"N\"], -90) + polar(NI,120&nbsp;) + polar(HN, 180) + polar(JN,60) + polar(CN,-120)}</p>\n<p>Joint O: &nbsp;{polar(f[\"O\"], -90) + polar(KO, 60) + polar(LO,&nbsp;0) + polar(JO,120) + polar(DO, -60)}</p>\n</div>", "advice": "<p>Look for situations like &nbsp;1a) and 2a) in the diagram below. &nbsp;</p>\n<p></p>\n<p></p>\n<p><img src=\"resources/question-resources/FBD_kZRowVa.png\" width=\"613\" height=\"405\"/></p>\n<p></p>\n<p>In figure 1a), members $AB$ and $AC$ share the same line of action and member $AD$ is zero-force. &nbsp;If a load is added to $A$, then member $AD$&nbsp;must pick up load to support it and will not be zero-force.</p>\n<p>If figure 2a), members $AB$ and $AC$ do not share the same line of action and both must be zero-force to maintain equilibrium of joint $A$. &nbsp;If a load is added at $A$ as shown in figure 2b) then $AB$ and $AC$ will pick up load to maintain equilibrium.</p>\n<p>When a member is identified as zero-force, then it may produce zero-force members at adjacent joints.</p>", "rulesets": {}, "extensions": ["geogebra"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"num_ans": {"name": "num_ans", "group": "setup", "definition": "length(filter(m,m,zeroForce))", "description": "<p>This counts the number of zero force members</p>", "templateType": "anything", "can_override": false}, "IJ": {"name": "IJ", "group": "members", "definition": "HI + f[\"I\"]* cos(radians(60))", "description": "", "templateType": "anything", "can_override": false}, "DO": {"name": "DO", "group": "members", "definition": "F[\"D\"] / 2.0/  cos(radians(30)) + DE - CD", "description": "", "templateType": "anything", "can_override": false}, "x": {"name": "x", "group": "setup", "definition": "[\"A\":0,\"B\":2,\"C\":4,\"D\":8,\"E\":10,\"F\":12,\n  \"G\":1.5,\"H\":3,\"I\":4.5,\"J\":6,\"K\":7.5,\"L\":9,\n\"M\":10.5,\"N\":5,\"O\":7]", "description": "<p>horizontal location as dictionary</p>", "templateType": "anything", "can_override": false}, "GH": {"name": "GH", "group": "members", "definition": "0.5 f[\"G\"] + AG", "description": "", "templateType": "anything", "can_override": false}, "EL": {"name": "EL", "group": "members", "definition": "F[\"E\"]/sin(radians(60)) - EM", "description": "", "templateType": "anything", "can_override": false}, "BH": {"name": "BH", "group": "members", "definition": "F[\"B\"]/sin(radians(60)) - BG", "description": "", "templateType": "anything", "can_override": false}, "NI": {"name": "NI", "group": "members", "definition": "-f[\"I\"] * cos(radians(30))", "description": "<ol>\n<li>not alphabetical (IN) becasue in is reserved word</li>\n</ol>", "templateType": "anything", "can_override": false}, "FM": {"name": "FM", "group": "members", "definition": "F[\"F\"] *2.0", "description": "", "templateType": "anything", "can_override": false}, "CH": {"name": "CH", "group": "members", "definition": "CD - BC + F[\"C\"]/2.0/sin(radians(60))", "description": "", "templateType": "anything", "can_override": false}, "KO": {"name": "KO", "group": "members", "definition": "-f[\"K\"] * cos(radians(30))", "description": "", "templateType": "anything", "can_override": false}, "DL": {"name": "DL", "group": "members", "definition": "F[\"D\"]/2.0/cos(radians(30)) - DE + CD", "description": "", "templateType": "anything", "can_override": false}, "CN": {"name": "CN", "group": "members", "definition": "f[\"C\"]/sin(radians(60)) - CH", "description": "", "templateType": "anything", "can_override": false}, "m": {"name": "m", "group": "setup", "definition": "dict([[\"AB\", precround(AB,5)],\n [\"AG\", precround(AG,5)],\n [\"BC\", precround(BC,5)],\n [\"BG\", precround(BG,5)],\n [\"BH\", precround(BH,5)],\n [\"CD\", precround(CD,5)],\n [\"CH\", precround(CH,5)],\n [\"CN\", precround(CN,5)],\n [\"DE\", precround(DE,5)],\n [\"DL\", precround(DL,5)],\n [\"DO\", precround(DO,5)],\n [\"EF\", precround(EF,5)],\n [\"EL\", precround(EL,5)],\n [\"EM\", precround(EM,5)],\n [\"FM\", precround(FM,5)],\n [\"GH\", precround(GH,5)],\n [\"HI\", precround(HI,5)],\n [\"HN\", precround(HN,5)],\n [\"IJ\", precround(IJ,5)],\n [\"JK\", precround(JK,5)],\n [\"JO\", precround(JO,5)],\n [\"JN\", precround(JN,5)],\n [\"KL\", precround(KL,5)],\n [\"KO\", precround(KO,5)],\n [\"LO\", precround(LO,5)],\n [\"LM\", precround(LM,5)],\n [\"NI\", precround(NI,5)]])", "description": "<p>forces in members as dictionary</p>", "templateType": "anything", "can_override": false}, "AB": {"name": "AB", "group": "members", "definition": "-AG cos(radians(30))", "description": "", "templateType": "anything", "can_override": false}, "loads": {"name": "loads", "group": "setup", "definition": "shuffle(set(points)-set(supports))[0..2]\n//[\"J\",\"B\"]//", "description": "<p>2 loads, anywhere but at the supports</p>\n<p>passed to geogebra</p>", "templateType": "anything", "can_override": false}, "JN": {"name": "JN", "group": "members", "definition": "NI + CN + HN/cos(radians(60))", "description": "", "templateType": "anything", "can_override": false}, "zeroForce": {"name": "zeroForce", "group": "setup", "definition": "map(if(m[pt]=0,1,0),pt,members)", "description": "<p>This makes a list of true/false values indicating which members are zero-force</p>", "templateType": "anything", "can_override": false}, "JK": {"name": "JK", "group": "members", "definition": "KL + F[\"K\"]* cos(radians(60))", "description": "", "templateType": "anything", "can_override": false}, "KL": {"name": "KL", "group": "members", "definition": "2.0 F[\"L\"] + 2.0 (EL + DL) cos(radians(30)) + LM", "description": "", "templateType": "anything", "can_override": false}, "LM": {"name": "LM", "group": "members", "definition": "0.5 F[\"M\"] + FM", "description": "", "templateType": "anything", "can_override": false}, "points": {"name": "points", "group": "setup", "definition": "[\"A\",\"B\",\"C\",\"D\",\"E\", \"F\",\"G\",\"H\",\"I\",\"J\", \"K\",\"L\",\"M\",\"N\",\"O\"]", "description": "<p>names of the points</p>", "templateType": "anything", "can_override": false}, "EM": {"name": "EM", "group": "members", "definition": "- F[\"M\"] * cos(radians(30))", "description": "", "templateType": "anything", "can_override": false}, "EF": {"name": "EF", "group": "members", "definition": "-FM cos(radians(30))", "description": "", "templateType": "anything", "can_override": false}, "AG": {"name": "AG", "group": "members", "definition": "2.0 f[\"A\"] ", "description": "", "templateType": "anything", "can_override": false}, "BC": {"name": "BC", "group": "members", "definition": "AB + 0.5(BG-BH)", "description": "", "templateType": "anything", "can_override": false}, "LO": {"name": "LO", "group": "members", "definition": "-( 2.0 f[\"L\"] * cos(radians(30)) + 2.0 DL + EL)", "description": "", "templateType": "anything", "can_override": false}, "CD": {"name": "CD", "group": "members", "definition": "-(6 * f[\"A\"] + 4 * f[\"B\"] + 2*  f[\"C\"]\n  + 4.5 * f[\"G\"] + 3 * f[\"H\"] + 1.5 * f[\"I\"] + f[\"N\"]) / (6 tan(radians(30)))", "description": "<p>sum m at j</p>", "templateType": "anything", "can_override": false}, "members": {"name": "members", "group": "setup", "definition": "[\"AB\",\"AG\",\"BG\", \"BC\",\"BH\",\"GH\",\"CH\",\"CN\", \"CD\", \"HN\",\"HI\",\"NI\",\"JN\",\"IJ\",\"JK\",\"JO\",\n  \"KO\", \"KL\", \"LO\",\"DO\",\"DL\",\"DE\",\"EL\",\"LM\",\"EM\",\n  \"EF\",\"FM\"]\n  ", "description": "<p>names of the members</p>", "templateType": "anything", "can_override": false}, "BG": {"name": "BG", "group": "members", "definition": "- F[\"G\"] * cos(radians(30))", "description": "", "templateType": "anything", "can_override": false}, "f": {"name": "f", "group": "setup", "definition": "dict(map([pt, 0], pt, set(points)-set(supports) - set(loads))) +\ndict(map([supports[pt],reactions[pt]],pt,[0,1]))+\ndict(map([loads[pt],[13,17][pt]], pt, [0,1]))", "description": "<p>forces as dictionary &nbsp;</p>\n<p>downward forces are positive</p>\n<p>Loads have magnitude 1</p>\n<p></p>", "templateType": "anything", "can_override": false}, "JO": {"name": "JO", "group": "members", "definition": "f[\"O\"]/2/cos(radians(30)) + LO + DO", "description": "", "templateType": "anything", "can_override": false}, "HI": {"name": "HI", "group": "members", "definition": "0.5 F[\"H\"] +(BH - HN) cos(radians(30)) + GH", "description": "", "templateType": "anything", "can_override": false}, "DE": {"name": "DE", "group": "members", "definition": "EF + 0.5(EM - EL)", "description": "", "templateType": "anything", "can_override": false}, "reactions": {"name": "reactions", "group": "setup", "definition": "[ -(13 (x[loads[0]] - x[supports[1]]) +\n17 (x[loads[1]] - x[supports[1]]))/(x[supports[0]]-x[supports[1]]),\n  -(13(x[loads[0]] - x[supports[0]])+\n17 (x[loads[1]] - x[supports[0]]))/(x[supports[1]]-x[supports[0]])\n]\n\n", "description": "<p>sum of moments at the supports</p>\n<p>reactions at supports[0] and supports[1]</p>\n<p>Loads assumed to be 13 and 17</p>", "templateType": "anything", "can_override": false}, "supports": {"name": "supports", "group": "setup", "definition": "shuffle([\"A\",\"B\",\"C\",\"D\",\"E\",\"F\"])[0..2]\n//[\"C\",\"D\"]", "description": "<p>reactions -- along the bottom</p>\n<p>passed to geogebra</p>", "templateType": "anything", "can_override": false}, "HN": {"name": "HN", "group": "members", "definition": "-(2.0 CH + BH + 2.0 f[\"H\"] * cos(radians(30)))", "description": "", "templateType": "anything", "can_override": false}, "answers": {"name": "answers", "group": "Ungrouped variables", "definition": "map(if(m[pt]=0,20 /num_ans,0),pt,members)", "description": "<p>array of point values for marking&nbsp;</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["answers"], "variable_groups": [{"name": "setup", "variables": ["points", "members", "loads", "supports", "f", "m", "x", "reactions", "zeroForce", "num_ans"]}, {"name": "members", "variables": ["AB", "AG", "BC", "BG", "BH", "CD", "CH", "CN", "DE", "DL", "DO", "EF", "EL", "EM", "FM", "GH", "HI", "HN", "IJ", "JK", "JO", "JN", "KL", "KO", "LO", "LM", "NI"]}], "functions": {"polar": {"parameters": [["mag", "number"], ["dir", "number"]], "type": "vector", "language": "jme", "definition": "vector([mag * cos(radians(dir)), mag * sin(radians(dir))])"}, "applet": {"parameters": [], "type": "ggbapplet", "language": "javascript", "definition": "// Create the worksheet. \n// This function returns an object with a container `element` and a `promise` resolving to a GeoGebra applet.\nvar params = {\n  //filename: 'resources/question-resources/centroid_F00fWDR.ggb',\n  material_id: 'frtfqyat',\n  //width: 250,\n  //height: 250\n}\n\nvar result = Numbas.extensions.geogebra.createGeogebraApplet(params);\n\n// Once the applet has loaded, run some commands to manipulate the worksheet.\nresult.promise.then(function(d) {\n  var app = d.app;\n  var v = question.scope;\n  question.applet = d;\n  \n function setGGBNumber(name) {\n    // Sets number in GGB to a Numbas Variable\n    var n = v.evaluate(name).value;\n    app.setValue(name,n);\n  }\n  \nfunction setGGBPoint(name) {\n    // moves point in GGB to location of Numbas Vector Variable\n    var pt = question.scope.evaluate(name).value\n    app.setFixed(name,false,false);\n    app.setCoords(name, pt[0], pt[1]);\n    app.setFixed(name,true,true);\n  }\n\n  //initialize pass the locations of the loads and supports to geogebra\n  var s0 = v.evaluate(\"supports[0]\").value;\n  var s1 = v.evaluate(\"supports[1]\").value;\n  app.evalCommand(`supports={\"${s0}\",\"${s1}\"}`);\n  var p0 = v.evaluate(\"loads[0]\").value;\n  var p1 = v.evaluate(\"loads[1]\").value;\n  app.evalCommand(`loads={\"${p0}\",\"${p1}\"}`);\n \n});\n\n// This function returns the result of `createGeogebraApplet` as an object \n// with the JME data type 'ggbapplet', which can be substituted into the question's content.\nreturn new Numbas.jme.types.ggbapplet(result);"}}, "preamble": {"js": "question.signals.on('adviceDisplayed',function() {\n\n // change look of zero force members\n var v = question.scope;\n  try{\n    var app = question.applet.app;\n \n\n for (index = 0; index < 27; index++) { \n    var link = v.evaluate(\"members[\"+index+\"]\").value;\n    var load = v.evaluate(link).value;\n    if(load*load < 0.00005) {\n    \n    app.setVisible(`${link}_1`, false);\n    app.setColor(`${link}_2`, 200,200,200);\n    }\n  } \n\n\n  \n  }\n  catch(err){}  \n})\n\n", "css": ""}, "parts": [{"type": "m_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Select all {num_ans} zero-force members to receive full credit.</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "checkbox", "displayColumns": "5", "minAnswers": "num_ans", "maxAnswers": "num_ans", "warningType": "prevent", "showCellAnswerState": false, "markingMethod": "sum ticked cells", "choices": "members", "matrix": "answers"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}]}], "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}