// Numbas version: finer_feedback_settings
{"name": "Internal force: Overhanging beam", "extensions": ["geogebra", "jsxgraph", "shear-and-bending-moment-diagrams", "quantities"], "custom_part_types": [{"source": {"pk": 19, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/19/edit"}, "name": "Engineering Accuracy with units", "short_name": "engineering-answer", "description": "<p>A value with units marked right if within an adjustable % error of the correct value. &nbsp;Marked close if within a wider margin of error.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\n\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\n\n\ncorrect_units:\nunits(correct_quantity)\n\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\nreplace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n\n\nstudent_quantity:\nswitch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n\n\npercent_error:\ntry(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   \n\nright:\npercent_error <= settings['right']\n\n\nclose:\nright_sign and percent_error <= settings['close']\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)\n\n"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]\n\n"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)\n"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "<p>Modify&nbsp;the&nbsp;unit portion of&nbsp;the student's answer by</p>\n<p>1. replacing \"ohms\" with \"ohm\" &nbsp;case insensitive</p>\n<p>2.&nbsp;replacing '-'&nbsp;with ' '&nbsp;</p>\n<p>3. replacing '&deg;' with ' deg'&nbsp;</p>\n<p>to allow answers like 10 ft-lb and 30&deg;</p>", "definition": "replace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n"}, {"name": "student_quantity", "description": "<p>This fixes the student answer for two common errors. &nbsp;</p>\n<p>If student_units are wrong&nbsp;&nbsp;- replace with correct units</p>\n<p>If student_scalar has the wrong sign - replace with right sign</p>\n<p>If student makes both errors, only one gets fixed.</p>", "definition": "switch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n"}, {"name": "percent_error", "description": "", "definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   "}, {"name": "right", "description": "", "definition": "percent_error <= settings['right']\n"}, {"name": "close", "description": "<p>Only marked close if the student actually has the right sign.</p>", "definition": "right_sign and percent_error <= settings['close']"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity) "}], "settings": [{"name": "correctAnswer", "label": "Correct Quantity.", "help_url": "", "hint": "The correct answer given as a JME quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "right", "label": "% Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "0.2", "evaluate": true}, {"name": "close", "label": "% Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "1.0", "evaluate": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units. &nbsp;if correct answer is 100 N and close is &plusmn;1%,<br />99 &nbsp;N is accepted.", "input_type": "percent", "default_value": "75"}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.<br />If the correct answer is 100 N, both 100 and -100 N are accepted.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value but forgotten units.<br />This value would be close&nbsp;if the expected units were provided. &nbsp;If the correct answer is 100 N, and close is &plusmn;1%,<br />99 is accepted.", "input_type": "percent", "default_value": "25"}], "public_availability": "always", "published": true, "extensions": ["quantities"]}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Internal force: Overhanging beam", "tags": ["bending moment", "distributed load", "internal forces", "Mechanics", "mechanics", "shear", "Statics", "statics"], "metadata": {"description": "<p>Calculate reactions and shear and bending moment at a point for&nbsp;an overhanging beam with a constant&nbsp;or uniformly varying distributed load.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>{loadDiagram}</p>\n<p style=\"padding: 3px;\">The $\\var{distance(L)}$ beam shown supports a load that varies uniformly from $\\var{load(Wa)}$ at the left end to $\\var{load(Wb)}$ at the right end. Point $C$ is located at $x =\\var{distance(C)}$.</p>\n<ul></ul>", "advice": "<p><strong>1. &nbsp;Replace the distributed load with an equivalent concentrated load and draw a free-body diagram of the entire beam.</strong></p>\n<p>{fbd1}</p>\n<p>Recall that the equivalent force of a distributed load is the 'area' and it acts at the centroid of the shaded area above.</p>\n<p>\\[ W = \\var{force(W)},\\qquad &nbsp; &nbsp; &nbsp;\\bar{x}=\\var{distance(xbarW)}\\]</p>\n<p><strong>2. &nbsp;Apply equilibrium equations to find the reactions at $A$ and $B$.</strong></p>\n<p>\\[\\begin{align} \\Sigma M_A &amp;= 0 &amp; &nbsp;\\Sigma F_y &amp;=0 \\\\<br/>R_B\\cdot \\var{distance(B)} &amp;= &nbsp;W \\cdot \\bar{x} &amp; &nbsp;R_A + R_B &amp;= \\var{W}\\\\<br/>R_B &amp;= \\var{force(R_B)} \\uparrow &amp; R_A &amp;= \\var{force(abs(R_A))} &nbsp;\\var{if(R_A&gt;0,latex('\\\\uparrow'),latex('\\\\downarrow'))}\\end{align}\\]</p>\n<p><strong>3. Take an imaginary cut at point $C$, and draw a FBD of the portion of the beam &nbsp;to the left of $C$ and use it to find the shear and bending moment at the cut.</strong></p>\n<p>{fbd2}</p>\n<p style=\"padding-left: 30px;\"><strong>a. &nbsp;Use similar triangles to find $w_C$, &nbsp;the distributed load at point $C$.</strong></p>\n<p style=\"padding-left: 60px;\">Knowing $w_A = \\var{load(wA)} $, $w_B = \\var{load(wB)} $.</p>\n<p style=\"padding-left: 60px;\">\\[ \\begin{align}<br/>\\dfrac{w_C -w_A}{\\var{distance(C)}} &amp;= \\dfrac{w_B-w_A}{\\var{distance(L)}}\\\\<br/>&nbsp;w_C &amp;= w_A + \\left(\\var{siground(c/L,4)} \\right)\\left( w_B - w_A \\right) \\\\<br/>&amp;= \\var{load(WC)}<br/>\\end{align}\\]</p>\n<p style=\"padding-left: 20px;\"><strong>b. &nbsp;Find the equivalent force due to the distributed load.</strong></p>\n<p style=\"padding-left: 20px;\">&nbsp;\\[ \\begin{align}<br/>&nbsp; W' &amp;= (\\var{distance(C)}) \\left(\\dfrac{W_A + W_C}{2}\\right) \\\\<br/>&nbsp; &nbsp; &nbsp; &amp; = \\var{force(W')}<br/>\\end{align} \\]</p>\n<p style=\"padding-left: 20px;\"><strong>c. &nbsp;Locate the centroid of the equivalent concentrated load.</strong></p>\n<p style=\"padding-left: 60px;\">\\[ \\bar{x} = \\var{force(xbarW')}\\]</p>\n<p style=\"padding-left: 20px;\"><strong>d. Apply equilibrium equations to solve for the shear and moment at $C$.</strong></p>\n<p style=\"padding-left: 40px;\">\\[\\begin{align} \\Sigma F_y &amp;=0\\\\ <br/>V_C &amp;= \\var{force(FV)} \\end{align}\\]</p>\n<div data-jme-visible=\"B&gt;C\">\n<p style=\"padding-left: 40px;\">\\[\\begin{align} <br/>\\Sigma M_C &amp;= 0 \\\\ <br/>M_C &nbsp;&amp; = R_A \\cdot \\var{distance(C)} - W' &nbsp;\\cdot (\\var{distance(C)} -\\bar{x}) &nbsp;\\\\<br/>&amp;= \\left( \\var{force(R_A)}\\right) &nbsp;\\left(\\var{distance(C)}\\right) - \\left(\\var{force(W')}\\right) \\left(\\var{distance(d)}\\right) &nbsp; \\\\<br/>M_C &amp;= \\var{moment(M_C)} &nbsp;\\end{align}\\]</p>\n<p style=\"padding-left: 40px;\"></p>\n</div>\n<div data-jme-visible=\"B&lt;C\">\n<p style=\"padding-left: 40px;\">\\[\\begin{align} <br/>\\Sigma M_C &amp;= 0 \\\\ <br/>M_C &nbsp;&amp; = R_A \\cdot \\var{distance(C)} - W' &nbsp;\\cdot (\\var{distance(C)} -\\bar{x}) &nbsp;+R_B \\cdot d_\\perp) \\\\<br/>&amp;= \\left( \\var{force(R_A)}\\right) &nbsp;\\left(\\var{distance(C)}\\right) - \\left(\\var{force(W')}\\right) \\left(\\var{distance(d)}\\right)+\\left(\\var{force(R_B)}\\right) \\left(\\var{distance(C-B)}\\right) &nbsp;\\\\<br/>M_C &amp;= \\var{moment(M_C)} &nbsp;\\end{align}\\]</p>\n</div>\n<p></p>", "rulesets": {}, "extensions": ["geogebra", "jsxgraph", "quantities", "shear-and-bending-moment-diagrams"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"L": {"name": "L", "group": "Quantities", "definition": "random(12..20#2)", "description": "<p>overall length of the beam.</p>", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "functions", "definition": "random(['N','m', 'N*m', 'N/m'],['lb','ft', 'ft*lb', 'lb/ft'])", "description": "", "templateType": "anything", "can_override": false}, "debug": {"name": "debug", "group": "Ungrouped variables", "definition": "false", "description": "", "templateType": "anything", "can_override": false}, "FV": {"name": "FV", "group": "Unnamed group", "definition": "siground(R_A + if(B<C,R_B,0)  - W',5)", "description": "<p>shear force at C, Signed</p>", "templateType": "anything", "can_override": false}, "M_C": {"name": "M_C", "group": "Unnamed group", "definition": "siground(R_A * C - W' *(C - xbarW') + if(B<C, R_B * (C-B), 0),4) ", "description": "<p>moment at D, signed</p>\n<p>&minus;\ud835\udc34\u2113&minus;\ud835\udc4a&prime;\ud835\udc51&perp;&minus;\ud835\udc36\ud835\udc512</p>", "templateType": "anything", "can_override": false}, "C": {"name": "C", "group": "Quantities", "definition": "random(2..L#2 except[L,B])", "description": "<p>position of cut</p>", "templateType": "anything", "can_override": false}, "size": {"name": "size", "group": "Quantities", "definition": "random(50,100,200)", "description": "<p>Random load value used to make actual loads Wa and Wb.</p>", "templateType": "anything", "can_override": false}, "WC": {"name": "WC", "group": "Quantities", "definition": "WA +  (WB-WA) C / L ", "description": "<p>distributed load value at point C</p>", "templateType": "anything", "can_override": false}, "WB": {"name": "WB", "group": "Quantities", "definition": "size random(0..2#0.5)", "description": "<p>distributed load value at point A, right end.</p>", "templateType": "anything", "can_override": false}, "WA": {"name": "WA", "group": "Quantities", "definition": "size random(0..2#0.5)", "description": "<p>distributed load value at point A, left end</p>", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Unnamed group", "definition": "c-xbarw'", "description": "<p>distance from cut to equivalent load</p>", "templateType": "anything", "can_override": false}, "force": {"name": "force", "group": "functions", "definition": "(f)-> siground(qty(f, units[0]),4)", "description": "", "templateType": "anything", "can_override": false}, "distance": {"name": "distance", "group": "functions", "definition": "(d)->siground(qty(d,units[1]),4)", "description": "", "templateType": "anything", "can_override": false}, "load": {"name": "load", "group": "functions", "definition": "(l)->siground(qty(l,units[3]),4)", "description": "", "templateType": "anything", "can_override": false}, "properties": {"name": "properties", "group": "jsxgraph", "definition": "[beamLength: L, loads: [w1], forces: [], moments: [], reactions: [hide(RA),hide(RB)], symbols: symbols]", "description": "", "templateType": "anything", "can_override": false}, "W1": {"name": "W1", "group": "jsxgraph", "definition": "[[x: 0, value: wA, label: WA+if(WA<>WB, \" to \" + string(load(WB)) , ''), visible: true],[x: L, value: WB, label: \"D\", visible: true],]", "description": "", "templateType": "anything", "can_override": false}, "LoadDiagram": {"name": "LoadDiagram", "group": "jsxgraph", "definition": "vmloaddiagram(properties)", "description": "", "templateType": "anything", "can_override": false}, "symbols": {"name": "symbols", "group": "jsxgraph", "definition": "[[x: C, type: \"dot\", visible: true, label: \"$C$\"],[x: B, type: \"roller\", visible: true , label: \"$B$\"], [x: 0, type: 'pin', visible: true, label: \"$A$\"]]", "description": "", "templateType": "anything", "can_override": false}, "moment": {"name": "moment", "group": "functions", "definition": "(m)-> siground(qty(m, units[2]),4)", "description": "", "templateType": "anything", "can_override": false}, "B": {"name": "B", "group": "Quantities", "definition": "round(random(L/2..L))", "description": "", "templateType": "anything", "can_override": false}, "xbar": {"name": "xbar", "group": "functions", "definition": "(w) -> let (xa, w[0][\"x\"], xb, w[1][\"x\"], ya, w[0][\"value\"], yb, w[1][\"value\"] , if(xa+xb=0, 0, xa+(xb - xa)*(ya + 2 yb)/3/(ya + yb)))", "description": "", "templateType": "anything", "can_override": false}, "xbarW": {"name": "xbarW", "group": "jsxgraph", "definition": "xbar(W1)", "description": "", "templateType": "anything", "can_override": false}, "area": {"name": "area", "group": "functions", "definition": "w -> let (xa, w[0][\"x\"], xb, w[1][\"x\"], ya, w[0][\"value\"], yb, w[1][\"value\"] ,(xb-xa)(ya+yb)/2)", "description": "", "templateType": "anything", "can_override": false}, "W": {"name": "W", "group": "jsxgraph", "definition": "area(W1)", "description": "<p>equivalent force of entire load</p>", "templateType": "anything", "can_override": false}, "W1'": {"name": "W1'", "group": "Unnamed group", "definition": "[[x: 0, value: wA, label: '', visible: true],[x: C, value: WC, label: \"C\", visible: true],]", "description": "", "templateType": "anything", "can_override": false}, "xbarW'": {"name": "xbarW'", "group": "Unnamed group", "definition": "xbar(w1')", "description": "", "templateType": "anything", "can_override": false}, "W'": {"name": "W'", "group": "Unnamed group", "definition": "area(W1')", "description": "<p>equivalent force of part load</p>", "templateType": "anything", "can_override": false}, "EqW": {"name": "EqW", "group": "diagrams", "definition": "[x: xbar(w1), value: area(W1), label: \"$W$\", visible: true]", "description": "", "templateType": "anything", "can_override": false}, "EqW'": {"name": "EqW'", "group": "Unnamed group", "definition": "[x: xbarW', value: W', label: \"$W'$\", visible: true]", "description": "", "templateType": "anything", "can_override": false}, "R_A": {"name": "R_A", "group": "Quantities", "definition": "let(equivalent_loads, eqw,(sum(map(f->cross( vector(B-f[\"x\"],0,0),vector(0,-f[\"value\"],0))[2],forces+equivalent_loads))\n- sum(map(m->m['value'], moments)))/(A-B))\n", "description": "<p>Reaction at A</p>", "templateType": "anything", "can_override": false}, "check": {"name": "check", "group": "Quantities", "definition": "R_A + R_B = EqW[\"value\"]", "description": "", "templateType": "anything", "can_override": false}, "shearDiagram": {"name": "shearDiagram", "group": "jsxgraph", "definition": "vmsheardiagram(properties,debug)", "description": "", "templateType": "anything", "can_override": false}, "momentDiagram": {"name": "momentDiagram", "group": "jsxgraph", "definition": "vmmomentdiagram(properties,debug)", "description": "", "templateType": "anything", "can_override": false}, "reactions": {"name": "reactions", "group": "jsxgraph", "definition": "[[x: 0, value: R_A, label: \"$R_A$\", visible: false],[x: B, value: R_B, label: \"$R_B$\", visible: false]]", "description": "", "templateType": "anything", "can_override": false}, "forces": {"name": "forces", "group": "Ungrouped variables", "definition": "[]", "description": "", "templateType": "anything", "can_override": false}, "moments": {"name": "moments", "group": "Ungrouped variables", "definition": "[]", "description": "", "templateType": "anything", "can_override": false}, "properties_fbd1": {"name": "properties_fbd1", "group": "diagrams", "definition": "[beamLength: L, loads: [[hide(relabel(w1[0], \"\")),w1[1]]], forces: [eqw], reactions: [[x: 0, value: abs(R_A), label: \"$R_A$\", visible: true],RB], moments: [], symbols: [[x: C, type: \"dot\", visible: true, label: \"$C$\"],[x: xbarw, type: \"dot\", label: \"$\\\\bar{x}$\", visible: true]]]", "description": "", "templateType": "anything", "can_override": false}, "fbd1": {"name": "fbd1", "group": "diagrams", "definition": "vmloaddiagram(properties_fbd1)", "description": "", "templateType": "anything", "can_override": false}, "relabel": {"name": "relabel", "group": "functions", "definition": "(dict, label) -> merge(dict, [label: label])", "description": "", "templateType": "anything", "can_override": false}, "hide": {"name": "hide", "group": "functions", "definition": "(dict) -> merge(dict, [visible: false])", "description": "", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "Quantities", "definition": "0", "description": "", "templateType": "anything", "can_override": false}, "RA": {"name": "RA", "group": "jsxgraph", "definition": "[x: 0, value: R_A, label: \"$R_A$\", visible: true]", "description": "", "templateType": "anything", "can_override": false}, "RB": {"name": "RB", "group": "jsxgraph", "definition": "[x: B, value: R_B, label: \"$R_B$\", visible: true]", "description": "", "templateType": "anything", "can_override": false}, "properties_fbd2": {"name": "properties_fbd2", "group": "Unnamed group", "definition": "[beamLength: C, loads: [[hide(w1'[0]),w1'[1]]], forces: [eqw'], reactions: [relabel(RA, string(force(abs(RA[\"value\"])))),V, relabel(RB, string(force(abs(RB[\"value\"]))))], moments: [M], symbols: [[x: xbarw', type: \"dot\", label: \"$\\\\bar{x}$\", visible: true], [x: B, type: \"dot\", label: \"$B$\", visible: true]]]", "description": "", "templateType": "anything", "can_override": false}, "fbd2": {"name": "fbd2", "group": "Unnamed group", "definition": "vmloaddiagram(properties_fbd2)", "description": "", "templateType": "anything", "can_override": false}, "V": {"name": "V", "group": "Unnamed group", "definition": "[x: C, value: -abs(fv), label: \"$V_C$\", visible: true]", "description": "<p>shear force points down on fbd</p>", "templateType": "anything", "can_override": false}, "M": {"name": "M", "group": "Unnamed group", "definition": "[x: C, value: 1, label: \"$M_C$\", visible: true]", "description": "", "templateType": "anything", "can_override": false}, "R_B": {"name": "R_B", "group": "Quantities", "definition": "-map(f->cross( vector(A-f[\"x\"],0,0),vector(0,-f[\"value\"],0))[2],forces+eqw)[0]/(A-B)\n", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "WA<>WB //always trapezoidal", "maxRuns": 100}, "ungrouped_variables": ["debug", "forces", "moments"], "variable_groups": [{"name": "Quantities", "variables": ["L", "A", "B", "C", "size", "WA", "WB", "WC", "R_A", "R_B", "check"]}, {"name": "vectors", "variables": []}, {"name": "jsxgraph", "variables": ["properties", "LoadDiagram", "shearDiagram", "momentDiagram", "W1", "symbols", "xbarW", "reactions", "W", "RA", "RB"]}, {"name": "functions", "variables": ["units", "force", "distance", "load", "moment", "area", "xbar", "relabel", "hide"]}, {"name": "diagrams", "variables": ["EqW", "properties_fbd1", "fbd1"]}, {"name": "Unnamed group", "variables": ["properties_fbd2", "fbd2", "W1'", "W'", "xbarW'", "EqW'", "FV", "M_C", "d", "V", "M"]}], "functions": {"display": {"parameters": [["q", "quantity"]], "type": "string", "language": "jme", "definition": "string(siground(q,4))"}, "applet": {"parameters": [["app_width", "number"], ["app_height", "number"], ["show_fbd", "boolean"]], "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  material_id: 'susdzdmr',\n  width: app_width,\n  height: app_height\n};\n//geogebra_applet('susdzdmr') old ggb file\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  question.applet = d;\n  app.setGridVisible(false);\n  \n  function 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 function setGGBNumber(name) {\n    // Sets number in GGB to a Numbas Variable\n    var n = question.scope.evaluate(name).value;\n    app.setValue(name,n);\n  }\n  \n  setGGBPoint(\"C\");\n  setGGBPoint(\"D\");\n  app.setValue('fbd',show_fbd);\n  app.setAxesVisible(false,false);\n  app.enableShiftDragZoom(false);\n  setGGBNumber(\"w_A\");\n  setGGBNumber(\"w_B\");\n  \n \n  \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);"}, "showfbds": {"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  material_id: 'susdzdmr',\n  width: 500,\n  height: 500\n};\n//geogebra_applet('susdzdmr') old ggb file\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  question.applet = d;\n  app.setGridVisible(false);\n  \n  function 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 function setGGBNumber(name) {\n    // Sets number in GGB to a Numbas Variable\n    var n = question.scope.evaluate(name).value;\n    app.setValue(name,n);\n  }\n  \n  setGGBPoint(\"C\");\n  setGGBPoint(\"D\");\n  app.setValue('fbd',true);\n  app.setAxesVisible(false,false);\n  app.enableShiftDragZoom(false);\n  setGGBNumber(\"w_A\");\n  setGGBNumber(\"w_B\");\n  \n \n  \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);"}, "trapezoid": {"parameters": [["a", "number"], ["b", "number"], ["w", "number"]], "type": "vector", "language": "jme", "definition": "[(a+b)/2 * w, (w/3)*(a + 2b)/(a+b)] // a = left height, b = right height, w = width.... returns area and xbar"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Reactions", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Determine the reactions at pin $A$ and roller $B$. &nbsp;Let positive values indicate upward forces.</p>\n<p>$A$ =&nbsp;[[0]]&nbsp; &nbsp;<span data-jme-visible=\"debug\"> $\\var{force(R_A)}$</span></p>\n<p>$B$ = [[1]]&nbsp; &nbsp;<span data-jme-visible=\"debug\">$\\var{force(R_B)}$</span></p>", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "$R_A$", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "force(R_A)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "$R_B$", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "Force(R_B)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Internal Load", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Determine the internal shear and bending moment at a section passing through point $C$. Use the standard convention for the meaning of positive shears and bending moments.&nbsp;</p>\n<p>$V_C$ &nbsp;= [[0]]&nbsp; &nbsp; <span data-jme-visible=\"debug\">$\\var{force(FV)}$</span></p>\n<p>$M_C$ = [[1]] &nbsp;&nbsp; <span data-jme-visible=\"debug\">$\\var{moment(M_C)}$</span></p>", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "$V_C$", "marks": "15", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "force(FV)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "$M_C$", "marks": "15", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "moment(M_C)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "resources": []}]}], "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}