A value with units marked right if within an adjustable % error of the correct value. Marked close if within a wider margin of error.
", "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\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)\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": "Modify the unit portion of the student's answer by
\n1. replacing \"ohms\" with \"ohm\" case insensitive
\n2. replacing '-' with ' '
\n3. replacing '°' with ' deg'
\nto allow answers like 10 ft-lb and 30°
", "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": "This fixes the student answer for two common errors.
\nIf student_units are wrong - replace with correct units
\nIf student_scalar has the wrong sign - replace with right sign
\nIf student makes both errors, only one gets fixed.
", "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": "Only marked close if the student actually has the right sign.
", "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. if correct answer is 100 N and close is ±1%,Calculate reactions and shear and bending moment at a point for an overhanging beam with a constant or uniformly varying distributed load.
", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "{applet(500,215,false)}
\nThe beam shown supports a uniformly distributed load of $w$ = {Wa}. load that varies uniformly from {Wa} at the left end to {Wb} at the right end.
\nThe lengths of the beam segments are $d_1$ = {display(d_1)}, $d_2$ = {display(d_2)}, and $d_3$ = {display(d_3)}.
", "advice": "1. Draw a FBD of the entire beam and find reactions at A and C.
\n{applet(500,566,true)}
\na. Replace distributed load with an equivalent concentrated load.
\n$W$ = {W_t}, $d$ = {display(dw)}
\nb. Apply equilibrium equations.
\n$\\begin{align} \\Sigma M_A &= 0 & \\Sigma F_y &=0 \\\\C \\cdot\\var{if(C[0]<D[0],latex('d_1'),latex('(d_1+d_2)'))} &= W \\cdot d & \\simplify{{if(scalar(FA)<0,-1,1)} A} + C &= W = \\var{W_t}\\\\ C &= \\var{display(FC)} \\uparrow & A &= \\var{display(abs(FA))} \\var{if(F_A[1]>0,latex('\\\\uparrow'),latex('\\\\downarrow'))}\\end{align}$
\n2. Draw a FBD of the portion of the beam between A and D and find the shear and bending moment.
\na. Determine the distributed load above point D.
\nLet $w_A$, $w_B$, and $w_D$ be the magnitude of the distributed load at points $A$, $B$, and $D$ respectively, and $L$ the length of the beam.
\nGiven: $w_A = \\var{wA},\\qquad w_B = \\var{wB}\\qquad L = (d_1 + d_2 + d_3) = \\var{L}$
\n$w_D = \\var{display(wD)}$
\nUsing similar triangles: $w_D = w_A + \\dfrac{\\var{if(C[0]>D[0],latex('d_1'),latex('(d_1+d_2)'))}}{L} \\left( w_B - w_A \\right) = \\var{display(wD)}$
\nb. Replace distributed load with an equivalent concentrated load.
\n$W'$ = {display(W_p)}, $d'$ = {display(dw')}
\nc. Apply equilibrium equations.
\nLet $\\ell = \\var{if(C[0]>D[0],latex('d_1'),latex('d_1+d_2'))} = \\var{display(Dx)}\\text{, and} \\qquad d_\\perp = (\\ell - d') = \\var{display(Dx - dw')}$
\n$\\begin{align} \\Sigma M_D &= 0 & \\Sigma F_y &=0 \\\\ \\simplify{{if(scalar(FA)<0,1,-1)} A} \\ell + W' d_\\perp \\var{if(Cx < Dx, latex('+C d_2'),'')} + M_D&= 0 & \\simplify{{if(scalar(FA)<0,-1,1)} A} \\var{if(Cx < Dx, latex('+ C'),'')} - W' - V &=0 \\\\ M_D &= \\simplify{{if(scalar(FA)>0,1,-1)} A} \\ell - W' d_\\perp \\var{if(Cx < Dx, latex('C d_2'),'')} & V &= \\simplify{{if(scalar(FA)<0,-1,1) }A} \\var{if(Cx < Dx, latex('+ C'),'')} - W' \\\\ &= \\var{display(M_D)} & V &= \\var{display(FV)} \\end{align}$
\n\n=
", "rulesets": {}, "extensions": ["geogebra", "quantities"], "variables": {"F_Wt": {"name": "F_Wt", "group": "vectors", "definition": "vector(0,-scalar(W_t))", "description": "", "templateType": "anything"}, "L": {"name": "L", "group": "Quantities", "definition": "qty(random(6,8,12,16,20,24),units[1])", "description": "overall length of the beam.
", "templateType": "anything"}, "d_2": {"name": "d_2", "group": "Quantities", "definition": "abs(Dx-Cx)", "description": "length of second beam segment
", "templateType": "anything"}, "units": {"name": "units", "group": "Ungrouped variables", "definition": "random(['N','m'],['lb','ft'])", "description": "", "templateType": "anything"}, "debug": {"name": "debug", "group": "Ungrouped variables", "definition": "false", "description": "", "templateType": "anything"}, "A": {"name": "A", "group": "Ungrouped variables", "definition": "Vector(0,0)\n", "description": "", "templateType": "anything"}, "F_V": {"name": "F_V", "group": "vectors", "definition": "(F_A + F_Wp + if(C[0]x position of point A
", "templateType": "anything"}, "Bx": {"name": "Bx", "group": "Quantities", "definition": "L", "description": "x position of point B (right end)
", "templateType": "anything"}, "h2": {"name": "h2", "group": "Quantities", "definition": "abs(W_a-W_b) Wmax", "description": "height of triangular portion of load
", "templateType": "anything"}, "FA": {"name": "FA", "group": "Quantities", "definition": "W_t * (Cx-dw) /Cx", "description": "Force at A, signed
", "templateType": "anything"}, "FC": {"name": "FC", "group": "Quantities", "definition": "W_t dw/Cx", "description": "Force at roller C, always up
", "templateType": "anything"}, "FV": {"name": "FV", "group": "Quantities", "definition": "FA - W_p + if(C[0]partial load to the left of point d
", "templateType": "anything"}, "M_D": {"name": "M_D", "group": "Quantities", "definition": "FA Dx - W_p * (Dx - dw') + if(Cx−\ud835\udc34\u2113−\ud835\udc4a′\ud835\udc51⊥−\ud835\udc36\ud835\udc512
", "templateType": "anything"}, "dw": {"name": "dw", "group": "Quantities", "definition": "(Wa / 6 + Wb /3 ) L L /W_T", "description": "distance to equivalent load's centroid for whole beam
", "templateType": "anything"}, "W_t": {"name": "W_t", "group": "Quantities", "definition": "(Wa + Wb)/2 L", "description": "Equivalent load on beam, down
", "templateType": "anything"}, "F_A": {"name": "F_A", "group": "vectors", "definition": "- (F_C + F_Wt)", "description": "", "templateType": "anything"}, "C": {"name": "C", "group": "Ungrouped variables", "definition": "vector(random(2..10#2),0)", "description": "", "templateType": "anything"}, "Wmax": {"name": "Wmax", "group": "Quantities", "definition": "qty(random(100,200,400,500,800,1000),units[0] +\"/\" + units[1])", "description": "Random load value which gets scaled geogebra_values w_a and w_b to make actual loads Wa and Wb.
", "templateType": "anything"}, "h1": {"name": "h1", "group": "Quantities", "definition": "min(W_a,W_b) Wmax", "description": "height of rectangular portion of the load
", "templateType": "anything"}, "Wd": {"name": "Wd", "group": "Quantities", "definition": "wA + (wb-wa) * if(C[0]>D[0],d_1, d_1+d_2) / L ", "description": "distributed load value at point D
", "templateType": "anything"}, "B": {"name": "B", "group": "Ungrouped variables", "definition": "vector(12,0)\n", "description": "", "templateType": "anything"}, "w_A": {"name": "w_A", "group": "Ungrouped variables", "definition": "random(0..2#0.5)", "description": "", "templateType": "anything"}, "Wb": {"name": "Wb", "group": "Quantities", "definition": "Wmax w_b", "description": "distributed load value at point A, right end.
", "templateType": "anything"}, "F_C": {"name": "F_C", "group": "vectors", "definition": "vector(0,scalar(FC))", "description": "", "templateType": "anything"}, "dw'": {"name": "dw'", "group": "Quantities", "definition": "(Wa / 6 + Wd /3 ) Dx Dx /W_p", "description": "distance from A to partial load W_p
", "templateType": "anything"}, "Cx": {"name": "Cx", "group": "Quantities", "definition": "C[0]/12 Bx\n ", "description": "x position of point C (roller)
", "templateType": "anything"}, "Wa": {"name": "Wa", "group": "Quantities", "definition": "Wmax w_a", "description": "distributed load value at point A, left end
", "templateType": "anything"}, "D": {"name": "D", "group": "Ungrouped variables", "definition": "vector(random(2..10#2),0)", "description": "", "templateType": "anything"}, "d_1": {"name": "d_1", "group": "Quantities", "definition": "qty(min(scalar(Cx),scalar(Dx)),units[1])", "description": "length of first beam segment.
", "templateType": "anything"}, "ggb_points": {"name": "ggb_points", "group": "Ungrouped variables", "definition": "[\n ['C',C],['D',D],['w_A',w_a],['w_B',w_b], ['fbd','false']\n]", "description": "", "templateType": "anything"}, "d_3": {"name": "d_3", "group": "Quantities", "definition": "Bx-d_1-d_2", "description": "length of third beam segment
", "templateType": "anything"}}, "variablesTest": {"condition": "abs(C[0]-D[0])>1 and // not too close to each other\nw_a+w_b <> 0 and // must not both be zero = no load\nD[0] > 2 // not too close to end", "maxRuns": 100}, "ungrouped_variables": ["A", "B", "C", "D", "w_A", "w_B", "ggb_points", "units", "debug"], "variable_groups": [{"name": "Quantities", "variables": ["L", "Ax", "Bx", "Cx", "Dx", "d_1", "d_2", "d_3", "Wmax", "Wa", "Wd", "Wb", "h1", "h2", "dw", "W_t", "FC", "FA", "dw'", "W_p", "FV", "M_D"]}, {"name": "vectors", "variables": ["F_C", "F_Wt", "F_A", "F_Wp", "F_V"]}], "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);"}}, "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": "Determine the reactions at pin $A$ and roller $C$. Let positive values indicate upward forces.
\n$A$ = [[0]] {display(FA)}
\n$C$ = [[1]] {display(FC)}
", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "$F_A$", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "FA", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "$F_C$", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "FC", "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": "Determine the internal shear and bending moment at a section passing through point $D$. Use the standard convention for the meaning of positive shears and bending moments.
\n$V_D$ = [[0]] {display(FV)}
\n$M_D$ = [[1]] {display(M_D)}
", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "$V$", "marks": "15", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "FV", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "$M_D$", "marks": "15", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "M_D", "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/"}]}]}], "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}