// Numbas version: finer_feedback_settings
{"name": "22. Distributed Loads", "metadata": {"description": "<p>Homework set. &nbsp;Uniformly and uniformly varying distributed loads.</p>", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", ""], "variable_overrides": [[], [], []], "questions": [{"name": "Reactions for beam with uniformly distributed load", "extensions": ["jsxgraph", "quantities", "shear-and-bending-moment-diagrams"], "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}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": [], "metadata": {"description": "<p>Find the reactions for a beam with a uniformly distributed load.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>{loadDiagram}</p>\n<p>A $\\var{distance(L)}$ long beam is subjected uniformly distributed load, as shown. Assume the weight of the beam is negligible.</p>\n<p><span data-jme-visible=\"debug\">w: {loading} W: {w} &nbsp;$F_A$: {FA} &nbsp;$F_B$ {FB}</span></p>", "advice": "<ol>\n<li>To solve, replace the distributed load with an equivalent concentrated load. &nbsp;The equivalent concentrated load acts at the centroid of the rectangle, and its magnitude is the \"area\" of the rectangle. &nbsp;\\[ W_R = \\var{udl(loading)} \\times \\var{distance((D-C))} = \\var{force(w)} \\]</li>\n<li>Once replaced, draw a free body diagram; {fbd}</li>\n<li>Take moments at $A$ to find $B$ and vice-versa. &nbsp;</li>\n<li>Check your work by applying $\\Sigma F_y = 0$.</li>\n</ol>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"x": {"name": "x", "group": "Ungrouped variables", "definition": "(C+D)/2", "description": "<p>midpoint of load</p>", "templateType": "anything", "can_override": false}, "loading": {"name": "loading", "group": "inputs", "definition": "random(1,2,3,4,5,6)* random(10, 20, 50, 100)", "description": "<p>magnitude of distributed loading [force/length]</p>", "templateType": "anything", "can_override": false}, "D": {"name": "D", "group": "inputs", "definition": "random(C..L)", "description": "<p>distributed load ends here</p>\n<p>D-C &gt; 3 and B-A &gt; L/2 and A&lt;&gt;C and B&lt;&gt;D</p>", "templateType": "anything", "can_override": false}, "C": {"name": "C", "group": "inputs", "definition": "random(0..L/2)", "description": "<p>distributed load starts here</p>", "templateType": "anything", "can_override": false}, "FA": {"name": "FA", "group": "Ungrouped variables", "definition": "W-FB", "description": "<p>reaction at A</p>", "templateType": "anything", "can_override": false}, "B": {"name": "B", "group": "inputs", "definition": "random(L/2..L)", "description": "<p>location of right hand support</p>", "templateType": "anything", "can_override": false}, "W": {"name": "W", "group": "Ungrouped variables", "definition": "loading * (D-C)", "description": "<p>Downward force</p>", "templateType": "anything", "can_override": false}, "L": {"name": "L", "group": "inputs", "definition": "random(8,10,12,14,16)", "description": "<p>length of beam</p>", "templateType": "anything", "can_override": false}, "debug": {"name": "debug", "group": "Ungrouped variables", "definition": "false", "description": "", "templateType": "anything", "can_override": false}, "FB": {"name": "FB", "group": "Ungrouped variables", "definition": "(x-A) * W / (B-A)\n", "description": "<p>reaction at B</p>", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "inputs", "definition": "random(['lb','ft', 'lb/ft'],['N','m', 'N/m'])", "description": "", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "inputs", "definition": "random(0..L/2)", "description": "<p>location of left hand support</p>", "templateType": "anything", "can_override": false}, "Force": {"name": "Force", "group": "Ungrouped variables", "definition": "(f)-> siground(qty(F,units[0]),4)", "description": "", "templateType": "anything", "can_override": false}, "distance": {"name": "distance", "group": "Ungrouped variables", "definition": "(d)-> siground(qty(d,units[1]),4)", "description": "", "templateType": "anything", "can_override": false}, "udl": {"name": "udl", "group": "Ungrouped variables", "definition": "(w)->siground(qty(w,units[2]),4)", "description": "", "templateType": "anything", "can_override": false}, "loadProperties": {"name": "loadProperties", "group": "diagrams", "definition": "[ beamLength: L, symbols: LoadSymbols, loads: loads, reactions: [], forces: [], moments: []]", "description": "", "templateType": "anything", "can_override": false}, "loadDiagram": {"name": "loadDiagram", "group": "diagrams", "definition": "vmloaddiagram(loadProperties)", "description": "", "templateType": "anything", "can_override": false}, "loadSymbols": {"name": "loadSymbols", "group": "diagrams", "definition": "[[type: \"pin\", x: A ,label: \"$R_A$\", visible: true], [type: \"roller\", x: b, label: \"$R_B$\", visible: true]]", "description": "", "templateType": "anything", "can_override": false}, "fbdproperties": {"name": "fbdproperties", "group": "diagrams", "definition": "[beamLength: L, reactions: FBDreactions, forces: FBDforces,  moments: [], loads: fbdLoads, symbols: [[type: \"dot\", x: x ,label: string(distance(x)), visible: true]]]", "description": "", "templateType": "anything", "can_override": false}, "FBDforces": {"name": "FBDforces", "group": "diagrams", "definition": "[[x: x, value: W, label: \"$W_R$\", visible: true]]", "description": "", "templateType": "anything", "can_override": false}, "FBDreactions": {"name": "FBDreactions", "group": "diagrams", "definition": "[[x: A, value: FA, label: \"$A$\", visible: true],[x: B, value: FB, label: \"$B$\", visible: true]]", "description": "", "templateType": "anything", "can_override": false}, "fbd": {"name": "fbd", "group": "diagrams", "definition": "vmloaddiagram(fbdproperties)", "description": "", "templateType": "anything", "can_override": false}, "fbdLoads": {"name": "fbdLoads", "group": "diagrams", "definition": "[[[x: C, value: 1, label:\"\", visible: false],[x: D, value: 1, label: \"\", visible: false]]]", "description": "", "templateType": "anything", "can_override": false}, "loads": {"name": "loads", "group": "diagrams", "definition": "[[[x: C, value: 1, label: string(udl(loading)), visible: true],[x: D, value: 1, label: \"\", visible: true]]]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "D-C > 3 and B-A > L/2 and A<>C and B<>D", "maxRuns": 100}, "ungrouped_variables": ["W", "FB", "x", "FA", "debug", "Force", "distance", "udl"], "variable_groups": [{"name": "inputs", "variables": ["A", "B", "C", "D", "loading", "units", "L"]}, {"name": "diagrams", "variables": ["loadProperties", "loads", "loadDiagram", "loadSymbols", "fbdproperties", "FBDforces", "FBDreactions", "fbd", "fbdLoads"]}, {"name": "Unnamed group", "variables": []}], "functions": {}, "preamble": {"js": "", "css": ".jsxgraph-board {width: 200px; height: 100px;}"}, "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 $A$ and $B$.</p>\n<p>$A$ =&nbsp;[[0]]&nbsp;&nbsp;$B$ =&nbsp;[[1]]&nbsp;</p>", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "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(FA)", "right": "0.1", "close": "1.0", "C1": "80", "C2": "80", "C3": "60"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "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(FB)", "right": "0.1", "close": "1.0", "C1": "80", "C2": "80", "C3": "60"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Reactions for beam with uniformly varying load", "extensions": ["jsxgraph", "quantities", "shear-and-bending-moment-diagrams"], "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": ["question-resources/dist-load.ggb"], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["mechanics, statics, reactions, distributed load, uniformly varying load"], "metadata": {"description": "<p>Find the reactions for a beam with a uniformly varying distributed load.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>{loadDiagram}</p>\n<p>A {qty(L, units[1]) } long beam is subjected to a load which varies uniformly from $\\var{uvl(wc)}$ at $C$ to $\\var{uvl(wd)}$ at $D$. The beam itself weighs $\\var{uvl(w_b)}$.</p>\n<p><span data-jme-visible=\"debug\">W: {w} &nbsp;beam: {wb} xbar: {x} check: {check}</span></p>\n<p><span data-jme-visible=\"debug\">$F_A$: {precround(FA,4)} &nbsp;$F_B$ {precround(FB,4)}</span></p>", "advice": "<ol>\n<li>To solve, divide the trapazoid into a rectangle and a triangle or two triangles, then replace each&nbsp;with an equivalent concentrated load. &nbsp;The equivalent concentrated load acts at the centroid of each&nbsp;shape, and its magnitude is the \"area\" of the shape. &nbsp;</li>\n<li>Treat the beam as a uniformly distributed load, and place the weight of the beam at the&nbsp;center.</li>\n<li>Once replaced, draw a free body diagram; then take moments at $A$ to find $B$ and vice-versa. &nbsp;Check your work by applying $\\Sigma F_y = 0$.</li>\n</ol>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"D": {"name": "D", "group": "inputs", "definition": "random(L-3.. L)", "description": "<p>distributed load ends here</p>", "templateType": "anything", "can_override": false}, "L": {"name": "L", "group": "inputs", "definition": "random(10,15, 18)", "description": "<p>length of beam</p>\n<p></p>", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "inputs", "definition": "random(['lb', 'ft', 'lb/ft'],['kN', 'm', 'kN/m'])", "description": "", "templateType": "anything", "can_override": false}, "loading": {"name": "loading", "group": "inputs", "definition": "random(10..50#10)", "description": "<p>distributed loading [force/length]</p>", "templateType": "anything", "can_override": false}, "FA": {"name": "FA", "group": "Ungrouped variables", "definition": "(W + WB)-FB", "description": "<p>reaction at A</p>", "templateType": "anything", "can_override": false}, "debug": {"name": "debug", "group": "Ungrouped variables", "definition": "false", "description": "", "templateType": "anything", "can_override": false}, "wc": {"name": "wc", "group": "inputs", "definition": "random(0..2#0.5 except 0.5) loading", "description": "", "templateType": "anything", "can_override": false}, "W": {"name": "W", "group": "Ungrouped variables", "definition": "precround((wc+wd)/2 * (D-C),5)", "description": "<p>Downward force due to load</p>", "templateType": "anything", "can_override": false}, "B": {"name": "B", "group": "inputs", "definition": "if(D=L, random(L-1..L-4), L)", "description": "<p>location of right hand support</p>", "templateType": "anything", "can_override": false}, "C": {"name": "C", "group": "inputs", "definition": "random(0..5)", "description": "<p>distributed load starts here</p>", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "inputs", "definition": "if(C=0, random(1..4), 0)", "description": "<p>location of left hand support</p>", "templateType": "anything", "can_override": false}, "wd": {"name": "wd", "group": "inputs", "definition": "random(0..2#0.5 except 0.5) loading", "description": "", "templateType": "anything", "can_override": false}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "C + (wc / 6 + wd/ 3)(D-C) * 2/(wc+wd)", "description": "<p>midpoint of load</p>", "templateType": "anything", "can_override": false}, "FB": {"name": "FB", "group": "Ungrouped variables", "definition": "precround(((x-A) * W + (CG-A) *  WB) / (B-A),5)\n", "description": "<p>reaction at B</p>", "templateType": "anything", "can_override": false}, "w_b": {"name": "w_b", "group": "inputs", "definition": "siground(random(0.1..1 #0.1) loading,3)", "description": "<p>Weight of the beam in W/L units</p>", "templateType": "anything", "can_override": false}, "CG": {"name": "CG", "group": "Ungrouped variables", "definition": "L/2", "description": "<p>center of the beam</p>", "templateType": "anything", "can_override": false}, "WB": {"name": "WB", "group": "Ungrouped variables", "definition": "w_b L ", "description": "<p>Weight of the beam itself</p>", "templateType": "anything", "can_override": false}, "check": {"name": "check", "group": "Ungrouped variables", "definition": "(W + WB)= (FA+FB)", "description": "", "templateType": "anything", "can_override": false}, "points": {"name": "points", "group": "inputs", "definition": "sort(deal(L)[0..2])", "description": "", "templateType": "anything", "can_override": false}, "properties": {"name": "properties", "group": "Unnamed group", "definition": "[beamLength: L, loads: distributedLoad, symbols: symbols, forces: [], moments: [], reactions: []]", "description": "", "templateType": "anything", "can_override": false}, "loadDiagram": {"name": "loadDiagram", "group": "Unnamed group", "definition": "vmloaddiagram(properties)", "description": "", "templateType": "anything", "can_override": false}, "symbols": {"name": "symbols", "group": "Unnamed group", "definition": "[[x: A, type: \"pin\", label: \"$A$\", visible: true],[x: B, type: \"roller\", label: \"$B$\", visible: true], [x: C, type: \"dot\", label: \"$C$\", visible: true], [x: D, type: \"dot\", label: \"$D$\", visible: true]]\n", "description": "", "templateType": "anything", "can_override": false}, "distributedLoad": {"name": "distributedLoad", "group": "Unnamed group", "definition": "[[[x: C, value: wC ,  label: loadWords(wc,wd), visible: true], [x: D, value: wd , label: \"\", visible: true]]]", "description": "", "templateType": "anything", "can_override": false}, "loadWords": {"name": "loadWords", "group": "Unnamed group", "definition": "(w1,w2) -> w1 + \" to \" + w2  + \" \"  + units[2]", "description": "", "templateType": "anything", "can_override": false}, "UVL": {"name": "UVL", "group": "Unnamed group", "definition": "w -> qty(w, units[2])", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "D-C > L/3 and \nwc<>wd", "maxRuns": 100}, "ungrouped_variables": ["W", "FB", "x", "FA", "debug", "CG", "WB", "check"], "variable_groups": [{"name": "inputs", "variables": ["A", "B", "C", "D", "loading", "units", "L", "wc", "wd", "w_b", "points"]}, {"name": "ggb", "variables": []}, {"name": "Unnamed group", "variables": ["properties", "loadDiagram", "symbols", "distributedLoad", "loadWords", "UVL"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Find 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 $A$ and $B$.</p>\n<p>$A$ =&nbsp;[[0]]&nbsp; </p>\n<p>$B$ =&nbsp;[[1]]&nbsp;&nbsp;</p>", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "A", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(precround(FA,4),units[0])", "right": "0.1", "close": "1.0", "C1": "80", "C2": "80", "C3": "60"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "B", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(siground(FB,4),units[0])", "right": "0.1", "close": "1.0", "C1": "80", "C2": "80", "C3": "60"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Distributed Loads: trapezoidal loading", "extensions": ["jsxgraph", "quantities", "shear-and-bending-moment-diagrams"], "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}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["beam", "distributed load", "Equilibrium", "equilibrium", "Mechanics", "mechanics", "Statics", "statics"], "metadata": {"description": "<p>Find the reactions of a simply-supported beam with a trapazoidal distributed load.</p>", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "statement": "<p>{loadDiagram}</p>\n<p>$\\var{distance(L)}$ long beam $AB$ is subjected to a distributed load which varies as shown.</p>\n<p>Determine the reactions at $A$ and $B$.</p>", "advice": "<p></p>\n<ol>\n<li>Determine locations of the centroids and the 'area' under the loading curve for each part.\n<p>$\\begin{align}\\\\ L &amp;= \\var{distance(L)}\\\\W_R &amp;= \\var{force(xr)} &amp; x_R &amp;= \\var{distance(xr)} \\\\<br/>&nbsp;W_T &amp;= \\var{force(wt)} &amp;x_T &amp;= \\var{distance(xt)}\\end{align}$</p>\n</li>\n<li>\n<p>Draw a free body diagram of the beam, replacing the distributed loads with equivalent concentrated loads at the centroids of the triangle and rectangle.</p>\n<p>{fbd}</p>\n</li>\n<li>Find the reactions\n<p>$\\begin{align}\\\\ <br/>\\Sigma M_A &amp;= 0 &nbsp;\\\\<br/>W_R (x_r) + W_T (x_T) &amp;=&nbsp;&nbsp;B (L )\\\\<br/>B &amp;= \\frac{W_R( x_r) + W_T( x_T)}{L} &nbsp;\\\\<br/>&amp;= \\var{force(rb)} \\\\ \\\\ <br/>\\Sigma F_y &amp;= 0 \\\\ A + B &amp;= W_T + W_R \\\\ A &amp;= W_T + W_R - B \\\\ <br/>&amp;= \\var{force(ra)} \\end{align}$</p>\n</li>\n<li>You may check your answer by finding $A$ using $\\Sigma M_B = 0$. &nbsp;You should get the same result either way.</li>\n</ol>\n<p></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"w": {"name": "w", "group": "Ungrouped variables", "definition": "random(50..150#10)", "description": "<p>Max value of loading &nbsp;in &nbsp;[force/distance]</p>", "templateType": "anything", "can_override": false}, "WT": {"name": "WT", "group": "solution", "definition": "triangle_base w /2", "description": "<p>weight of the triangular load</p>", "templateType": "anything", "can_override": false}, "WR": {"name": "WR", "group": "solution", "definition": "rectangle_base w", "description": "<p>weight of the rectangular load</p>", "templateType": "anything", "can_override": false}, "WTot": {"name": "WTot", "group": "solution", "definition": "WT + WR", "description": "<p>Total weight of load</p>", "templateType": "anything", "can_override": false}, "xR": {"name": "xR", "group": "solution", "definition": "rectangle_base/2 + rectangle[0]", "description": "<p>location of centroid of rect</p>", "templateType": "anything", "can_override": false}, "xT": {"name": "xT", "group": "solution", "definition": "if(type=0,triangle_base/3, 2 triangle_base/3) + triangle[0]\n ", "description": "<p>Centroid of triangle</p>", "templateType": "anything", "can_override": false}, "L": {"name": "L", "group": "Ungrouped variables", "definition": "random([16,20,24])", "description": "<p>length of beam</p>", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "Ungrouped variables", "definition": "random([['ft','lb', 'lb/ft'],['m','kN', 'kN/m']])", "description": "", "templateType": "anything", "can_override": false}, "RB": {"name": "RB", "group": "solution", "definition": "(WR xR + WT xT)/ L", "description": "", "templateType": "anything", "can_override": false}, "RA": {"name": "RA", "group": "solution", "definition": "(WT * (L-xT) + WR * (L-xR ))/ L", "description": "", "templateType": "anything", "can_override": false}, "check": {"name": "check", "group": "solution", "definition": "RA + RB = Wtot", "description": "", "templateType": "anything", "can_override": false}, "properties": {"name": "properties", "group": "diagram", "definition": "[beamLength: L,  loads: loads, symbols: symbols ,  forces: [], moments: [], reactions: []]", "description": "", "templateType": "anything", "can_override": false}, "loads": {"name": "loads", "group": "diagram", "definition": "[\n[ [x: rectangle[0], value: w, label: w + \" \" + units[2], visible: true], \n  [x: rectangle[1], value: w, label: \"\" ] ],\n[ [x: triangle[0], value: if(type=0,w,0), label: \"\" , visible: true], \n  [x: triangle[1], value: if(type=0,0,w), label: \"\" ]\n]\n]\n", "description": "<p>choses between triangle-rectangle and rectangle triangle</p>", "templateType": "anything", "can_override": false}, "symbols": {"name": "symbols", "group": "diagram", "definition": "[[type: \"pin\", x: 0, label: \"$A$\", visible: true], [type: \"roller\", x: L, label: \"$B$\", visible: true]]", "description": "", "templateType": "anything", "can_override": false}, "LoadDiagram": {"name": "LoadDiagram", "group": "diagram", "definition": "vmloaddiagram(properties)", "description": "", "templateType": "anything", "can_override": false}, "uniquePoint": {"name": "uniquePoint", "group": "Ungrouped variables", "definition": "sort(shuffle(0..L)[0..3])", "description": "", "templateType": "anything", "can_override": false}, "type": {"name": "type", "group": "Ungrouped variables", "definition": "random(0,1)", "description": "<p>0 &nbsp;= rect then triangle</p>\n<p>1 = triangle then rect</p>", "templateType": "anything", "can_override": false}, "Rectangle": {"name": "Rectangle", "group": "Ungrouped variables", "definition": "if(type=0,\n  [load_start, load_start+ rectangle_base],\n  [load_start+triangle_base, load_start+triangle_base+rectangle_base])", "description": "", "templateType": "anything", "can_override": false}, "triangle": {"name": "triangle", "group": "Ungrouped variables", "definition": "if(type=0,\n  [load_start+rectangle_base, load_start+ rectangle_base + triangle_base],\n  [load_start, load_start+triangle_base])", "description": "", "templateType": "anything", "can_override": false}, "Triangle_base": {"name": "Triangle_base", "group": "Ungrouped variables", "definition": "6", "description": "", "templateType": "anything", "can_override": false}, "rectangle_base": {"name": "rectangle_base", "group": "Ungrouped variables", "definition": "random(4..L-triangle_base)", "description": "", "templateType": "anything", "can_override": false}, "Load_start": {"name": "Load_start", "group": "Ungrouped variables", "definition": "random(0..L-triangle_base-rectangle_base)", "description": "", "templateType": "anything", "can_override": false}, "distance": {"name": "distance", "group": "quantities", "definition": "d -> qty(d, units[0])", "description": "", "templateType": "anything", "can_override": false}, "force": {"name": "force", "group": "quantities", "definition": "f -> siground(qty(f,units[1]),4)", "description": "", "templateType": "anything", "can_override": false}, "load": {"name": "load", "group": "quantities", "definition": "w -> qty(w,units[2])", "description": "", "templateType": "anything", "can_override": false}, "FBDProperties": {"name": "FBDProperties", "group": "diagram", "definition": "[beamLength: L,  reactions: fbdReactions, loads: fbdloads, symbols: fbdsymbols, moments: [], forces: fbdEquivalentloads]", "description": "", "templateType": "anything", "can_override": false}, "FBDSymbols": {"name": "FBDSymbols", "group": "diagram", "definition": "[[type: \"dot\", x: xt, label: xt, visible: true], [type: \"dot\", x: xr, label: xr, visible: true]]", "description": "", "templateType": "anything", "can_override": false}, "fbd": {"name": "fbd", "group": "diagram", "definition": "vmloaddiagram(fbdproperties)", "description": "", "templateType": "anything", "can_override": false}, "fbdReactions": {"name": "fbdReactions", "group": "diagram", "definition": "[[x: 0, value: ra, label: \"$A$\", visible: true], [x: L, value: rb, label: \"$B$\", visible: true]]\n", "description": "", "templateType": "anything", "can_override": false}, "fbdEquivalentLoads": {"name": "fbdEquivalentLoads", "group": "diagram", "definition": "[[x: xr, value: wr, label: \"$W_R$\", visible: true], [x: xt, value: wt, label: \"$W_T$\", visible: true]]", "description": "", "templateType": "anything", "can_override": false}, "fbdLoads": {"name": "fbdLoads", "group": "diagram", "definition": "[\n[ [x: rectangle[0], value: w, label: \"\" , visible: false], \n  [x: rectangle[1], value: w, label: \"\" ] ],\n[ [x: triangle[0], value: if(type=0,w,0), label: \"\" , visible: false], \n  [x: triangle[1], value: if(type=0,0,w), label: \"\" ]\n]\n]\n", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["w", "L", "units", "uniquePoint", "type", "Rectangle", "triangle", "Triangle_base", "rectangle_base", "Load_start"], "variable_groups": [{"name": "solution", "variables": ["WT", "WR", "WTot", "xR", "xT", "RB", "RA", "check"]}, {"name": "quantities", "variables": ["distance", "force", "load"]}, {"name": "diagram", "variables": ["properties", "loads", "symbols", "FBDProperties", "FBDSymbols", "fbdReactions", "fbdEquivalentLoads", "fbdLoads", "fbd", "LoadDiagram"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Find Reactions", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$A = $&nbsp;[[0]]&nbsp; <br/><br/>$B = $&nbsp;[[1]]&nbsp;&nbsp;</p>", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "$A$", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "force(ra)", "right": "0.2", "close": "1.0", "C1": "80", "C2": "80", "C3": "65"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "$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(rb)", "right": "0.2", "close": "1.0", "C1": "80", "C2": "80", "C3": "65"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "allowPrinting": true, "navigation": {"allowregen": true, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": false, "navigatemode": "sequence", "onleave": {"action": "none", "message": ""}, "preventleave": true, "typeendtoleave": false, "startpassword": "", "autoSubmit": true, "allowAttemptDownload": false, "downloadEncryptionKey": "", "showresultspage": "oncompletion"}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"enterreviewmodeimmediately": true, "showactualmarkwhen": "always", "showtotalmarkwhen": "always", "showanswerstatewhen": "always", "showpartfeedbackmessageswhen": "always", "showexpectedanswerswhen": "inreview", "showadvicewhen": "inreview", "allowrevealanswer": true, "intro": "", "end_message": "", "results_options": {"printquestions": true, "printadvice": true}, "feedbackmessages": [], "reviewshowexpectedanswer": true, "showanswerstate": true, "reviewshowfeedback": true, "showactualmark": true, "showtotalmark": true, "reviewshowscore": true, "reviewshowadvice": true}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "extensions": ["jsxgraph", "quantities", "shear-and-bending-moment-diagrams"], "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": [["question-resources/dist-load.ggb", "/srv/numbas/media/question-resources/dist-load.ggb"]]}