// Numbas version: finer_feedback_settings
{"name": "V&M: Triangular loading", "extensions": ["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\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": "<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/triangle_ndXLH1l.svg", "/srv/numbas/media/question-resources/triangle_ndXLH1l.svg"], ["question-resources/hw_2_ISSDAce.png", "/srv/numbas/media/question-resources/hw_2_ISSDAce.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "V&M: Triangular loading", "tags": ["Mechanics", "mechanics", "shear and bending moment diagram.", "Statics", "statics"], "metadata": {"description": "<p>Derive the expressions for&nbsp;the shear and bending moment as functions of $x$ for a cantilever beam with a uniformly varying (triangular) load.</p>", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "statement": "<p>A cantilever beam supports a uniformly varying distributed load as shown.</p>\n<p><img src=\"resources/question-resources/triangle_ndXLH1l.svg\" width=\"441\" height=\"190\"/></p>", "advice": "<p><strong>Draw a free body diagram.</strong></p>\n<p style=\"padding-left: 30px;\">For a general solution, take an imaginary cut at $x$ and draw a free body diagram of the portion of the beam to the left of that point. &nbsp;$V(x)$ and $M(x)$ are drawn in the positive directions for shear and bending moment. &nbsp;</p>\n<p style=\"padding-left: 30px;\"></p>\n<p><img src=\"resources/question-resources/hw_2_ISSDAce.png\" width=\"459\" height=\"170\"/></p>\n<p style=\"padding-left: 30px;\">At location&nbsp;$x$ the downward loading is proportionally less than the maximum loading at the wall, $w$.</p>\n<p style=\"padding-left: 30px;\">$w(x) = \\left(\\frac{x}{L}\\right) w$</p>\n<p><strong>Determine equivalent load, $W$, by finding the area and centroid of the triangular load.</strong></p>\n<p style=\"padding-left: 30px;\">$W&nbsp;= \\dfrac{(w&nbsp;x/L) (x)}{2} = \\dfrac {w x^2}{2 L}$ acting at a distance of $\\dfrac{2 x}{3}$ from the left, or $\\dfrac{x}{3}$ from the cut.</p>\n<p><strong>Apply equations of equilibrium to the free body diagram.</strong></p>\n<p style=\"padding-left: 30px;\">$\\begin{align} \\Sigma F_y &amp;= 0 &amp; \\Sigma M_{cut} &amp;= 0\\\\ -W&nbsp;- V(x) &amp;=0 &amp; (W)(x/3) + M(x) &amp;=0\\\\ V(x) &amp;=-\\dfrac {w x^2}{2 L}&amp; M(x) &amp;= -\\dfrac {w x^3}{6 L}&nbsp;&nbsp;\\end{align}$</p>\n<p><strong>Evaluating for given values,&nbsp;&nbsp;$w = \\var{qty(w, unitsW)}$ and $L = \\var{qty(L, unitsL)}$.</strong></p>\n<p style=\"padding-left: 30px;\">$\\begin{align} V(x) &amp;=-\\simplify[all]{{w}/2/{L}} x^2 &amp; M(x) &amp;= -\\simplify[all]{{w}/6/{L}} x^3 \\end{align}$</p>\n<p><strong>Evaluate functions at $x = \\var{qty(L/2,unitsL)}$.</strong></p>\n<p style=\"padding-left: 30px;\">$\\begin{align} V(\\var{L/2}) &amp;=\\var{Vmp}&nbsp;&nbsp;&amp; M(\\var{L/2}) &amp;= \\var{Mmp}\\end{align}$</p>", "rulesets": {}, "extensions": ["quantities"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"unitsL": {"name": "unitsL", "group": "Ungrouped variables", "definition": "'ft'", "description": "", "templateType": "anything", "can_override": false}, "unitsW": {"name": "unitsW", "group": "Ungrouped variables", "definition": "unitsF+'/'+unitsL", "description": "<p>Shear at midpoint</p>", "templateType": "anything", "can_override": false}, "L": {"name": "L", "group": "Ungrouped variables", "definition": "random(5,10,12,15,16,18,20,24)", "description": "", "templateType": "anything", "can_override": false}, "w": {"name": "w", "group": "Ungrouped variables", "definition": "random(20..200#10)", "description": "", "templateType": "anything", "can_override": false}, "Vmp": {"name": "Vmp", "group": "Ungrouped variables", "definition": "qty(-w L/8, unitsF)", "description": "", "templateType": "anything", "can_override": false}, "unitsF": {"name": "unitsF", "group": "Ungrouped variables", "definition": "'lb'", "description": "", "templateType": "anything", "can_override": false}, "Mmp": {"name": "Mmp", "group": "Ungrouped variables", "definition": "siground(qty(- w l^2/48, unitsF + ' ' + unitsL),5)", "description": "<p>moment at midpoint</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["unitsF", "unitsL", "unitsW", "L", "w", "Vmp", "Mmp"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Functions", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Derive expressions for shear and bending moments as a function of $x$. &nbsp;<em> Use the standard sign convention for shear and bending moments.</em></p>\n<p>$V(x) =$&nbsp;[[0]] &nbsp;$\\qquad M(x) = $&nbsp;[[1]]</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "V(x)", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "-{W} x^2/(2 * {L})", "showPreview": true, "checkingType": "sigfig", "checkingAccuracy": 3, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}, {"type": "jme", "useCustomName": true, "customName": "M(x)", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "- {w} x^3/(6 * {L})", "showPreview": true, "checkingType": "sigfig", "checkingAccuracy": 3, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Values at midpoint.", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Evaluate the shear and bending moment functions at $x = \\var{qty(L/2,unitsL)}$.&nbsp;</p>\n<p>$V(\\var{L/2}) =$&nbsp;[[0]] &nbsp;$\\qquad M(\\var{L/2}) = $&nbsp;[[1]]</p>", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "V({L/2})", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "Vmp", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "M({L/2})", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "Mmp", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "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/"}]}