// Numbas version: exam_results_page_options
{"name": "35. Internal Forces", "metadata": {"description": "<p>Homework set. &nbsp;Find internal shear force, normal force, and bending moment at a designated point in a rigid body.</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": ["geogebra", "quantities", "weh"], "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": [], "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>{geogebra_applet('kuhdcgxv',[ 'a': scalar(A),'b':&nbsp;scalar(B),'c':&nbsp;scalar(C),'d':&nbsp;scalar(D),'l':&nbsp;scalar(L)])}</p>\n<p>A&nbsp;{L} long beam is subjected to a {loading} uniformly distributed load.&nbsp;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": "<p>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.</p>\n<p>Once replaced, draw a free body diagram; then take moments at <em>A</em> to find<em> B</em> and vice-versa. &nbsp;Check your work by applying $\\Sigma F_y = 0$.</p>", "rulesets": {}, "variables": {"x": {"name": "x", "group": "Ungrouped variables", "definition": "(C+D)/2", "description": "<p>midpoint of load</p>", "templateType": "anything"}, "loading": {"name": "loading", "group": "inputs", "definition": "qty(random(1,2,3,4,5,6)* random(10, 20, 50, 100),units[0]+\"/\"+units[1])", "description": "<p>magnitude of distributed loading [force/length]</p>", "templateType": "anything"}, "D": {"name": "D", "group": "inputs", "definition": "qty(random(scalar(C)..scalar(L)),units[1])", "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"}, "C": {"name": "C", "group": "inputs", "definition": "qty(random(0..scalar(L)),units[1])", "description": "<p>distributed load starts here</p>", "templateType": "anything"}, "FA": {"name": "FA", "group": "Ungrouped variables", "definition": "W-FB", "description": "<p>reaction at A</p>", "templateType": "anything"}, "B": {"name": "B", "group": "inputs", "definition": "qty(random(scalar(A)..scalar(L)),units[1])", "description": "<p>location of right hand support</p>", "templateType": "anything"}, "W": {"name": "W", "group": "Ungrouped variables", "definition": "loading * (D-C)", "description": "<p>Downward force</p>", "templateType": "anything"}, "L": {"name": "L", "group": "inputs", "definition": "qty(random(8,10,12,14,16),units[1])", "description": "<p>length of beam</p>", "templateType": "anything"}, "debug": {"name": "debug", "group": "Ungrouped variables", "definition": "false", "description": "", "templateType": "anything"}, "FB": {"name": "FB", "group": "Ungrouped variables", "definition": "(x-A) * W / (B-A)\n", "description": "<p>reaction at B</p>", "templateType": "anything"}, "units": {"name": "units", "group": "inputs", "definition": "random(['lb','ft'],['N','m'])", "description": "", "templateType": "anything"}, "A": {"name": "A", "group": "inputs", "definition": "qty(random(0..scalar(L)/2),units[1])", "description": "<p>location of left hand support</p>", "templateType": "anything"}}, "variablesTest": {"condition": "D-C > qty(3,units[1]) and B-A > L/2 and A<>C and B<>D", "maxRuns": 100}, "ungrouped_variables": ["W", "FB", "x", "FA", "debug"], "variable_groups": [{"name": "inputs", "variables": ["A", "B", "C", "D", "loading", "units", "L"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Reactions", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Determine the reactions at $A$ 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": "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": "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": "Internal Force: distributed load", "extensions": ["geogebra", "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": [], "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 shear, normal force and bending moment at a point in a beam supporting a uniformly distributed load.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>The frame shown supports a uniformly distributed load $w = \\var{load}$. &nbsp;Member $BC$&nbsp;is {BC} long. &nbsp;</p>\n<p>Determine the internal forces at point $D$&nbsp;which is located {BD} to the right of point $B$.</p>\n<p width=\"50%\">{applet}</p>", "advice": "<p><strong>Find the reactions <em>B</em> and&nbsp;<em>C</em>.&nbsp;</strong></p>\n<p style=\"padding-left: 40px;\">Draw a Free body diagram of beam $BC$. &nbsp;</p>\n<p>{fbd1}</p>\n<p style=\"padding-left: 30px;\">Note that member&nbsp;$AB$&nbsp;is a two-force member, so force $AB$ acts along its axis.</p>\n<p style=\"padding-left: 30px;\">Replace the distributed load with an equivalent concentrated. The equivalent load acts at the center of member $BC$ with magnitude:</p>\n<p style=\"padding-left: 30px;\">$W = w \\cdot \\overline{BC} = (\\var{load}) (\\var{BC}) = \\var{Q_W}$.</p>\n<p></p>\n<p style=\"padding-left: 30px;\">Let the length of member &nbsp;$BC = \\ell = \\var{BC}$, then solve the equilibrium equations to find the reactions at $B$ and $C$.</p>\n<p style=\"padding-left: 30px;\">$\\begin{align}\\Sigma M_C &amp; = 0 &amp;\\Sigma F_x&nbsp;&amp;= 0 &amp;\\Sigma F_y &amp;= 0\\\\AB_y &nbsp;\\cdot \\ell&nbsp;&amp;= W \\cdot \\dfrac {\\ell}{2} &nbsp;&amp; &nbsp; C_x &amp;=AB_x &nbsp;&amp; C_y &amp;= W -AB_y&nbsp;\\\\AB \\sin \\var{abs(alpha)}&deg;&amp; = \\dfrac{ W }{2}&amp; C_x &amp;= AB \\cos \\var{abs(alpha)}&deg; &amp;&nbsp;C_y &amp;= W - AB&nbsp;\\sin \\var{abs(alpha)}&deg; \\\\ AB &amp;= \\var{display(Q_AB)}&nbsp;&amp; C_x &amp;= \\var{display(abs(Q_cx))}\\var{if(F_AB[0]&gt;0,latex('\\\\leftarrow'),latex('\\\\rightarrow'))} &amp; C_y &amp;= \\var{display(Q_Cy)} \\var{if(F_AB[1]&gt;0,latex('\\\\uparrow'),latex('\\\\downarrow'))}\\end{align}$</p>\n<p style=\"padding-left: 30px;\"></p>\n<p><strong>Take an imaginary cut through member <em>BC</em> at point&nbsp;<em>D</em> and draw a free body diagram of the right (or left) portion. </strong></p>\n<p>{fbd2}&nbsp;</p>\n<p style=\"padding-left: 40px;\">The length of segment $DC$ is $\\var{CD}$. There will be unknown internal shear ($V$), bending moment ($M_D$) and normal force&nbsp;($P$)&nbsp;at the cut. Assume that they act&nbsp;in the 'positive' directions established by the sign convention for shear and bending moments. &nbsp;</p>\n<p style=\"padding-left: 40px;\">Note that the downward force on this section of the beam&nbsp;($W'$) is&nbsp;due to the distributed force acting on this portion of the beam only and acts at the centroid of the loading.</p>\n<p style=\"padding-left: 40px;\">$W' = w \\cdot \\overline{DC} = (\\var{load}) (\\var{BC-BD}) = \\var{display(Q_W')}$</p>\n<p><strong>Solve for the internal forces at <em>D</em>.</strong></p>\n<p style=\"padding-left: 30px;\">$\\begin{align}\\Sigma M_D &amp; = 0 &amp;\\Sigma F_x &amp;= 0 &amp;\\Sigma F_y &amp;= 0\\\\ M_D&nbsp; &amp;= C_y (\\var{CD}) - W'(\\var{CD/2})&amp; &nbsp; P &amp;= \\var{if(F_AB[0]&gt;0,latex('-'),'')} C_x &nbsp;&amp; V&nbsp;&amp;= W'-C_y\\\\ &amp;= \\var{display(Q_MD)} &amp; &amp;= \\var{display(-Q_Cx)} &amp; &amp;= \\var{display(Q_V)}&nbsp;\\end{align}$</p>\n<p>&nbsp;&nbsp;</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"BC": {"name": "BC", "group": "Inputs", "definition": "qty(random(4..12#2),units[1])", "description": "", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "Ungrouped variables", "definition": "['lb','ft']", "description": "", "templateType": "anything", "can_override": false}, "load": {"name": "load", "group": "Inputs", "definition": "qty(random(10..50#5), units[0\n  ]+\"/\"+units[1])", "description": "", "templateType": "anything", "can_override": false}, "Q_W'": {"name": "Q_W'", "group": "soon", "definition": "CD Load\n", "description": "", "templateType": "anything", "can_override": false}, "Q_V": {"name": "Q_V", "group": "soon", "definition": "Q_W'-Q_Cy", "description": "", "templateType": "anything", "can_override": false}, "Q_Cy": {"name": "Q_Cy", "group": "soon", "definition": "Q_W - qty(F_AB[1], units[0])", "description": "", "templateType": "anything", "can_override": false}, "Q_AB": {"name": "Q_AB", "group": "soon", "definition": "qty(abs(F_AB), units[0])", "description": "", "templateType": "anything", "can_override": false}, "params": {"name": "params", "group": "Ungrouped variables", "definition": "[alpha: [definition: radians(alpha), visible: false],\nn: [definition: n, visible: false],\nshow: [definition: 0, visible: false],\n]", "description": "<p>n = 1..10 &nbsp;</p>", "templateType": "anything", "can_override": false}, "F_AB": {"name": "F_AB", "group": "soon", "definition": "precround(scalar(Q_W)/2 * vector(1/tan(radians(alpha+180)), 1),4)", "description": "<p>alpha is defined from negative x axis,&nbsp;</p>", "templateType": "anything", "can_override": false}, "BD": {"name": "BD", "group": "Inputs", "definition": "n/10 BC\n", "description": "<p>n/10 is fraction of length BC</p>", "templateType": "anything", "can_override": false}, "Q_W": {"name": "Q_W", "group": "soon", "definition": "load * bc", "description": "<p>W</p>", "templateType": "anything", "can_override": false}, "alpha": {"name": "alpha", "group": "Inputs", "definition": "random(-60..60#5 except [0, -5, 5])", "description": "", "templateType": "anything", "can_override": false}, "sum": {"name": "sum", "group": "soon", "definition": "precround(F_AB+F_C+F_W,3)", "description": "<p>check</p>", "templateType": "anything", "can_override": false}, "Q_Cx": {"name": "Q_Cx", "group": "soon", "definition": "qty((F_AB[0]), units[0])", "description": "", "templateType": "anything", "can_override": false}, "F_W": {"name": "F_W", "group": "soon", "definition": "vector(-scalar(Q_W),0)", "description": "", "templateType": "anything", "can_override": false}, "CD": {"name": "CD", "group": "Inputs", "definition": "BC-BD", "description": "", "templateType": "anything", "can_override": false}, "Q_MD": {"name": "Q_MD", "group": "soon", "definition": "(CD Q_Cy - CD Q_W'/2)", "description": "<p>Q</p>", "templateType": "anything", "can_override": false}, "F_C": {"name": "F_C", "group": "soon", "definition": "precround(-(F_AB+F_W),4)", "description": "", "templateType": "anything", "can_override": false}, "applet": {"name": "applet", "group": "Ungrouped variables", "definition": "geogebra_applet( 'pt6wrf9n', params)", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Inputs", "definition": "random(2..8# 0.5)", "description": "<p>Position of cut as ratio of BC</p>", "templateType": "anything", "can_override": false}, "fbd1": {"name": "fbd1", "group": "Ungrouped variables", "definition": "geogebra_applet('pt6wrf9n', params + [show: [definition: 1, visible: false]])", "description": "", "templateType": "anything", "can_override": false}, "fbd2": {"name": "fbd2", "group": "Ungrouped variables", "definition": "geogebra_applet('pt6wrf9n', params + \n[show: [definition: 2, visible: false],\n n: [definition: min(5,n), visible: false]\n])", "description": "<p>just setting n=5 to make the diagram larger</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["units", "applet", "params", "fbd1", "fbd2"], "variable_groups": [{"name": "soon", "variables": ["Q_W", "F_AB", "F_W", "F_C", "sum", "Q_AB", "Q_Cx", "Q_Cy", "Q_MD", "Q_W'", "Q_V"]}, {"name": "Inputs", "variables": ["BC", "alpha", "load", "n", "BD", "CD"]}], "functions": {"display": {"parameters": [["q", "quantity"]], "type": "string", "language": "jme", "definition": "string(siground(q,4))"}}, "preamble": {"js": "question.signals.on('adviceDisplayed',function() {\n try{\n    var app = question.scope.variables.applet.app;  \n    app.setVisible(\"fbd\", true,false);\n    app.setValue(\"fbd\", 1);\n  }\n  catch(err){}  \n})\n", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<table style=\"height: 98px; width: 411px;\">\n<tbody>\n<tr style=\"height: 23px;\">\n<td style=\"width: 157.375px; height: 17px;\">Shear force:</td>\n<td style=\"width: 220.640625px; height: 17px;\">\n<p>$P_D = $ [[0]]</p>\n</td>\n</tr>\n<tr style=\"height: 23px;\">\n<td style=\"width: 157.375px; height: 39px;\">Normal force:</td>\n<td style=\"width: 220.640625px; height: 39px;\">$V_D &nbsp;= $ [[1]]</td>\n</tr>\n<tr style=\"height: 23px;\">\n<td style=\"width: 157.375px; height: 42px;\">Bending moment:&nbsp;</td>\n<td style=\"width: 220.640625px; height: 42px;\">$M_D =$ [[2]]</td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p></p>", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "$P_D$", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "-Q_Cx", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "$V_D$", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "Q_V", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "$M_D$", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "Q_MD", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Internal force: overhanging beam", "extensions": ["geogebra", "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": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["bending moment", "distributed load", "internal forces", "Mechanics", "mechanics", "shear", "Statics", "statics"], "metadata": {"description": "<p>Calculate reactions and shear and bending moment at a point for&nbsp;an overhanging beam with a constant&nbsp;or uniformly varying distributed load.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>{applet(500,215,false)}</p>\n<p style=\"padding: 3px;\">The beam shown supports a<span data-jme-visible=\"Wa=Wb\"> uniformly distributed load of $w$ = {Wa}.</span><span data-jme-visible=\"Wa&lt;&gt;Wb\"> load that varies&nbsp;uniformly from {Wa} at the left end to {Wb} at the right end.</span>&nbsp;</p>\n<p style=\"padding-left: 30px;\">The lengths of the beam segments are $d_1$ = {display(d_1)}, $d_2$ = {display(d_2)}, and $d_3$ = {display(d_3)}.</p>", "advice": "<p><strong>1.</strong>&nbsp;<strong>Draw a FBD of the entire beam and find&nbsp;reactions at <em>A</em>&nbsp;and <em>C</em>.</strong></p>\n<p style=\"padding-left: 30px;\">{applet(500,566,true)}</p>\n<p style=\"padding-left: 30px;\"><strong>a. &nbsp;Replace distributed load with an equivalent concentrated load.</strong></p>\n<p style=\"padding-left: 30px;\">$W$ = {W_t}, &nbsp; &nbsp;&nbsp;$d$ = {display(dw)}</p>\n<p style=\"padding-left: 30px;\"><strong>b. &nbsp;Apply equilibrium equations.</strong></p>\n<p style=\"padding-left: 30px;\">$\\begin{align} \\Sigma M_A &amp;= 0 &amp; &nbsp;\\Sigma F_y &amp;=0 \\\\C \\cdot\\var{if(C[0]&lt;D[0],latex('d_1'),latex('(d_1+d_2)'))} &amp;= &nbsp;W&nbsp;\\cdot&nbsp;d &nbsp;&amp; &nbsp;\\simplify{{if(scalar(FA)&lt;0,-1,1)}&nbsp;A} + C &nbsp;&amp;= W = \\var{W_t}\\\\ C &amp;= \\var{display(FC)} \\uparrow &amp;&nbsp;A &amp;= \\var{display(abs(FA))} &nbsp;\\var{if(F_A[1]&gt;0,latex('\\\\uparrow'),latex('\\\\downarrow'))}\\end{align}$</p>\n<p><strong>2. Draw a FBD of the portion of the beam between <em>A</em> and <em>D</em> and find the shear and bending moment.</strong></p>\n<p style=\"padding-left: 30px;\"><strong>a. &nbsp;Determine the&nbsp;distributed load above point D.</strong></p>\n<p style=\"padding-left: 60px;\">Let $w_A$, $w_B$, and $w_D$ be the magnitude of the distributed load at points $A$, $B$, and $D$ respectively, and $L$ the length of the beam.</p>\n<p style=\"padding-left: 60px;\">Given: $w_A = \\var{wA},\\qquad w_B = \\var{wB}\\qquad L = (d_1 + d_2 + d_3) = \\var{L}$ &nbsp;</p>\n<p style=\"padding-left: 60px;\" data-jme-visible=\"wa=wb\">$w_D = \\var{display(wD)}$</p>\n<p style=\"padding-left: 60px;\" data-jme-visible=\"wa&lt;&gt;wb\">Using similar triangles: &nbsp;$w_D = w_A + \\dfrac{\\var{if(C[0]&gt;D[0],latex('d_1'),latex('(d_1+d_2)'))}}{L} \\left( w_B - w_A \\right) = \\var{display(wD)}$</p>\n<p style=\"padding-left: 30px;\"><strong>b. Replace distributed load with an equivalent concentrated load.</strong></p>\n<p style=\"padding-left: 60px;\">$W'$ = {display(W_p)}, &nbsp; &nbsp; $d'$ = {display(dw')}</p>\n<p style=\"padding-left: 30px;\"><strong>c. Apply equilibrium equations.</strong></p>\n<p style=\"padding-left: 60px;\">Let $\\ell = &nbsp;\\var{if(C[0]&gt;D[0],latex('d_1'),latex('d_1+d_2'))} = \\var{display(Dx)}\\text{, and} \\qquad d_\\perp = (\\ell - d') = \\var{display(Dx - dw')}$</p>\n<p style=\"padding-left: 60px;\">$\\begin{align} \\Sigma M_D &amp;= 0 &amp; \\Sigma F_y &amp;=0 \\\\&nbsp;\\simplify{{if(scalar(FA)&lt;0,1,-1)} A} \\ell + W' d_\\perp \\var{if(Cx &lt; Dx, latex('+C d_2'),'')} + M_D&amp;= 0&nbsp;&amp; \\simplify{{if(scalar(FA)&lt;0,-1,1)} A} \\var{if(Cx &lt; Dx, latex('+ C'),'')} - W' -&nbsp;V&nbsp;&amp;=0 \\\\ M_D &amp;= \\simplify{{if(scalar(FA)&gt;0,1,-1)} A} \\ell -&nbsp;W' d_\\perp&nbsp;\\var{if(Cx &lt; Dx, latex('C d_2'),'')}&nbsp;&amp; V&nbsp;&amp;= \\simplify{{if(scalar(FA)&lt;0,-1,1) }A} \\var{if(Cx &lt; Dx, latex('+ C'),'')} - W'&nbsp;\\\\ &amp;= \\var{display(M_D)}&nbsp;&amp; V &amp;= \\var{display(FV)}&nbsp;\\end{align}$</p>\n<p style=\"padding-left: 60px;\"></p>\n<p>=</p>", "rulesets": {}, "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": "<p>overall length of the beam.</p>", "templateType": "anything"}, "d_2": {"name": "d_2", "group": "Quantities", "definition": "abs(Dx-Cx)", "description": "<p>length of second beam segment</p>", "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]<D[0], F_C, vector(0,0)))", "description": "", "templateType": "anything"}, "F_Wp": {"name": "F_Wp", "group": "vectors", "definition": "vector(0,-scalar(W_p))", "description": "", "templateType": "anything"}, "Dx": {"name": "Dx", "group": "Quantities", "definition": "D[0]/12 Bx", "description": "<p>x position of point d (cut)</p>", "templateType": "anything"}, "Ax": {"name": "Ax", "group": "Quantities", "definition": "qty(0,units[1])", "description": "<p>x position of point A</p>", "templateType": "anything"}, "Bx": {"name": "Bx", "group": "Quantities", "definition": "L", "description": "<p>x position of point B (right end)</p>", "templateType": "anything"}, "h2": {"name": "h2", "group": "Quantities", "definition": "abs(W_a-W_b) Wmax", "description": "<p>height of triangular portion of load</p>", "templateType": "anything"}, "FA": {"name": "FA", "group": "Quantities", "definition": "W_t * (Cx-dw) /Cx", "description": "<p>Force at A, signed</p>", "templateType": "anything"}, "FC": {"name": "FC", "group": "Quantities", "definition": "W_t dw/Cx", "description": "<p>Force at roller C, always up</p>", "templateType": "anything"}, "FV": {"name": "FV", "group": "Quantities", "definition": "FA - W_p + if(C[0]<D[0],FC,qty(0, units[0]))", "description": "<p>shear force at D, Signed</p>", "templateType": "anything"}, "w_B": {"name": "w_B", "group": "Ungrouped variables", "definition": "random(0..2#0.5)", "description": "", "templateType": "anything"}, "W_p": {"name": "W_p", "group": "Quantities", "definition": "(Wa + Wd)/2 Dx", "description": "<p>partial load to the left of point d</p>", "templateType": "anything"}, "M_D": {"name": "M_D", "group": "Quantities", "definition": "FA Dx - W_p * (Dx - dw') + if(Cx<Dx,FC,qty(0,units[0])) d_2", "description": "<p>moment at D, signed</p>\n<p>&minus;\ud835\udc34\u2113&minus;\ud835\udc4a&prime;\ud835\udc51&perp;&minus;\ud835\udc36\ud835\udc512</p>", "templateType": "anything"}, "dw": {"name": "dw", "group": "Quantities", "definition": "(Wa / 6 + Wb  /3 ) L L /W_T", "description": "<p>distance to equivalent load's centroid for whole beam</p>", "templateType": "anything"}, "W_t": {"name": "W_t", "group": "Quantities", "definition": "(Wa + Wb)/2 L", "description": "<p>Equivalent load on beam, down</p>", "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": "<p>Random load value which gets scaled geogebra_values w_a and w_b to make actual loads Wa and Wb.</p>", "templateType": "anything"}, "h1": {"name": "h1", "group": "Quantities", "definition": "min(W_a,W_b) Wmax", "description": "<p>height of rectangular portion of the load</p>", "templateType": "anything"}, "Wd": {"name": "Wd", "group": "Quantities", "definition": "wA +  (wb-wa) * if(C[0]>D[0],d_1, d_1+d_2) / L ", "description": "<p>distributed load value at point D</p>", "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": "<p>distributed load value at point A, right end.</p>", "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": "<p>distance from A to partial load W_p</p>", "templateType": "anything"}, "Cx": {"name": "Cx", "group": "Quantities", "definition": "C[0]/12 Bx\n ", "description": "<p>x position of point&nbsp;C (roller)</p>", "templateType": "anything"}, "Wa": {"name": "Wa", "group": "Quantities", "definition": "Wmax w_a", "description": "<p>distributed load value at point A, left end</p>", "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": "<p>length of first beam segment.</p>", "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": "<p>length of third beam segment</p>", "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": "<p>Determine the reactions at pin $A$ and roller $C$. &nbsp;Let positive values indicate upward forces.</p>\n<p>$A$ =&nbsp;[[0]] <span data-jme-visible=\"debug\">{display(FA)}</span></p>\n<p>$C$ =&nbsp;[[1]] <span data-jme-visible=\"debug\">{display(FC)}</span></p>", "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": "<p>Determine the&nbsp;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.&nbsp;</p>\n<p>$V_D$ &nbsp;=&nbsp;[[0]] <span data-jme-visible=\"debug\">{display(FV)}</span></p>\n<p>$M_D$ =&nbsp;[[1]] <span data-jme-visible=\"debug\">{display(M_D)}</span></p>", "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"}]}], "allowPrinting": true, "navigation": {"allowregen": true, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": false, "showresultspage": "oncompletion", "navigatemode": "sequence", "onleave": {"action": "none", "message": ""}, "preventleave": true, "startpassword": ""}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"showactualmark": true, "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": true, "advicethreshold": 0, "intro": "", "reviewshowscore": true, "reviewshowfeedback": true, "reviewshowexpectedanswer": true, "reviewshowadvice": true, "feedbackmessages": []}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "extensions": ["geogebra", "quantities", "weh"], "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": []}