// Numbas version: finer_feedback_settings
{"name": "Moment of inertia: 2 channels and 2 plates", "extensions": ["geogebra", "polynomials", "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/channel_EfJjxiR.png", "/srv/numbas/media/question-resources/channel_EfJjxiR.png"], ["question-resources/builtupbeam.ggb", "/srv/numbas/media/question-resources/builtupbeam.ggb"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Moment of inertia: 2 channels and 2 plates", "tags": ["built-up beam", "Mechanics", "mechanics", "moment of inertia", "radius of gyration", "standard sections", "Statics", "statics"], "metadata": {"description": "<p>Find moment of inertia and radius of gyration for a built-up beam made of two channels and two plates.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>A built-up beam is constructed by welding two channels separated by a distance $b = \\var{b}$ to two ({w} $\\times$ {h}) plates.</p>\n<table height=\"34\" style=\"width: 548px;\">\n<tbody>\n<tr>\n<td style=\"width: 223.390625px; text-align: left;\">{geogebra_applet('rgft4vzy',[\"b\":ggb(b),'bf': ggb(bf),'w': ggb(w) ,'d': ggb(d),'t': ggb(t),'h': ggb(h)])}</td>\n<td style=\"width: 501.609375px; text-align: left;\">\n<div style=\"float: right;\">\n<p><strong>Channel properties:</strong></p>\n<p>$\\begin{align}\\var{desc}\\\\\\text{Area}&amp;= \\var{A_C} \\\\D&nbsp;&amp;= \\var{d} \\\\b_f &amp;= \\var{bf}\\\\\\bar{x} &amp;= \\var{xbar}\\\\\\bar{I}_{xx} &amp;= \\var{Ibarx_C} \\\\\\bar{I}_{yy} &amp;= \\var{Ibary_C}\\end{align}$</p>\n</div>\n</td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p></p>", "advice": "<p><strong></strong><strong>Determine moment of inertia with respect to the <em>x</em>-axis</strong></p>\n<p style=\"padding-left: 30px;\"><strong></strong>For the channel, since the&nbsp;x-axis passes through its centroid:</p>\n<p style=\"padding-left: 60px;\">$(I_x)_C = \\bar{I}_{xx} =&nbsp;\\var{Ibarx_C} $</p>\n<p style=\"padding-left: 30px;\">For the plate, the <em>x</em>-axis does not pass through its&nbsp;centroid&nbsp;so&nbsp;the parallel axis theorem must be used.</p>\n<p style=\"padding-left: 60px;\">$(I_x)_R = [\\bar{I} + A d^2] $ where,</p>\n<p style=\"padding-left: 90px;\">$\\bar{I} = \\dfrac{b h^3}{12} = \\dfrac{(\\var{w})(\\var{h})^3}{12} = \\var{siground(Ibarx_R,4)}$</p>\n<p style=\"padding-left: 90px;\">$A &nbsp;= b h = (\\var{w})\\,(\\var{h}) = \\var{A_r}$</p>\n<p style=\"padding-left: 90px;\">$d = D/2 + h/2 = \\dfrac{\\var{d}+ \\var{h}}{2} = \\var{d_y} $</p>\n<p style=\"padding-left: 60px;\">$(I_x)_R = \\var{disp(Ix_R)}$</p>\n<p style=\"padding-left: 30px;\">For the composite shape,</p>\n<p style=\"padding-left: 60px;\">$A = 2 [A_C + A_R] = \\var{disp(A_T)}$</p>\n<p style=\"padding-left: 60px;\">$I_x = 2 [ (I_x)_C + (I_x)_R ] = \\var{disp(Ix)}$, and &nbsp;$k_x = \\sqrt{\\dfrac{I_x}{A}} = \\var{disp(kx)}$</p>\n<p style=\"padding-left: 90px;\"></p>\n<p><strong>Determine moment of inertia with respect to the <em>y-</em>axis</strong></p>\n<p style=\"padding-left: 30px;\">For the rectangle, since the y-axis passes through its centroid:</p>\n<p style=\"padding-left: 60px;\">$(I_y)_R = \\dfrac{h b^3}{12}&nbsp;= \\dfrac{(\\var{h}) (\\var{w})^3}{12} = \\var{disp(Ibary_r)}$</p>\n<p style=\"padding-left: 30px;\">For the channel, the y-axis does not pass through its centroid so the parallel axis theorem must be used.</p>\n<p style=\"padding-left: 60px;\">$(I_y)_C = [\\bar{I} + A d^2] $ where,</p>\n<p style=\"padding-left: 90px;\">$\\bar{I} = \\bar{I}_{yy} = \\var{Ibary_C}$</p>\n<p style=\"padding-left: 90px;\">$A = A_C&nbsp;= \\var{A_C}$</p>\n<p style=\"padding-left: 90px;\">$d = b/2 + \\bar{x}&nbsp;= \\dfrac{\\var{b}}{2} + \\var{xbar}= \\var{d_x} $</p>\n<p style=\"padding-left: 90px;\">$(I_y)_C = \\var{disp(Iy_C)}$</p>\n<p style=\"padding-left: 30px;\">For the composite shape,</p>\n<p style=\"padding-left: 60px;\">$A = 2 [A_C + A_R] = \\var{disp(A_T)}$</p>\n<p style=\"padding-left: 60px;\">$I_y = 2 [ (I_y)_C + (I_y)_R ] = \\var{disp(Iy)}$, and&nbsp;$k_y = \\sqrt{\\dfrac{I_y}{A}} = \\var{disp(ky)}$</p>\n<p style=\"padding-left: 60px;\"><strong>&nbsp;</strong></p>\n<p style=\"padding-left: 60px;\"></p>", "rulesets": {}, "extensions": ["geogebra", "polynomials", "quantities"], "variables": {"xbar": {"name": "xbar", "group": "Channel Properties", "definition": "qty(C_data['x'][unit], if(unit=0,'in','mm'))", "description": "<p>horizontal distance to centroid from flange</p>", "templateType": "anything"}, "A_t": {"name": "A_t", "group": "Solution", "definition": "2(A_r+A_C)", "description": "", "templateType": "anything"}, "Ibarx_c": {"name": "Ibarx_c", "group": "Channel Properties", "definition": "C_data['Ix'][unit] * if(unit=0,qty('in^4'),qty(10^6,'mm^4'))", "description": "", "templateType": "anything"}, "ky": {"name": "ky", "group": "Solution", "definition": "sqrt(scalar(Iy/A_t)) units", "description": "", "templateType": "anything"}, "d_y": {"name": "d_y", "group": "Solution", "definition": "d/2 + h/2", "description": "", "templateType": "anything"}, "index": {"name": "index", "group": "Ungrouped variables", "definition": "random(0..length(data)-1)", "description": "<p>random channel index</p>", "templateType": "anything"}, "A_r": {"name": "A_r", "group": "Solution", "definition": "w h", "description": "", "templateType": "anything"}, "C_data": {"name": "C_data", "group": "Channel Properties", "definition": "data[index]", "description": "<p>hash of data for selected channel</p>", "templateType": "anything"}, "kx": {"name": "kx", "group": "Solution", "definition": "sqrt(scalar(Ix/A_t)) units", "description": "", "templateType": "anything"}, "A_C": {"name": "A_C", "group": "Channel Properties", "definition": "qty(C_data['A'][unit], if(unit=0,'in^2','mm^2'))", "description": "<p>area of channel</p>", "templateType": "anything"}, "unit": {"name": "unit", "group": "Ungrouped variables", "definition": "random(0,1)", "description": "<p>0 = inches, 1 = mm</p>", "templateType": "anything"}, "Iy_C": {"name": "Iy_C", "group": "Solution", "definition": "Ibary_C + A_c d_x d_x", "description": "", "templateType": "anything"}, "Ix": {"name": "Ix", "group": "Solution", "definition": "2 (Ibarx_c + Ix_r)", "description": "", "templateType": "anything"}, "bf": {"name": "bf", "group": "Channel Properties", "definition": "qty(C_data['bf'][unit], if(unit=0,'in','mm'))", "description": "<p>flange width</p>", "templateType": "anything"}, "Iy": {"name": "Iy", "group": "Solution", "definition": "2 (Iy_C + Ibary_R)", "description": "", "templateType": "anything"}, "w": {"name": "w", "group": "Ungrouped variables", "definition": "round ((b/2 + bf + t ) 2 , if(unit=0,'1 in', '10 mm'))", "description": "<p>width&nbsp;of plate &nbsp;a little longer than necessary</p>", "templateType": "anything"}, "t": {"name": "t", "group": "Channel Properties", "definition": "qty(C_data['tf'][unit], if(unit=0,'in','mm'))", "description": "", "templateType": "anything"}, "d_x": {"name": "d_x", "group": "Solution", "definition": "b/2 + xbar", "description": "", "templateType": "anything"}, "d": {"name": "d", "group": "Channel Properties", "definition": "qty(C_data['d'][unit], if(unit=0,'in','mm'))", "description": "<p>depth of channel</p>", "templateType": "anything"}, "Ibary_c": {"name": "Ibary_c", "group": "Channel Properties", "definition": "C_data['Iy'][unit] * if(unit=0,qty('in^4'),qty(10^6,'mm^4'))", "description": "<p>centroidal momentof inertia</p>", "templateType": "anything"}, "Desc": {"name": "Desc", "group": "Channel Properties", "definition": "C_data['DESC'][unit] ", "description": "<p>designation</p>", "templateType": "anything"}, "Ix_R": {"name": "Ix_R", "group": "Solution", "definition": "Ibarx_r + A_r d_y d_y", "description": "", "templateType": "anything"}, "h": {"name": "h", "group": "Ungrouped variables", "definition": "round(random(1..3#0.1)t,if(unit=0,'0.125 in', '5 mm'))", "description": "<p>width of plate</p>", "templateType": "anything"}, "Ibarx_r": {"name": "Ibarx_r", "group": "Solution", "definition": "w h h h /12", "description": "", "templateType": "anything"}, "units": {"name": "units", "group": "Channel Properties", "definition": "qty(if(unit=0,'in','mm'))", "description": "", "templateType": "anything"}, "Ibary_R": {"name": "Ibary_R", "group": "Solution", "definition": "h w w w /12", "description": "", "templateType": "anything"}, "data": {"name": "data", "group": "Channel Properties", "definition": "json_decode(safe(\"[\\n  {\\n    \\\"DESC\\\": [\\n      \\\"C15$\\\\\\\\times$50\\\",\\n      \\\"C380$\\\\\\\\times$74\\\"\\n    ],\\n    \\\"W\\\": [\\n      50,\\n      74\\n    ],\\n    \\\"A\\\": [\\n      14.7,\\n      9480\\n    ],\\n    \\\"d\\\": [\\n      15,\\n      381\\n    ],\\n    \\\"bf\\\": [\\n      3.72,\\n      94.5\\n    ],\\n    \\\"tw\\\": [\\n      0.716,\\n      18.2\\n    ],\\n    \\\"tf\\\": [\\n      0.65,\\n      16.5\\n    ],\\n    \\\"x\\\": [\\n      0.799,\\n      20.3\\n    ],\\n    \\\"Ix\\\": [\\n      404,\\n      168\\n    ],\\n    \\\"Iy\\\": [\\n      11,\\n      4.58\\n    ]\\n  },\\n  {\\n    \\\"DESC\\\": [\\n      \\\"C15$\\\\\\\\times$40\\\",\\n      \\\"C380$\\\\\\\\times$60\\\"\\n    ],\\n    \\\"W\\\": [\\n      40,\\n      60\\n    ],\\n    \\\"A\\\": [\\n      11.8,\\n      7610\\n    ],\\n    \\\"d\\\": [\\n      15,\\n      381\\n    ],\\n    \\\"bf\\\": [\\n      3.52,\\n      89.4\\n    ],\\n    \\\"tw\\\": [\\n      0.52,\\n      13.2\\n    ],\\n    \\\"tf\\\": [\\n      0.65,\\n      16.5\\n    ],\\n    \\\"x\\\": [\\n      0.778,\\n      19.8\\n    ],\\n    \\\"Ix\\\": [\\n      348,\\n      145\\n    ],\\n    \\\"Iy\\\": [\\n      9.17,\\n      3.82\\n    ]\\n  },\\n  {\\n    \\\"DESC\\\": [\\n      \\\"C15$\\\\\\\\times$33.9\\\",\\n      \\\"C380$\\\\\\\\times$50.4\\\"\\n    ],\\n    \\\"W\\\": [\\n      33.9,\\n      50.4\\n    ],\\n    \\\"A\\\": [\\n      10,\\n      6450\\n    ],\\n    \\\"d\\\": [\\n      15,\\n      381\\n    ],\\n    \\\"bf\\\": [\\n      3.4,\\n      86.4\\n    ],\\n    \\\"tw\\\": [\\n      0.4,\\n      10.2\\n    ],\\n    \\\"tf\\\": [\\n      0.65,\\n      16.5\\n    ],\\n    \\\"x\\\": [\\n      0.788,\\n      20\\n    ],\\n    \\\"Ix\\\": [\\n      315,\\n      131\\n    ],\\n    \\\"Iy\\\": [\\n      8.07,\\n      3.36\\n    ]\\n  },\\n  {\\n    \\\"DESC\\\": [\\n      \\\"C12$\\\\\\\\times$30\\\",\\n      \\\"C310$\\\\\\\\times$45\\\"\\n    ],\\n    \\\"W\\\": [\\n      30,\\n      45\\n    ],\\n    \\\"A\\\": [\\n      8.81,\\n      5680\\n    ],\\n    \\\"d\\\": [\\n      12,\\n      305\\n    ],\\n    \\\"bf\\\": [\\n      3.17,\\n      80.5\\n    ],\\n    \\\"tw\\\": [\\n      0.51,\\n      13\\n    ],\\n    \\\"tf\\\": [\\n      0.501,\\n      12.7\\n    ],\\n    \\\"x\\\": [\\n      0.674,\\n      17.1\\n    ],\\n    \\\"Ix\\\": [\\n      162,\\n      67.4\\n    ],\\n    \\\"Iy\\\": [\\n      5.12,\\n      2.13\\n    ]\\n  },\\n  {\\n    \\\"DESC\\\": [\\n      \\\"C12$\\\\\\\\times$25\\\",\\n      \\\"C310$\\\\\\\\times$37\\\"\\n    ],\\n    \\\"W\\\": [\\n      25,\\n      37\\n    ],\\n    \\\"A\\\": [\\n      7.34,\\n      4740\\n    ],\\n    \\\"d\\\": [\\n      12,\\n      305\\n    ],\\n    \\\"bf\\\": [\\n      3.05,\\n      77.5\\n    ],\\n    \\\"tw\\\": [\\n      0.387,\\n      9.83\\n    ],\\n    \\\"tf\\\": [\\n      0.501,\\n      12.7\\n    ],\\n    \\\"x\\\": [\\n      0.674,\\n      17.1\\n    ],\\n    \\\"Ix\\\": [\\n      144,\\n      59.9\\n    ],\\n    \\\"Iy\\\": [\\n      4.45,\\n      1.85\\n    ]\\n  },\\n  {\\n    \\\"DESC\\\": [\\n      \\\"C12$\\\\\\\\times$20.7\\\",\\n      \\\"C310$\\\\\\\\times$30.8\\\"\\n    ],\\n    \\\"W\\\": [\\n      20.7,\\n      30.8\\n    ],\\n    \\\"A\\\": [\\n      6.08,\\n      3920\\n    ],\\n    \\\"d\\\": [\\n      12,\\n      305\\n    ],\\n    \\\"bf\\\": [\\n      2.94,\\n      74.7\\n    ],\\n    \\\"tw\\\": [\\n      0.282,\\n      7.16\\n    ],\\n    \\\"tf\\\": [\\n      0.501,\\n      12.7\\n    ],\\n    \\\"x\\\": [\\n      0.698,\\n      17.7\\n    ],\\n    \\\"Ix\\\": [\\n      129,\\n      53.7\\n    ],\\n    \\\"Iy\\\": [\\n      3.86,\\n      1.61\\n    ]\\n  },\\n  {\\n    \\\"DESC\\\": [\\n      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