// Numbas version: finer_feedback_settings
{"name": "Momentkapacitet balk - h\u00e5llfasthetsdom\u00e4nen", "extensions": [], "custom_part_types": [{"source": {"pk": 1, "author": {"name": "Christian Lawson-Perfect", "pk": 7}, "edit_page": "/part_type/1/edit"}, "name": "Yes/no", "short_name": "yes-no", "description": "<p>The student is shown two radio choices: \"Yes\" and \"No\". One of them is correct.</p>", "help_url": "", "input_widget": "radios", "input_options": {"correctAnswer": "if(eval(settings[\"correct_answer_expr\"]), 0, 1)", "hint": {"static": true, "value": ""}, "choices": {"static": true, "value": ["Yes", "No"]}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nif(studentanswer=correct_answer,\n  correct(),\n  incorrect()\n)\n\ninterpreted_answer:\nstudentAnswer=0\n\ncorrect_answer:\nif(eval(settings[\"correct_answer_expr\"]),0,1)", "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": "if(studentanswer=correct_answer,\n  correct(),\n  incorrect()\n)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "studentAnswer=0"}, {"name": "correct_answer", "description": "", "definition": "if(eval(settings[\"correct_answer_expr\"]),0,1)"}], "settings": [{"name": "correct_answer_expr", "label": "Is the answer \"Yes\"?", "help_url": "", "hint": "An expression which evaluates to <code>true</code> or <code>false</code>.", "input_type": "mathematical_expression", "default_value": "true", "subvars": false}], "public_availability": "always", "published": true, "extensions": []}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Momentkapacitet balk - h\u00e5llfasthetsdom\u00e4nen", "tags": [], "metadata": {"description": "<p>Calculation of bending resistance of wooden beams exposed to fire. The students have to calculate charring and effective cross sections ending in the bending resistance of the cross section.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>Klarar tr&auml;balken krav motsvarande R {rKrav}?</p>\n<ol>\n<li>Virkeskvalitet: $\\var{gl}$</li>\n<li>Bredd: $b=\\var{b}$ $mm$</li>\n<li>H&ouml;jd: $h=\\var{h}$ $mm$</li>\n<li>Verksamheten ovan bj&auml;lklaget &auml;r {occupancy}</li>\n<li>Egentyngden f&ouml;r bj&auml;lklaget &auml;r {gk} kN/m&sup2;</li>\n<li>Centrumavst&aring;nd mellan balkar, $cc$ - {cc} m</li>\n<li>Balken kan anses fritt upplagd med l&auml;ngden $l$ - {length} m</li>\n<li>S&auml;kerhetsklass {SK_rand}</li>\n</ol>\n<p>Antag att balken &auml;r brandutsatt p&aring; 3 sidor (under och p&aring; sidorna) samt att ingen vippning kan ske, dvs $k_{crit} = 1$. Anv&auml;nd metoden reducerat tv&auml;rsnitt.</p>", "advice": "<h2>$M_{Ed,fi}$</h2>\n<p>Momentp&aring;k&auml;nningen f&ouml;r en fritt upplagd balk ber&auml;knas som</p>\n<p style=\"text-align: center;\">$M_{Ed,fi}=\\frac{qL^2}{8}$</p>\n<p style=\"text-align: left;\">D&auml;r $q$ &auml;r den utbredda lasten vilken ber&auml;knas utifr&aring;n den dimensionerande lasten i brandfallet.</p>\n<p style=\"text-align: center;\">$E_{d,fi}=g_k+\\psi_1 q_k$</p>\n<p>F&ouml;r {occupancy} &auml;r $q_k$ = {qk} kN/m&sup2; och ur tabell kan vi l&auml;sa att $\\psi_1$ = {psi_1}. D&aring; egentyngden, $g_k$, ges i uppgiften till {gk} kN/m&sup2; ber&auml;knas $E_{d,fi}$ till</p>\n<p style=\"text-align: center;\">$E_{d,fi}=\\var{precround(gk,1)}+\\var{psi_1}\\cdot \\var{qk}=\\var{precround(Ed_fi,1)}$ $kN/m&sup2;$</p>\n<p style=\"text-align: left;\">Ett centrumavst&aring;nd motsvarande {cc} meter g&ouml;r att $E_{d,fi}$ kan antas som</p>\n<p style=\"text-align: center;\">$\\var{precround(Ed_fi,1)}\\cdot \\var{precround(cc,1)} = \\var{precround(Ed_fi_tot,1)}$ $kN/m$</p>\n<p style=\"text-align: left;\">Den f&ouml;rsta ekvationen kan d&auml;rf&ouml;r justeras till</p>\n<p style=\"text-align: center;\">$M_{Ed,fi}=\\frac{E_{d,fi}L^2}{8}=\\frac{\\var{precround(Ed_fi_tot,1)}\\cdot\\var{length}^2}{8}=\\var{precround(MEd_fi,1)}$ $kNm$</p>\n<h2>$M_{Rd,fi}$</h2>\n<h3>Inbr&auml;nningshastighet</h3>\n<p>I f&ouml;rsta steget ber&auml;knas inbr&auml;nningshastigheten genom att ber&auml;kna den minsta bredd, $b_{min}$, som kr&auml;vs f&ouml;r att rundningen av h&ouml;rnen inte ska tas med</p>\n<p style=\"text-align: center;\"><span data-jme-visible=\"t0&gt;=13\">$b_{min}=\\huge\\{ \\normalsize{2d_{char,0}+80 \\atop 8.15d_{char,0}}\\text{ &nbsp;&nbsp; }{d_{char,0}\\geq13\\text{ }mm \\atop d_{char,0}&lt;13\\text{ }mm}\\Rightarrow b_{min}=2 t_R \\beta _0+80=\\var{bmin}$ $mm$</span></p>\n<p style=\"text-align: center;\"><span data-jme-visible=\"t0&lt;13\">$b_{min}=\\huge\\{ \\normalsize{2d_{char,0}+80 \\atop 8.15d_{char,0}}\\text{ &nbsp;&nbsp; }{d_{char,0}\\geq13\\text{ }mm \\atop d_{char,0}&lt;13\\text{ }mm}\\Rightarrow b_{min}=8.15d_{char,0}=\\var{bmin}$ $mm$</span></p>\n<p>med $t_R = \\var{rkrav}\\text{ }min$ och $\\beta_0 = \\var{beta0}\\text{ }mm/min$ blir $b_{min} = \\var{bMin}\\text{ }mm$ vilket &auml;r $\\var{betaTrue}$ &auml;n $b=\\var{b}\\text{ }mm$ varf&ouml;r $\\beta_{design}=\\underline{\\underline{\\var{betaDesign}\\text{ }mm/min}}$.</p>\n<h3>Effektivt tv&auml;rsnitt och b&ouml;jmotst&aring;nd</h3>\n<p style=\"text-align: left;\">Med tresidig inbr&auml;nning ber&auml;knas $b_{eff}$ som:</p>\n<p style=\"text-align: center;\">$b_{eff}=b-2(\\beta_{design}t_R+k_0d_0)=\\var{b}-2\\left(\\var{betaDesign}\\cdot\\var{rKrav}+\\var{kZero}\\cdot\\var{dZero}\\right)=\\var{precround(bEff,1)}$ $mm$</p>\n<p>och $h_{eff}$ som</p>\n<p style=\"text-align: center;\">$h_{eff}=h-(\\beta_{design}t_R+k_0d_0)=\\var{h}-\\left(\\var{betaDesign}\\cdot\\var{rKrav}+\\var{kZero}\\cdot\\var{dZero}\\right)=\\var{precround(hEff,1)}$ $mm$</p>\n<p>Utifr&aring;n det ber&auml;knas b&ouml;jmotst&aring;ndet som:</p>\n<p style=\"text-align: center;\">$W_{eff}=\\frac{b_{eff}h_{eff}^2}{6}=\\frac{\\var{bEff}\\cdot\\var{hEff}^2}{6}=\\underline{\\underline{\\var{precround(wEff,1)}\\text{ }mm^3}}$</p>\n<h3 style=\"text-align: left;\">Materialegenskaper</h3>\n<p style=\"text-align: left;\">I brandfallet ber&auml;knas dimensionerande materialv&auml;rden med:</p>\n<p style=\"text-align: center;\">$f_{md,fi}=k_{mod,fi}\\frac{k_{fi}f_{mk}}{\\gamma_{M,fi}}=1\\frac{\\var{kFi}\\cdot\\var{fm}}{1}=\\underline{\\underline{\\var{precround(fmFi,1)}\\text{ }MPa}}$</p>\n<h3 style=\"text-align: left;\">Momentkapacitet</h3>\n<p style=\"text-align: left;\">Med $k_{crit}$ = 1, ber&auml;knas $M_{Rd,fi}$ som:</p>\n<p style=\"text-align: center;\">$M_{Rd,fi}=k_{crit}f_{md,fi}W_{eff}=1\\cdot\\var{precround(fmFi,1)}\\cdot\\var{precround(wEff,1)}=\\underline{\\underline{\\var{precround(mToT,1)}\\text{ }kNm}}$</p>\n<h2 style=\"text-align: left;\">Sammanfattning</h2>\n<p>Kontrollera om h&aring;llfastheten, $M_{Rd,fi}$, &auml;r st&ouml;rre &auml;n belastningen, $M_{Ed,fi}$, dvs.</p>\n<p style=\"text-align: center;\">$M_{Ed,fi}\\leq M_{Rd,fi}$</p>\n<p style=\"text-align: center;\">$\\var{precround(MEd_Fi,1)}\\leq\\var{precround(Mtot,1)}$</p>\n<p style=\"text-align: left;\">Om ovanst&aring;ende &auml;r sant s&aring; kan konstruktionen anses klara krav motsvarande R {rKrav}.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"rKrav": {"name": "rKrav", "group": "Ungrouped variables", "definition": "random(15, 30, 60, 90, 120)", "description": "<p>Klassificeringstid</p>", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(42, 56, 66, 78, 90, 115, 140, 165, 190, 215)", "description": "<p>Tv&auml;rsnittsbredd</p>", "templateType": "anything", "can_override": false}, "h": {"name": "h", "group": "Ungrouped variables", "definition": "random(90, 115, 135, 180, 225, 270, 315, 360, 405, 450, 495, 540)", "description": "", "templateType": "anything", "can_override": false}, "beta0": {"name": "beta0", "group": "Ungrouped variables", "definition": "0.65", "description": "", "templateType": "anything", "can_override": false}, "betaN": {"name": "betaN", "group": "Ungrouped variables", "definition": "0.7", "description": "", "templateType": "anything", "can_override": false}, "bMin": {"name": "bMin", "group": "Ungrouped variables", "definition": "if(beta0*rKrav<13,8.15*beta0*rKrav,2*beta0*rKrav+80)", "description": "", "templateType": "anything", "can_override": false}, "betaDesign": {"name": "betaDesign", "group": "Ungrouped variables", "definition": "if(bMin<b,beta0,betaN)", "description": "", "templateType": "anything", "can_override": false}, "bEff": {"name": "bEff", "group": "Ungrouped variables", "definition": "max(0,b-2*(betaDesign*rKrav+kZero*dZero))", "description": "", "templateType": "anything", "can_override": false}, "hEff": {"name": "hEff", "group": "Ungrouped variables", "definition": "max(0,h-(betaDesign*rKrav+kZero*dZero))", "description": "", "templateType": "anything", "can_override": false}, "wEff": {"name": "wEff", "group": "Ungrouped variables", "definition": "hEff^2*bEff/6", "description": "", "templateType": "anything", "can_override": false}, "kMod": {"name": "kMod", "group": "Ungrouped variables", "definition": "1", "description": "", "templateType": "anything", "can_override": false}, "kFi": {"name": "kFi", "group": "Ungrouped variables", "definition": "1.15", "description": "", "templateType": "anything", "can_override": false}, "fmFi": {"name": "fmFi", "group": "Ungrouped variables", "definition": "fmList[kvalitet]*kFi", "description": "", "templateType": "anything", "can_override": false}, "mTot": {"name": "mTot", "group": "Ungrouped variables", "definition": "fmFi*wEff/1000000", "description": "", "templateType": "anything", "can_override": false}, "t0": {"name": "t0", "group": "Ungrouped variables", "definition": "rKrav * beta0", "description": "", "templateType": "anything", "can_override": false}, "betaTrue": {"name": "betaTrue", "group": "Ungrouped variables", "definition": "if(betaDesign=beta0,\"mindre\",\"st\u00f6rre\")", "description": "", "templateType": "anything", "can_override": false}, "kZero": {"name": "kZero", "group": "Ungrouped variables", "definition": "min(1.0,rKrav/20)", "description": "", "templateType": "anything", "can_override": false}, "dZero": {"name": "dZero", "group": "Ungrouped variables", "definition": "7.0", "description": "", "templateType": "anything", "can_override": false}, "wEffInt": {"name": "wEffInt", "group": "Ungrouped variables", "definition": "Int(wEff*10)", "description": "", "templateType": "anything", "can_override": false}, "mTotInt": {"name": "mTotInt", "group": "Ungrouped variables", "definition": "Int(mTot*10)", "description": "", "templateType": "anything", "can_override": false}, "mTotPrecision": {"name": "mTotPrecision", "group": "Ungrouped variables", "definition": "mTotInt/10.0", "description": "", "templateType": "anything", "can_override": false}, "kCrit": {"name": "kCrit", "group": "Ungrouped variables", "definition": "1.0*if(lambdaRel<0.75,1,min(1,if(lambdaRel>1.4,1/lambdaRel^2,1.56-0.75*lambdaRel)))", "description": "", "templateType": "anything", "can_override": false}, "fmList": {"name": "fmList", "group": "Ungrouped variables", "definition": "[28,30,32]", "description": "", "templateType": "anything", "can_override": false}, "fcList": {"name": "fcList", "group": "Ungrouped variables", "definition": "[24,24.5,26.5]", "description": "", "templateType": "anything", "can_override": false}, "ftList": {"name": "ftList", "group": "Ungrouped variables", "definition": "[16.5,19.5,19.5]", "description": "", "templateType": "anything", "can_override": false}, "eList": {"name": "eList", "group": "Ungrouped variables", "definition": "[10400,10800,11100]", "description": "", "templateType": "anything", "can_override": false}, "gList": {"name": "gList", "group": "Ungrouped variables", "definition": "[720,540,780]", "description": "", "templateType": "anything", "can_override": false}, "kvalitet": {"name": "kvalitet", "group": "Ungrouped variables", "definition": "if(b > 80, 1, 0)", "description": "", "templateType": "anything", "can_override": false}, "fcFi": {"name": "fcFi", "group": "Ungrouped variables", "definition": "fcList[kvalitet] *kFi", "description": "", "templateType": "anything", "can_override": false}, "eModulFi": {"name": "eModulFi", "group": "Ungrouped variables", "definition": "eList[kvalitet] * kFi", "description": "", "templateType": "anything", "can_override": false}, "gModulFi": {"name": "gModulFi", "group": "Ungrouped variables", "definition": "gList[kvalitet] * kFi", "description": "", "templateType": "anything", "can_override": false}, "lambdaRel": {"name": "lambdaRel", "group": "Ungrouped variables", "definition": "sqrt(fcFi*1000000/sigmaCritFi)  ", "description": "", "templateType": "anything", "can_override": false}, "iFi": {"name": "iFi", "group": "Ungrouped variables", "definition": "(hEff/1000)^3*(bEff/1000)/12", "description": "", "templateType": "anything", "can_override": false}, "iTorFi": {"name": "iTorFi", "group": "Ungrouped variables", "definition": "hEff/2000*(bEff/2000)^3*(16/3-3.36*(bEff/2000)/(hEff/2000)*(1-(bEff/2000)^4/(12*(hEff/2000))^4))", "description": "", "templateType": "anything", "can_override": false}, "sigmaCritFi": {"name": "sigmaCritFi", "group": "Ungrouped variables", "definition": "pi*sqrt(eModulFi*iFi*gModulFi*iTorFi)/(0.9*elementLength*5*wEff/1000000000)*1000000  ", "description": "", "templateType": "anything", "can_override": false}, "elementLength": {"name": "elementLength", "group": "Ungrouped variables", "definition": "1.0", "description": "", "templateType": "anything", "can_override": false}, "fm": {"name": "fm", "group": "Ungrouped variables", "definition": "fmList[kvalitet]", "description": "", "templateType": "anything", "can_override": false}, "gl": {"name": "gl", "group": "Ungrouped variables", "definition": "if(h > 180, \"GL\"+fm+\"c\", \"GL\"+fm+\"h\")", "description": "", "templateType": "anything", "can_override": false}, "length": {"name": "length", "group": "Ungrouped variables", "definition": "random(5..7#1)", "description": "", "templateType": "anything", "can_override": false}, "occupancy": {"name": "occupancy", "group": "Ungrouped variables", "definition": "[\"kontor\", \"bostad\"][randomizer]", "description": "", "templateType": "anything", "can_override": false}, "sk_rand": {"name": "sk_rand", "group": "Ungrouped variables", "definition": "random(1..3#1)", "description": "", "templateType": "anything", "can_override": false}, "cc": {"name": "cc", "group": "Ungrouped variables", "definition": "random(3..6#1)", "description": "", "templateType": "anything", "can_override": false}, "randomizer": {"name": "randomizer", "group": "Ungrouped variables", "definition": "random(0,1)", "description": "", "templateType": "anything", "can_override": false}, "psi_1": {"name": "psi_1", "group": "Ungrouped variables", "definition": "[0.5, 0.5][randomizer]", "description": "", "templateType": "anything", "can_override": false}, "STR_B": {"name": "STR_B", "group": "Ungrouped variables", "definition": "SK*(1.35*0.89*gk+1.5*qk)", "description": "", "templateType": "anything", "can_override": false}, "gk": {"name": "gk", "group": "Ungrouped variables", "definition": "0.5", "description": "", "templateType": "anything", "can_override": false}, "qk": {"name": "qk", "group": "Ungrouped variables", "definition": "[2.5, 2.0][randomizer]", "description": "", "templateType": "anything", "can_override": false}, "sk": {"name": "sk", "group": "Ungrouped variables", "definition": "[0,0.89,0.93,1.0][sk_rand]", "description": "", "templateType": "anything", "can_override": false}, "eta_fi": {"name": "eta_fi", "group": "Ungrouped variables", "definition": "Ed_fi / max(str_a, str_b)", "description": "", "templateType": "anything", "can_override": false}, "ed_fi": {"name": "ed_fi", "group": "Ungrouped variables", "definition": "gk+psi_1*qk", "description": "", "templateType": "anything", "can_override": false}, "str_a": {"name": "str_a", "group": "Ungrouped variables", "definition": "SK*1.35*gk", "description": "", "templateType": "anything", "can_override": false}, "MEd_fi": {"name": "MEd_fi", "group": "Ungrouped variables", "definition": "Ed_fi_tot * length^2 / 8", "description": "", "templateType": "anything", "can_override": false}, "compliance": {"name": "compliance", "group": "Ungrouped variables", "definition": "med_fi<mtot", "description": "", "templateType": "anything", "can_override": false}, "Ed_fi_tot": {"name": "Ed_fi_tot", "group": "Ungrouped variables", "definition": "cc * Ed_fi", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "h > b\nand\nbeff > 0\nand\nmTot>0\nand\nkCrit = 1", "maxRuns": 100}, "ungrouped_variables": ["rKrav", "b", "h", "kvalitet", "elementLength", "beta0", "betaN", "bMin", "betaDesign", "kZero", "bEff", "hEff", "kMod", "kFi", "t0", "betaTrue", "dZero", "wEff", "mTot", "wEffInt", "mTotInt", "mTotPrecision", "kCrit", "fmList", "fcList", "ftList", "eList", "gList", "fmFi", "fcFi", "eModulFi", "gModulFi", "lambdaRel", "iFi", "iTorFi", "sigmaCritFi", "fm", "gl", "length", "occupancy", "sk_rand", "cc", "randomizer", "psi_1", "STR_B", "gk", "qk", "sk", "eta_fi", "ed_fi", "str_a", "MEd_fi", "compliance", "Ed_fi_tot"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": true, "customName": "Momentp\u00e5k\u00e4nning", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Vad &auml;r den dimensionerande momentp&aring;k&auml;nningen, $M_{Ed,fi}$? Svara i kNm.</p>", "minValue": "MEd_fi", "maxValue": "MEd_fi", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": "0", "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": "0", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "plain-eu"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Momentkapacitet", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": "0.5", "exploreObjective": null, "prompt": "<p>Antag att $k_{crit}$ = 1, vad &auml;r momentkapaciteten, $M_{Rd,fi}$ f&ouml;r tv&auml;rsnittet? Svara i $kNm$.</p>", "minValue": "mTot", "maxValue": "mTot", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "1", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "plain-eu"], "correctAnswerStyle": "plain-eu"}, {"type": "yes-no", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Klarar konstruktionen krav motsvarande R {rKrav}?</p>", "settings": {"correct_answer_expr": "compliance"}}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "Joakim Sandstr\u00f6m", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7645/"}], "resources": []}]}], "contributors": [{"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "Joakim Sandstr\u00f6m", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7645/"}]}