// Numbas version: exam_results_page_options
{"name": "problema 3 - tema 3 - clase 4", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "problema 3 - tema 3 - clase 4", "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>Sea un s&oacute;lido el&aacute;stico, lineal e is&oacute;tropo de m&oacute;dulo el&aacute;stico E=1000 Pa y coeficiente de Poisson $\\nu=1/4$. En un punto determinado del mismo se conocen los siguientes datos:</p>\n<ul>\n<li>Hay un estado de deformaci&oacute;n tal que $\\varepsilon_{13}=0$, $\\varepsilon_{23}=0$<span style=\"display: inline !important; float: none; background-color: #ffffff; color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;\"> y $\\varepsilon_{33}=0$</span><span style=\"display: inline !important; float: none; background-color: #ffffff; color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;\">.</span></li>\n<li><span style=\"display: inline !important; float: none; background-color: #ffffff; color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;\">La tensi&oacute;n media es positiva</span></li>\n<li><span style=\"display: inline !important; float: none; background-color: #ffffff; color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;\">La tensi&oacute;n normal al plano $X_2-X_3$ vale $\\var{sigma_11}$ Pa</span></li>\n<li><span style=\"display: inline !important; float: none; background-color: #ffffff; color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;\">La energ&iacute;a de deformaci&oacute;n el&aacute;stica debida a la parte volum&eacute;trica de tensiones y deformaciones vale $\\hat{u}^{vol}=\\var{uvol}$ J/m$^3$.</span></li>\n<li><span style=\"display: inline !important; float: none; background-color: #ffffff; color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;\">La direcci&oacute;n, en el plano $X_1-X_2$, que forma 60&ordm; ($\\curvearrowleft$) con la direcci&oacute;n $X_1$ es direcci&oacute;n principal del tensor de tensiones</span></li>\n</ul>\n<p><em><span style=\"text-align: left; color: #000000; text-transform: none; text-indent: 0px; letter-spacing: normal; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-variant: normal; font-weight: 400; text-decoration: none; word-spacing: 0px; display: inline !important; white-space: normal; orphans: 2; float: none; -webkit-text-stroke-width: 0px; background-color: #ffffff;\">Utiliza maple para imponer las ecuaciones que te dar&aacute;n las componentes del tensor de tensiones y el resto de preguntas. Cuando hayas respondido revisa en moodle que se te ha subido la nota correcta. Si el sistema hubiese subido un 0, haz de nuevo el ejercicio (simplemente cambia en maple los nuevos datos del problema y ejecuta los comandos).</span></em></p>", "advice": "", "rulesets": {}, "extensions": [], "variables": {"sigma_1": {"name": "sigma_1", "group": "Ungrouped variables", "definition": "random(-9,-8,-7,-6,-5,-4,-3,-2,-1,1,2,3,4,5,6,7,8,9)", "description": "", "templateType": "anything"}, "sigma_2": {"name": "sigma_2", "group": "Ungrouped variables", "definition": "random(-9,-8,-7,-6,-5,-4,-3,-2,-1,1,2,3,4,5,6,7,8,9)", "description": "", "templateType": "anything"}, "sigma_3": {"name": "sigma_3", "group": "Ungrouped variables", "definition": "(1/4)*(sigma_1+sigma_2)", "description": "", "templateType": "anything"}, "sigmam": {"name": "sigmam", "group": "Ungrouped variables", "definition": "(sigma_1 + sigma_2 + sigma_3)/3", "description": "", "templateType": "anything"}, "uvol": {"name": "uvol", "group": "Ungrouped variables", "definition": "1/7680*(sigma_1 + sigma_2)^2", "description": "", "templateType": "anything"}, "sigma_11": {"name": "sigma_11", "group": "Ungrouped variables", "definition": "1/4*sigma_1 + 3/4*sigma_2", "description": "", "templateType": "anything"}, "sigma_12": {"name": "sigma_12", "group": "Ungrouped variables", "definition": "1/4*sqrt(3)*sigma_1 - 1/4*sqrt(3)*sigma_2", "description": "", "templateType": "anything"}, "sigma_22": {"name": "sigma_22", "group": "Ungrouped variables", "definition": "3/4*sigma_1 + 1/4*sigma_2", "description": "", "templateType": "anything"}, "sigma_33": {"name": "sigma_33", "group": "Ungrouped variables", "definition": "sigma_3", "description": "", "templateType": "anything"}, "epsilon_11": {"name": "epsilon_11", "group": "Ungrouped variables", "definition": "1/1600*sigma_2", "description": "", "templateType": "anything"}, "epsilon_12": {"name": "epsilon_12", "group": "Ungrouped variables", "definition": "1/3200*sqrt(3)*sigma_1 - 1/3200*sqrt(3)*sigma_2", "description": "", "templateType": "anything"}, "epsilon_22": {"name": "epsilon_22", "group": "Ungrouped variables", "definition": "1/1600*sigma_1", "description": "", "templateType": "anything"}, "epsilon_33": {"name": "epsilon_33", "group": "Ungrouped variables", "definition": "0", "description": "", "templateType": "anything"}, "epsilon_1": {"name": "epsilon_1", "group": "Ungrouped variables", "definition": "3/3200*sigma_1 - 1/3200*sigma_2", "description": "", "templateType": "anything"}, "epsilon_2": {"name": "epsilon_2", "group": "Ungrouped variables", "definition": "-1/3200*sigma_1 + 3/3200*sigma_2", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "((sigma_1+sigma_2+sigma_3)>0)and(sigma_1>sigma_2)and(sigma_2>sigma_3)", "maxRuns": 100}, "ungrouped_variables": ["sigma_1", "sigma_2", "sigma_3", "sigmam", "uvol", "sigma_11", "sigma_12", "sigma_22", "sigma_33", "epsilon_11", "epsilon_12", "epsilon_22", "epsilon_33", "epsilon_1", "epsilon_2"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "matrix", "useCustomName": true, "customName": "Cuesti\u00f3n 1.", "marks": "5", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Obtener las componentes del tensor de tensiones $\\mathbf{\\sigma}$ <em>(responde redondeando a 1 decimal)</em></p>", "correctAnswer": "matrix([[sigma_11,sigma_12,0],[sigma_12,sigma_22,0],[0,0,sigma_33]])", "correctAnswerFractions": false, "numRows": "3", "numColumns": "3", "allowResize": false, "tolerance": 0, "markPerCell": false, "allowFractions": false, "precisionType": "dp", "precision": "1", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false}, {"type": "matrix", "useCustomName": true, "customName": "Cuesti\u00f3n 2.", "marks": "4", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Obtener el valor de las tensiones principales (ord&eacute;nalas de mayor a menor al introducir el resultado)&nbsp;<span style=\"display: inline !important; float: none; background-color: #ffffff; color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-style: italic; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;\">(responde redondeando a 1 decimal)</span></p>", "correctAnswer": "matrix([[sigma_1,sigma_2,sigma_3]])", "correctAnswerFractions": false, "numRows": 1, "numColumns": "3", "allowResize": false, "tolerance": 0, "markPerCell": false, "allowFractions": false, "precisionType": "dp", "precision": "1", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false}, {"type": "matrix", "useCustomName": true, "customName": "Cuesti\u00f3n 3.", "marks": "3", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Obtener las componentes del tensor de deformaciones $\\mathbf{\\varepsilon}$&nbsp;<span style=\"display: inline !important; float: none; background-color: #ffffff; color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-style: italic; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;\">(responde redondeando a 4 decimales)</span></p>", "correctAnswer": "matrix([[epsilon_11,epsilon_12,0],[epsilon_12,epsilon_22,0],[0,0,0]])", "correctAnswerFractions": false, "numRows": "3", "numColumns": "3", "allowResize": false, "tolerance": 0, "markPerCell": false, "allowFractions": false, "precisionType": "dp", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false}, {"type": "matrix", "useCustomName": true, "customName": "Cuesti\u00f3n 4", "marks": "3", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Obtener el valor de las deformaciones principales (ord&eacute;nalas de mayor a menor)&nbsp;<span style=\"display: inline !important; float: none; background-color: #ffffff; color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-style: italic; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;\">(responde redondeando a 4 decimales)</span></p>", "correctAnswer": "matrix([[epsilon_1,epsilon_2,0]])", "correctAnswerFractions": false, "numRows": 1, "numColumns": "3", "allowResize": false, "tolerance": 0, "markPerCell": false, "allowFractions": false, "precisionType": "dp", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false}], "contributors": [{"name": "Sergio Blanco", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2217/"}]}]}], "contributors": [{"name": "Sergio Blanco", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2217/"}]}