{"id":93960,"date":"2025-04-11T11:55:22","date_gmt":"2025-04-11T09:55:22","guid":{"rendered":"https:\/\/sdcverifier.com\/sin-categoria\/evaluacion-del-pandeo-de-placas-segun-lr-csr-2024-calculos-manuales-frente-a-validacion-del-sdc-verifier\/"},"modified":"2026-03-31T17:19:05","modified_gmt":"2026-03-31T15:19:05","slug":"evaluacion-del-pandeo-de-placas-segun-lr-csr-2024-calculos-manuales-frente-a-validacion-del-sdc-verifier","status":"publish","type":"post","link":"https:\/\/sdcverifier.com\/es\/benchmarks\/evaluacion-del-pandeo-de-placas-segun-lr-csr-2024-calculos-manuales-frente-a-validacion-del-sdc-verifier\/","title":{"rendered":"Evaluaci\u00f3n del pandeo de placas seg\u00fan LR CSR (2024) &#8211; C\u00e1lculos manuales frente a validaci\u00f3n del SDC Verifier"},"content":{"rendered":"<p class=\"\" data-start=\"359\" data-end=\"667\">Este punto de referencia eval\u00faa la precisi\u00f3n y fiabilidad del an\u00e1lisis de pandeo de placas realizado con <strong data-start=\"456\" data-end=\"472\">SDC Verifier<\/strong> compar\u00e1ndolo con <strong data-start=\"503\" data-end=\"524\">c\u00e1lculos manuales<\/strong> detallados basados en las Normas Estructurales Comunes (CSR) de LR para graneleros y petroleros (edici\u00f3n 2024), concretamente <strong data-start=\"634\" data-end=\"666\">la Parte 1, Cap\u00edtulo 8 &#8211; Pandeo<\/strong>.<\/p>\n<p class=\"\" data-start=\"669\" data-end=\"1092\">Se model\u00f3 una placa de prueba con unas dimensiones <strong data-start=\"698\" data-end=\"725\">de 10,2 \u00d7 5,4 \u00d7 1,1 metros<\/strong> y se carg\u00f3 con una combinaci\u00f3n de fuerzas axiales, transversales y de cizallamiento. Una de las placas superiores -de 3<strong data-start=\"830\" data-end=\"872\">,4 \u00d7 1,35 metros y 12 mm de grosor-<\/strong>se seleccion\u00f3 para una comprobaci\u00f3n focalizada. El material utilizado fue <strong data-start=\"942\" data-end=\"956\">acero dulce<\/strong> y todas las condiciones de contorno, escenarios de carga y coeficientes basados en el c\u00f3digo se aplicaron de forma coherente en ambos m\u00e9todos de c\u00e1lculo.  <\/p>\n<p class=\"\" data-start=\"1094\" data-end=\"1115\">El objetivo era:<\/p>\n<ul data-start=\"1116\" data-end=\"1408\">\n<li class=\"\" data-start=\"1116\" data-end=\"1150\">\n<p class=\"\" data-start=\"1118\" data-end=\"1150\">Verifique los requisitos de esbeltez,<\/p>\n<\/li>\n<li class=\"\" data-start=\"1151\" data-end=\"1215\">\n<p class=\"\" data-start=\"1153\" data-end=\"1215\">Calcule la tensi\u00f3n de pandeo el\u00e1stico y los factores de tensi\u00f3n cr\u00edtica,<\/p>\n<\/li>\n<li class=\"\" data-start=\"1216\" data-end=\"1275\">\n<p class=\"\" data-start=\"1218\" data-end=\"1275\">Resuelva anal\u00edticamente las cuatro ecuaciones de estado l\u00edmite LR CSR,<\/p>\n<\/li>\n<li class=\"\" data-start=\"1276\" data-end=\"1335\">\n<p class=\"\" data-start=\"1278\" data-end=\"1335\">Derive las tensiones \u00faltimas de pandeo y el factor de utilizaci\u00f3n,<\/p>\n<\/li>\n<li class=\"\" data-start=\"1336\" data-end=\"1408\">\n<p class=\"\" data-start=\"1338\" data-end=\"1408\">Valide los resultados mediante una <strong data-start=\"1366\" data-end=\"1407\">simulaci\u00f3n MEF<\/strong> completa <strong data-start=\"1366\" data-end=\"1407\">y una comprobaci\u00f3n del SDC Verifier<\/strong>.<\/p>\n<\/li>\n<\/ul>\n<style>.kb-table-of-content-nav.kb-table-of-content-id76469_8ce96a-36 .kb-table-of-content-wrap{padding-top:var(--global-kb-spacing-sm, 1.5rem);padding-right:var(--global-kb-spacing-sm, 1.5rem);padding-bottom:var(--global-kb-spacing-sm, 1.5rem);padding-left:var(--global-kb-spacing-sm, 1.5rem);}.kb-table-of-content-nav.kb-table-of-content-id76469_8ce96a-36 .kb-table-of-contents-title-wrap{padding-top:0px;padding-right:0px;padding-bottom:0px;padding-left:0px;}.kb-table-of-content-nav.kb-table-of-content-id76469_8ce96a-36 .kb-table-of-contents-title{font-weight:regular;font-style:normal;}.kb-table-of-content-nav.kb-table-of-content-id76469_8ce96a-36 .kb-table-of-content-wrap .kb-table-of-content-list{font-weight:regular;font-style:normal;margin-top:var(--global-kb-spacing-sm, 1.5rem);margin-right:0px;margin-bottom:0px;margin-left:0px;}<\/style><div class=\"split\"> <\/div>\n<p class=\"\" data-start=\"219\" data-end=\"324\">Se dise\u00f1\u00f3 un modelo de placa de prueba con unas dimensiones <strong data-start=\"243\" data-end=\"265\">de 10,2 \u00d7 5,4 \u00d7 1,1 m<\/strong> para realizar este an\u00e1lisis comparativo:<\/p>\n<p class=\"\" data-start=\"326\" data-end=\"351\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-73464\" src=\"https:\/\/sdcverifier.com\/wp-content\/uploads\/2025\/04\/Screenshot-2025-04-10-173719.png\" alt=\"\" width=\"798\" height=\"262\"><\/p>\n<p class=\"\" data-start=\"353\" data-end=\"511\">El modelo se constri\u00f1\u00f3 en las cuatro esquinas inferiores donde se conectan las placas laterales. Se aplicaron fuerzas en los bordes de la placa superior con los siguientes valores: <\/p>\n<ul data-start=\"513\" data-end=\"642\">\n<li class=\"\" data-start=\"513\" data-end=\"556\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi mathvariant=\"normal\">\u2223<\/mi><msubsup><mi>F<\/mi><mi>L<\/mi><mo>+<\/mo><\/msubsup><mi mathvariant=\"normal\">\u2223<\/mi><mo>=<\/mo><mi mathvariant=\"normal\">\u2223<\/mi><msubsup><mi>F<\/mi><mi>L<\/mi><mo>&#8211;<\/mo><\/msubsup><mi mathvariant=\"normal\">\u2223<\/mi><mo>=<\/mo><mn>3000<\/mn><mtext>  kN<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">|F_L^+| = |F_L^-| = 3000 texto{kN}<\/annotation><\/semantics><\/math><\/li>\n<li class=\"\" data-start=\"557\" data-end=\"600\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi mathvariant=\"normal\">\u2223<\/mi><msubsup><mi>F<\/mi><mi>S<\/mi><mo>+<\/mo><\/msubsup><mi mathvariant=\"normal\">\u2223<\/mi><mo>=<\/mo><mi mathvariant=\"normal\">\u2223<\/mi><msubsup><mi>F<\/mi><mi>S<\/mi><mo>&#8211;<\/mo><\/msubsup><mi mathvariant=\"normal\">\u2223<\/mi><mo>=<\/mo><mn>2550<\/mn><mtext>  kN<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">|F_S^+| = |F_S^-| = 2550 texto{kN}<\/annotation><\/semantics><\/math><\/li>\n<li class=\"\" data-start=\"601\" data-end=\"642\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi mathvariant=\"normal\">\u2223<\/mi><msubsup><mi>F<\/mi><mi>P<\/mi><mo>+<\/mo><\/msubsup><mi mathvariant=\"normal\">\u2223<\/mi><mo>=<\/mo><mi mathvariant=\"normal\">\u2223<\/mi><msubsup><mi>F<\/mi><mi>P<\/mi><mo>&#8211;<\/mo><\/msubsup><mi mathvariant=\"normal\">\u2223<\/mi><mo>=<\/mo><mn>2500<\/mn><mtext>  kN<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">|F_P^+| = |F_P^-| = 2500 texto{kN}<\/annotation><\/semantics><\/math><\/li>\n<\/ul>\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/sdcverifier.com\/wp-content\/uploads\/2025\/04\/Screenshot-2025-04-10-173755.png\" alt=\"\" class=\"wp-image-73465\"\/><\/figure>\n<div class=\"split\"> <\/div>\n<h2 data-start=\"73\" data-end=\"115\">Selected Plate and Material Properties<\/h2>\n<p class=\"\" data-start=\"117\" data-end=\"201\"><strong data-start=\"117\" data-end=\"201\">One of the top plates was chosen for all the calculations included in the check.<\/strong><\/p>\n<p class=\"\" data-start=\"203\" data-end=\"227\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-73466\" src=\"https:\/\/sdcverifier.com\/wp-content\/uploads\/2025\/04\/Screenshot-2025-04-10-173926.png\" alt=\"\" width=\"548\" height=\"252\" \/><\/p>\n<p class=\"\" data-start=\"229\" data-end=\"250\"><strong data-start=\"229\" data-end=\"250\">Plate dimensions:<\/strong><\/p>\n<ul data-start=\"252\" data-end=\"358\">\n<li class=\"\" data-start=\"252\" data-end=\"286\">\n<p class=\"\" data-start=\"254\" data-end=\"286\"><strong data-start=\"254\" data-end=\"265\">Length:<\/strong><\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>a<\/mi><mo>=<\/mo><mn>3.400<\/mn><mtext> <\/mtext><mi>m<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">a = 3.400 m<\/annotation><\/semantics><\/math><\/li>\n<li class=\"\" data-start=\"287\" data-end=\"320\">\n<p class=\"\" data-start=\"289\" data-end=\"320\"><strong data-start=\"289\" data-end=\"299\">Width:<\/strong><\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>b<\/mi><mo>=<\/mo><mn>1.350<\/mn><mtext> <\/mtext><mi>m<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">b = 1.350 m<\/annotation><\/semantics><\/math><\/li>\n<li class=\"\" data-start=\"321\" data-end=\"358\">\n<p class=\"\" data-start=\"323\" data-end=\"358\"><strong data-start=\"323\" data-end=\"337\">Thickness:<\/strong><\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>t<\/mi><mi>p<\/mi><\/msub><mo>=<\/mo><mn>0.012<\/mn><mtext> <\/mtext><mi>m<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">t_p = 0.012 m<\/annotation><\/semantics><\/math><\/li>\n<\/ul>\n<p data-start=\"360\" data-end=\"395\"><span data-teams=\"true\"><div class=\"su-spacer\" style=\"height:20px\"><\/div><\/span><\/p>\n<p class=\"\" data-start=\"360\" data-end=\"395\"><strong data-start=\"360\" data-end=\"395\">Mild steel material properties:<\/strong><\/p>\n<ul data-start=\"397\" data-end=\"622\">\n<li class=\"\" data-start=\"397\" data-end=\"440\">\n<p class=\"\" data-start=\"399\" data-end=\"440\"><strong data-start=\"399\" data-end=\"419\">Young\u2019s Modulus:<\/strong><\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>E<\/mi><mo>=<\/mo><mn>210<\/mn><mtext> <\/mtext><mi>G<\/mi><mi>P<\/mi><mi>a<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">E = 210 GPa<\/annotation><\/semantics><\/math><\/li>\n<li class=\"\" data-start=\"441\" data-end=\"481\">\n<p class=\"\" data-start=\"443\" data-end=\"481\"><strong data-start=\"443\" data-end=\"463\">Poisson\u2019s Ratio:<\/strong><\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\u03bd<\/mi><mo>=<\/mo><mn>0.3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">nu = 0.3<\/annotation><\/semantics><\/math><\/li>\n<li class=\"\" data-start=\"482\" data-end=\"529\">\n<p class=\"\" data-start=\"484\" data-end=\"529\"><strong data-start=\"484\" data-end=\"501\">Mass Density:<\/strong><\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\u03c1<\/mi><mo>=<\/mo><mn>7850<\/mn><mtext> <\/mtext><mi>k<\/mi><mi>g<\/mi><mi mathvariant=\"normal\">\/<\/mi><msup><mi>m<\/mi><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">rho = 7850 kg\/m^3<\/annotation><\/semantics><\/math><\/li>\n<li class=\"\" data-start=\"530\" data-end=\"576\">\n<p class=\"\" data-start=\"532\" data-end=\"576\"><strong data-start=\"532\" data-end=\"553\">Tensile Strength:<\/strong><\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>R<\/mi><mi>m<\/mi><\/msub><mo>=<\/mo><mn>360<\/mn><mtext> <\/mtext><mi>M<\/mi><mi>P<\/mi><mi>a<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">R_m = 360 MPa<\/annotation><\/semantics><\/math><\/li>\n<li class=\"\" data-start=\"577\" data-end=\"622\">\n<p class=\"\" data-start=\"579\" data-end=\"622\"><strong data-start=\"579\" data-end=\"596\">Yield Stress:<\/strong><\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>R<\/mi><mrow><mi>e<\/mi><mi>H<\/mi><mo separator=\"true\"><\/mo><mi>_P<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>235<\/mn><mtext> <\/mtext><mi>M<\/mi><mi>P<\/mi><mi>a<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">R_{eH,P} = 235 MPa<\/annotation><\/semantics><\/math><\/li>\n<\/ul>\n<p data-start=\"59\" data-end=\"161\"><span data-teams=\"true\"><div class=\"su-spacer\" style=\"height:20px\"><\/div><\/span><\/p>\n<p class=\"\" data-start=\"59\" data-end=\"161\"><strong data-start=\"59\" data-end=\"161\">Due to the complexity of the model, all required stress values were obtained with the help of FEM.<\/strong><\/p>\n<p class=\"\" data-start=\"163\" data-end=\"183\"><strong data-start=\"163\" data-end=\"183\">Obtained values:<\/strong><\/p>\n<ul data-start=\"185\" data-end=\"274\">\n<li class=\"\" data-start=\"185\" data-end=\"216\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03c3<\/mi><mi>x<\/mi><\/msub><mo>=<\/mo><mn>37.14<\/mn><mtext> <\/mtext><mi>M<\/mi><mi>P<\/mi><mi>a<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">sigma_x = 37.14 MPa<\/annotation><\/semantics><\/math><\/li>\n<li class=\"\" data-start=\"217\" data-end=\"248\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03c3<\/mi><mi>y<\/mi><\/msub><mo>=<\/mo><mn>25.12<\/mn><mtext> <\/mtext><mi>M<\/mi><mi>P<\/mi><mi>a<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">sigma_y = 25.12 MPa<\/annotation><\/semantics><\/math><\/li>\n<li class=\"\" data-start=\"249\" data-end=\"274\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\u03c4<\/mi><mo>=<\/mo><mn>16.34<\/mn><mtext> <\/mtext><mi>M<\/mi><mi>P<\/mi><mi>a<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">tau = 16.34 MPa<\/annotation><\/semantics><\/math><\/li>\n<\/ul>\n<p class=\"\" data-start=\"88\" data-end=\"170\"><strong data-start=\"88\" data-end=\"170\">In order to check the results, analytical calculations were first carried out.<\/strong><\/p>\n<p data-start=\"172\" data-end=\"240\">Slenderness requirement check (Pt. 1, Ch. 8, Sec. 2 \/ [2.2.1]):<\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>t<\/mi><mi>p<\/mi><\/msub><mo>&gt;<\/mo><mfrac><mi>b<\/mi><mi>c<\/mi><\/mfrac><msqrt><mfrac><msub><mi>R<\/mi><mrow><mi>e<\/mi><mi>H<\/mi><\/mrow><\/msub><mn>235<\/mn><\/mfrac><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">t_p &gt; frac{b}{c} sqrt{frac{R_{eH}}{235}}<\/annotation><\/semantics><\/math><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>12<\/mn><mtext> <\/mtext><mi>m<\/mi><mi>m<\/mi><mo>&gt;<\/mo><mfrac><mn>1350<\/mn><mn>125<\/mn><\/mfrac><mo>\u22c5<\/mo><msqrt><mfrac><mn>235<\/mn><mn>235<\/mn><\/mfrac><\/msqrt><mtext> <\/mtext><mi>m<\/mi><mi>m<\/mi><\/mrow><\/semantics><\/math><\/p>\n<p class=\"\" data-start=\"359\" data-end=\"380\">\u2705 <strong data-start=\"361\" data-end=\"380\">12 mm &gt; 10.8 mm<\/strong><\/p>\n<p data-start=\"76\" data-end=\"114\"><span data-teams=\"true\"><div class=\"su-spacer\" style=\"height:20px\"><\/div><\/span><\/p>\n<p data-start=\"76\" data-end=\"114\">Final Equations for Limit States<\/p>\n<p class=\"\" data-start=\"115\" data-end=\"168\"><em data-start=\"115\" data-end=\"167\">(According to code Pt. 1, Ch. 8, Sec. 5 \/ [2.2.1])<\/em>:<\/p>\n<p class=\"\" data-start=\"170\" data-end=\"178\"><strong data-start=\"170\" data-end=\"176\">I.<\/strong><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mrow><mo fence=\"true\">(<\/mo><mfrac><mrow><msub><mi>\u03b3<\/mi><mrow><mi>c<\/mi><mn>1<\/mn><\/mrow><\/msub><msub><mi>\u03c3<\/mi><mi>x<\/mi><\/msub><mi>S<\/mi><\/mrow><msubsup><mi>\u03c3<\/mi><mrow><mi>c<\/mi><mi>x<\/mi><\/mrow><mo lspace=\"0em\" mathvariant=\"normal\" rspace=\"0em\">\u2032<\/mo><\/msubsup><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><msub><mi>e<\/mi><mn>0<\/mn><\/msub><\/msup><mo>\u2212<\/mo><mi>B<\/mi><msup><mrow><mo fence=\"true\">(<\/mo><mfrac><mrow><msub><mi>\u03b3<\/mi><mrow><mi>c<\/mi><mn>1<\/mn><\/mrow><\/msub><msub><mi>\u03c3<\/mi><mi>x<\/mi><\/msub><mi>S<\/mi><\/mrow><msubsup><mi>\u03c3<\/mi><mrow><mi>c<\/mi><mi>x<\/mi><\/mrow><mo lspace=\"0em\" mathvariant=\"normal\" rspace=\"0em\">\u2032<\/mo><\/msubsup><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mfrac><msub><mi>e<\/mi><mn>0<\/mn><\/msub><mn>2<\/mn><\/mfrac><\/msup><msup><mrow><mo fence=\"true\">(<\/mo><mfrac><mrow><msub><mi>\u03b3<\/mi><mrow><mi>c<\/mi><mn>1<\/mn><\/mrow><\/msub><msub><mi>\u03c3<\/mi><mi>y<\/mi><\/msub><mi>S<\/mi><\/mrow><msubsup><mi>\u03c3<\/mi><mrow><mi>c<\/mi><mi>y<\/mi><\/mrow><mo lspace=\"0em\" mathvariant=\"normal\" rspace=\"0em\">\u2032<\/mo><\/msubsup><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mfrac><msub><mi>e<\/mi><mn>0<\/mn><\/msub><mn>2<\/mn><\/mfrac><\/msup><mo>+<\/mo><msup><mrow><mo fence=\"true\">(<\/mo><mfrac><mrow><msub><mi>\u03b3<\/mi><mrow><mi>c<\/mi><mn>1<\/mn><\/mrow><\/msub><msub><mi>\u03c3<\/mi><mi>y<\/mi><\/msub><mi>S<\/mi><\/mrow><msubsup><mi>\u03c3<\/mi><mrow><mi>c<\/mi><mi>y<\/mi><\/mrow><mo lspace=\"0em\" mathvariant=\"normal\" rspace=\"0em\">\u2032<\/mo><\/msubsup><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><msub><mi>e<\/mi><mn>0<\/mn><\/msub><\/msup><mo>+<\/mo><msup><mrow><mo fence=\"true\">(<\/mo><mfrac><mrow><msub><mi>\u03b3<\/mi><mrow><mi>c<\/mi><mn>1<\/mn><\/mrow><\/msub><mi mathvariant=\"normal\">\u2223<\/mi><mi>\u03c4<\/mi><mi mathvariant=\"normal\">\u2223<\/mi><mi>S<\/mi><\/mrow><msubsup><mi>\u03c4<\/mi><mi>c<\/mi><mo lspace=\"0em\" mathvariant=\"normal\" rspace=\"0em\">\u2032<\/mo><\/msubsup><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><msub><mi>e<\/mi><mn>0<\/mn><\/msub><\/msup><mo>=<\/mo><mn>1<\/mn><\/mrow><\/semantics><\/math><\/p>\n<p class=\"\" data-start=\"526\" data-end=\"564\"><strong data-start=\"526\" data-end=\"533\">II.<\/strong> (when<\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03c3<\/mi><mi>x<\/mi><\/msub><mo>\u2265<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">sigma_x geq 0<\/annotation><\/semantics><\/math><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mrow><mo fence=\"true\">(<\/mo><mfrac><mrow><msub><mi>\u03b3<\/mi><mrow><mi>c<\/mi><mn>2<\/mn><\/mrow><\/msub><msub><mi>\u03c3<\/mi><mi>x<\/mi><\/msub><mi>S<\/mi><\/mrow><msubsup><mi>\u03c3<\/mi><mrow><mi>c<\/mi><mi>x<\/mi><\/mrow><mo lspace=\"0em\" mathvariant=\"normal\" rspace=\"0em\">\u2032<\/mo><\/msubsup><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mfrac><mn>2<\/mn><msubsup><mi>\u03b2<\/mi><mi>p<\/mi><mn>0.25<\/mn><\/msubsup><\/mfrac><\/msup><mo>+<\/mo><msup><mrow><mo fence=\"true\">(<\/mo><mfrac><mrow><msub><mi>\u03b3<\/mi><mrow><mi>c<\/mi><mn>2<\/mn><\/mrow><\/msub><mi mathvariant=\"normal\">\u2223<\/mi><mi>\u03c4<\/mi><mi mathvariant=\"normal\">\u2223<\/mi><mi>S<\/mi><\/mrow><msubsup><mi>\u03c4<\/mi><mi>c<\/mi><mo lspace=\"0em\" mathvariant=\"normal\" rspace=\"0em\">\u2032<\/mo><\/msubsup><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mfrac><mn>2<\/mn><msubsup><mi>\u03b2<\/mi><mi>p<\/mi><mn>0.25<\/mn><\/msubsup><\/mfrac><\/msup><mo>=<\/mo><mn>1<\/mn><\/mrow><\/semantics><\/math><\/p>\n<p class=\"\" data-start=\"739\" data-end=\"778\"><strong data-start=\"739\" data-end=\"747\">III.<\/strong> (when<\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03c3<\/mi><mi>y<\/mi><\/msub><mo>\u2265<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">sigma_y geq 0<\/annotation><\/semantics><\/math><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mrow><mo fence=\"true\">(<\/mo><mfrac><mrow><msub><mi>\u03b3<\/mi><mrow><mi>c<\/mi><mn>3<\/mn><\/mrow><\/msub><msub><mi>\u03c3<\/mi><mi>y<\/mi><\/msub><mi>S<\/mi><\/mrow><msubsup><mi>\u03c3<\/mi><mrow><mi>c<\/mi><mi>y<\/mi><\/mrow><mo lspace=\"0em\" mathvariant=\"normal\" rspace=\"0em\">\u2032<\/mo><\/msubsup><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mfrac><mn>2<\/mn><msubsup><mi>\u03b2<\/mi><mi>p<\/mi><mn>0.25<\/mn><\/msubsup><\/mfrac><\/msup><mo>+<\/mo><msup><mrow><mo fence=\"true\">(<\/mo><mfrac><mrow><msub><mi>\u03b3<\/mi><mrow><mi>c<\/mi><mn>3<\/mn><\/mrow><\/msub><mi mathvariant=\"normal\">\u2223<\/mi><mi>\u03c4<\/mi><mi mathvariant=\"normal\">\u2223<\/mi><mi>S<\/mi><\/mrow><msubsup><mi>\u03c4<\/mi><mi>c<\/mi><mo lspace=\"0em\" mathvariant=\"normal\" rspace=\"0em\">\u2032<\/mo><\/msubsup><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mfrac><mn>2<\/mn><msubsup><mi>\u03b2<\/mi><mi>p<\/mi><mn>0.25<\/mn><\/msubsup><\/mfrac><\/msup><mo>=<\/mo><mn>1<\/mn><\/mrow><\/semantics><\/math><\/p>\n<p class=\"\" data-start=\"953\" data-end=\"962\"><strong data-start=\"953\" data-end=\"960\">IV.<\/strong><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mfrac><mrow><msub><mi>\u03b3<\/mi><mrow><mi>c<\/mi><mn>4<\/mn><\/mrow><\/msub><mi mathvariant=\"normal\">\u2223<\/mi><mi>\u03c4<\/mi><mi mathvariant=\"normal\">\u2223<\/mi><mi>S<\/mi><\/mrow><msubsup><mi>\u03c4<\/mi><mi>c<\/mi><mo lspace=\"0em\" mathvariant=\"normal\" rspace=\"0em\">\u2032<\/mo><\/msubsup><\/mfrac><mo>=<\/mo><mn>1<\/mn><\/mrow><\/semantics><\/math><\/p>\n<p data-start=\"58\" data-end=\"95\">Aspect Ratio of the Plate Panel<\/p>\n<p class=\"\" data-start=\"96\" data-end=\"130\"><em data-start=\"96\" data-end=\"130\">(Pt. 1, Ch. 8, Sec. 5 \/ Symbols)<\/em><\/p>\n<p class=\"\" data-start=\"132\" data-end=\"244\">The aspect ratio <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\u03b1<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">alpha<\/annotation><\/semantics><\/math> of the plate panel is defined as the ratio of its length <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>a<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">a<\/annotation><\/semantics><\/math> to width <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">b<\/annotation><\/semantics><\/math>:<\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\u03b1<\/mi><mo>=<\/mo><mfrac><mi>a<\/mi><mi>b<\/mi><\/mfrac><mspace width=\"2em\"><\/mspace><mi>\u03b1<\/mi><mo>=<\/mo><mfrac><mn>3.40<\/mn><mn>1.35<\/mn><\/mfrac><mspace width=\"2em\"><\/mspace><mi>\u03b1<\/mi><mo>=<\/mo><mn>2.519<\/mn><\/mrow><\/semantics><\/math><\/p>\n<p data-start=\"66\" data-end=\"105\">Elastic Buckling Reference Stress<\/p>\n<p class=\"\" data-start=\"106\" data-end=\"140\"><em data-start=\"106\" data-end=\"140\">(Pt. 1, Ch. 8, Sec. 5 \/ Symbols)<\/em><\/p>\n<p data-start=\"142\" data-end=\"228\"><span data-teams=\"true\"><div class=\"su-spacer\" style=\"height:20px\"><\/div><\/span><\/p>\n<p class=\"\" data-start=\"142\" data-end=\"228\">The elastic buckling reference stress <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03c3<\/mi><mi>E<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">sigma_E<\/annotation><\/semantics><\/math> was calculated using the formula:<\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03c3<\/mi><mi>E<\/mi><\/msub><mo>=<\/mo><mfrac><mrow><msup><mi>\u03c0<\/mi><mn>2<\/mn><\/msup><mi>E<\/mi><\/mrow><mrow><mn>12<\/mn><mo stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>\u2212<\/mo><msup><mi>\u03bd<\/mi><mn>2<\/mn><\/msup><mo stretchy=\"false\">)<\/mo><\/mrow><\/mfrac><msup><mrow><mo fence=\"true\">(<\/mo><mfrac><msub><mi>t<\/mi><mi>p<\/mi><\/msub><mi>b<\/mi><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mn>2<\/mn><\/msup><\/mrow><\/semantics><\/math><\/p>\n<p class=\"\" data-start=\"307\" data-end=\"337\">Substituting the known values:<\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03c3<\/mi><mi>E<\/mi><\/msub><mo>=<\/mo><mfrac><mrow><msup><mi>\u03c0<\/mi><mn>2<\/mn><\/msup><mo>\u22c5<\/mo><mn>210<\/mn><mo>\u22c5<\/mo><msup><mn>10<\/mn><mn>9<\/mn><\/msup><\/mrow><mrow><mn>12<\/mn><mo>\u22c5<\/mo><mo stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>\u2212<\/mo><msup><mn>0.3<\/mn><mn>2<\/mn><\/msup><mo stretchy=\"false\">)<\/mo><\/mrow><\/mfrac><msup><mrow><mo fence=\"true\">(<\/mo><mfrac><mn>0.012<\/mn><mn>1.35<\/mn><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mn>2<\/mn><\/msup><mtext> Pa<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">sigma_E = frac{pi^2 cdot 210 cdot 10^9}{12 cdot (1 &#8211; 0.3^2)} left(frac{0.012}{1.35}right)^2 text{Pa}<\/annotation><\/semantics><\/math><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03c3<\/mi><mi>E<\/mi><\/msub><mo>=<\/mo><mn>14<\/mn><mtext>\u2009<\/mtext><mn>996<\/mn><mtext>\u2009<\/mtext><mn>549.9<\/mn><mtext> Pa<\/mtext><\/mrow><\/semantics><\/math><\/p>\n<p data-start=\"72\" data-end=\"118\"><span data-teams=\"true\"><div class=\"su-spacer\" style=\"height:20px\"><\/div><\/span><\/p>\n<p data-start=\"72\" data-end=\"118\">Edge Stress Ratio and Correction Factors<\/p>\n<ul data-start=\"120\" data-end=\"588\">\n<li class=\"\" data-start=\"120\" data-end=\"334\">\n<p class=\"\" data-start=\"122\" data-end=\"313\"><strong data-start=\"122\" data-end=\"143\">Edge stress ratio<\/strong><\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\u03c8<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">psi<\/annotation><\/semantics><\/math><\/p>\n<p>was set as 1 in both directions:<br data-start=\"187\" data-end=\"190\" \/><em data-start=\"192\" data-end=\"311\">(Pt. 1, Ch. 8, Sec. 5 \/ Symbols; stresses calculated using weighted average approach, Pt. 1, Ch. 8, App. 1 \/ [2.2.1])<\/em><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\u03c8<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><\/semantics><\/math><\/li>\n<\/ul>\n<p><span data-teams=\"true\"><div class=\"su-spacer\" style=\"height:20px\"><\/div><\/span><\/p>\n<ul data-start=\"120\" data-end=\"588\">\n<li class=\"\" data-start=\"336\" data-end=\"463\">\n<p class=\"\" data-start=\"338\" data-end=\"438\"><strong data-start=\"338\" data-end=\"359\">Correction factor<\/strong><\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>F<\/mi><mrow><mi>l<\/mi><mi>o<\/mi><mi>n<\/mi><mi>g<\/mi><\/mrow><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">F_{long}<\/annotation><\/semantics><\/math><\/p>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span> was set as 1:<br data-start=\"388\" data-end=\"391\" \/><em data-start=\"393\" data-end=\"436\">(Pt. 1, Ch. 8, Sec. 5 \/ [2.2.4]; Table 2)<\/em><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>F<\/mi><mrow><mi>l<\/mi><mi>o<\/mi><mi>n<\/mi><mi>g<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>1<\/mn><\/mrow><\/semantics><\/math><\/li>\n<\/ul>\n<p><span data-teams=\"true\"><div class=\"su-spacer\" style=\"height:20px\"><\/div><\/span><\/p>\n<ul data-start=\"120\" data-end=\"588\">\n<li class=\"\" data-start=\"465\" data-end=\"588\">\n<p class=\"\" data-start=\"467\" data-end=\"563\"><strong data-start=\"467\" data-end=\"488\">Correction factor<\/strong><\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>F<\/mi><mrow><mi>t<\/mi><mi>r<\/mi><mi>a<\/mi><mi>n<\/mi><\/mrow><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">F_{tran}<\/annotation><\/semantics><\/math><\/p>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span> was also set as 1:<br data-start=\"522\" data-end=\"525\" \/><em data-start=\"527\" data-end=\"561\">(Pt. 1, Ch. 8, Sec. 5 \/ [2.2.5])<\/em><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>F<\/mi><mrow><mi>t<\/mi><mi>r<\/mi><mi>a<\/mi><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>1<\/mn><\/mrow><\/semantics><\/math><\/li>\n<\/ul>\n<p class=\"\" data-start=\"590\" data-end=\"681\">Ultimate buckling stresses were calculated in 3 cases:<br data-start=\"644\" data-end=\"647\" \/><em data-start=\"647\" data-end=\"681\">(Pt. 1, Ch. 8, Sec. 5 \/ Table 3)<\/em><\/p>\n<div class=\"split\"> <\/div>\n<h3 data-start=\"76\" data-end=\"114\"><strong>Case 1: <\/strong><\/h3>\n<p data-start=\"76\" data-end=\"114\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-73474\" src=\"https:\/\/sdcverifier.com\/wp-content\/uploads\/2025\/04\/Screenshot-2025-04-10-192824.png\" alt=\"\" width=\"312\" height=\"146\" \/><\/p>\n<p data-start=\"116\" data-end=\"143\">Plate Buckling Setup<\/p>\n<p class=\"\" data-start=\"144\" data-end=\"235\">The plate is compressed along the <strong data-start=\"178\" data-end=\"193\">x-direction<\/strong> with an edge stress ratio <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\u03c8<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">psi = 1<\/annotation><\/semantics><\/math>.<\/p>\n<p data-start=\"237\" data-end=\"266\">Intermediate Parameters:<\/p>\n<ul data-start=\"268\" data-end=\"706\">\n<li class=\"\" data-start=\"268\" data-end=\"386\">\n<p class=\"\" data-start=\"270\" data-end=\"298\"><strong data-start=\"270\" data-end=\"296\">Effective width factor<\/strong><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>c<\/mi><mo>=<\/mo><mi>min<\/mi><mo>\u2061<\/mo><mrow><mo fence=\"true\">(<\/mo><mo stretchy=\"false\">(<\/mo><mn>1.25<\/mn><mo>\u2212<\/mo><mn>0.12<\/mn><mi>\u03c8<\/mi><mo stretchy=\"false\">)<\/mo><mo separator=\"true\">,<\/mo><mtext> <\/mtext><mn>1.25<\/mn><mo fence=\"true\">)<\/mo><\/mrow><mo>=<\/mo><mi>min<\/mi><mo>\u2061<\/mo><mo stretchy=\"false\">(<\/mo><mn>1.13<\/mn><mo separator=\"true\">,<\/mo><mtext> <\/mtext><mn>1.25<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>1.13<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">c = min left( (1.25 &#8211; 0.12psi), 1.25 right) = min(1.13, 1.25) = 1.13<\/annotation><\/semantics><\/math><\/li>\n<li class=\"\" data-start=\"388\" data-end=\"571\">\n<p class=\"\" data-start=\"390\" data-end=\"417\"><strong data-start=\"390\" data-end=\"415\">Slenderness parameter<\/strong><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03bb<\/mi><mi>c<\/mi><\/msub><mo>=<\/mo><mfrac><mi>c<\/mi><mn>2<\/mn><\/mfrac><mrow><mo fence=\"true\">(<\/mo><mn>1<\/mn><mo>+<\/mo><msqrt><mrow><mn>1<\/mn><mo>\u2212<\/mo><mfrac><mn>0.88<\/mn><mi>c<\/mi><\/mfrac><\/mrow><\/msqrt><mo fence=\"true\">)<\/mo><\/mrow><mo>=<\/mo><mfrac><mn>1.13<\/mn><mn>2<\/mn><\/mfrac><mrow><mo fence=\"true\">(<\/mo><mn>1<\/mn><mo>+<\/mo><msqrt><mrow><mn>1<\/mn><mo>\u2212<\/mo><mfrac><mn>0.88<\/mn><mn>1.13<\/mn><\/mfrac><\/mrow><\/msqrt><mo fence=\"true\">)<\/mo><\/mrow><mo>=<\/mo><mn>0.831<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">lambda_c = frac{c}{2} left( 1 + sqrt{1 &#8211; frac{0.88}{c}} right) = frac{1.13}{2} left( 1 + sqrt{1 &#8211; frac{0.88}{1.13}} right) = 0.831<\/annotation><\/semantics><\/math><\/li>\n<li class=\"\" data-start=\"573\" data-end=\"706\">\n<p class=\"\" data-start=\"575\" data-end=\"616\"><strong data-start=\"575\" data-end=\"614\">Buckling factor in x-direction<\/strong><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>K<\/mi><mi>x<\/mi><\/msub><mo>=<\/mo><msub><mi>F<\/mi><mrow><mi>l<\/mi><mi>o<\/mi><mi>n<\/mi><mi>g<\/mi><\/mrow><\/msub><mo>\u22c5<\/mo><mfrac><mn>8.4<\/mn><mrow><mi>\u03c8<\/mi><mo>+<\/mo><mn>1.1<\/mn><\/mrow><\/mfrac><mo>=<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><mfrac><mn>8.4<\/mn><mrow><mn>1<\/mn><mo>+<\/mo><mn>1.1<\/mn><\/mrow><\/mfrac><mo>=<\/mo><mn>4<\/mn><\/mrow><\/semantics><\/math><\/li>\n<\/ul>\n<p data-start=\"78\" data-end=\"131\"><span data-teams=\"true\"><div class=\"su-spacer\" style=\"height:20px\"><\/div><\/span><\/p>\n<p data-start=\"78\" data-end=\"131\">Reference Degree of Slenderness in x-direction<\/p>\n<p class=\"\" data-start=\"132\" data-end=\"166\"><em data-start=\"132\" data-end=\"166\">(Pt. 1, Ch. 8, Sec. 5 \/ [2.2.2])<\/em><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03bb<\/mi><mi>x<\/mi><\/msub><mo>=<\/mo><msqrt><mfrac><msub><mi>R<\/mi><mrow><mi>e<\/mi><mi>H<\/mi><mo separator=\"true\">,<\/mo><mi>P<\/mi><\/mrow><\/msub><mrow><msub><mi>K<\/mi><mi>x<\/mi><\/msub><mo>\u22c5<\/mo><msub><mi>\u03c3<\/mi><mi>E<\/mi><\/msub><\/mrow><\/mfrac><\/msqrt><\/mrow><\/semantics><\/math><\/p>\n<p class=\"\" data-start=\"232\" data-end=\"252\">Substituting values:<\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03bb<\/mi><mi>x<\/mi><\/msub><mo>=<\/mo><msqrt><mfrac><mrow><mn>235<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mn>6<\/mn><\/msup><\/mrow><mrow><mn>4<\/mn><mo>\u00d7<\/mo><mn>14996549.9<\/mn><\/mrow><\/mfrac><\/msqrt><mo>=<\/mo><mn>1.979<\/mn><\/mrow><\/semantics><\/math><\/p>\n<p data-start=\"70\" data-end=\"129\">Reduction Factor for Stress in x-direction<\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>C<\/mi><mi>x<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">C_x<\/annotation><\/semantics><\/math><\/p>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p class=\"\" data-start=\"130\" data-end=\"164\"><em data-start=\"130\" data-end=\"164\">(Pt. 1, Ch. 8, Sec. 5 \/ Table 3)<\/em><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>C<\/mi><mi>x<\/mi><\/msub><mo>=<\/mo><mi>c<\/mi><mrow><mo fence=\"true\">(<\/mo><mfrac><mn>1<\/mn><msub><mi>\u03bb<\/mi><mi>x<\/mi><\/msub><\/mfrac><mo>\u2212<\/mo><mfrac><mn>0.22<\/mn><msubsup><mi>\u03bb<\/mi><mi>x<\/mi><mn>2<\/mn><\/msubsup><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">C_x = c left( frac{1}{lambda_x} &#8211; frac{0.22}{lambda_x^2} right)<\/annotation><\/semantics><\/math><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>C<\/mi><mi>x<\/mi><\/msub><mo>=<\/mo><mn>1.13<\/mn><mo>\u00d7<\/mo><mrow><mo fence=\"true\">(<\/mo><mfrac><mn>1<\/mn><mn>1.979<\/mn><\/mfrac><mo>\u2212<\/mo><mfrac><mn>0.22<\/mn><msup><mn>1.979<\/mn><mn>2<\/mn><\/msup><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mo>=<\/mo><mn>0.507<\/mn><\/mrow><\/semantics><\/math><\/p>\n<div class=\"split\"> <\/div>\n<h3 data-start=\"79\" data-end=\"90\">Case 2:<\/h3>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-73475\" src=\"https:\/\/sdcverifier.com\/wp-content\/uploads\/2025\/04\/Screenshot-2025-04-10-195111.png\" alt=\"\" width=\"315\" height=\"205\" \/><\/p>\n<ul>\n<li data-start=\"155\" data-end=\"171\"><strong>Parameters:<\/strong><\/li>\n<\/ul>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>c<\/mi><mo>=<\/mo><mi>min<\/mi><mo>\u2061<\/mo><mo stretchy=\"false\">(<\/mo><mo stretchy=\"false\">(<\/mo><mn>1.25<\/mn><mo>\u2212<\/mo><mn>0.12<\/mn><mi>\u03c8<\/mi><mo stretchy=\"false\">)<\/mo><mo separator=\"true\">,<\/mo><mn>1.25<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>min<\/mi><mo>\u2061<\/mo><mo stretchy=\"false\">(<\/mo><mo stretchy=\"false\">(<\/mo><mn>1.25<\/mn><mo>\u2212<\/mo><mn>0.12<\/mn><mo>\u22c5<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><mo separator=\"true\">,<\/mo><mn>1.25<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>1.13<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">c = min((1.25 &#8211; 0.12psi), 1.25) = min((1.25 &#8211; 0.12 cdot 1), 1.25) = 1.13<\/annotation><\/semantics><\/math><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03bb<\/mi><mi>c<\/mi><\/msub><mo>=<\/mo><mfrac><mi>c<\/mi><mn>2<\/mn><\/mfrac><mrow><mo fence=\"true\">(<\/mo><mn>1<\/mn><mo>+<\/mo><msqrt><mrow><mn>1<\/mn><mo>\u2212<\/mo><mfrac><mn>0.88<\/mn><mi>c<\/mi><\/mfrac><\/mrow><\/msqrt><mo fence=\"true\">)<\/mo><\/mrow><mo>=<\/mo><mfrac><mn>1.13<\/mn><mn>2<\/mn><\/mfrac><mrow><mo fence=\"true\">(<\/mo><mn>1<\/mn><mo>+<\/mo><msqrt><mrow><mn>1<\/mn><mo>\u2212<\/mo><mfrac><mn>0.88<\/mn><mn>1.13<\/mn><\/mfrac><\/mrow><\/msqrt><mo fence=\"true\">)<\/mo><\/mrow><mo>=<\/mo><mn>0.831<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">lambda_c = frac{c}{2} left( 1 + sqrt{1 &#8211; frac{0.88}{c}} right) = frac{1.13}{2} left( 1 + sqrt{1 &#8211; frac{0.88}{1.13}} right) = 0.831<\/annotation><\/semantics><\/math><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>f<\/mi><mn>1<\/mn><\/msub><mo>=<\/mo><mo stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mi>\u03c8<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">(<\/mo><mi>\u03b1<\/mi><mo>\u2212<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mo stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">(<\/mo><mn>2.519<\/mn><mo>\u2212<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>0<\/mn><\/mrow><\/semantics><\/math><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>K<\/mi><mi>y<\/mi><\/msub><mo>=<\/mo><msub><mi>F<\/mi><mrow><mi>t<\/mi><mi>r<\/mi><mi>a<\/mi><mi>n<\/mi><\/mrow><\/msub><mo>\u22c5<\/mo><mfrac><mrow><mn>2<\/mn><msup><mrow><mo fence=\"true\">(<\/mo><mn>1<\/mn><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mi>\u03b1<\/mi><mn>2<\/mn><\/msup><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mn>2<\/mn><\/msup><\/mrow><mrow><mn>1<\/mn><mo>+<\/mo><mi>\u03c8<\/mi><mo>+<\/mo><mfrac><mrow><mn>1<\/mn><mo>\u2212<\/mo><mi>\u03c8<\/mi><\/mrow><mn>100<\/mn><\/mfrac><mrow><mo fence=\"true\">(<\/mo><mfrac><mn>2.4<\/mn><msup><mi>\u03b1<\/mi><mn>2<\/mn><\/msup><\/mfrac><mo>+<\/mo><mn>6.9<\/mn><msub><mi>f<\/mi><mn>1<\/mn><\/msub><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><\/mfrac><\/mrow><\/semantics><\/math><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>K<\/mi><mi>y<\/mi><\/msub><mo>=<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><mfrac><mrow><mn>2<\/mn><msup><mrow><mo fence=\"true\">(<\/mo><mn>1<\/mn><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mn>2.519<\/mn><mn>2<\/mn><\/msup><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mn>2<\/mn><\/msup><\/mrow><mrow><mn>1<\/mn><mo>+<\/mo><mn>1<\/mn><mo>+<\/mo><mfrac><mrow><mn>1<\/mn><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><mn>100<\/mn><\/mfrac><mrow><mo fence=\"true\">(<\/mo><mfrac><mn>2.4<\/mn><msup><mn>2.519<\/mn><mn>2<\/mn><\/msup><\/mfrac><mo>+<\/mo><mn>6.9<\/mn><mo>\u22c5<\/mo><mn>0<\/mn><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><\/mfrac><\/mrow><\/semantics><\/math><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>K<\/mi><mi>y<\/mi><\/msub><mo>=<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><mfrac><mrow><mn>2<\/mn><msup><mrow><mo fence=\"true\">(<\/mo><mn>1<\/mn><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mn>2.519<\/mn><mn>2<\/mn><\/msup><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mn>2<\/mn><\/msup><\/mrow><mrow><mn>1<\/mn><mo>+<\/mo><mn>1<\/mn><mo>+<\/mo><mfrac><mrow><mn>1<\/mn><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><mn>100<\/mn><\/mfrac><mrow><mo fence=\"true\">(<\/mo><mfrac><mn>2.4<\/mn><msup><mn>2.519<\/mn><mn>2<\/mn><\/msup><\/mfrac><mo>+<\/mo><mn>6.9<\/mn><mo>\u22c5<\/mo><mn>0<\/mn><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><\/mfrac><\/mrow><\/semantics><\/math><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>K<\/mi><mi>y<\/mi><\/msub><mo>=<\/mo><mn>1.340<\/mn><\/mrow><\/semantics><\/math><\/p>\n<p data-start=\"105\" data-end=\"160\">Reference Degree of Slenderness in Y Direction \u03bb\u1d67<\/p>\n<p class=\"\" data-start=\"161\" data-end=\"195\"><em data-start=\"161\" data-end=\"195\">(Pt. 1, Ch. 8, Sec. 5 \/ [2.2.2])<\/em><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03bb<\/mi><mi>y<\/mi><\/msub><mo>=<\/mo><msqrt><mfrac><msub><mi>R<\/mi><mrow><mi>e<\/mi><mi>H<\/mi><mo separator=\"true\">,<\/mo><mi>P<\/mi><\/mrow><\/msub><mrow><msub><mi>K<\/mi><mi>y<\/mi><\/msub><mo>\u22c5<\/mo><msub><mi>\u03c3<\/mi><mi>E<\/mi><\/msub><\/mrow><\/mfrac><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">lambda_y = sqrt{ frac{R_{eH,P}}{K_y cdot sigma_E} }<\/annotation><\/semantics><\/math><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03bb<\/mi><mi>y<\/mi><\/msub><mo>=<\/mo><msqrt><mfrac><mrow><mn>235<\/mn><mo>\u22c5<\/mo><msup><mn>10<\/mn><mn>6<\/mn><\/msup><\/mrow><mrow><mn>1.340<\/mn><mo>\u22c5<\/mo><mn>14996549.9<\/mn><\/mrow><\/mfrac><\/msqrt><mo>=<\/mo><mn>3.419<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">lambda_y = sqrt{ frac{235 cdot 10^6}{1.340 cdot 14996549.9} } = 3.419<\/annotation><\/semantics><\/math><\/p>\n<p data-start=\"65\" data-end=\"87\">Factor <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>c<\/mi><mn>1<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">c_1<\/annotation><\/semantics><\/math><\/p>\n<p class=\"\" data-start=\"88\" data-end=\"122\"><em data-start=\"88\" data-end=\"122\">(Pt. 1, Ch. 8, Sec. 5 \/ [2.2.3])<\/em><\/p>\n<p data-start=\"124\" data-end=\"198\"><span data-teams=\"true\"><div class=\"su-spacer\" style=\"height:20px\"><\/div><\/span><\/p>\n<p class=\"\" data-start=\"124\" data-end=\"198\">The coefficient <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>c<\/mi><mn>1<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">c_1<\/annotation><\/semantics><\/math> was calculated appropriately to chosen the SP-A assessment method:<\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>c<\/mi><mn>1<\/mn><\/msub><mo>=<\/mo><mrow><mo fence=\"true\">(<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mfrac><mn>1<\/mn><mi>\u03b1<\/mi><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mo separator=\"true\">,<\/mo><mspace width=\"1em\"><\/mspace><mtext>and <\/mtext><msub><mi>c<\/mi><mn>1<\/mn><\/msub><mo>\u2265<\/mo><mn>0<\/mn><\/mrow><\/semantics><\/math><\/p>\n<ul>\n<li data-start=\"277\" data-end=\"290\"><strong>Substituting:<\/strong><\/li>\n<\/ul>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>c<\/mi><mn>1<\/mn><\/msub><mo>=<\/mo><mrow><mo fence=\"true\">(<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mfrac><mn>1<\/mn><mn>2.519<\/mn><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mo>=<\/mo><mn>0.603<\/mn><\/mrow><\/semantics><\/math><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>R<\/mi><mo>=<\/mo><mn>0.220<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">R = 0.220<\/annotation><\/semantics><\/math><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msubsup><mi>\u03bb<\/mi><mi>p<\/mi><mn>2<\/mn><\/msubsup><mo>=<\/mo><msubsup><mi>\u03bb<\/mi><mi>y<\/mi><mn>2<\/mn><\/msubsup><mo>\u2212<\/mo><mn>0.5<\/mn><mspace width=\"1em\"><\/mspace><mtext>and<\/mtext><mspace width=\"1em\"><\/mspace><mn>1<\/mn><mo>\u2264<\/mo><msubsup><mi>\u03bb<\/mi><mi>p<\/mi><mn>2<\/mn><\/msubsup><mo>\u2264<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\lambda_p^2 = \\lambda_y^2 &#8211; 0.5 \\quad \\text{and} \\quad 1 \\leq \\lambda_p^2 \\leq 3<\/annotation><\/semantics><\/math><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msubsup><mi>\u03bb<\/mi><mi>p<\/mi><mn>2<\/mn><\/msubsup><mo>=<\/mo><msup><mn>3.419<\/mn><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>0.5<\/mn><mspace width=\"1em\"><\/mspace><mtext>and<\/mtext><mspace width=\"1em\"><\/mspace><mn>1<\/mn><mo>\u2264<\/mo><msubsup><mi>\u03bb<\/mi><mi>p<\/mi><mn>2<\/mn><\/msubsup><mo>\u2264<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\lambda_p^2 = 3.419^2 &#8211; 0.5 \\quad \\text{and} \\quad 1 \\leq \\lambda_p^2 \\leq 3<\/annotation><\/semantics><\/math><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msubsup><mi>\u03bb<\/mi><mi>p<\/mi><mn>2<\/mn><\/msubsup><mo>=<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\lambda_p^2 = 3<\/annotation><\/semantics><\/math><\/p>\n<p data-start=\"352\" data-end=\"379\"><span data-teams=\"true\"><div class=\"su-spacer\" style=\"height:20px\"><\/div><\/span><\/p>\n<p data-start=\"352\" data-end=\"379\">Calculation of <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>F<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">F<\/annotation><\/semantics><\/math><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>F<\/mi><mo>=<\/mo><mrow><mo fence=\"true\">(<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mrow><mo fence=\"true\">(<\/mo><mfrac><msub><mi>K<\/mi><mi>y<\/mi><\/msub><mn>0.91<\/mn><\/mfrac><mo>\u2212<\/mo><mn>1<\/mn><mo fence=\"true\">)<\/mo><\/mrow><mfrac><mn>1<\/mn><msubsup><mi>\u03bb<\/mi><mi>p<\/mi><mn>2<\/mn><\/msubsup><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mo>\u22c5<\/mo><msub><mi>c<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><mspace width=\"1em\"><\/mspace><mi>F<\/mi><mo>\u2265<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">F = left( 1 &#8211; left( frac{K_y}{0.91} &#8211; 1 right) frac{1}{lambda_p^2} right) cdot c_1, quad F geq 0<\/annotation><\/semantics><\/math><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>F<\/mi><mo>=<\/mo><mrow><mo fence=\"true\">(<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mrow><mo fence=\"true\">(<\/mo><mfrac><mn>1.340<\/mn><mn>0.91<\/mn><\/mfrac><mo>\u2212<\/mo><mn>1<\/mn><mo fence=\"true\">)<\/mo><\/mrow><mo>\u22c5<\/mo><mfrac><mn>1<\/mn><mn>3<\/mn><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mo>\u22c5<\/mo><mn>0.603<\/mn><mo>=<\/mo><mn>0.508<\/mn><\/mrow><\/semantics><\/math><\/p>\n<p data-start=\"599\" data-end=\"626\"><span data-teams=\"true\"><div class=\"su-spacer\" style=\"height:20px\"><\/div><\/span><\/p>\n<p data-start=\"599\" data-end=\"626\">Calculation of <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>T<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">T<\/annotation><\/semantics><\/math><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>T<\/mi><mo>=<\/mo><msub><mi>\u03bb<\/mi><mi>y<\/mi><\/msub><mo>+<\/mo><mfrac><mn>14<\/mn><mrow><mn>15<\/mn><msub><mi>\u03bb<\/mi><mi>y<\/mi><\/msub><\/mrow><\/mfrac><mo>+<\/mo><mfrac><mn>1<\/mn><mn>3<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">T = lambda_y + frac{14}{15lambda_y} + frac{1}{3}<\/annotation><\/semantics><\/math><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>T<\/mi><mo>=<\/mo><mn>3.419<\/mn><mo>+<\/mo><mfrac><mn>14<\/mn><mrow><mn>15<\/mn><mo>\u22c5<\/mo><mn>3.419<\/mn><\/mrow><\/mfrac><mo>+<\/mo><mfrac><mn>1<\/mn><mn>3<\/mn><\/mfrac><mo>=<\/mo><mn>4.026<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">T = 3.419 + frac{14}{15 cdot 3.419} + frac{1}{3} = 4.026<\/annotation><\/semantics><\/math><\/p>\n<p data-start=\"753\" data-end=\"780\"><span data-teams=\"true\"><div class=\"su-spacer\" style=\"height:20px\"><\/div><\/span><\/p>\n<p data-start=\"753\" data-end=\"780\">Calculation of <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>H<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">H<\/annotation><\/semantics><\/math><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>H<\/mi><mo>=<\/mo><msub><mi>\u03bb<\/mi><mi>y<\/mi><\/msub><mo>\u2212<\/mo><mfrac><mrow><mn>2<\/mn><msub><mi>\u03bb<\/mi><mi>y<\/mi><\/msub><\/mrow><mrow><mi>c<\/mi><mo stretchy=\"false\">(<\/mo><mi>T<\/mi><mo>+<\/mo><msqrt><mrow><msup><mi>T<\/mi><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>4<\/mn><\/mrow><\/msqrt><mo stretchy=\"false\">)<\/mo><\/mrow><\/mfrac><mo separator=\"true\">,<\/mo><mspace width=\"1em\"><\/mspace><mi>H<\/mi><mo>\u2265<\/mo><mi>R<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">H = lambda_y &#8211; frac{2lambda_y}{c(T + sqrt{T^2 &#8211; 4})}, quad H geq R<\/annotation><\/semantics><\/math><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>H<\/mi><mo>=<\/mo><mn>3.419<\/mn><mo>\u2212<\/mo><mfrac><mrow><mn>2<\/mn><mo>\u22c5<\/mo><mn>3.419<\/mn><\/mrow><mrow><mn>1.13<\/mn><mo>\u22c5<\/mo><mo stretchy=\"false\">(<\/mo><mn>4.026<\/mn><mo>+<\/mo><msqrt><mrow><msup><mn>4.026<\/mn><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>4<\/mn><\/mrow><\/msqrt><mo stretchy=\"false\">)<\/mo><\/mrow><\/mfrac><mo>=<\/mo><mn>2.614<\/mn><mspace width=\"1em\"><\/mspace><mtext>(valid since <\/mtext><mi>H<\/mi><mo>&gt;<\/mo><mi>R<\/mi><mo>=<\/mo><mn>0.22<\/mn><mtext>)<\/mtext><\/mrow><\/semantics><\/math><\/p>\n<p data-start=\"107\" data-end=\"165\">Reduction Factor for Stress in Y Direction <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>C<\/mi><mi>y<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">C_y<\/annotation><\/semantics><\/math><\/p>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p class=\"\" data-start=\"166\" data-end=\"200\"><em data-start=\"166\" data-end=\"200\">(Pt. 1, Ch. 8, Sec. 5 \/ Table 3)<\/em><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>C<\/mi><mi>y<\/mi><\/msub><mo>=<\/mo><mi>c<\/mi><mrow><mo fence=\"true\">(<\/mo><mfrac><mn>1<\/mn><msub><mi>\u03bb<\/mi><mi>y<\/mi><\/msub><\/mfrac><mo>\u2212<\/mo><mfrac><mrow><mi>R<\/mi><mo>+<\/mo><msup><mi>F<\/mi><mn>2<\/mn><\/msup><mo stretchy=\"false\">(<\/mo><mi>H<\/mi><mo>\u2212<\/mo><mi>R<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><msubsup><mi>\u03bb<\/mi><mi>y<\/mi><mn>2<\/mn><\/msubsup><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><\/semantics><\/math><\/p>\n<ul>\n<li data-start=\"289\" data-end=\"308\"><strong>Substituted values:<\/strong><\/li>\n<\/ul>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>C<\/mi><mi>y<\/mi><\/msub><mo>=<\/mo><mn>1.13<\/mn><mo>\u22c5<\/mo><mrow><mo fence=\"true\">(<\/mo><mfrac><mn>1<\/mn><mn>3.419<\/mn><\/mfrac><mo>\u2212<\/mo><mfrac><mrow><mn>0.22<\/mn><mo>+<\/mo><msup><mn>0.508<\/mn><mn>2<\/mn><\/msup><mo>\u22c5<\/mo><mo stretchy=\"false\">(<\/mo><mn>2.614<\/mn><mo>\u2212<\/mo><mn>0.22<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><msup><mn>3.419<\/mn><mn>2<\/mn><\/msup><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">C_y = 1.13 cdot left( frac{1}{3.419} &#8211; frac{0.22 + 0.508^2 cdot (2.614 &#8211; 0.22)}{3.419^2} right)<\/annotation><\/semantics><\/math><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>C<\/mi><mi>y<\/mi><\/msub><mo>=<\/mo><mn>0.250<\/mn><\/mrow><\/semantics><\/math><\/p>\n<div class=\"split\"> <\/div>\n<h3 class=\"\" data-start=\"105\" data-end=\"157\">Case 15:<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/h3>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>K<\/mi><mi>\u03c4<\/mi><\/msub><mo>=<\/mo><msqrt><mn>3<\/mn><\/msqrt><mrow><mo fence=\"true\">(<\/mo><mn>5.34<\/mn><mo>+<\/mo><mfrac><mn>4<\/mn><msup><mi>\u03b1<\/mi><mn>2<\/mn><\/msup><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><\/semantics><\/math><\/p>\n<ul>\n<li data-start=\"225\" data-end=\"244\"><strong>Substituted values:<\/strong><\/li>\n<\/ul>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>K<\/mi><mi>\u03c4<\/mi><\/msub><mo>=<\/mo><msqrt><mn>3<\/mn><\/msqrt><mrow><mo fence=\"true\">(<\/mo><mn>5.34<\/mn><mo>+<\/mo><mfrac><mn>4<\/mn><msup><mn>2.519<\/mn><mn>2<\/mn><\/msup><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">K_tau = sqrt{3} left( 5.34 + frac{4}{2.519^2} right)<\/annotation><\/semantics><\/math><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>K<\/mi><mi>\u03c4<\/mi><\/msub><mo>=<\/mo><mn>10.341<\/mn><\/mrow><\/semantics><\/math><\/p>\n<p data-start=\"126\" data-end=\"204\">Reference degree of slenderness in <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><mi>y<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">xy<\/annotation><\/semantics><\/math>  direction <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03bb<\/mi><mi>\u03c4<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">lambda_tau<\/annotation><\/semantics><\/math><\/p>\n<p class=\"\" data-start=\"205\" data-end=\"239\"><em data-start=\"205\" data-end=\"239\">(Pt. 1, Ch. 8, Sec. 5 \/ [2.2.2])<\/em><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03bb<\/mi><mi>\u03c4<\/mi><\/msub><mo>=<\/mo><msqrt><mfrac><msub><mi>R<\/mi><mrow><mi>e<\/mi><mi>H<\/mi><mo separator=\"true\">,<\/mo><mi>P<\/mi><\/mrow><\/msub><mrow><msub><mi>K<\/mi><mi>\u03c4<\/mi><\/msub><mo>\u22c5<\/mo><msub><mi>\u03c3<\/mi><mi>E<\/mi><\/msub><\/mrow><\/mfrac><\/msqrt><\/mrow><\/semantics><\/math><\/p>\n<p data-start=\"309\" data-end=\"328\"><span data-teams=\"true\"><div class=\"su-spacer\" style=\"height:20px\"><\/div><\/span><\/p>\n<ul>\n<li data-start=\"309\" data-end=\"328\"><strong>Substituted values:<\/strong><\/li>\n<\/ul>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03bb<\/mi><mi>\u03c4<\/mi><\/msub><mo>=<\/mo><msqrt><mfrac><mrow><mn>235<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mn>6<\/mn><\/msup><\/mrow><mrow><mn>10.341<\/mn><mo>\u00d7<\/mo><mn>14996549.9<\/mn><\/mrow><\/mfrac><\/msqrt><mo>=<\/mo><mn>1.231<\/mn><\/mrow><\/semantics><\/math><\/p>\n<p data-start=\"122\" data-end=\"190\">Reduction factor for stress in <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><mi>y<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">xy<\/annotation><\/semantics><\/math> direction <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>C<\/mi><mi>\u03c4<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">C_tau<\/annotation><\/semantics><\/math><\/p>\n<p class=\"\" data-start=\"191\" data-end=\"225\"><em data-start=\"191\" data-end=\"225\">(Pt. 1, Ch. 8, Sec. 5 \/ Table 3)<\/em><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>C<\/mi><mi>\u03c4<\/mi><\/msub><mo>=<\/mo><mfrac><mn>0.84<\/mn><msub><mi>\u03bb<\/mi><mi>\u03c4<\/mi><\/msub><\/mfrac><\/mrow><\/semantics><\/math><\/p>\n<ul>\n<li data-start=\"269\" data-end=\"288\"><strong>Substituted values:<\/strong><\/li>\n<\/ul>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>C<\/mi><mi>\u03c4<\/mi><\/msub><mo>=<\/mo><mfrac><mn>0.84<\/mn><mn>1.231<\/mn><\/mfrac><mo>=<\/mo><mn>0.682<\/mn><\/mrow><\/semantics><\/math><\/p>\n<p data-start=\"86\" data-end=\"118\">Ultimate buckling stresses<\/p>\n<p class=\"\" data-start=\"119\" data-end=\"153\"><em data-start=\"119\" data-end=\"153\">(Pt. 1, Ch. 8, Sec. 5 \/ [2.2.3])<\/em><\/p>\n<p class=\"\" data-start=\"155\" data-end=\"226\"><strong data-start=\"155\" data-end=\"226\"><span data-teams=\"true\"><div class=\"su-spacer\" style=\"height:20px\"><\/div><\/span><\/strong><\/p>\n<ul>\n<li data-start=\"155\" data-end=\"226\"><strong data-start=\"155\" data-end=\"226\">In the direction parallel to the longer edge of the buckling panel:<\/strong><\/li>\n<\/ul>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msubsup><mi>\u03c3<\/mi><mrow><mi>c<\/mi><mi>x<\/mi><\/mrow><mo lspace=\"0em\" mathvariant=\"normal\" rspace=\"0em\">\u2032<\/mo><\/msubsup><mo>=<\/mo><msub><mi>C<\/mi><mi>x<\/mi><\/msub><msub><mi>R<\/mi><mrow><mi>e<\/mi><mi>H<\/mi><mo separator=\"true\">,<\/mo><mi>P<\/mi><\/mrow><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">sigma&#8217;_{cx} = C_x R_{eH,P}<\/annotation><\/semantics><\/math><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msubsup><mi>\u03c3<\/mi><mrow><mi>c<\/mi><mi>x<\/mi><\/mrow><mo lspace=\"0em\" mathvariant=\"normal\" rspace=\"0em\">\u2032<\/mo><\/msubsup><mo>=<\/mo><mn>0.507<\/mn><mo>\u22c5<\/mo><mn>235<\/mn><mtext> <\/mtext><mi>M<\/mi><mi>P<\/mi><mi>a<\/mi><mo>=<\/mo><mrow><mn mathvariant=\"bold\">119.145<\/mn><mtext> <\/mtext><mi mathvariant=\"bold\">M<\/mi><mi mathvariant=\"bold\">P<\/mi><mi mathvariant=\"bold\">a<\/mi><\/mrow><\/mrow><\/semantics><\/math><\/p>\n<ul>\n<li data-start=\"331\" data-end=\"403\"><strong data-start=\"331\" data-end=\"403\">In the direction parallel to the shorter edge of the buckling panel:<\/strong><\/li>\n<\/ul>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msubsup><mi>\u03c3<\/mi><mrow><mi>c<\/mi><mi>y<\/mi><\/mrow><mo lspace=\"0em\" mathvariant=\"normal\" rspace=\"0em\">\u2032<\/mo><\/msubsup><mo>=<\/mo><msub><mi>C<\/mi><mi>y<\/mi><\/msub><msub><mi>R<\/mi><mrow><mi>e<\/mi><mi>H<\/mi><mo separator=\"true\">,<\/mo><mi>P<\/mi><\/mrow><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">sigma&#8217;_{cy} = C_y R_{eH,P}<\/annotation><\/semantics><\/math><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msubsup><mi>\u03c3<\/mi><mrow><mi>c<\/mi><mi>y<\/mi><\/mrow><mo lspace=\"0em\" mathvariant=\"normal\" rspace=\"0em\">\u2032<\/mo><\/msubsup><mo>=<\/mo><mn>0.250<\/mn><mo>\u22c5<\/mo><mn>235<\/mn><mtext> <\/mtext><mi>M<\/mi><mi>P<\/mi><mi>a<\/mi><mo>=<\/mo><mrow><mn mathvariant=\"bold\">58.750<\/mn><mtext> <\/mtext><mi mathvariant=\"bold\">M<\/mi><mi mathvariant=\"bold\">P<\/mi><mi mathvariant=\"bold\">a<\/mi><\/mrow><\/mrow><\/semantics><\/math><\/p>\n<ul>\n<li data-start=\"507\" data-end=\"517\"><strong data-start=\"507\" data-end=\"517\">Shear:<\/strong><\/li>\n<\/ul>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msubsup><mi>\u03c4<\/mi><mi>c<\/mi><mo lspace=\"0em\" mathvariant=\"normal\" rspace=\"0em\">\u2032<\/mo><\/msubsup><mo>=<\/mo><msub><mi>C<\/mi><mi>\u03c4<\/mi><\/msub><mo>\u22c5<\/mo><mfrac><msub><mi>R<\/mi><mrow><mi>e<\/mi><mi>H<\/mi><mo separator=\"true\">,<\/mo><mi>P<\/mi><\/mrow><\/msub><msqrt><mn>3<\/mn><\/msqrt><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">tau&#8217;_c = C_tau cdot frac{R_{eH,P}}{sqrt{3}}<\/annotation><\/semantics><\/math><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msubsup><mi>\u03c4<\/mi><mi>c<\/mi><mo lspace=\"0em\" mathvariant=\"normal\" rspace=\"0em\">\u2032<\/mo><\/msubsup><mo>=<\/mo><mn>0.682<\/mn><mo>\u22c5<\/mo><mfrac><mrow><mn>235<\/mn><mtext> <\/mtext><mi>M<\/mi><mi>P<\/mi><mi>a<\/mi><\/mrow><msqrt><mn>3<\/mn><\/msqrt><\/mfrac><mo>=<\/mo><mrow><mn mathvariant=\"bold\">92.532<\/mn><mtext> <\/mtext><mi mathvariant=\"bold\">M<\/mi><mi mathvariant=\"bold\">P<\/mi><mi mathvariant=\"bold\">a<\/mi><\/mrow><\/mrow><\/semantics><\/math><\/p>\n<p data-start=\"88\" data-end=\"161\">The rest of the input parameters for final equations were calculated:<\/p>\n<p data-start=\"163\" data-end=\"232\"><span data-teams=\"true\"><div class=\"su-spacer\" style=\"height:20px\"><\/div><\/span><\/p>\n<ul>\n<li data-start=\"163\" data-end=\"232\"><strong data-start=\"163\" data-end=\"194\">Plate slenderness parameter<\/strong><br data-start=\"194\" data-end=\"197\" \/><em data-start=\"197\" data-end=\"232\">(Pt. 1, Ch. 8, Sec. 5 \/ [2.2.1]):<\/em><\/li>\n<\/ul>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03b2<\/mi><mi>p<\/mi><\/msub><mo>=<\/mo><mfrac><mi>b<\/mi><msub><mi>t<\/mi><mi>p<\/mi><\/msub><\/mfrac><msqrt><mfrac><msub><mi>R<\/mi><mrow><mi>e<\/mi><mi>H<\/mi><mo separator=\"true\">,<\/mo><mi>P<\/mi><\/mrow><\/msub><mi>E<\/mi><\/mfrac><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">beta_p = frac{b}{t_p} sqrt{frac{R_{eH,P}}{E}}<\/annotation><\/semantics><\/math><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03b2<\/mi><mi>p<\/mi><\/msub><mo>=<\/mo><mfrac><mn>1.350<\/mn><mn>0.012<\/mn><\/mfrac><mo>\u22c5<\/mo><msqrt><mfrac><mrow><mn>235<\/mn><mo>\u22c5<\/mo><msup><mn>10<\/mn><mn>6<\/mn><\/msup><\/mrow><mrow><mn>210<\/mn><mo>\u22c5<\/mo><msup><mn>10<\/mn><mn>9<\/mn><\/msup><\/mrow><\/mfrac><\/msqrt><mo>=<\/mo><mn mathvariant=\"bold\">3.763<\/mn><\/mrow><\/semantics><\/math><\/p>\n<p data-start=\"74\" data-end=\"99\">Coefficient <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>B<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">B<\/annotation><\/semantics><\/math><\/p>\n<p class=\"\" data-start=\"100\" data-end=\"135\"><em data-start=\"100\" data-end=\"135\">(Pt. 1, Ch. 8, Sec. 5 \/ Table 1):<\/em><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>B<\/mi><mo>=<\/mo><mn>0.7<\/mn><mo>\u2212<\/mo><mfrac><mrow><mn>0.3<\/mn><mo>\u22c5<\/mo><msub><mi>\u03b2<\/mi><mi>p<\/mi><\/msub><\/mrow><msup><mi>\u03b1<\/mi><mn>2<\/mn><\/msup><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">B = 0.7 &#8211; frac{0.3 cdot beta_p}{alpha^2}<\/annotation><\/semantics><\/math><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>B<\/mi><mo>=<\/mo><mn>0.7<\/mn><mo>\u2212<\/mo><mfrac><mrow><mn>0.3<\/mn><mo>\u22c5<\/mo><mn>3.763<\/mn><\/mrow><msup><mn>2.519<\/mn><mn>2<\/mn><\/msup><\/mfrac><mo>=<\/mo><mn mathvariant=\"bold\">0.522<\/mn><\/mrow><\/semantics><\/math><\/p>\n<p data-start=\"81\" data-end=\"108\">Coefficient <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>e<\/mi><mn>0<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">e_0<\/annotation><\/semantics><\/math><\/p>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p class=\"\" data-start=\"109\" data-end=\"144\"><em data-start=\"109\" data-end=\"144\">(Pt. 1, Ch. 8, Sec. 5 \/ Table 1):<\/em><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>e<\/mi><mn>0<\/mn><\/msub><mo>=<\/mo><mfrac><mn>2<\/mn><msubsup><mi>\u03b2<\/mi><mi>p<\/mi><mn>0.25<\/mn><\/msubsup><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">e_0 = frac{2}{beta_p^{0.25}}<\/annotation><\/semantics><\/math><\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>e<\/mi><mn>0<\/mn><\/msub><mo>=<\/mo><mfrac><mn>2<\/mn><msup><mn>3.763<\/mn><mn>0.25<\/mn><\/msup><\/mfrac><mo>=<\/mo><mn mathvariant=\"bold\">1.436<\/mn><\/mrow><\/semantics><\/math><\/p>\n<p data-start=\"125\" data-end=\"163\"><span data-teams=\"true\"><div class=\"su-spacer\" style=\"height:20px\"><\/div><\/span><\/p>\n<p data-start=\"125\" data-end=\"163\">Final Equations for Limit States<\/p>\n<p class=\"\" data-start=\"164\" data-end=\"280\"><em data-start=\"164\" data-end=\"280\">(Pt. 1, Ch. 8, Sec. 5 \/ [2.2.1]) \u2014 Transformed to calculate stress multiplier factors acting on loads <\/em><\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\u03b3<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">gamma<\/annotation><\/semantics><\/math><\/p>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">\u03b3<\/span><\/span><\/span><\/p>\n<p data-start=\"282\" data-end=\"291\">I.<\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03b3<\/mi><mrow><mi>c<\/mi><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><msup><mrow><mo fence=\"true\">(<\/mo><mfrac><mn>1<\/mn><mrow><msup><mrow><mo fence=\"true\">(<\/mo><mfrac><mrow><msub><mi>\u03c3<\/mi><mi>x<\/mi><\/msub><mi>S<\/mi><\/mrow><msubsup><mi>\u03c3<\/mi><mrow><mi>c<\/mi><mi>x<\/mi><\/mrow><mo lspace=\"0em\" mathvariant=\"normal\" rspace=\"0em\">\u2032<\/mo><\/msubsup><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><msub><mi>e<\/mi><mn>0<\/mn><\/msub><\/msup><mo>\u2212<\/mo><mi>B<\/mi><msup><mrow><mo fence=\"true\">(<\/mo><mfrac><mrow><msub><mi>\u03c3<\/mi><mi>x<\/mi><\/msub><mi>S<\/mi><\/mrow><msubsup><mi>\u03c3<\/mi><mrow><mi>c<\/mi><mi>x<\/mi><\/mrow><mo lspace=\"0em\" mathvariant=\"normal\" rspace=\"0em\">\u2032<\/mo><\/msubsup><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mfrac><msub><mi>e<\/mi><mn>0<\/mn><\/msub><mn>2<\/mn><\/mfrac><\/msup><msup><mrow><mo fence=\"true\">(<\/mo><mfrac><mrow><msub><mi>\u03c3<\/mi><mi>y<\/mi><\/msub><mi>S<\/mi><\/mrow><msubsup><mi>\u03c3<\/mi><mrow><mi>c<\/mi><mi>y<\/mi><\/mrow><mo lspace=\"0em\" mathvariant=\"normal\" rspace=\"0em\">\u2032<\/mo><\/msubsup><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mfrac><msub><mi>e<\/mi><mn>0<\/mn><\/msub><mn>2<\/mn><\/mfrac><\/msup><mo>+<\/mo><msup><mrow><mo fence=\"true\">(<\/mo><mfrac><mrow><msub><mi>\u03c3<\/mi><mi>y<\/mi><\/msub><mi>S<\/mi><\/mrow><msubsup><mi>\u03c3<\/mi><mrow><mi>c<\/mi><mi>y<\/mi><\/mrow><mo lspace=\"0em\" mathvariant=\"normal\" rspace=\"0em\">\u2032<\/mo><\/msubsup><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><msub><mi>e<\/mi><mn>0<\/mn><\/msub><\/msup><mo>+<\/mo><msup><mrow><mo fence=\"true\">(<\/mo><mfrac><mrow><mi mathvariant=\"normal\">\u2223<\/mi><mi>\u03c4<\/mi><mi mathvariant=\"normal\">\u2223<\/mi><mi>S<\/mi><\/mrow><msubsup><mi>\u03c4<\/mi><mi>c<\/mi><mo lspace=\"0em\" mathvariant=\"normal\" rspace=\"0em\">\u2032<\/mo><\/msubsup><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><msub><mi>e<\/mi><mn>0<\/mn><\/msub><\/msup><\/mrow><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mfrac><mn>1<\/mn><msub><mi>e<\/mi><mn>0<\/mn><\/msub><\/mfrac><\/msup><\/mrow><\/semantics><\/math><\/p>\n<p data-start=\"630\" data-end=\"640\">II.<\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03b3<\/mi><mrow><mi>c<\/mi><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><msup><mrow><mo fence=\"true\">(<\/mo><mfrac><mn>1<\/mn><mrow><msup><mrow><mo fence=\"true\">(<\/mo><mfrac><mrow><msub><mi>\u03c3<\/mi><mi>x<\/mi><\/msub><mi>S<\/mi><\/mrow><msubsup><mi>\u03c3<\/mi><mrow><mi>c<\/mi><mi>x<\/mi><\/mrow><mo lspace=\"0em\" mathvariant=\"normal\" rspace=\"0em\">\u2032<\/mo><\/msubsup><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mfrac><mn>2<\/mn><msubsup><mi>\u03b2<\/mi><mi>p<\/mi><mn>0.25<\/mn><\/msubsup><\/mfrac><\/msup><mo>+<\/mo><msup><mrow><mo fence=\"true\">(<\/mo><mfrac><mrow><mi mathvariant=\"normal\">\u2223<\/mi><mi>\u03c4<\/mi><mi mathvariant=\"normal\">\u2223<\/mi><mi>S<\/mi><\/mrow><msubsup><mi>\u03c4<\/mi><mi>c<\/mi><mo lspace=\"0em\" mathvariant=\"normal\" rspace=\"0em\">\u2032<\/mo><\/msubsup><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mfrac><mn>2<\/mn><msubsup><mi>\u03b2<\/mi><mi>p<\/mi><mn>0.25<\/mn><\/msubsup><\/mfrac><\/msup><\/mrow><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mfrac><msubsup><mi>\u03b2<\/mi><mi>p<\/mi><mn>0.25<\/mn><\/msubsup><mn>2<\/mn><\/mfrac><\/msup><\/mrow><\/semantics><\/math><\/p>\n<p data-start=\"857\" data-end=\"868\">III.<\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03b3<\/mi><mrow><mi>c<\/mi><mn>3<\/mn><\/mrow><\/msub><mo>=<\/mo><msup><mrow><mo fence=\"true\">(<\/mo><mfrac><mn>1<\/mn><mrow><msup><mrow><mo fence=\"true\">(<\/mo><mfrac><mrow><msub><mi>\u03c3<\/mi><mi>y<\/mi><\/msub><mi>S<\/mi><\/mrow><msubsup><mi>\u03c3<\/mi><mrow><mi>c<\/mi><mi>y<\/mi><\/mrow><mo lspace=\"0em\" mathvariant=\"normal\" rspace=\"0em\">\u2032<\/mo><\/msubsup><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mfrac><mn>2<\/mn><msubsup><mi>\u03b2<\/mi><mi>p<\/mi><mn>0.25<\/mn><\/msubsup><\/mfrac><\/msup><mo>+<\/mo><msup><mrow><mo fence=\"true\">(<\/mo><mfrac><mrow><mi mathvariant=\"normal\">\u2223<\/mi><mi>\u03c4<\/mi><mi mathvariant=\"normal\">\u2223<\/mi><mi>S<\/mi><\/mrow><msubsup><mi>\u03c4<\/mi><mi>c<\/mi><mo lspace=\"0em\" mathvariant=\"normal\" rspace=\"0em\">\u2032<\/mo><\/msubsup><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mfrac><mn>2<\/mn><msubsup><mi>\u03b2<\/mi><mi>p<\/mi><mn>0.25<\/mn><\/msubsup><\/mfrac><\/msup><\/mrow><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mfrac><msubsup><mi>\u03b2<\/mi><mi>p<\/mi><mn>0.25<\/mn><\/msubsup><mn>2<\/mn><\/mfrac><\/msup><\/mrow><\/semantics><\/math><\/p>\n<p data-start=\"1085\" data-end=\"1095\">IV.<\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03b3<\/mi><mrow><mi>c<\/mi><mn>4<\/mn><\/mrow><\/msub><mo>=<\/mo><mfrac><msubsup><mi>\u03c4<\/mi><mi>c<\/mi><mo lspace=\"0em\" mathvariant=\"normal\" rspace=\"0em\">\u2032<\/mo><\/msubsup><mrow><mi mathvariant=\"normal\">\u2223<\/mi><mi>\u03c4<\/mi><mi mathvariant=\"normal\">\u2223<\/mi><mi>S<\/mi><\/mrow><\/mfrac><\/mrow><\/semantics><\/math><\/p>\n<p data-start=\"52\" data-end=\"107\">Partial Safety Factor and Stress Multiplier Factors<\/p>\n<p data-start=\"109\" data-end=\"193\"><span data-teams=\"true\"><div class=\"su-spacer\" style=\"height:20px\"><\/div><\/span><\/p>\n<p class=\"\" data-start=\"109\" data-end=\"193\">The <strong data-start=\"113\" data-end=\"138\">partial safety factor <\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>S<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">S<\/annotation><\/semantics><\/math><\/p>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">S<\/span><\/span><\/span> <em data-start=\"147\" data-end=\"181\">(Pt. 1, Ch. 8, Sec. 5 \/ Symbols)<\/em> was set as:<\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>S<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><\/semantics><\/math><\/p>\n<p class=\"\" data-start=\"208\" data-end=\"302\">Then the <strong data-start=\"217\" data-end=\"256\">values of stress multiplier factors<\/strong> acting on loads <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\u03b3<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">gamma<\/annotation><\/semantics><\/math><\/p>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">\u03b3<\/span><\/span><\/span> were calculated:<\/p>\n<p data-start=\"304\" data-end=\"313\">I.<\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03b3<\/mi><mrow><mi>c<\/mi><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>1.763<\/mn><\/mrow><\/semantics><\/math><\/p>\n<p data-start=\"341\" data-end=\"351\">II.<\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03b3<\/mi><mrow><mi>c<\/mi><mn>2<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>2.486<\/mn><\/mrow><\/semantics><\/math><\/p>\n<p data-start=\"379\" data-end=\"390\">III.<\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03b3<\/mi><mrow><mi>c<\/mi><mn>3<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>1.968<\/mn><\/mrow><\/semantics><\/math><\/p>\n<p data-start=\"418\" data-end=\"428\">IV.<\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03b3<\/mi><mrow><mi>c<\/mi><mn>4<\/mn><\/mrow><\/msub><mo>=<\/mo><mn>5.663<\/mn><\/mrow><\/semantics><\/math><\/p>\n<p data-start=\"52\" data-end=\"111\">\n<p data-start=\"52\" data-end=\"111\"><span data-teams=\"true\"><div class=\"su-spacer\" style=\"height:20px\"><\/div><\/span><\/p>\n<p data-start=\"52\" data-end=\"111\">Minimum Stress Multiplier Factor and Utilization Factor<\/p>\n<p class=\"\" data-start=\"113\" data-end=\"238\">The <strong data-start=\"117\" data-end=\"153\">minimum stress multiplier factor<\/strong> from above \u2013 the <strong data-start=\"171\" data-end=\"210\">stress multiplier factor at failure <\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03b3<\/mi><mi>c<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">gamma_c<\/annotation><\/semantics><\/math> \u2013 was found:<\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03b3<\/mi><mi>c<\/mi><\/msub><mo>=<\/mo><mn>1.763<\/mn><\/mrow><\/semantics><\/math><\/p>\n<p class=\"\" data-start=\"264\" data-end=\"358\">The <strong data-start=\"268\" data-end=\"290\">utilization factor <\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03b7<\/mi><mrow><mi>a<\/mi><mi>c<\/mi><mi>t<\/mi><\/mrow><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">eta_{act}<\/annotation><\/semantics><\/math> was calculated <em data-start=\"323\" data-end=\"357\">(Pt. 1, Ch. 8, Sec. 1 \/ [3.2.2])<\/em>:<\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03b7<\/mi><mrow><mi>a<\/mi><mi>c<\/mi><mi>t<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mn>1<\/mn><msub><mi>\u03b3<\/mi><mi>c<\/mi><\/msub><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><mn>1.763<\/mn><\/mfrac><mo>=<\/mo><mi><mn mathvariant=\"bold\">0.567<\/mn><\/mi><\/mrow><\/semantics><\/math><\/p>\n<div class=\"split\"> <\/div>\n<h2 data-start=\"51\" data-end=\"73\">SDC Verifier Setup<\/h2>\n<p class=\"\" data-start=\"75\" data-end=\"233\">In <strong data-start=\"78\" data-end=\"94\">SDC Verifier<\/strong>, the standard was added using the <strong data-start=\"129\" data-end=\"149\">same assumptions<\/strong> as in the analytical calculation. The check was then performed based on this setup.<\/p>\n<h3 data-start=\"235\" data-end=\"264\">1. Mild Steel Properties<\/h3>\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/sdcverifier.com\/wp-content\/uploads\/2025\/04\/Screenshot-2025-04-10-204603.png\" alt=\"\" class=\"wp-image-73476\"\/><\/figure>\n\n<h3 class=\"\" data-start=\"52\" data-end=\"88\">Propiedades de la placa superior (T = 12 mm)<\/h3>\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/sdcverifier.com\/wp-content\/uploads\/2025\/04\/Screenshot-2025-04-10-204645.png\" alt=\"\" class=\"wp-image-73477\"\/><\/figure>\n\n<h3 class=\"\" data-start=\"71\" data-end=\"95\">Resumen de propiedades<\/h3>\n<p class=\"\" data-start=\"96\" data-end=\"144\"><em data-start=\"96\" data-end=\"144\">Calculado para el CSys \u00ab0..B\u00e1sico Rectangular\u00bb<\/em><\/p>\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/sdcverifier.com\/wp-content\/uploads\/2025\/04\/Screenshot-2025-04-10-204813.png\" alt=\"\" class=\"wp-image-73478\"\/><\/figure>\n\n<h3 class=\"\" data-start=\"77\" data-end=\"92\">Cargas FEM<\/h3>\n<p class=\"\" data-start=\"93\" data-end=\"160\"><em data-start=\"93\" data-end=\"160\">Este p\u00e1rrafo contiene informaci\u00f3n sobre las cargas aplicadas al modelo.<\/em><\/p>\n<p data-start=\"162\" data-end=\"180\">1. Bordes largos<\/p>\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/sdcverifier.com\/wp-content\/uploads\/2025\/04\/Screenshot-2025-04-10-204925.png\" alt=\"\" class=\"wp-image-73479\"\/><\/figure>\n\n<h3>2. Bordes cortos<\/h3>\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/sdcverifier.com\/wp-content\/uploads\/2025\/04\/Screenshot-2025-04-10-205047.png\" alt=\"\" class=\"wp-image-73480\"\/><\/figure>\n\n<h3>3. Bordes largos paralelos<\/h3>\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/sdcverifier.com\/wp-content\/uploads\/2025\/04\/Screenshot-2025-04-10-205219.png\" alt=\"\" class=\"wp-image-73481\"\/><\/figure>\n\n<h3 class=\"\" data-start=\"74\" data-end=\"89\">Restricciones<\/h3>\n<p class=\"\" data-start=\"91\" data-end=\"164\">Este p\u00e1rrafo contiene informaci\u00f3n sobre las partes limitadas del modelo.<\/p>\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/sdcverifier.com\/wp-content\/uploads\/2025\/04\/Screenshot-2025-04-10-205344.png\" alt=\"\" class=\"wp-image-73482\"\/><\/figure>\n\n<div class=\"split\"> <\/div>\n<h3 class=\"\" data-start=\"83\" data-end=\"96\">Resultados<\/h3>\n<p data-start=\"97\" data-end=\"112\">1..Trabajo 1<\/p>\n<p data-start=\"113\" data-end=\"128\">Conjuntos de carga<\/p>\n<p class=\"\" data-start=\"129\" data-end=\"212\">En este apartado se describe la influencia de las diferentes combinaciones de carga.<\/p>\n<p data-start=\"214\" data-end=\"245\">Cargar conjunto &#8216;1..Cargar conjunto 1&#8217;<\/p>\n<p data-start=\"246\" data-end=\"281\">3..LR Pandeo de la placa CSR (2024)<\/p>\n<p class=\"\" data-start=\"283\" data-end=\"484\"><strong data-start=\"283\" data-end=\"320\">Norma aplicada seg\u00fan <\/strong><strong data-start=\"323\" data-end=\"401\">LR Reglas estructurales comunes para graneleros y petroleros, enero de 2024 <\/strong><em data-start=\"404\" data-end=\"449\">basado en la siguiente parte de la norma <\/em><strong data-start=\"452\" data-end=\"484\">Parte 1, Cap\u00edtulo 8 &#8211; Pandeo<\/strong><\/p>\n<p data-start=\"486\" data-end=\"677\"><span data-teams=\"true\"><div class=\"su-spacer\" style=\"height:20px\"><\/div><\/span><\/p>\n<p class=\"\" data-start=\"486\" data-end=\"677\"><strong data-start=\"486\" data-end=\"501\">Sistema de unidades<\/strong><br data-start=\"501\" data-end=\"504\">Sistema de unidades de corriente = MKS (Metro\/Kg\/Segundo). Se utiliza en los c\u00e1lculos de las siguientes normas:<br data-start=\"604\" data-end=\"607\">API RP 2A, ISO 19902, Norsok N004, DIN 15018, FEM 1.001 y Euroc\u00f3digo3. <\/p>\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/sdcverifier.com\/wp-content\/uploads\/2025\/04\/Screenshot-2025-04-10-205504.png\" alt=\"\" class=\"wp-image-73483\"\/><\/figure>\n\n<p data-start=\"52\" data-end=\"169\">Resultados intermedios de <sub>\u03c3\u2032cx<\/sub>, <sub>\u03c3\u2032cy<\/sub> y <sub>\u03c4\u2032c<\/sub> a partir de los detalles de c\u00e1lculo del control<\/p>\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/sdcverifier.com\/wp-content\/uploads\/2025\/04\/Screenshot-2025-04-10-205631.png\" alt=\"\" class=\"wp-image-73484\"\/><\/figure>\n\n<div class=\"split\"> <\/div>\n<h3 data-start=\"79\" data-end=\"143\"><strong data-start=\"83\" data-end=\"143\">Comparaci\u00f3n de los c\u00e1lculos manuales y los resultados del SDC Verifier<\/strong><\/h3>\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><strong>Par\u00e1metro<\/strong><\/td><td><strong>C\u00e1lculos manuales<\/strong><\/td><td><strong>SDC Verifier<\/strong><\/td><\/tr><tr><td><strong>Requisito de esbeltez<\/strong> <\/td><td>Aprobado<\/td><td>Aprobado<\/td><\/tr><\/tbody><\/table><\/figure>\n\n<p><strong data-start=\"155\" data-end=\"191\">Tensiones \u00faltimas de pandeo [MPa]<\/strong><\/p>\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>Par\u00e1metro<\/td><td>C\u00e1lculos manuales<\/td><td>SDC Verifier<\/td><\/tr><tr><td><sub>\u03c3\u2032cx<\/sub><\/td><td>119.145<\/td><td>119.252<\/td><\/tr><tr><td><sub>\u03c3\u2032cy<\/sub><\/td><td>58.750<\/td><td>58.631<\/td><\/tr><tr><td><strong><strong>\u03c3<\/strong><\/strong><sub>\u2032c<\/sub><\/td><td>92.932<\/td><td>92.585<\/td><\/tr><\/tbody><\/table><\/figure>\n\n<p><strong>Inversa de los factores multiplicadores de tensi\u00f3n que act\u00faan sobre las cargas<\/strong><\/p>\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>Par\u00e1metro<\/td><td>C\u00e1lculos manuales<\/td><td>SDC Verifier<\/td><\/tr><tr><td><sub>1\/\u03b3c1<\/sub><\/td><td>0.567<\/td><td>0.562<\/td><\/tr><tr><td><sub>1\/\u03b3c2<\/sub><\/td><td>0.402<\/td><td>0.396<\/td><\/tr><tr><td><sub>1\/\u03b3c3<\/sub><\/td><td>0.508<\/td><td>0.504<\/td><\/tr><tr><td><sub>1\/\u03b3c4<\/sub><\/td><td>0.177<\/td><td>0.169<\/td><\/tr><\/tbody><\/table><\/figure>\n\n<p><strong data-start=\"846\" data-end=\"868\">Factor de utilizaci\u00f3n<\/strong><\/p>\n<p>&nbsp;<\/p>\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>Par\u00e1metro<\/td><td>C\u00e1lculos manuales<\/td><td>SDC Verifier<\/td><\/tr><tr><td><sub>\u03b7act<\/sub> = 1 \/ <sub>\u03b3c1<\/sub><\/td><td>0.567<\/td><td>0.562<\/td><\/tr><\/tbody><\/table><\/figure>\n\n<p><strong data-start=\"802\" data-end=\"811\">Nota: <\/strong><em data-start=\"814\" data-end=\"896\" data-is-last-node=\"\">Los resultados del SDC Verifier son los mismos que los obtenidos con c\u00e1lculos manuales.<\/em><\/p>\n\n<div class=\"split\"> <\/div>\n<h2 data-start=\"1415\" data-end=\"1436\"><strong data-start=\"1422\" data-end=\"1436\">Conclusi\u00f3n<\/strong><\/h2>\n<p class=\"\" data-start=\"1438\" data-end=\"1554\">La evaluaci\u00f3n comparativa confirma un <strong data-start=\"1463\" data-end=\"1490\">alto nivel de concordancia<\/strong> entre los c\u00e1lculos manuales y la comprobaci\u00f3n automatizada del SDC Verifier:<\/p>\n<ul data-start=\"1556\" data-end=\"1902\">\n<li class=\"\" data-start=\"1556\" data-end=\"1604\">\n<p class=\"\" data-start=\"1558\" data-end=\"1604\"><strong data-start=\"1562\" data-end=\"1603\">Se cumpli\u00f3 el requisito de esbeltez<\/strong>.<\/p>\n<\/li>\n<li class=\"\" data-start=\"1556\" data-end=\"1604\">\n<p class=\"\" data-start=\"1558\" data-end=\"1604\">Las diferencias en <strong data-start=\"1622\" data-end=\"1652\">las tensiones \u00faltimas de pandeo<\/strong> y los <strong data-start=\"1657\" data-end=\"1686\">factores multiplicadores de<\/strong> tensi\u00f3n estuvieron dentro de <strong data-start=\"1699\" data-end=\"1708\">&lt;0<\/strong> <strong data-start=\"1699\" data-end=\"1708\">,2%<\/strong>, lo que indica una coherencia precisa.<\/p>\n<\/li>\n<li class=\"\" data-start=\"1742\" data-end=\"1902\">\n<p class=\"\" data-start=\"1744\" data-end=\"1902\">El <strong data-start=\"1748\" data-end=\"1770\">factor de utilizaci\u00f3n<\/strong> obtenido fue casi id\u00e9ntico:<br data-start=\"1801\" data-end=\"1804\">\u2192 C\u00e1lculos manuales: <strong data-start=\"1827\" data-end=\"1854\"><sub>\u03b7act<\/sub><\/strong> <strong data-start=\"1827\" data-end=\"1854\">= 0,567<\/strong><br data-start=\"1854\" data-end=\"1857\">\u2192 SDC Verifier: <strong data-start=\"1875\" data-end=\"1902\"><sub>\u03b7act<\/sub><\/strong> <strong data-start=\"1875\" data-end=\"1902\">= 0,562<\/strong><\/p>\n<\/li>\n<\/ul>\n<p class=\"\" data-start=\"1904\" data-end=\"2123\">Esta validaci\u00f3n demuestra que <strong data-start=\"1938\" data-end=\"2023\">SDC Verifier aplica con precisi\u00f3n los procedimientos de evaluaci\u00f3n de pandeo LR CSR 2024<\/strong>, lo que lo convierte en una herramienta fiable para las comprobaciones de integridad estructural en aplicaciones mar\u00edtimas y de alta mar.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Este punto de referencia eval\u00faa la precisi\u00f3n y fiabilidad del an\u00e1lisis de pandeo de placas realizado con SDC Verifier compar\u00e1ndolo con c\u00e1lculos manuales detallados basados en las Normas Estructurales Comunes (CSR) de LR para graneleros y petroleros (edici\u00f3n 2024), concretamente la Parte 1, Cap\u00edtulo 8 &#8211; Pandeo. Se model\u00f3 una placa de prueba con unas [&hellip;]<\/p>\n","protected":false},"author":16,"featured_media":93961,"parent":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[626],"tags":[],"class_list":["post-93960","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-benchmarks"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/sdcverifier.com\/es\/wp-json\/wp\/v2\/posts\/93960","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sdcverifier.com\/es\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sdcverifier.com\/es\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sdcverifier.com\/es\/wp-json\/wp\/v2\/users\/16"}],"replies":[{"embeddable":true,"href":"https:\/\/sdcverifier.com\/es\/wp-json\/wp\/v2\/comments?post=93960"}],"version-history":[{"count":0,"href":"https:\/\/sdcverifier.com\/es\/wp-json\/wp\/v2\/posts\/93960\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/sdcverifier.com\/es\/wp-json\/wp\/v2\/media\/93961"}],"wp:attachment":[{"href":"https:\/\/sdcverifier.com\/es\/wp-json\/wp\/v2\/media?parent=93960"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sdcverifier.com\/es\/wp-json\/wp\/v2\/categories?post=93960"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sdcverifier.com\/es\/wp-json\/wp\/v2\/tags?post=93960"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}