31:Tf93,specimen = ({ ////////////// // MATERIAL // ////////////// f_cm: 40, // Mean Compressive Strength at 28th day (MPa) E_cm: 35000, // Elastic Modulus at 28th day (MPa) cement_hardtype: "N", // Cement Hardening Type (CEB-FIP 90 only; Choices: "SL", "N", "R", "RS") cement_strengthclass: "32.5N", // Strength Class (fib MC 2010 only) // Choices: "32.5N", "32.5R", "42.5N", "42.5R", "52.5N", "52.5R" cement_type: "I", // Cement Type (CEB-FIP 90 Updated Knowledge and Model B3 only) // Choices: "I", "II", "III" // (Model BAZANT B4 uses different notation for cement type and for this // model according to explanation just after the equation 43 (RILEM-B4 document) // R: Type I, SL: Type II, RS: Type III are assumed to be consistent with the // other codes.) ////////////// // GEOMETRY // ////////////// V_S: 150, // Volume to surface area ratio (mm) L: 1000, // Specimen Length (mm) notional_thickness_coef: 1.5, // notional thickness coefficient (CEB-FIP 78 only) ///////////////// // ENVIRONMENT // ///////////////// RH: 60, // Relative Humidity (%) T: 35, // Temperature (C; CEB-FIP90, CEB-FIP2010, EN1992, and IRC2020 only) Consider_Temperature_Adjusted_Age_of_Concrete: "No", // Options : "Yes" , "No" // For CEB-FIP90, CEB-FIP2010, // IRC112 2020 and EN1992/Eurocode 2004 includeHighStressEffect: "No", // Options: "Yes", "No" // For CEB-FIP90, CEB-FIP2010, and EN1992/Eurocode 2004 ////////////////// // CONSTRUCTION // ////////////////// t_s: 0, // age when shrinkage starts t_0: 16, // age of loading ////////// // LOAD // ////////// P: -10000000, // Applied axial load (N) Sigma: -20.833333, // Axial Compressive Stress (MPa) (P/(b*d)) //////////////////////////////////////////////// // ADDITIONAL PARAMETERS FOR MODELS B3 and B4 // //////////////////////////////////////////////// // Material c: 350, // Cement content (in kg/m^3) = 13.69 lb/ft^3 a_c: 5, // Aggregate to cement ratio w_c: 0.5, // Water to cement ratio w: 175, // Water content (kg/m^3; Model B3 only) aggregate_type: "Unknown", // Aggregate type of concrete (Model B4 only) // Choices: Diabase, Quartzite, Limestone, Sandstone, Granite, QuartzDiorite, Unknown density: 2350, // density of concrete (Model B4 only) simplifiedDesign: true, // (Model B4 only) //If designer knows admixture class composition of concrete admixtureClass_Shrinkage: "", // Admixture Class admixtureClass_Creep: "", // Geometry specimen_geometry: "infinite square prism", // "infinite slab", "infinite cylinder", "infinite square prism", "sphere", "cube" // Environment T_cur: 20, // Ambient temperature while curing (Model B4 only) curing_condition: "normalcuring", // Choices: "normalcuring", "steamcuring", "curedinwater" (Model B3 only) // Construction t_c: 16, // age when drying starts (for creep) UH_R: 4000, // activation energy of hydration where R is the gas constant (Model B4 only) US_R: 4000, // activation energy of moisture diffusion and of creep where R is the gas constant (Model B4 only) /////////////////////////////////////////// // ADDITIONAL PARAMETERS FOR AS3600-2009 // /////////////////////////////////////////// environmentVariable: 0.6, // (k4) Choices: 0.7 for arid, 0.65 for interior, 0.60 for temperate inland basicCreepCoef: 0, // 3.1.8.2 (phi_cbb) if "basicCreepCoef: 0", default values are used based on Table 3.1.8.2 basicDryingShrinkageStrain: 0.0008, //3.1.7.2 });32:T8de, CreepExample = function(t) { let material = _.clone(specimen); return [ //CEB-FIP 78 Code: {Code: "CEB-FIP 78" , "Creep Displacement": CEB_FIP_78_Eps_cc(material, t).value.toLocaleString (undefined, {minimumFractionDigits: 3}), "Note": CEB_FIP_78_Eps_cc(material, t).message}, // CEB-FIP 90 Code: {Code: "CEB-FIP 90", "Creep Displacement": CEB_FIP_90_Eps_cc(material, t).value.toLocaleString (undefined, {minimumFractionDigits: 3}), "Note": CEB_FIP_90_Eps_cc(material, t).message}, // CEB-FIP 2010 Code: {Code: "fib MC 2010", "Creep Displacement": CEB_FIP_2010_Eps_cc (material, t).value.toLocaleString (undefined, {minimumFractionDigits: 3}), "Note": CEB_FIP_2010_Eps_cc (material, t).message}, // EN1992/EuroCode 2004: {Code: "EN1992/Eurocode 2004", "Creep Displacement": EN_1992_1_1_2004_Eps_cc(material, t).value.toLocaleString (undefined, {minimumFractionDigits: 3}), "Note": EN_1992_1_1_2004_Eps_cc(material, t).message}, // AASHTO v6: {Code: "AASHTO v6", "Creep Displacement": AASHTO_v6_Eps_cc(material, t).value.toLocaleString (undefined, {minimumFractionDigits: 3}), "Note": AASHTO_v6_Eps_cc(material, t).message}, // AASHTO v7 & v8: {Code: "AASHTO v7/v8", "Creep Displacement": AASHTO_v7_v8_Eps_cc(material, t).value.toLocaleString (undefined, {minimumFractionDigits: 3}), "Note": AASHTO_v7_v8_Eps_cc(material, t).message}, // Bazant B3: {Code: "Model B3", "Creep Displacement": BAZANT_B3_Eps_cc (material, t).value.toLocaleString (undefined, {minimumFractionDigits: 3}), "Note": BAZANT_B3_Eps_cc(material, t).message}, // Bazant B4: {Code: "Model B4" , "Creep Displacement": BAZANT_B4_Eps_cc(material, t).value.toLocaleString (undefined, {minimumFractionDigits: 3}), "Note": BAZANT_B4_Eps_cc(material, t).message}, //AS3600-2009 {Code: "AS3600-2009", "Creep Displacement": AS3600_2009_Eps_cc(material, t).value.toLocaleString (undefined, {minimumFractionDigits: 3}), "Note": AS3600_2009_Eps_cc(material, t).message}, //IRC 112 2020 {Code: "IRC 112 2020", "Creep Displacement": IRC_112_2020_Eps_cc(material,t).value.toLocaleString (undefined, {minimumFractionDigits: 3}), "Note": IRC_112_2020_Eps_cc(material,t).message} ] }33:T1143,ShrinkageExampleA = function(t) { let material = _.clone(specimen); return [ {Code: "CEB-FIP 78", "Shrinkage Displacement": (CEB_FIP_78_Eps_sh (material,t,material.t_s).value-CEB_FIP_78_Eps_sh (material,1, material.t_s).value).toLocaleString (undefined, {minimumFractionDigits: 3}), "LARSA 4D Assumptions" : "t_s >0 " , " LARSA 4D Shrinkage Displacement": (CEB_FIP_78_Eps_sh(material,t,material.t_s).value-CEB_FIP_78_Eps_sh(material,1,material.t_s).value) .toLocaleString (undefined, {minimumFractionDigits: 3}), "Note": "-" }, {Code: "CEB-FIP 90 updated knowledge ", "Shrinkage Displacement": (CEB_FIP_90_upd_Eps_sh(material,t).value-CEB_FIP_90_upd_Eps_sh(material,1).value).toLocaleString (undefined, {minimumFractionDigits: 3}), "LARSA 4D Assumptions" : "- " , " LARSA 4D Shrinkage Displacement": "-", "Note": "-"}, {Code: "CEB-FIP 90 ", "Shrinkage Displacement": (CEB_FIP_90_Eps_sh(material, t, material.t_s).value-CEB_FIP_90_Eps_sh(material, 1, material.t_s).value) .toLocaleString (undefined, {minimumFractionDigits: 3}), "LARSA 4D Assumptions" : "t_s =3 " , " LARSA 4D Shrinkage Displacement": (CEB_FIP_90_Eps_sh(material, t, 3).value - CEB_FIP_90_Eps_sh(material, 1, 1).value) .toLocaleString (undefined, {minimumFractionDigits: 3}), "Note": "-" }, {Code: "fib MC 2010", "Shrinkage Displacement": (CEB_FIP_2010_Eps_sh(material,t,material.t_s).value-CEB_FIP_2010_Eps_sh(material,1,material.t_s).value).toLocaleString (undefined, {minimumFractionDigits: 3}), "LARSA 4D Assumptions" : "t_s =3 ", " LARSA 4D Shrinkage Displacement": (CEB_FIP_2010_Eps_sh(material,t,3).value - CEB_FIP_2010_Eps_sh(material,1,1).value) .toLocaleString (undefined, {minimumFractionDigits: 3}), "Note": "-" }, {Code: "EN1992/Eurocode 2004 ", "Shrinkage Displacement": (EN_1992_1_1_2004_Eps_sh(material,t,material.t_s).value - EN_1992_1_1_2004_Eps_sh(material,1,material.t_s).value) .toLocaleString (undefined, {minimumFractionDigits: 3}), "LARSA 4D Assumptions" : "t_s =14 ", " LARSA 4D Shrinkage Displacement": (EN_1992_1_1_2004_Eps_sh(material,t,14).value - EN_1992_1_1_2004_Eps_sh(material,1,1).value) .toLocaleString (undefined, {minimumFractionDigits: 3}), "Note": "-" }, {Code: "AASHTO v6 ", "Shrinkage Displacement": (AASHTO_v6_Eps_sh(material,t).value - AASHTO_v6_Eps_sh(material,1).value) .toLocaleString (undefined, {minimumFractionDigits: 3}), "LARSA 4D Assumptions" : "t_s =0 ", " LARSA 4D Shrinkage Displacement": (AASHTO_v6_Eps_sh(material,t).value - AASHTO_v6_Eps_sh(material,1).value) .toLocaleString (undefined, {minimumFractionDigits: 3}), "Note": "-" }, {Code: "AASHTO v7/v8 ", "Shrinkage Displacement": (AASHTO_v7_v8_Eps_sh(material,t).value - AASHTO_v7_v8_Eps_sh(material,1).value) .toLocaleString (undefined, {minimumFractionDigits: 5}), "LARSA 4D Assumptions" : "- ", " LARSA 4D Shrinkage Displacement": "- ", "Note": "-"}, {Code: "BAZANT B3 ", "Shrinkage Displacement": (BAZANT_B3_Eps_sh(material,t).value - BAZANT_B3_Eps_sh (material,1).value) .toLocaleString (undefined, {minimumFractionDigits: 3}), "LARSA 4D Assumptions" : "- ", " LARSA 4D Shrinkage Displacement at age of 100 days": "- ", "Note": "-" }, {Code: "BAZANT B4 ", "Shrinkage Displacement": (BAZANT_B4_Eps_sh (material,t).value - BAZANT_B4_Eps_sh (material,1).value ).toLocaleString (undefined, {minimumFractionDigits: 3}), "LARSA 4D Assumptions" : "- ", " LARSA 4D Shrinkage Displacement": "- ", "Note": BAZANT_B4_Eps_sh(material,t).message }, {Code: "AS3600-2009 ", "Shrinkage Displacement": (AS3600_2009_Eps_sh(material,t,material.t_s).value - AS3600_2009_Eps_sh(material,1,material.t_s).value ).toLocaleString (undefined, {minimumFractionDigits: 5}), "LARSA 4D Assumptions" : "t_s = 0 ", " LARSA 4D Shrinkage Displacement": (AS3600_2009_Eps_sh(material,t,0).value - AS3600_2009_Eps_sh(material,1,0).value ).toLocaleString (undefined, {minimumFractionDigits: 3}), "Note": AS3600_2009_Eps_sh(material,t,material.t_s).message }, {Code: "IRC 112 2020", "Shrinkage Displacement": (IRC_112_2020_Eps_sh (material,t,material.t_s).value - IRC_112_2020_Eps_sh (material,1,material.t_s).value ).toLocaleString (undefined, {minimumFractionDigits: 3}), "LARSA 4D Assumptions" : " - ", " LARSA 4D Shrinkage Displacement": " - ", "Note": " - " } ]; }34:T118b,ShrinkageExampleB = function(t) { let material = _.clone(specimen); return [ {Code: "CEB-FIP 78", "Shrinkage Displacement": [CEB_FIP_78_Eps_sh (material,t, material.t_s).value-CEB_FIP_78_Eps_sh(material,15, material.t_s).value] .toLocaleString (undefined, {minimumFractionDigits: 3}), "LARSA 4D Assumptions" : "t_s >0 " , " LARSA 4D Shrinkage Displacement": [CEB_FIP_78_Eps_sh(material,t, material.t_s).value-CEB_FIP_78_Eps_sh(material,15, material.t_s).value] .toLocaleString (undefined, {minimumFractionDigits: 3}), "Note": "-" }, {Code: "CEB-FIP 90 updated knowledge ", "Shrinkage Displacement": [CEB_FIP_90_upd_Eps_sh(material,t).value-CEB_FIP_90_upd_Eps_sh(material,15).value] .toLocaleString (undefined, {minimumFractionDigits: 3}), "LARSA 4D Assumptions" : "- " , " LARSA 4D Shrinkage Displacement": "-", "Note": "-"}, {Code: "CEB-FIP 90 ", "Shrinkage Displacement": [CEB_FIP_90_Eps_sh(material, t, material.t_s).value - CEB_FIP_90_Eps_sh(material, 15, material.t_s).value] .toLocaleString (undefined, {minimumFractionDigits: 3}), "LARSA 4D Assumptions" : "t_s =3 " , " LARSA 4D Shrinkage Displacement": [CEB_FIP_90_Eps_sh(material, t, 3).value - CEB_FIP_90_Eps_sh(material, 15, 3).value] .toLocaleString (undefined, {minimumFractionDigits: 3}), "Note": "-" }, {Code: "fib MC 2010", "Shrinkage Displacement": [CEB_FIP_2010_Eps_sh(material,t,material.t_s).value - CEB_FIP_2010_Eps_sh(material,15,material.t_s).value] .toLocaleString (undefined, {minimumFractionDigits: 3}), "LARSA 4D Assumptions" : "t_s =3 ", " LARSA 4D Shrinkage Displacement": [CEB_FIP_2010_Eps_sh(material,t,3).value - CEB_FIP_2010_Eps_sh(material,15,3).value].toLocaleString (undefined, {minimumFractionDigits: 3}), "Note": "-" }, {Code: "EN1992/Eurocode 2004 ", "Shrinkage Displacement": [EN_1992_1_1_2004_Eps_sh(material,t,material.t_s).value - EN_1992_1_1_2004_Eps_sh(material,15,material.t_s).value].toLocaleString (undefined, {minimumFractionDigits: 3}), "LARSA 4D Assumptions" : "t_s =14 ", " LARSA 4D Shrinkage Displacement": [EN_1992_1_1_2004_Eps_sh(material,t,14).value - EN_1992_1_1_2004_Eps_sh(material,15,14).value] .toLocaleString (undefined, {minimumFractionDigits: 3}), "Note": "-" }, {Code: "AASHTO v6 ", "Shrinkage Displacement": [AASHTO_v6_Eps_sh(material,t).value - AASHTO_v6_Eps_sh(material,15).value] .toLocaleString (undefined, {minimumFractionDigits: 3}), "LARSA 4D Assumptions" : "t_s =0 ", " LARSA 4D Shrinkage Displacement": [AASHTO_v6_Eps_sh(material,t).value - AASHTO_v6_Eps_sh(material,15).value] .toLocaleString (undefined, {minimumFractionDigits: 3}), "Note": "-" }, {Code: "AASHTO v7/v8 ", "Shrinkage Displacement": [AASHTO_v7_v8_Eps_sh(material,t).value - AASHTO_v7_v8_Eps_sh(material,15).value] .toLocaleString (undefined, {minimumFractionDigits: 3}), "LARSA 4D Assumptions" : "- ", " LARSA 4D Shrinkage Displacement": "- ", "Note": "-" }, {Code: "BAZANT B3 ", "Shrinkage Displacement": [BAZANT_B3_Eps_sh(material,t).value - BAZANT_B3_Eps_sh(material,15).value] .toLocaleString (undefined, {minimumFractionDigits: 3}), "LARSA 4D Assumptions" : "- ", " LARSA 4D Shrinkage Displacement at age of 100 days": "- ", "Note": "-" } , {Code: "BAZANT B4 ", "Shrinkage Displacement": [BAZANT_B4_Eps_sh (material,t).value - BAZANT_B4_Eps_sh (material,15).value].toLocaleString (undefined, {minimumFractionDigits: 3}) , "LARSA 4D Assumptions" : "- ", " LARSA 4D Shrinkage Displacement": "- ", "Note": BAZANT_B4_Eps_sh(material,t).message }, {Code: "AS3600-2009 ", "Shrinkage Displacement": [AS3600_2009_Eps_sh (material,t,material.t_s).value - AS3600_2009_Eps_sh (material,15,material.t_s).value].toLocaleString (undefined, {minimumFractionDigits: 3}) , "LARSA 4D Assumptions" : "t_s =0 ", " LARSA 4D Shrinkage Displacement":[AS3600_2009_Eps_sh (material,t,0).value - AS3600_2009_Eps_sh (material,15,0).value].toLocaleString (undefined, {minimumFractionDigits: 3}), "Note": AS3600_2009_Eps_sh(material,t,material.t_s).message }, {Code: "IRC 112 2020", "Shrinkage Displacement": (IRC_112_2020_Eps_sh (material,t,material.t_s).value - IRC_112_2020_Eps_sh (material,15,material.t_s).value).toLocaleString (undefined, {minimumFractionDigits: 3}), "LARSA 4D Assumptions" : " - ", " LARSA 4D Shrinkage Displacement": " - ", "Note": " - " } ]; }35:T550,CEB_FIP_78_Eps_sh = function(material,t,t_s) { let msg = ""; // holds warning messages let h = 2*material.V_S; let h_0 = (h*material.notional_thickness_coef)/10; //[e.9] let alpha = 1 // Clause e.1.5 & Clause e.1.4 (for shrinkage alpha = 1 for all cement hard type classes) let t_adj; // Clause e.1.4 & [e.8] if (material.Consider_Temperature_Adjusted_Age_of_Concrete == "Yes") t_adj = alpha / 30 * (material.T + 10) * t; else t_adj = t; let ts_adj; // Clause e.1.4 & [e.8] if (material.Consider_Temperature_Adjusted_Age_of_Concrete == "Yes") ts_adj = alpha / 30 * (material.T + 10) * t_s; else ts_adj = t_s; let Eps_s1 = (0.000775*material.RH**3 - 0.1565*material.RH**2 + 11.0325*material.RH - 303.25)*0.00001; //(D-9) let Eps_s2 = Math.exp( 0.00174 * h_0 - 0.32 / h_0 - Math.log(h_0 ** 0.251 / 1.9)); //(D-10) let Eps_s0 = Eps_s1 * Eps_s2; // taken from explanation of [e.7] let K_3 = 11.8 * h_0 + 16; //(D-8.2) let K_4 = Math.exp(-0.00257 * h_0 + 0.32 / h_0 + Math.log(0.22 * h_0 ** 0.4)); //(D-8.3) let Beta_s_t = (t_adj / (t_adj + K_3)) ** K_4; //(D-8.1) let Beta_s_t0 = (ts_adj/(ts_adj + K_3)) ** K_4; //(D-8.1) let CEB_FIP_78_Eps_sh = Eps_s0*(Beta_s_t - Beta_s_t0); //[e.7] let disp = CEB_FIP_78_Eps_sh*material.L; return {value:disp, message: msg}; }36:Tab3,CEB_FIP_78_Eps_cc = function(material, t) { let msg = ""; let dbg = "CEB FIP 78 Creep"; let h = 2*material.V_S; dbg = Utility_Add(dbg, "h", h); let h_0 = (h *material.notional_thickness_coef) / 10; // [e.9] dbg = Utility_Add(dbg, "h_0", h_0); let K_1 = Math.exp(5.02 / h_0 + Math.log(6.95 * h_0 ** 1.25)); // (D-5.2) dbg = Utility_Add(dbg, "K_1", K_1); let K_2 = Math.exp(0.00144 * h_0 - 1.1 / h_0 - Math.log(1.005 * h_0 ** 0.2954)); // (D-5.3) dbg = Utility_Add(dbg, "K_2", K_2); let alpha; // Clause e.1.5 if (material.cement_hardtype == "SL" || material.cement_hardtype == "N") alpha = 1; else if (material.cement_hardtype == "R") alpha = 2; else if (material.cement_hardtype == "RS") alpha = 3; let t_adj; // Clause e.1.3.2 & [e.8] if (material.Consider_Temperature_Adjusted_Age_of_Concrete == "Yes") t_adj = alpha / 30 * (material.T + 10) * t; else t_adj = t * alpha; dbg = Utility_Add(dbg, "t_adj", t_adj); let t0_adj; // Clause e.1.3.2 & [e.8] if (material.Consider_Temperature_Adjusted_Age_of_Concrete == "Yes") t0_adj = alpha / 30 * (material.T + 10) * material.t_0; else t0_adj = material.t_0 * alpha; dbg = Utility_Add(dbg, "t0_adj", t0_adj); let Beta_f_t = (t_adj / (t_adj + K_1)) ** K_2; // (D-5.1) dbg = Utility_Add(dbg, "Beta_f_t", Beta_f_t); let Beta_f_t0 = (t0_adj / (t0_adj + K_1)) ** K_2; // (D-5.1) dbg = Utility_Add(dbg, "Beta_f_t0", Beta_f_t0); let Beta_d = ((t_adj - t0_adj) / (t_adj - t0_adj + 328)) ** (1/4.2); //(D-4) dbg = Utility_Add(dbg, "Beta_d", Beta_d); let Beta_a = 0.8 * (1 - (t0_adj / (t0_adj + 47)) ** (1 / 2.45)); // [e.4] Beta_a = 0.0; // (LARSA 4D assumption) msg += "Beta_a is taken as 0 (LARSA 4D assumption), "; dbg = Utility_Add(dbg, "Beta_a", Beta_a); let Phi_f1 = 4.45 - 0.035 * material.RH; //(D-6) dbg = Utility_Add(dbg, "Phi_f1", Phi_f1); let Phi_f2 = Math.exp(4.4 * 0.00001 * h_0 - 0.35 / h_0 - Math.log(h_0 ** 0.1667 / 2.6)); // (D-7) dbg = Utility_Add(dbg, "Phi_f2", Phi_f2); let Phi_f = Phi_f1 * Phi_f2; // taken form expalantion of [e.4] dbg = Utility_Add(dbg, "Phi_f", Phi_f); let Phi_d = 0.4; //denotes delayed modulus of elasticity, taken form expalantion of [e.4] dbg = Utility_Add(dbg, "Phi_d", Phi_d); let Phi_t_t0 = Beta_a + Phi_d * Beta_d + Phi_f * (Beta_f_t - Beta_f_t0); // [e.4] dbg = Utility_Add(dbg, "Phi_t_t0", Phi_t_t0); let CEB_FIP_78_Eps_cc = (material.Sigma * Phi_t_t0) / material.E_cm; // [e.1] let disp = CEB_FIP_78_Eps_cc*material.L; if (-material.Sigma > 0.4*(material.f_cm-8)) msg += "Applied stress is larger than 0.4f_ck"; return ({value:disp, message:msg, debug:dbg}); }37:T79b,CEB_FIP_90_upd_Eps_sh = function(material,t) { let msg = ""; // holds the warning messages let Alpha_as; // talen from explanation of eq (3.1-16 b) if (material.cement_type == "I") Alpha_as = 700; else if (material.cement_type == "II") Alpha_as = 800; else if (material.cement_type == "III") Alpha_as = 600; else return "Undefined Cement Type"; let t_1 = 1; let f_cm_0 = 10; let RH_0 = 100; let h_0 = 100; let Beta_as = 1-Math.exp(-0.2*(t/t_1)**0.5); // eq(3.1-16 b) let Eps_caso = -Alpha_as*((material.f_cm/f_cm_0)/(6+material.f_cm/f_cm_0))**2.5 *10**-6; // eq(3.1-16 a) //Autogeneous shrinkage let Eps_cas = Eps_caso * Beta_as; // eq(3.1-15 b) let alpha_ds1; // taken from explanation of eq(3.1-17 d) if (material.cement_type == "I") alpha_ds1 = 4; else if (material.cement_type == "II") alpha_ds1 = 3; else if (material.cement_type == "III") alpha_ds1 = 6; else return "Undefined Cement Type"; let alpha_ds2; // taken from explanation of eq(3.1-17 d) if (material.cement_type == "I") alpha_ds2 = 0.11; else if (material.cement_type == "II") alpha_ds2 = 0.13; else if (material.cement_type == "III") alpha_ds2 =0.12; else return "Undefined Cement Type"; let Eps_cdso = (220+110*alpha_ds1)*Math.exp((-alpha_ds2*material.f_cm)/f_cm_0)*0.000001; // eq(3.1-17 a) let Beta_s1 = ((3.5*f_cm_0)/material.f_cm)** 0.1; // eq(3.1-17 d) let Beta_RH; // eq(3.1-17 b) if (material.RH < 99*Beta_s1) Beta_RH = -1.55*(1 -(material.RH/RH_0)**3); else Beta_RH = 0.25; let h = 2*material.V_S; let Beta_ds =((t-material.t_s)/t_1/(350*(h/h_0)**2+(t-material.t_s)/t_1))**0.5; // eq(3.1-17 c) // Drying shrinkage let Eps_cds = Eps_cdso * Beta_RH * Beta_ds; // eq(3.1-15 c) let CEB_FIP_90_upd_Eps_sh = Eps_cas + Eps_cds; // eq(3.1-15 a) let disp = CEB_FIP_90_upd_Eps_sh*material.L; return {value:disp, message: msg}; }38:T4f1,CEB_FIP_90_Eps_sh = function(material,t,t_s) { let msg = ""; // holds the warning messages if (t <= t_s) { msg += "t <= ts"; return ({value:0.0, message:msg}); } let RH_0 = 100; let f_cm_0 = 10; let Beta_sRH = 1-(material.RH /RH_0) ** 3; // eq(2.1-79) let Beta_RH; // eq(2.1-78) if (material.RH >= 40 && material.RH < 99) Beta_RH = -1.55 * Beta_sRH; else if (material.RH >= 99) Beta_RH = 0.25; else return "Undefined Relative Humidity - Beta_RH parameter"; let Beta_sc; // taken from explanation of eq(2.1-76) if (material.cement_hardtype == "SL") Beta_sc = 4; else if (material.cement_hardtype == "N" || material.cement_hardtype == "R") Beta_sc = 5; else if (material.cement_hardtype == "RS") Beta_sc = 8; else return "Undefined Cement Type - Beta_sc parameter"; let Eps_s = (160 + 10 * Beta_sc * (9 - material.f_cm / f_cm_0)) * 0.000001; // eq(2.1-76) let Eps_cso = Eps_s * Beta_RH; // eq(2.1-75) let t_1=1; let h = 2*material.V_S; let h_0 = 100; let Beta_s =((t-t_s)/t_1/(350*(h/h_0)**2+(t-t_s)/t_1))**0.5; // eq(2.1-79) let CEB_FIP_90_Eps_sh = Eps_cso * Beta_s; //eq(2.1-74) let disp = CEB_FIP_90_Eps_sh*material.L; return {value: disp, message: msg}; }39:Tb43,CEB_FIP_90_Eps_cc = function(material, t) { let msg = ""; let dbgOutput = "CEB-FIP 90 Creep:"; let t_0_adj = material.t_0; dbgOutput = Utility_Add(dbgOutput, "TempAdjTime",t_0_adj); if (material.Consider_Temperature_Adjusted_Age_of_Concrete == "Yes") t_0_adj = t_0_adj * Math.exp(13.65-(4000./(273.+material.T))); // eq(2.1-86) dbgOutput = Utility_Add(dbgOutput, "TempAdjTime",t_0_adj); let Alpha; // taken from explanation of eq(9-40) if (material.cement_hardtype =="SL") Alpha = -1; else if (material.cement_hardtype == "R" || material.cement_hardtype == "N") Alpha = 0; else if (material.cement_hardtype == "RS") Alpha = 1; else return ({value:0.0, message:"Undefined Strength Class - Alpha parameter", debug:dbgOutput}); t_0_adj = t_0_adj*((9/(2+t_0_adj**(1.2)))+1)**Alpha; // eq(2.1-72) dbgOutput = Utility_Add(dbgOutput, "t0",t_0_adj); let RH_0 =100; // taken from explanation on page 55 let f_cm_0 = 10; // taken from explanation on page 55 let h_0 = 100; // taken from explanation on page 55 let t_1= 1; // taken from explanation on page 55 let h = 2*material.V_S; let Beta_H; // eq(2.1-71) if ((150*(1+(1.2*material.RH/RH_0)** 18)*(h/h_0) +250) <= 1500) Beta_H =150*(1+(1.2*material.RH / RH_0)** 18)*(h/h_0)+250; else Beta_H = 1500; dbgOutput = Utility_Add(dbgOutput, "Beta_H", Beta_H); let Beta_c =(((t - t_0_adj)/t_1)/(Beta_H + (t-t_0_adj)/t_1))**0.3; // eq(2.1-70) dbgOutput = Utility_Add(dbgOutput, "Beta_c", Beta_c); let Beta_t0 = 1 / (0.1+(t_0_adj / t_1)**0.2); //eq (2.1-68) dbgOutput = Utility_Add(dbgOutput, "Beta_t0", Beta_t0); let Beta_fcm = 5.3/(material.f_cm/f_cm_0)**0.5; // eq(2.1-67) dbgOutput = Utility_Add(dbgOutput, "Beta_fcm", Beta_fcm); let Phi_RH =1 +(1-material.RH/RH_0)/(0.46 *(h/h_0)**(1/3)); // eq(2.1-66) dbgOutput = Utility_Add(dbgOutput, "Phi_RH", Phi_RH); let Phi_0 = Phi_RH * Beta_fcm * Beta_t0; // eq(2.1-65) dbgOutput = Utility_Add(dbgOutput, "Phi_0", Phi_0); let Phi = Phi_0 * Beta_c; // eq(2.1-64) dbgOutput = Utility_Add(dbgOutput, "Phi", Phi); //Effect of High Stress let Phi_corrected = Phi; if (material.includeHighStressEffect == "Yes") // if high stress effect is included { if (-material.Sigma<=0.4*material.f_cm) Phi_corrected = Phi; // eq(2.1-73b) else Phi_corrected = Phi*Math.exp(1.5*(-material.Sigma/material.f_cm-0.4)); // eq(2.1-73a) } dbgOutput = Utility_Add(dbgOutput, "Phi_corrected", Phi_corrected); let CEB_FIP_90_Eps_cc = (material.Sigma * Phi_corrected) / material.E_cm; // eq(2.1-61) let disp = CEB_FIP_90_Eps_cc *material.L; if (-material.Sigma> 0.6*material.f_cm) msg += "Applied stress is larger than 0.6f_cm"; return ({value:disp, message:msg, debug:dbgOutput}); }3a:Ta83,CEB_FIP_2010_Eps_sh = function(material,t,t_s) { let msg = ""; // holds the warning messages let Beta_s1; // eq(9-14) if ((35 / material.f_cm) ** 0.1 <= 1) Beta_s1 = (35 / material.f_cm) ** 0.1; else Beta_s1 = 1; let Beta_RH; // eq(9-14) if (material.RH < 99 * Beta_s1 && material.RH >= 40 * Beta_s1) Beta_RH = -1.55 * (1 - (material.RH / 100) ** 3); else if (material.RH >= 99 * Beta_s1) Beta_RH = 0.25; else return "Undefined Relative Humidity - Beta_RH parameter"; let h = 2*material.V_S; let Beta_ds =((t -t_s) /(0.035 * h ** 2 + (t -t_s))) ** 0.5; //eq(9-15) let Alpha_ds1; // Table(9-2) if (material.cement_strengthclass == "32.5N") Alpha_ds1 = 3; else if (material.cement_strengthclass == "32.5R" || material.cement_strengthclass == "42.5N") Alpha_ds1 = 4; else if (material.cement_strengthclass == "42.5R" ||material.cement_strengthclass == "52.5N" ||material.cement_strengthclass == "52.5R") Alpha_ds1 = 6; else return "Undefined Cement Type - Alpha_ds1 parameter"; let Alpha_ds2; // Table(9-2) if (material.cement_strengthclass == "32.5N") Alpha_ds2 = 0.013; else if (material.cement_strengthclass == "32.5R" || material.cement_strengthclass == "42.5N") Alpha_ds2 = 0.012; else if (material.cement_strengthclass == "42.5R" ||material.cement_strengthclass == "52.5N" ||material.cement_strengthclass == "52.5R") Alpha_ds2 = 0.012; else return "Undefined Cement Type - Alpha_ds2 parameter"; let Eps_cds0 = ((220 + 110 * Alpha_ds1) * Math.exp(-Alpha_ds2 * material.f_cm) )* 0.000001; // eq(9-13) let Eps_cds = Eps_cds0 * Beta_RH * Beta_ds; //drying shrinkage at time t. eq(9-10 c) let Alpha_bs; // Table(9-2) if (material.cement_strengthclass == "32.5N") Alpha_bs = 800; else if (material.cement_strengthclass == "32.5R" || material.cement_strengthclass == "42.5N") Alpha_bs = 700; else if (material.cement_strengthclass == "42.5R" ||material.cement_strengthclass == "52.5N" ||material.cement_strengthclass == "52.5R") Alpha_bs = 600; else return "Undefined Cement Type - Alpha_bs parameter"; if (material.cement_hardtype == "SL") Alpha_ds2 = 0.013; else if (material.cement_hardtype == "N") Alpha_ds2 = 0.012; else Alpha_ds2 = 0.012; let Eps_cbs0 = -Alpha_bs * (((material.f_cm / 10 )/ (6 + material.f_cm / 10))**2.5) * 0.000001; // eq(9-11) let Beta_bs = (1-Math.exp(-0.2*Math.sqrt(t))); // eq(9.12) let Eps_cbs = Eps_cbs0 * Beta_bs; // basic shrinkage at time t. eq(9-10 b) let CEB_FIP_2010_Eps_sh = Eps_cbs + Eps_cds; // eq(9-10 a) let disp = CEB_FIP_2010_Eps_sh*material.L; return {value: disp, message: msg}; }3b:T8bf,CEB_FIP_2010_Eps_cc =function(material, t) { let t_0_adj = material.t_0; if (material.Consider_Temperature_Adjusted_Age_of_Concrete == "Yes") { t_0_adj = material.t_0 * Math.exp(13.65-(4000./(273.+material.T))); } let Alpha; // taken from explanation of eq(9-40) if (material.cement_strengthclass =="32.5N") Alpha = -1; else if (material.cement_strengthclass == "32.5R" || material.cement_strengthclass == "42.5N") Alpha = 0; else if (material.cement_strengthclass == "42.5R" || material.cement_strengthclass == "52.5N" || material.cement_strengthclass == "52.5R") Alpha = 1; else return "Undefined Strength Class - Alpha parameter"; t_0_adj = t_0_adj*((9/(2+t_0_adj**(1.2)))+1)**Alpha; // eq(9-40) let Gamma_t0 = 1/(2.3+3.5/t_0_adj**0.5); // eq(9-37) let Beta_dc_t0 = 1/(0.1+t_0_adj**0.2); // eq(9-35) let Alpha_fcm = (35/material.f_cm)**0.5; // eq(9-39) let h = 2*material.V_S; let Beta_h; // eq(9-38) if (1.5*h+250*Alpha_fcm <= 1500*Alpha_fcm) Beta_h= 1.5*h+250*Alpha_fcm; else Beta_h= 1500*Alpha_fcm; let Beta_dc_tt0 = ((t-material.t_0)/(Beta_h+(t-material.t_0)))**Gamma_t0; // eq(9.36) let Beta_RH = (1-material.RH/100)/(0.1*h/100)**(1/3); // eq(9-34) let Beta_dc_fcm = 412/material.f_cm**1.4; // eq(9-33) let Phi_dc = Beta_dc_fcm*Beta_RH*Beta_dc_t0*Beta_dc_tt0; // eq(9-32) let Beta_bc_tt0 = Math.log((30/t_0_adj+0.035)**2*(t-material.t_0)+1); // eq(9-31) let Beta_bc_fcm = 1.8/material.f_cm**0.7; // eq(9-30) let Phi_bc = Beta_bc_tt0*Beta_bc_fcm; // eq(9-29) let Phi = Phi_bc +Phi_dc; // eq(9-28) //Effect of High Stress let Phi_corrected = Phi; if (material.includeHighStressEffect == "Yes") { if (-material.Sigma<=0.4*material.f_cm) Phi_corrected = Phi; else Phi_corrected = Phi*Math.exp(1.5*(-material.Sigma/material.f_cm-0.4)); // eq(5.1-74) } let CEB_FIP_2010_Eps_cc = Phi_corrected*material.Sigma/material.E_cm; // eq(9-20) let disp = CEB_FIP_2010_Eps_cc*material.L; let msg = ""; if (-material.Sigma> 0.6*material.f_cm) msg += "Applied stress is larger than 0.6f_cm"; return ({value:disp, message:msg}); }3c:Tdf5,EN_1992_1_1_2004_Eps_sh =function(material,t,t_s) { let msg = ""; // holds the warning messages let dbgOutput = "EN1992 2004 Shrinkage Strain:"; // holds the output of each row let h_0 = 2*material.V_S; dbgOutput = Utility_Add(dbgOutput,"h_0",h_0); let Beta_ds = (t-t_s)/((t-t_s)+0.04*Math.sqrt(h_0**3)); // eq(3.10) dbgOutput = Utility_Add(dbgOutput,"Beta_ds",Beta_ds); let k_h; // Table(3.3) if (h_0 >=100 && h_0<=200) k_h = Utility_Interpolation(100, h_0, 200, 1 ,0.85); else if (h_0 >200 && h_0<=300) k_h = Utility_Interpolation(200, h_0, 300, 0.85, 0.75); else if (h_0 >300 && h_0<=500) k_h = Utility_Interpolation(300, h_0, 500, 0.75, 0.7); else if (h_0 >= 500) k_h =0.7 else { k_h = 1; msg += " h_0 is less than 100mm. "; } dbgOutput = Utility_Add(dbgOutput,"k_h",k_h); let Alpha_ds1; // taken from explanation of eq.(B11) if (material.cement_hardtype == "SL") Alpha_ds1 = 3; else if (material.cement_hardtype == "N") Alpha_ds1 = 4; else if (material.cement_hardtype == "R" || material.cement_hardtype == "RS") Alpha_ds1 =6; else return "Undefined Cement Type - Alpha_ds1 parameter"; dbgOutput = Utility_Add(dbgOutput,"Alpha_ds1",Alpha_ds1); let Alpha_ds2; // taken from explanation of eq.(B11) if (material.cement_hardtype == "SL") Alpha_ds2 = 0.13; else if (material.cement_hardtype == "N") Alpha_ds2 = 0.12; else if (material.cement_hardtype == "R" || material.cement_hardtype == "RS") Alpha_ds2 = 0.11; else return "Undefined Cement Type - Alpha_ds2 parameter"; dbgOutput = Utility_Add(dbgOutput,"Alpha_ds2",Alpha_ds2); let RH_0 =100; let f_cm_0 =10; let Beta_RH = 1.55*(1-(material.RH/RH_0)**3); // eq(B.12) dbgOutput = Utility_Add(dbgOutput,"AlBeta_RHha_ds2",Beta_RH); let Eps_cd0 = 0.85*((220+110*Alpha_ds1)*Math.exp(-Alpha_ds2*material.f_cm/f_cm_0))*0.000001*Beta_RH; // eq(B11) dbgOutput = Utility_Add(dbgOutput,"Eps_cd0",Eps_cd0); let Eps_cd = Eps_cd0*Beta_ds*k_h; // eq(3.9) dbgOutput = Utility_Add(dbgOutput,"Eps_cd",Eps_cd); let Beta_as = (1-Math.exp(-0.2*t**0.5)); // eq(3.13) dbgOutput = Utility_Add(dbgOutput,"Beta_as",Beta_as); let f_ck= material.f_cm-8; // Table (3.1) dbgOutput = Utility_Add(dbgOutput,"f_ck",f_ck); let Eps_ca_inf = 0.0000025*(f_ck-10); // eq(3.12) dbgOutput = Utility_Add(dbgOutput,"Eps_ca_inf",Eps_ca_inf); let Eps_ca = Beta_as*Eps_ca_inf; // eq(3.11) dbgOutput = Utility_Add(dbgOutput,"Eps_ca",Eps_ca); let EN_1992_1_1_2004_Eps_sh = Eps_cd+Eps_ca; // eq(3.8) dbgOutput = Utility_Add(dbgOutput,"EN_1992_1_1_2004_Eps_sh",EN_1992_1_1_2004_Eps_sh); let disp = -EN_1992_1_1_2004_Eps_sh *material.L; dbgOutput = Utility_Add(dbgOutput,"disp",disp); let dbg = "EN1992 2004 Shrinkage" dbg = Utility_Add(dbg,"f_cm",material.f_cm); dbg = Utility_Add(dbg,"f_ck",f_ck); dbg = Utility_Add(dbg,"h_0",h_0); dbg = Utility_Add(dbg,"RH",material.RH); dbg = Utility_Add(dbg,"Alpha_ds1",Alpha_ds1); dbg = Utility_Add(dbg,"Alpha_ds2",Alpha_ds2); dbg = Utility_Add(dbg,"Beta_RH",Beta_RH); dbg = Utility_Add(dbg,"Eps_cd0",Eps_cd0); dbg = Utility_Add(dbg,"Eps_ca_inf",Eps_ca_inf); dbg = Utility_Add(dbg,"k_h",k_h); dbg = Utility_Add(dbg,"Beta_as",Beta_as); dbg = Utility_Add(dbg,"Eps_ca",Eps_ca); dbg = Utility_Add(dbg,"Beta_ds",Beta_ds); dbg = Utility_Add(dbg,"Eps_cd",Eps_cd); dbg = Utility_Add(dbg,"EN_1992_1_1_2004_Eps_sh",EN_1992_1_1_2004_Eps_sh); dbg = Utility_Add(dbg,"disp",disp); return ({value:disp, message:msg, debug:dbg}); } 3d:Tc5a,EN_1992_1_1_2004_Eps_cc = function(material, t) { let Alpha_1 = (35/material.f_cm)**0.7; // eq(B.8c) let Alpha_2 = (35/material.f_cm)**0.2; // eq(B.8c) let Alpha_3 = (35/material.f_cm)**0.5; // eq(B.8c) let h= 2*material.V_S; let Phi_RH; // eq(B.3a) & eq(B.3b) if (material.f_cm <= 35) Phi_RH = 1+(1-material.RH/100)/(0.1*h**(1/3)); else Phi_RH = (1+((1-material.RH/100)/(0.1*h**(1/3)))*Alpha_1)*Alpha_2; let Beta_fcm = 16.8/material.f_cm**0.5; // eq(B.4) let t_0 = material.t_0; if(material.Consider_Temperature_Adjusted_Age_of_Concrete == "Yes") { t_0 = (Math.exp(-(4000/(273+material.T)-13.65)))*t_0; // eq(B.10) } let Alpha; // taken from explanation of (B.9) if (material.cement_hardtype == "SL") Alpha = -1; else if (material.cement_hardtype == "N") Alpha = 0; else if (material.cement_hardtype == "R" || material.cement_hardtype == "RS") Alpha =1; else return ({value:0.0, message:"Undefined Cement Type - Alpha parameter"}); t_0 = t_0*(9/(2+t_0**1.2)+1)**Alpha; // eq(B.9) if (t_0 < 0.5) t_0 = 0.5; let Beta_t0 = 1/(0.1+t_0**0.2); // eq(B.5) let Phi_0 = Phi_RH*Beta_fcm*Beta_t0; // eq(B.2) let Beta_H; // eq(B.8a) & eq(B.8b) if (material.f_cm<=35) Beta_H= Math.min(1.5*(1+(0.012*material.RH)**18)*h+250, 1500.); else Beta_H= Math.min(1.5*(1+(0.012*material.RH)**18)*h+250*Alpha_3, 1500.*Alpha_3); let Beta_c = ((t-material.t_0)/(Beta_H+t-material.t_0))**0.3; // eq(B.7) let Phi = Phi_0*Beta_c; // eq(B.1) //Effect of High Stress let Phi_corrected = Phi; if (material.includeHighStressEffect == "Yes") { if (-material.Sigma<=0.45*material.f_cm) Phi_corrected = Phi; else Phi_corrected = Phi*Math.exp(1.5*(-material.Sigma/material.f_cm-0.45)); // eq(3.7) } let EN_1992_1_1_2004_Eps_cc = Phi_corrected*material.Sigma/material.E_cm; // eq(3.6) let disp = EN_1992_1_1_2004_Eps_cc *material.L; let msg = ""; if (-material.Sigma> 0.45*material.f_cm) msg += "Applied stress is larger than 0.45f_cm"; let dbgOutput = "EN_1992_1_1_2004 Creep" dbgOutput = Utility_Add(dbgOutput,"t_0_adjusted",t_0); dbgOutput = Utility_Add(dbgOutput,"f_cm",material.f_cm); dbgOutput = Utility_Add(dbgOutput,"h_0",h); dbgOutput = Utility_Add(dbgOutput,"RH",material.RH); dbgOutput = Utility_Add(dbgOutput,"Beta_fcm",Beta_fcm); dbgOutput = Utility_Add(dbgOutput,"Beta_t0",Beta_t0); dbgOutput = Utility_Add(dbgOutput,"Alpha_1",Alpha_1); dbgOutput = Utility_Add(dbgOutput,"Alpha_2",Alpha_2); dbgOutput = Utility_Add(dbgOutput,"Alpha_3",Alpha_3); dbgOutput = Utility_Add(dbgOutput,"Beta_H",Beta_H); dbgOutput = Utility_Add(dbgOutput,"Phi_RH",Phi_RH); dbgOutput = Utility_Add(dbgOutput,"Phi_0",Phi_0); dbgOutput = Utility_Add(dbgOutput,"Beta_c",Beta_c); dbgOutput = Utility_Add(dbgOutput,"Phi",Phi); dbgOutput = Utility_Add(dbgOutput,"EN_1992_1_1_2004_Eps_cc",EN_1992_1_1_2004_Eps_cc); dbgOutput = Utility_Add(dbgOutput,"disp",disp); return ({value:disp, message:msg, debug:dbgOutput}); }3e:T99f,//TESTS: { let tol = 1e-5; let output; // All inputs are converted to SI units let t = 100; // age of concrete let specimen = { // Geometry V_S: 150.0, // mm specimen_geometry: "infinite square prism", // Inifinite Slab L: 1000.0, // Specimen Length (mm) // Material cement_type: "I", // Type I f_cm: 40.0, // Mean Compressive Strength at 28th day (MPa) c: 350.0, // Cement content (in kg/m^3) = 13.69 lb/ft^3 w: 175.0, // Water content (in kg/m^3) = 8.23 lb/ft^3 a_c: 7, // Aggregate to cement ratio w_c: 0.6, // Water to cement ratio // Curing curing_condition: "normalcuring", // Cured in water (100% RH) // Ambient Conditions RH: 60, // Relative Humidity 100% // Age t: 100, // Age of testing t_s: 3, // age when shrinkage starts t_0: 16, // age of loading t_cons: 15, // age of construction t_c: 3, // Loading Sigma: -11.031612, // Axial Compressive Stress (MPa) E_cm: 24855.5 }; // Shrinkage let sh = BAZANT_B3_Eps_sh(specimen,t); output = "SHRINKAGE: "; output += "\nRes: " + sh.value; output += "\n\nMsg: " + sh.message; output += "\n\nDebug: " + sh.debug; // Creep let cr = BAZANT_B3_Eps_cc(specimen,t); output +=" CREEP: "; output += "\nRes: " + cr.value; output += "\n\nMsg: " + cr.message; output += "\n\nDebug: " + cr.debug; return output }3f:Tb08,//TESTS: { let tol = 1e-5; let output; // All inputs are converted to SI units let t = 112; // age of concrete let specimen = { // Geometry V_S: 19.05, // mm specimen_geometry: "infinite slab", // Inifinite Slab L: 1, // Specimen Length (mm) // Material cement_type: "I", // Type I f_cm: 27.57903, // Mean Compressive Strength at 28th day (MPa) c: 219.292764, // Cement content (in kg/m^3) = 13.69 lb/ft^3 w: 131.831954, // Water content (in kg/m^3) = 8.23 lb/ft^3 a_c: 7, // Aggregate to cement ratio w_c: 0.6, // Water to cement ratio // Curing curing_condition: "curedinwater", // Cured in water (100% RH) // Ambient Conditions RH: 100, // Relative Humidity 100% // Age t: 112, // Age of testing t_s: 28, // age when shrinkage starts t_0: 28, // age of loading t_cons: 28, // age of construction // Loading Sigma: -11.031612, // Axial Compressive Stress (MPa) E_cm: 24855.5 // Ecm 28 }; // Expected Values let shrinkage_disp_expected = 86.073e-6; // Negative Shrinkage Strain let creep_disp_expected = -212.58e-6; // total strain (creep strain + elastic strain) is given as -658e-6. when the elastic strain, -443.8e-6 (11.031612/24855.5), the creep strain becomes -212.58e-6 // Shrinkage let shrinkage_disp_current = BAZANT_B3_Eps_sh(specimen,t).value; output = "SHRINKAGE: "; output += Utility_CompareResults(shrinkage_disp_expected, shrinkage_disp_current, tol); // Creep let creep_disp_current = BAZANT_B3_Eps_cc(specimen,t).value; output +=" CREEP: "; output += Utility_CompareResults(creep_disp_expected, creep_disp_current, tol); return output }40:Tcd2,BAZANT_B3_Eps_sh = function(material,t) { let msg = ""; // holds warning messages let dbgOutput = "B3 Shrinkage Strain"; // holds output of each row for debug. if (t - material.t_s <= 0.0) return {value:0.0, message:"t <= ts", debug:" "}; let Alpha_1; // eq(1.21) if (material.cement_type == "I") Alpha_1 = 1; else if (material.cement_type == "II") Alpha_1 = 0.85; else if (material.cement_type == "III") Alpha_1 = 1.1; else return "Undefined Cement Type - Alpha_1 parameter"; dbgOutput = Utility_Add(dbgOutput, "Alpha_1", Alpha_1); let Alpha_2; // eq(1.22) if (material.curing_condition == "steamcuring") Alpha_2 = 0.75; else if (material.curing_condition == "normalcuring") Alpha_2 = 1.2; else if (material.curing_condition == "curedinwater") Alpha_2 = 1.0; else return "Undefined Curing Condition - Alpha_2 parameter"; dbgOutput = Utility_Add(dbgOutput, "Alpha_2", Alpha_2); let k_t = 8.5*material.t_s**(-0.08)*material.f_cm**(-1/4); // eq(1.20) dbgOutput = Utility_Add(dbgOutput, "k_t", k_t); let V_S = material.V_S/10; // converting units mm to cm dbgOutput = Utility_Add(dbgOutput, "V_S", V_S); let D = 2*V_S; // taken from explanation of eq(1.11) dbgOutput = Utility_Add(dbgOutput, "D", D); let k_s; // eq(1.12) if (material.specimen_geometry == "infinite slab") k_s =1.00; else if (material.specimen_geometry == "infinite cylinder") k_s=1.10; else if (material.specimen_geometry == "infinite square prism") k_s =1.25; else if (material.specimen_geometry == "sphere") k_s=1.30; else if (material.specimen_geometry == "cube") k_s=1.55; else return "Undefined specimen geometry - k_s parameter"; dbgOutput = Utility_Add(dbgOutput, "k_s", k_s); let T_sh = k_t*(k_s*D)**2; // eq(1.11) dbgOutput = Utility_Add(dbgOutput, "T_sh", T_sh); let Eps_s_inf = (-Alpha_1*Alpha_2*(1.9*10**(-2)*material.w**(2.1)*material.f_cm**(-0.28)+270))*10**(-6); // eq(1.19) dbgOutput = Utility_Add(dbgOutput, "Eps_s_inf", Eps_s_inf); let Ecm_28 = BAZANT_B3_Ecm28(material.f_cm); dbgOutput = Utility_Add(dbgOutput, "Ecm_28", Ecm_28); let E_607 = Ecm_28*(607/(4+0.85*607))**(1/2); // eq(1.13) dbgOutput = Utility_Add(dbgOutput, "E_607", E_607); let E_t_Tsh = Ecm_28*((material.t_s+T_sh)/(4+0.85*(material.t_s+T_sh)))**(1/2); // where E = E(t_0+T_sh) in eq(1.13) dbgOutput = Utility_Add(dbgOutput, "E_t_Tsh", E_t_Tsh); let Eps_sh_inf = -Eps_s_inf*E_607/E_t_Tsh; // eq(1.13) dbgOutput = Utility_Add(dbgOutput, "Eps_sh_inf", Eps_sh_inf); let k_h; // eq(1.10) if (material.RH <= 98) k_h = 1-(material.RH/100)**3; else if (material.RH == 100) k_h = -0.2; else k_h = 0.2-0.141192*(material.RH/100)/0.02; dbgOutput = Utility_Add(dbgOutput, "k_h", k_h); let S = Math.tanh(((t - material.t_s)/T_sh)**(0.5)); dbgOutput = Utility_Add(dbgOutput, "S", S); let BAZANT_B3_Eps_sh = -Eps_sh_inf*k_h*S; // eq(1.8) dbgOutput = Utility_Add(dbgOutput, "BAZANT_B3_Eps_sh", BAZANT_B3_Eps_sh); let disp = BAZANT_B3_Eps_sh*material.L; dbgOutput = Utility_Add(dbgOutput, "disp", disp); return {value:disp, message:msg, debug:dbgOutput}; } 41:T6ab,BAZANT_B3_Eps_cc = function(material, t) { let msg = ""; let dbgOutput = ""; if (t <= material.t_0) { msg += "t <= t0"; return ({value: 0.0, message: msg, debug: dbgOutput}); } let J_t_t0_str = BAZANT_B3_compliance(material,t); let J_t_t0 = J_t_t0_str.value; msg += J_t_t0_str.message; dbgOutput += J_t_t0_str.debug; let J_t0Delta_t0_str = BAZANT_B3_compliance(material,material.t_0+0.01); let J_t0Delta_t0 = J_t0Delta_t0_str.value; msg += J_t0Delta_t0_str.message; dbgOutput += J_t0Delta_t0_str.debug; let phi = (J_t_t0/J_t0Delta_t0) - 1.0; // Creep Coefficient dbgOutput = Utility_Add(dbgOutput, "J_t", J_t_t0); dbgOutput = Utility_Add(dbgOutput, "J_t0+Delta", J_t0Delta_t0); dbgOutput = Utility_Add(dbgOutput, "Creep Coef.", phi); dbgOutput = Utility_Add(dbgOutput, "Sigma", material.Sigma); dbgOutput = Utility_Add(dbgOutput, "E28", material.E_cm); let BAZANT_B3_Eps_cc = material.Sigma / material.E_cm * phi ; dbgOutput = Utility_Add(dbgOutput, "BAZANT_B3_Eps_cc", BAZANT_B3_Eps_cc); let disp = BAZANT_B3_Eps_cc*material.L dbgOutput = Utility_Add(dbgOutput, "disp", disp); if (-material.Sigma>0.45*material.f_cm) msg += " Applied stress is larger than 0.45f_cm"; let Eps_sig_c_1 = J_t_t0*material.Sigma; let Eps_sig_c_2 = material.Sigma / material.E_cm * (1.0 + phi); dbgOutput = Utility_Add(dbgOutput,"Eps_sig_c_1 (J*Sigma)",Eps_sig_c_1); dbgOutput = Utility_Add(dbgOutput,"Eps_sig_c_2 (Eps_elastic + Eps_cc)",Eps_sig_c_2); dbgOutput = Utility_Add(dbgOutput,"Eps_sig_c Error (%)", (Eps_sig_c_1-Eps_sig_c_2)/Eps_sig_c_1*100.0); return ({value:disp, message:msg, debug:dbgOutput}) ; }42:T1451,BAZANT_B3_compliance = function(material, t) { let msg=""; // holds warning messages. let dbgOutput= "B3_Creep_Strain"; // holds output of each row for debug. let a_c= material.a_c; // eq(1.1) if (material.a_c<2.5 || material.a_c >13.5) msg += " a_c is out of limit"; dbgOutput = Utility_Add(dbgOutput, "a_c", a_c); let w_c= material.w_c; // eq(1.1) if (material.w_c<0.35 || material.w_c>0.85) msg += " w_c is out of limit"; dbgOutput = Utility_Add(dbgOutput, "w_c", w_c); let c= material.c; // eq(1.2) if (material.c<160 || material.c>720) msg += " c is out of limit"; dbgOutput = Utility_Add(dbgOutput, "c", c); //Basic Creep let Q_f = (0.086*(material.t_0)**(2/9)+1.21*(material.t_0)**(4/9))**(-1); // eq(1.35) dbgOutput = Utility_Add(dbgOutput, "Q_f", Q_f); let Z = (material.t_0)**(-0.5)*(Math.log(1+(t-material.t_0)**(0.1))); // eq(1.36) dbgOutput = Utility_Add(dbgOutput, "Z", Z); let r = 1.7*(material.t_0)**(0.12)+8; // eq(1.36) dbgOutput = Utility_Add(dbgOutput, "r", r); let Q = Q_f*(1+(Q_f/Z)**r)**(-1/r); // eq(1.36) dbgOutput = Utility_Add(dbgOutput, "Q", Q); let E_c = BAZANT_B3_Ecm28(material.f_cm); dbgOutput = Utility_Add(dbgOutput, "E_c", E_c); let q_1 = 0.6*10**(6)/E_c; // eq(1.16) dbgOutput = Utility_Add(dbgOutput, "q_1", q_1); let q_2 = 185.4*c**(0.5)*material.f_cm**(-0.9); // eq(1.17) dbgOutput = Utility_Add(dbgOutput, "q_2", q_2); let q_3 = 0.29*(w_c)**4*q_2; // eq(1.18 dbgOutput = Utility_Add(dbgOutput, "q_3", q_3); let q_4 = 20.3*(a_c)**(-0.7); // eq(1.17) dbgOutput = Utility_Add(dbgOutput, "q_4", q_4); let C_0 = q_2*Q + q_3*(Math.log(1+(t-material.t_0)**(0.1)))+q_4*(Math.log(t/material.t_0)); // eq(1.7) dbgOutput = Utility_Add(dbgOutput, "C_0", C_0); // Additional drying creep let Alpha_1; // (eq1.21) if (material.cement_type == "I") Alpha_1 = 1; else if (material.cement_type == "II") Alpha_1 = 0.85; else if (material.cement_type == "III") Alpha_1 = 1.1; else return "Undefined Cement Type - Alpha_1 parameter"; dbgOutput = Utility_Add(dbgOutput, "Alpha_1", Alpha_1); let Alpha_2; // eq(1.22) if (material.curing_condition == "steamcuring") Alpha_2 = 0.75; else if (material.curing_condition == "normalcuring") Alpha_2 = 1.2; else if (material.curing_condition == "curedinwater") Alpha_2 = 1.0; else return "Undefined Curing Condition - Alpha_2 parameter"; dbgOutput = Utility_Add(dbgOutput, "Alpha_2", Alpha_2); let k_t = 8.5*material.t_c**(-0.08)*material.f_cm**(-1/4); // eq(1.20) dbgOutput = Utility_Add(dbgOutput, "k_t", k_t); let V_S = material.V_S/10; // converting units (mm to cm) dbgOutput = Utility_Add(dbgOutput, "V_S", V_S); let D = 2*V_S; // taken from explanation of eq(1.11) dbgOutput = Utility_Add(dbgOutput, "D", D); let k_s; // eq(1.12) if (material.specimen_geometry == "infinite slab") k_s =1.00; else if (material.specimen_geometry == "infinite cylinder") k_s=1.10; else if (material.specimen_geometry == "infinite square prism") k_s =1.25; else if (material.specimen_geometry == "sphere") k_s=1.30; else if (material.specimen_geometry == "cube") k_s=1.55; dbgOutput = Utility_Add(dbgOutput, "k_s", k_s); let T_sh = k_t*(k_s*D)**2; // eq(1.11) dbgOutput = Utility_Add(dbgOutput, "T_sh", T_sh); let Eps_s_inf = -Alpha_1*Alpha_2*(0.019*material.w**(2.1)*material.f_cm**(-0.28)+270)*1e-6; // eq(1.19) dbgOutput = Utility_Add(dbgOutput, "Eps_s_inf", Eps_s_inf); let Ecm_28 = BAZANT_B3_Ecm28(material.f_cm); dbgOutput = Utility_Add(dbgOutput, "Ecm_28", Ecm_28); let E_607 = Ecm_28*(607/(4+0.85*607))**(1/2); // eq(1.13) dbgOutput = Utility_Add(dbgOutput, "E_607", E_607); let E_t_Tsh = Ecm_28*((material.t_c+T_sh)/(4+0.85*(material.t_c+T_sh)))**(1/2); // where E = E(t_0+T_sh) in eq(1.13) dbgOutput = Utility_Add(dbgOutput, "E_t_Tsh", E_t_Tsh); let Eps_sh_inf = -Eps_s_inf*E_607/E_t_Tsh; // eq(1.13) dbgOutput = Utility_Add(dbgOutput, "Eps_sh_inf", Eps_sh_inf); let q_5 = 7.57*100000*material.f_cm**(-1)*(Math.abs(Eps_sh_inf*1e6))**(-0.6); // eq(1.23) dbgOutput = Utility_Add(dbgOutput, "q_5", q_5); let t__0 = Math.max(material.t_0, material.t_c); // eq(1.14) dbgOutput = Utility_Add(dbgOutput, "t__0", t__0); let S_t = Math.tanh(((t-material.t_c)/T_sh)**(0.5)); // eq(1.9) dbgOutput = Utility_Add(dbgOutput, "S_t", S_t); let S_t0 = Math.tanh(((t__0-material.t_c)/T_sh)**(0.5)); // eq(1.9) dbgOutput = Utility_Add(dbgOutput, "S_t0", S_t0); let H_t = 1-(1-material.RH/100)*S_t; // eq(1.15) dbgOutput = Utility_Add(dbgOutput, "H_t", H_t); let H_t_0 = 1-(1-material.RH/100)*S_t0; // eq(1.15) dbgOutput = Utility_Add(dbgOutput, "H_t_0", H_t_0); let C_d; // eq(1.14) if (t>t__0) C_d = q_5*(Math.exp(-8*H_t)-Math.exp(-8*H_t_0))**(0.5); else C_d = 0; dbgOutput = Utility_Add(dbgOutput, "C_d", C_d); let J = (q_1+C_0+C_d)*0.000001; // eq(1.4) dbgOutput = Utility_Add(dbgOutput, "J", J); return ({value: J, message: msg, debug:dbgOutput}); }43:T1486,//TESTS: { let tol = 1e-5; let output = "Case 1:\n\n"; // SI units let t = 112; // age of concrete let specimen = { simplifiedDesign: false, // not use simplified design formulations // Geometry V_S: 19.05, // mm specimen_geometry: "infinite slab", // Inifinite Slab L: 1, // Specimen Length (mm) // Material cement_type: "I", // Type I f_cm: 27.6, // Mean Compressive Strength at 28th day (MPa) c: 219.3, // Cement content (in kg/m^3) = 13.69 lb/ft^3 a_c: 7, // Aggregate to cement ratio w_c: 0.6, // Water to cement ratio aggregate_type: "Unknown", // Aggregate type of concrete density: 2350, // density of concrete admixtureClass_Shrinkage: "", // Admixture Class admixtureClass_Creep: "", // Ambient Conditions RH: 50, // Relative Humidity 50% T_cur: 20, // Ambient temperature while curing // Age t: 112, // Age of testing t_s: 28, // age when shrinkage starts t_c: 28, // age when drying starts (for creep) t_0: 28, // age of loading UH_R: 4000, // activation energy of hydration where R is the gas constant US_R: 4000, // activation energy of moisture diffusion and of creep where R is the gas constant // Loading Sigma: -11.03 , // Axial Compressive Stress (MPa) E_cm: 24870.4 }; // Expected Values let shrinkage_disp_expected = -4.7167e-4; let creep_disp_expected = -1870e-6 - (specimen.Sigma/specimen.E_cm); // subtract the elastic strain to get ceep only strain // Shrinkage let shrinkage_disp_current = BAZANT_B4_Eps_sh(specimen,t).value; output += "SHRINKAGE: "; output += Utility_CompareResults(shrinkage_disp_expected, shrinkage_disp_current, tol); // Creep let creep_disp_current = BAZANT_B4_Eps_cc(specimen,t).value; output +=" CREEP: "; output += Utility_CompareResults(creep_disp_expected, creep_disp_current, tol); //------------------------------------------------------------------------------------------ // Add combination of fly ash (15-30% per unit weight of cement) //------------------------------------------------------------------------------------------ output += "-------------------------\nCase 2: Add Fly Ash...\n\n"; // Change material property specimen.admixtureClass_Shrinkage = "Fly(>15%, <=30%) - Super(<=5%)"; // Fly Ash (15-30% of cement) specimen.admixtureClass_Creep = "Fly(>=15%)"; // Expected Values shrinkage_disp_expected = -455.1e-6 - 45.11e-6; creep_disp_expected = -1996e-6 - (specimen.Sigma/specimen.E_cm); // Shrinkage shrinkage_disp_current = BAZANT_B4_Eps_sh(specimen,t).value; output += "SHRINKAGE: "; output += Utility_CompareResults(shrinkage_disp_expected, shrinkage_disp_current, tol); // Creep creep_disp_current = BAZANT_B4_Eps_cc(specimen,t).value; output +=" CREEP: "; output += Utility_CompareResults(creep_disp_expected, creep_disp_current, tol); //------------------------------------------------------------------------------------------ // Only the compressive strength of the concrete is known //------------------------------------------------------------------------------------------ output += "-------------------------\nCase 3: Only the compressive strength of the concrete is known...\n\n"; // Change material property specimen.simplifiedDesign = true; // Expected Values shrinkage_disp_expected = -585.1e-6 - 53.27e-6; creep_disp_expected = -2142e-6 - (specimen.Sigma/specimen.E_cm); // Shrinkage shrinkage_disp_current = BAZANT_B4_Eps_sh(specimen,t).value; output += "SHRINKAGE: "; output += Utility_CompareResults(shrinkage_disp_expected, shrinkage_disp_current, tol); // Creep creep_disp_current = BAZANT_B4_Eps_cc(specimen,t).value; output +=" CREEP: "; output += Utility_CompareResults(creep_disp_expected, creep_disp_current, tol); return output }44:T2dc4,BAZANT_B4_Eps_sh= function(material,t) { // equations are taken from J020A_2014_MASS_BAZ let msg = "" ; // holds the warning messages let dbgOutput = "B4 Shrinkage Strain"; // holds output of each row for debug. let V_S = material.V_S; // (6) mm if (material.V_S < 12 || material.V_S > 120) msg += " V_S is out of limit"; dbgOutput = Utility_Add(dbgOutput, "V_S", V_S); let w_c = material.w_c; // (1) if (material.w_c > 0.87 || material.w_c < 0.22) msg += " w_c is out of limit"; dbgOutput = Utility_Add(dbgOutput, "w_c", w_c); let a_c = material.a_c; // (1) if (material.a_c <1 || material.a_c > 13.2) msg += " a_c is out of limit"; dbgOutput = Utility_Add(dbgOutput, "a_c", a_c); let c = material.c; // (3) if (material.c <200 || material.c > 1500) msg += " c is out of limit"; dbgOutput = Utility_Add(dbgOutput, "c", c); let fc = material.f_cm // (3) if (material.f_cm < 15 || material.f_cm > 70) msg += " f_cm is out of limit"; dbgOutput = Utility_Add(dbgOutput, "fc", fc); let T_cur = material.T_cur; // (5) if (material.T_cur<20 || material.T_cur >30) msg += " T_cur is out of limit"; dbgOutput = Utility_Add(dbgOutput, "T_cur", T_cur); let Beta_TH = Math.exp(material.UH_R*(1/293-1/(T_cur+273))); // eq(8) dbgOutput = Utility_Add(dbgOutput, "Beta_TH", Beta_TH); let Beta_TS = Math.exp(material.US_R*(1/293-1/(T_cur+273))); // eq(9) dbgOutput = Utility_Add(dbgOutput, "Beta_TS", Beta_TS); let t_s_corrected = material.t_s*Beta_TH; //eq(8) dbgOutput = Utility_Add(dbgOutput, "t_s_corrected", t_s_corrected); let t_corrected = (t-material.t_s)*Beta_TS; // eq(9) dbgOutput = Utility_Add(dbgOutput, "t_corrected", t_corrected); // Multipliers in Table 4 let multiplier = BAZANT_B4_AdmixtureModificationForShrinkage (material); dbgOutput = Utility_Add(dbgOutput, "Admixture Multiplier->T_cem", multiplier.T_cem); dbgOutput = Utility_Add(dbgOutput, "Admixture Multiplier->Eps_au", multiplier.Eps_au); dbgOutput = Utility_Add(dbgOutput, "Admixture Multiplier->r_epsw", multiplier.r_epsw); dbgOutput = Utility_Add(dbgOutput, "Admixture Multiplier->r_alpha", multiplier.r_alpha); // Drying Shrinkage // Simplified Design let T_scem; // for simplified design form Table (8) if (material.cement_type == "I" || material.cement_type == "III") T_scem = 0.027; else if (material.cement_type == "II") T_scem = 0.032; else return "Undefined Cement Type - T_scem parameter"; dbgOutput = Utility_Add(dbgOutput, "T_scem", T_scem); let s_Tf; // for simplified design form Table (8) if (material.cement_type == "I") s_Tf = 0.21; else if (material.cement_type == "III") s_Tf = 1.55; else if ( material.cement_type == "II") s_Tf = -1.84; else return "Undefined Cement Type - s_Tf parameter"; dbgOutput = Utility_Add(dbgOutput, "s_Tf", s_Tf); let Eps_scem; // for simplified design taken from Table (8) if (material.cement_type == "I") Eps_scem = 0.00059; else if (material.cement_type == "III") Eps_scem = 0.00083; else if (material.cement_type == "II") Eps_scem = 0.00064; else return "Undefined Cement Type - Eps_scem parameter"; dbgOutput = Utility_Add(dbgOutput, "Eps_scem", Eps_scem); let s_Epsf; // for simplified design taken from Table (8) if (material.cement_type == "I") s_Epsf = -0.51; else if (material.cement_type == "III") s_Epsf = -0.84; else if (material.cement_type == "II") s_Epsf = -0.69; else return "Undefined Cement Type - s_Epsf parameter"; dbgOutput = Utility_Add(dbgOutput, "s_Epsf", s_Epsf); let T_cem; // Table 1 if (material.cement_type == "I") T_cem = 0.016; else if (material.cement_type == "III") T_cem = 0.080; else if (material.cement_type == "II") T_cem = 0.010; else return "Undefined Cement Type - T_cem parameter"; dbgOutput = Utility_Add(dbgOutput, "T_cem", T_cem); // Modify based on Table 4 T_cem *= multiplier.T_cem; dbgOutput = Utility_Add(dbgOutput, "T_cem_modified", T_cem); let P_Ta = -0.33; // Table 1 let P_Tw; // Table 1 if (material.cement_type == "I") P_Tw = -0.06; else if (material.cement_type == "III") P_Tw = -2.40; else if (material.cement_type == "II") P_Tw = 3.55; else return "Undefined Cement Type - R_Tw parameter"; dbgOutput = Utility_Add(dbgOutput, "P_Tw", P_Tw); let P_Tc; // Table 1 if (material.cement_type == "I") P_Tc = -0.10; else if (material.cement_type == "III") P_Tc = -2.70; else if (material.cement_type == "II") P_Tc = 3.80; else return "Undefined Cement Type - P_Tc parameter"; dbgOutput = Utility_Add(dbgOutput, "P_Tc", P_Tc); let T_0; if (material.simplifiedDesign) T_0 = T_scem*(fc/40)**s_Tf; // eq(45) for simplified design approach else T_0 = T_cem*(a_c/6)**P_Ta*(w_c/0.38)**P_Tw*(6.5*c/material.density)**P_Tc; // eq(22) dbgOutput = Utility_Add(dbgOutput, "T_0", T_0); let D = 2 * V_S; // taken from explanation of eq(21) dbgOutput = Utility_Add(dbgOutput, "D", D); let k_s; // eq(23) if (material.specimen_geometry == "infinite slab") k_s =1.00; else if (material.specimen_geometry == "infinite cylinder") k_s=1.10; else if (material.specimen_geometry == "infinite square prism") k_s =1.25; else if (material.specimen_geometry == "sphere") k_s=1.30; else if (material.specimen_geometry == "cube") k_s=1.55; else return "Undefined Specimen Geometry - k_s parameter"; dbgOutput = Utility_Add(dbgOutput, "k_s", k_s); let k_Ta; // Table 6 if (material.aggregate_type == "Diabase") k_Ta = 0.06; else if (material.aggregate_type == "Quartzite") k_Ta = 0.59; else if (material.aggregate_type == "Limestone") k_Ta = 1.80; else if (material.aggregate_type == "Sandstone" ) k_Ta = 2.30; else if (material.aggregate_type == "Granite" ) k_Ta = 4; else if (material.aggregate_type == "QuartzDiorite" ) k_Ta = 15; else if (material.aggregate_type == "Unknown") k_Ta =1; else return "Undefined Aggregate Type - k_Ta parameter"; dbgOutput = Utility_Add(dbgOutput, "k_Ta", k_Ta); let T_sh = T_0*k_Ta*(k_s*D)**2; // eq(21) dbgOutput = Utility_Add(dbgOutput, "T_sh", T_sh); let Eps_cem; // Table 1 if (material.cement_type == "I") Eps_cem = 0.00036; else if (material.cement_type == "III") Eps_cem = 0.00086; else if (material.cement_type == "II") Eps_cem = 0.00041; else return "Undefined Cement Type - Eps_cem parameter"; dbgOutput = Utility_Add(dbgOutput, "Eps_cem", Eps_cem); let P_Epsa = -0.80; // Table 1 let P_Epsw; // Table 1 if (material.cement_type == "I") P_Epsw = 1.10; else if (material.cement_type == "III") P_Epsw = -0.27; else if (material.cement_type == "II") P_Epsw = 1.00; else return "Undefined Cement Type - P_Epsw parameter"; dbgOutput = Utility_Add(dbgOutput, "P_Epsw", P_Epsw); let P_Epsc = 0.11; // Table 1 let Eps_0; if (material.simplifiedDesign) Eps_0 = Eps_scem*(fc/40)**s_Epsf; // for simplified design approach else Eps_0 = Eps_cem*(a_c/6)**P_Epsa*(w_c/0.38)**P_Epsw*(6.5*c/material.density)**P_Epsc; // eq(16) dbgOutput = Utility_Add(dbgOutput, "Eps_0", Eps_0); let k_Epsa; // Table 6 if (material.aggregate_type == "Diabase") k_Epsa = 0.76; else if (material.aggregate_type == "Quartzite") k_Epsa = 0.71; else if (material.aggregate_type == "Limestone") k_Epsa = 0.95; else if (material.aggregate_type == "Sandstone" ) k_Epsa = 1.60; else if (material.aggregate_type == "Granite" ) k_Epsa = 1.05; else if (material.aggregate_type == "QuartzDiorite" ) k_Epsa = 2.20; else if (material.aggregate_type == "Unknown") k_Epsa = 1.00; else return "Undefined Aggregate Type - k_Epsa parameter"; dbgOutput = Utility_Add(dbgOutput, "k_Epsa", k_Epsa); let E_28 = BAZANT_B4_Ecm28(fc)*0.001; dbgOutput = Utility_Add(dbgOutput, "E_28", E_28); let E_7TH_600TS = E_28*((Beta_TH*7+Beta_TS*600)/(4+(6/7)*(Beta_TH*7+Beta_TS*600)))**0.5; // eq(19) dbgOutput = Utility_Add(dbgOutput, "E_7TH_600TS", E_7TH_600TS); let E_t_Tsh_TS = E_28*((t_s_corrected+Beta_TS*T_sh)/(4+(6/7)*(t_s_corrected+Beta_TS*T_sh)))**0.5; // eq(19) dbgOutput = Utility_Add(dbgOutput, "E_t_Tsh_TS", E_t_Tsh_TS); let Eps_sh_inf = -(Eps_0*k_Epsa*E_7TH_600TS)/E_t_Tsh_TS; // eq(17) dbgOutput = Utility_Add(dbgOutput, "Eps_sh_inf", Eps_sh_inf); let k_h; // eq(20) if (material.RH <= 98) k_h = 1- (material.RH/100)**3; else k_h = 12.94*(1-material.RH/100)-0.2; dbgOutput = Utility_Add(dbgOutput, "Eps_sh_inf", Eps_sh_inf); let S_t = Math.tanh(Math.sqrt(t_corrected/T_sh)) ; // eq(15) dbgOutput = Utility_Add(dbgOutput, "S_t", S_t); let Eps_sh = Eps_sh_inf*k_h*S_t; // eq(14) dbgOutput = Utility_Add(dbgOutput, "Eps_sh", Eps_sh); //Autogenous Shrinkage // Simplfied Design let T_aucem = 2.26; // Table (7) let r_TF = 0.27; // Table (7) let Eps_aucem = 0.0000782; // Table (7) let r_Epsf = 1.03; // Table (7) let Alpha_s = 1.73; // Table (7) let r_ts = -1.73; // Table (7) let T_au_cem; // Table 2 if (material.cement_type == "I") T_au_cem = 1.00; else if (material.cement_type == "III") T_au_cem = 41.0; else if (material.cement_type == "II") T_au_cem =1.00; else return "Undefined Cement Type - T_au_cem parameter"; dbgOutput = Utility_Add(dbgOutput, "T_au_cem", T_au_cem); let r_Tw = 3.0; // Table 2 let T_au; if (material.simplifiedDesign) T_au = T_aucem*(fc/40)**r_TF; // eq(48) Simplified Design Approach else T_au = T_au_cem*(w_c/0.38)**r_Tw; // eq(26) dbgOutput = Utility_Add(dbgOutput, "T_au", T_au); let Eps_au_cem; // Table 2 if (material.cement_type == "I") Eps_au_cem = 0.00021; else if (material.cement_type == "III") Eps_au_cem = -0.000084; else if (material.cement_type == "II") Eps_au_cem = 0; else return "Undefined Cement Type - Eps_au_cem parameter"; dbgOutput = Utility_Add(dbgOutput, "Eps_au_cem", Eps_au_cem); // Modify based on Table 4 Eps_au_cem *= multiplier.Eps_au; dbgOutput = Utility_Add(dbgOutput, "Eps_au_cem_modified", Eps_au_cem); let r_Epsa = -0.75; // Table 2 r_Epsa *= multiplier.r_alpha; // Table 4 dbgOutput = Utility_Add(dbgOutput, "r_Epsa_modified", r_Epsa); let r_Epsw = -3.5; // Table 2 r_Epsw *= multiplier.r_epsw; // Table 4 dbgOutput = Utility_Add(dbgOutput, "r_Epsw_modified", r_Epsw); let Eps_au_inf; if (material.simplifiedDesign) Eps_au_inf = -Eps_aucem*(fc/40)**r_Epsf; // eq(47) for simplified design approach else Eps_au_inf = -Eps_au_cem*(a_c/6)**r_Epsa*(w_c/0.38)**r_Epsw; // eq(25) dbgOutput = Utility_Add(dbgOutput, "Eps_au_inf", Eps_au_inf); let r_alpha; // Table 2 if (material.cement_type == "I") r_alpha = 1.00; else if (material.cement_type == "III") r_alpha = 1.40; else if (material.cement_type == "II") r_alpha =1.00; else return "Undefined Cement Type - r_alpha parameter"; dbgOutput = Utility_Add(dbgOutput, "r_alpha", r_alpha); let Alpha = r_alpha*(w_c/0.38); // eq(24) dbgOutput = Utility_Add(dbgOutput, "Alpha", Alpha); let r_t = -4.5; // Table 2 let Eps_au; if (material.simplifiedDesign) Eps_au = Eps_au_inf*(1+(T_au/(t_corrected+t_s_corrected)**Alpha_s))**r_ts; // eq (46) else Eps_au = Eps_au_inf*(1+(T_au/(t_corrected+t_s_corrected)**Alpha))**r_t; // eq(24) dbgOutput = Utility_Add(dbgOutput, "Eps_au", Eps_au); let BAZANT_B4_Eps_sh = Eps_sh + Eps_au; // eq(13) dbgOutput = Utility_Add(dbgOutput, "BAZANT_B4_Eps_sh", BAZANT_B4_Eps_sh); // Shrinkage displacement (Total Length Change) let disp = BAZANT_B4_Eps_sh*material.L; dbgOutput = Utility_Add(dbgOutput, "disp", disp); return ({value: disp, message: msg, debug: dbgOutput}); } 45:T6ee,BAZANT_B4_Eps_cc = function(material, t) { let msg = "Simplified Design:" + material.simplifiedDesign + ", "; let dbgOutput = ""; if (t <= material.t_0) { msg += "t <= t_0"; return ({value:0.0, message: msg, debug:dbgOutput}); } let J_t_t0_str = BAZANT_B4_compliance(material,t); let J_t_t0 = J_t_t0_str.value; msg += J_t_t0_str.message; dbgOutput += J_t_t0_str.debug; let J_t0Delta_t0_str = BAZANT_B4_compliance(material,material.t_0+0.001); let J_t0Delta_t0 = J_t0Delta_t0_str.value; msg += J_t0Delta_t0_str.message; dbgOutput += J_t0Delta_t0_str.debug; let phi = (J_t_t0/J_t0Delta_t0) - 1.0; // Creep Coefficient dbgOutput = Utility_Add(dbgOutput, "J_t", J_t_t0); dbgOutput = Utility_Add(dbgOutput, "J_t0+Delta", J_t0Delta_t0); dbgOutput = Utility_Add(dbgOutput, "Creep Coef.", phi); dbgOutput = Utility_Add(dbgOutput, "Sigma", material.Sigma); dbgOutput = Utility_Add(dbgOutput, "E28", material.E_cm); let BAZANT_B4_Eps_cc = material.Sigma / material.E_cm * phi ; dbgOutput = Utility_Add(dbgOutput, "BAZANT_B4_Eps_cc", BAZANT_B4_Eps_cc); let disp = BAZANT_B4_Eps_cc*material.L dbgOutput = Utility_Add(dbgOutput, "disp", disp); if (-material.Sigma>0.45*material.f_cm) msg += " Applied stress is larger than 0.45f_cm"; let Eps_sig_c_1 = J_t_t0*material.Sigma; let Eps_sig_c_2 = material.Sigma / material.E_cm * (1.0 + phi); dbgOutput = Utility_Add(dbgOutput,"Eps_sig_c_1 (J*Sigma)",Eps_sig_c_1); dbgOutput = Utility_Add(dbgOutput,"Eps_sig_c_2 (Eps_elastic + Eps_cc)",Eps_sig_c_2); dbgOutput = Utility_Add(dbgOutput,"Eps_sig_c Error (%)", (Eps_sig_c_1-Eps_sig_c_2)/Eps_sig_c_1*100.0); return ({value:disp, message:msg, debug:dbgOutput}) ; }46:T3564,BAZANT_B4_compliance = function(material,t){ let msg = ""; // holds warning messages let dbgOutput = "B4 Creep Strain"; // holds output of each row for debug. let V_S = material.V_S; // (6) if (material.V_S < 12 || material.V_S > 120) msg += " V_S is out of limit"; dbgOutput = Utility_Add(dbgOutput, "V_S", V_S); let w_c = material.w_c; // (1) if (material.w_c > 0.87 || material.w_c < 0.22) msg += " w_c is out of limit"; dbgOutput = Utility_Add(dbgOutput, "w_c", w_c); let a_c = material.a_c; // (1) if (material.a_c<1 || material.a_c >13.2) msg+= " a_c is out of limit"; dbgOutput = Utility_Add(dbgOutput, "a_c", a_c); let c = material.c; // (3) if (material.c < 200 || material.c > 1500) msg += " c is out of limit"; dbgOutput = Utility_Add(dbgOutput, "c", c); let Beta_TH = Math.exp(material.UH_R*(1/293-1/(material.T_cur+273))); // eq(8) dbgOutput = Utility_Add(dbgOutput, "Beta_TH", Beta_TH); let Beta_TS = Math.exp(material.US_R*(1/293-1/(material.T_cur+273))); // eq(9) dbgOutput = Utility_Add(dbgOutput, "Beta_TS", Beta_TS); let t_c_corrected = material.t_c*Beta_TH; //eq(8) dbgOutput = Utility_Add(dbgOutput, "t_c_corrected", t_c_corrected); let t_corrected = t*Beta_TS; // eq(9) dbgOutput = Utility_Add(dbgOutput, "t_corrected", t_corrected); let t_0_corrected = material.t_0*Beta_TH // eq(8) dbgOutput = Utility_Add(dbgOutput, "t_0_corrected", t_0_corrected); // Multipliers in Table 5 let multiplier = BAZANT_B4_AdmixtureModificationForCreep(material); dbgOutput = Utility_Add(dbgOutput, "multiplier->p2", multiplier.p2); dbgOutput = Utility_Add(dbgOutput, "multiplier->p3", multiplier.p3); dbgOutput = Utility_Add(dbgOutput, "multiplier->p4", multiplier.p4); dbgOutput = Utility_Add(dbgOutput, "multiplier->p5", multiplier.p5); let p_1; // Table(3) if (material.cement_type == "I") p_1 = 0.70; else if (material.cement_type == "III") p_1 = 0.60; else if (material.cement_type == "II") p_1 = 0.80; else return "Undefined Cement Type - p_1 parameter"; dbgOutput = Utility_Add(dbgOutput, "p_1", p_1); let p_2; // Table(3) if (material.cement_type == "I") p_2 = 0.0586; else if (material.cement_type == "III") p_2 = 0.0174; else if (material.cement_type == "II") p_2 = 0.0405; else return "Undefined Cement Type - p_2 parameter"; dbgOutput = Utility_Add(dbgOutput, "p_2", p_2); // Modify based on Table 5 p_2 *= multiplier.p2; dbgOutput = Utility_Add(dbgOutput, "p_2_modified", p_2); let p_3 = 0.0393; // Table(3) // Modify based on Table 5 p_3 *= multiplier.p3; dbgOutput = Utility_Add(dbgOutput, "p_3_modified", p_3); let p_4 = 0.0034; // Table(3) // Modify based on Table 5 p_4 *= multiplier.p4; dbgOutput = Utility_Add(dbgOutput, "p_4_modified", p_4); let p_5; // Table(3) if (material.cement_type == "I") p_5 = 0.000777 ; else if (material.cement_type == "III") p_5 = 0.0000946; else if (material.cement_type == "II") p_5 = 0.000496; else return "Undefined Cement Type - p_5 parameter"; dbgOutput = Utility_Add(dbgOutput, "p_5", p_5); // Modify based on Table 5 p_5 *= multiplier.p5; dbgOutput = Utility_Add(dbgOutput, "p_5_modified", p_5); let p_5H; // Table(3) if (material.cement_type == "I" || material.cement_type == "II") p_5H = 8.00; else if (material.cement_type == "III") p_5H = 1.00; else return "Undefined Cement Type - p_5H parameter"; dbgOutput = Utility_Add(dbgOutput, "p_5H", p_5H); let p_2w = 3; // Table(3) let p_3a = -1.10; // Table(3) let p_3w = 0.40; // Table(3) let p_4a = -0.90; // Table(3) let p_4w = 2.45; // Table(3) let p_5Eps = -0.85; // Table(3) let p_5a = -1.00; // Table(3) let p_5w = 0.78; // Table(3) // parameters used for simplified design let s_2; // Table (9) if (material.cement_type == "I") s_2 = 0.0142; else if (material.cement_type == "III") s_2 = 0.0299; else if (material.cement_type == "II") s_2 =0.0112; else return "Undefined Cement Type - s_2 parameter"; dbgOutput = Utility_Add(dbgOutput, "s_2", s_2); let s_3 = 0.976; // Table (9) let s_4 = 0.004; // Table (9) let s_5; // Table (9) if (material.cement_type == "I") s_5 = 0.00154; else if (material.cement_type == "III") s_5 = 0.0000418; else if (material.cement_type == "II") s_5 = 0.000015; else return "Undefined Cement Type - s_5 parameter"; dbgOutput = Utility_Add(dbgOutput, "s_5", s_5); let s_2f = -1.58; // Table (9) let s_3f = -1.61; // Table (9) let s_4f = -1.16; // Table (9) let s_5f = -0.45; // Table (9) // Instantaneous Compliance let E_28 = BAZANT_B4_Ecm28(material.f_cm)*0.001; // Eq.29 dbgOutput = Utility_Add(dbgOutput, "E_28", E_28); let q_1 = (p_1/E_28)*0.001; // Eq.28 dbgOutput = Utility_Add(dbgOutput, "q_1", q_1); //Basic Creep let q_2; if (material.simplifiedDesign) q_2 = (s_2*(material.f_cm/40)**s_2f)*0.001; // eq(49) else q_2 = (p_2*((w_c/0.38)**p_2w))*0.001; // eq(40) dbgOutput = Utility_Add(dbgOutput, "q_2", q_2); let q_3; if (material.simplifiedDesign) q_3 = s_3*q_2*(material.f_cm/40)**s_3f; // eq(50) else q_3 = (p_3*q_2*((a_c/6)**p_3a)*((w_c/0.38)**p_3w)); // eq(41) dbgOutput = Utility_Add(dbgOutput, "q_3", q_3); let q_4; if (material.simplifiedDesign) q_4 = (s_4*(material.f_cm/40)**s_4f)*0.001; //eq(51) else q_4 = (p_4*((a_c/6)**p_4a)*((w_c/0.38)**p_4w))*0.001; // eq(42) dbgOutput = Utility_Add(dbgOutput, "q_4", q_4); let r_t = 1.7*(t_0_corrected)**0.12+8; // eq(35) dbgOutput = Utility_Add(dbgOutput, "r_t", r_t); let Z_t = t_0_corrected**(-0.5)*Math.log(1+(t_corrected-t_0_corrected)**0.1); // eq(34) dbgOutput = Utility_Add(dbgOutput, "Z_t", Z_t); let Q_f = (0.086*t_0_corrected**(2/9)+1.21*t_0_corrected**(4/9))**(-1); // eq(33) dbgOutput = Utility_Add(dbgOutput, "Q_f", Q_f); let Q_t = Q_f*(1+(Q_f/Z_t)**r_t)**(-1/r_t); // eq(32) dbgOutput = Utility_Add(dbgOutput, "Q_t", Q_t); let C_0 = q_2*Q_t + q_3*Math.log(1+(t_corrected-t_0_corrected)**(0.1)) + q_4*Math.log(t_corrected/t_0_corrected); // eq(31) dbgOutput = Utility_Add(dbgOutput, "C_0", C_0); // Drying Creep // Multipliers in Table 4 let multiplier2 = BAZANT_B4_AdmixtureModificationForShrinkage(material); //dbgOutput = Utility_Add(dbgOutput, "multiplier2", multiplier2); let k_h; // eq(20) if (material.RH/100 <=0.98) k_h = 1- (material.RH/100)**3; else k_h = 12.94*(1-material.RH/100)-0.2; dbgOutput = Utility_Add(dbgOutput, "k_h", k_h); let T_cem; // Table 1 if (material.cement_type == "I") T_cem = 0.016; else if (material.cement_type == "III") T_cem = 0.080; else if (material.cement_type == "II") T_cem = 0.010; else return "Undefined Cement Type - T_cem parameter"; dbgOutput = Utility_Add(dbgOutput, "T_cem", T_cem); // Modify based on Table 4 T_cem *= multiplier2.T_cem; dbgOutput = Utility_Add(dbgOutput, "T_cem_modified", T_cem); let T_scem; // for simplified design form Table (8) if (material.cement_type == "I" || material.cement_type == "III") T_scem = 0.027; else if (material.cement_type == "II") T_scem = 0.032; else return "Undefined Cement Type - T_scem parameter"; dbgOutput = Utility_Add(dbgOutput, "T_scem", T_scem); let s_Tf; // for simplified design form Table (8) if (material.cement_type == "I") s_Tf = 0.21; else if (material.cement_type == "III") s_Tf = 1.55; else if ( material.cement_type == "II") s_Tf = -1.84; else return "Undefined Cement Type - s_Tf parameter"; dbgOutput = Utility_Add(dbgOutput, "s_Tf", s_Tf); let P_Ta = -0.33; // Table 1 let P_Tw; // Table 1 if (material.cement_type == "I") P_Tw = -0.06; else if (material.cement_type == "III") P_Tw = -2.40; else if (material.cement_type == "II") P_Tw = 3.55; else return "Undefined Cement Type - P_Tw parameter"; dbgOutput = Utility_Add(dbgOutput, "P_Tw", P_Tw); let P_Tc; // Table 1 if (material.cement_type == "I") P_Tc = -0.10; else if (material.cement_type == "III") P_Tc = -2.70; else if (material.cement_type == "II") P_Tc = 3.80; else return "Undefined Cement Type - P_Tc parameter"; dbgOutput = Utility_Add(dbgOutput, "P_Tc", P_Tc); let T_0; if (material.simplifiedDesign) T_0 = T_scem*(material.f_cm/40)**s_Tf; // eq(45) else T_0 = T_cem*(a_c/6)**P_Ta*(w_c/0.38)**P_Tw*(6.5*c/material.density)**P_Tc; // eq(22) dbgOutput = Utility_Add(dbgOutput, "T_0", T_0); let D = 2*V_S; // taken from explanation of eq(21) dbgOutput = Utility_Add(dbgOutput, "D", D); let k_s; // eq(23) if (material.specimen_geometry == "infinite slab") k_s =1.00; else if (material.specimen_geometry == "infinite cylinder") k_s=1.10; else if (material.specimen_geometry == "infinite square prism") k_s =1.25; else if (material.specimen_geometry == "sphere") k_s=1.30; else if (material.specimen_geometry == "cube") k_s=1.55; else return "Undefined Specimen Geometry - k_s parameter"; dbgOutput = Utility_Add(dbgOutput, "k_s", k_s); let k_Ta; // Table 6 if (material.aggregate_type == "Diabase") k_Ta = 0.06; else if (material.aggregate_type == "Quartzite") k_Ta = 0.59; else if (material.aggregate_type == "Limestone") k_Ta = 1.80; else if (material.aggregate_type == "Sandstone" ) k_Ta = 2.30; else if (material.aggregate_type == "Granite" ) k_Ta = 4; else if (material.aggregate_type == "QuartzDiorite" ) k_Ta = 15; else if (material.aggregate_type == "Unknown") k_Ta =1; else return "Undefined Aggregate Type - k_Ta parameter"; dbgOutput = Utility_Add(dbgOutput, "k_Ta", k_Ta); let T_sh = T_0*k_Ta*(k_s*D)**2; // eq(21) dbgOutput = Utility_Add(dbgOutput, "T_sh", T_sh); let Eps_scem; // for simplified design taken from Table (8) if (material.cement_type == "I") Eps_scem = 0.00059; else if (material.cement_type == "III") Eps_scem = 0.00083; else if (material.cement_type == "II") Eps_scem = 0.00064; else return "Undefined Cement Type - Eps_scem parameter"; dbgOutput = Utility_Add(dbgOutput, "Eps_scem", Eps_scem); let s_Epsf; // for simplified design taken from Table (8) if (material.cement_type == "I") s_Epsf = -0.51; else if (material.cement_type == "III") s_Epsf = -0.84; else if (material.cement_type == "II") s_Epsf = -0.69; else return "Undefined Cement Type - s_Epsf parameter"; dbgOutput = Utility_Add(dbgOutput, "s_Epsf", s_Epsf); let Eps_cem; // Table 1 if (material.cement_type == "I") Eps_cem = 0.00036; else if (material.cement_type == "III") Eps_cem = 0.00086; else if (material.cement_type == "II") Eps_cem = 0.00041; else return "Undefined Cement Type - Eps_cem parameter"; dbgOutput = Utility_Add(dbgOutput, "Eps_cem", Eps_cem); let P_Epsa = -0.80; // Table 1 let P_Epsw; // Table 1 if (material.cement_type == "I") P_Epsw = 1.10; else if (material.cement_type == "III") P_Epsw = -0.27; else if (material.cement_type == "II") P_Epsw = 1.00; else return "Undefined Cement Type - P_Epsw parameter"; dbgOutput = Utility_Add(dbgOutput, "P_Epsw", P_Epsw); let P_Epsc = 0.11; // Table 1 let Eps_0; if (material.simplifiedDesign) Eps_0 = Eps_scem*(material.f_cm/40)**s_Epsf; // eq(44) else Eps_0 = Eps_cem*(a_c/6)**P_Epsa*(w_c/0.38)**P_Epsw*(6.5*c/material.density)**P_Epsc; // eq(16) dbgOutput = Utility_Add(dbgOutput, "Eps_0", Eps_0); let k_Epsa; // Table 6 if (material.aggregate_type == "Diabase") k_Epsa = 0.76; else if (material.aggregate_type == "Quartzite") k_Epsa = 0.71; else if (material.aggregate_type == "Limestone") k_Epsa = 0.95; else if (material.aggregate_type == "Sandstone" ) k_Epsa = 1.60; else if (material.aggregate_type == "Granite" ) k_Epsa = 1.05; else if (material.aggregate_type == "QuartzDiorite" ) k_Epsa = 2.20; else if (material.aggregate_type == "Unknown") k_Epsa = 1.00; else return "Undefined Aggregate Type - k_Epsa parameter"; dbgOutput = Utility_Add(dbgOutput, "k_Epsa", k_Epsa); let E_7TH_600TS = E_28*((Beta_TH*7+Beta_TS*600)/(4+(6/7)*(Beta_TH*7+Beta_TS*600)))**0.5; // eq(19) dbgOutput = Utility_Add(dbgOutput, "E_7TH_600TS", E_7TH_600TS); let E_t_Tsh_TS = E_28*((t_c_corrected+Beta_TS*T_sh)/(4+(6/7)*(t_c_corrected+Beta_TS*T_sh)))**0.5; // eq(19) dbgOutput = Utility_Add(dbgOutput, "E_t_Tsh_TS", E_t_Tsh_TS); let Eps_sh_inf = -(Eps_0*k_Epsa*E_7TH_600TS)/E_t_Tsh_TS; // eq(17) dbgOutput = Utility_Add(dbgOutput, "Eps_sh_inf", Eps_sh_inf); let q_5; if (material.simplifiedDesign) q_5 = (s_5*(material.f_cm/40)**s_5f)*0.001*(Math.abs(k_h*Eps_sh_inf))**p_5Eps; // eq(52) else q_5 = (p_5*((a_c/6)**p_5a)*((w_c/0.38)**p_5w))*0.001*((-k_h*Eps_sh_inf)**p_5Eps); // eq(43) dbgOutput = Utility_Add(dbgOutput, "q_5", q_5); let H = 1-(1-material.RH/100)*(Math.tanh(((t_corrected-t_0_corrected)/T_sh)**0.5)); // eq(37) dbgOutput = Utility_Add(dbgOutput, "H", H); let t__0 = Math.max(t_0_corrected, t_c_corrected); dbgOutput = Utility_Add(dbgOutput, "t__0", t__0); let H_c = 1-(1-material.RH/100)*Math.tanh(((t__0-t_0_corrected)/T_sh)**0.5); // eq(38) dbgOutput = Utility_Add(dbgOutput, "H_c", H_c); let C_d; // eq(36) if (t_corrected>= t__0) C_d = q_5*(Math.exp(-p_5H*H)-Math.exp(-p_5H*H_c))**0.5; else C_d = 0; dbgOutput = Utility_Add(dbgOutput, "C_d", C_d); let J_t = (q_1+ C_0+C_d); // eq(27) dbgOutput = Utility_Add(dbgOutput, "J_t", J_t); return ({value: J_t, message: msg, debug: dbgOutput}); }47:Tc98,BAZANT_B4_AdmixtureModificationForShrinkage = function(material) // Table 4 { let multiplier = {T_cem: 1, Eps_au: 1, r_epsw: 1, r_alpha: 1}; switch (material.admixtureClass_Shrinkage) { case ("Re(<=0.5%) - Fly(<=15%)"): {multiplier = {T_cem: 6.0, Eps_au: 0.58, r_epsw: 0.5, r_alpha: 2.6}; break;} case ("Re(>0.5%, <=0.6%) - Fly(<=15%)"): {multiplier = {T_cem: 2.0, Eps_au: 0.43, r_epsw: 0.59, r_alpha: 3.1}; break;} case ("Re(>0.5%, <=0.6%) - Fly(>15%, <=30%)"): {multiplier = {T_cem: 2.1, Eps_au: 0.72, r_epsw: 0.88, r_alpha: 3.4}; break;} case ("Re(>0.5%, <=0.6%) - Fly(>30%)"): {multiplier = {T_cem: 2.8, Eps_au: 0.87, r_epsw: 1.60, r_alpha: 5.0}; break;} case ("Re(>0.6%) - Fly(<=15%)"): {multiplier = {T_cem: 2.0, Eps_au: 0.26, r_epsw: 0.22, r_alpha: 0.95}; break;} case ("Re(>0.6%) - Fly(>15%, <=30%)"): {multiplier = {T_cem: 2.1, Eps_au: 1.1, r_epsw: 1.1, r_alpha: 3.3}; break;} case ("Re(>0.6%) - Fly(>30%)"): {multiplier = {T_cem: 2.1, Eps_au: 1.1, r_epsw: 0.97, r_alpha: 4.0}; break;} case ("Fly(<=15%) - Super(<=5%)"): {multiplier = {T_cem: 0.32, Eps_au: 0.71, r_epsw: 0.55, r_alpha: 1.71}; break;} case ("Fly(<=15%) - Super(>5%)"): {multiplier = {T_cem: 0.32, Eps_au: 0.55, r_epsw: 0.92, r_alpha: 2.30}; break;} case ("Fly(>15%, <=30%) - Super(<=5%)"): {multiplier = {T_cem: 0.5, Eps_au: 0.9, r_epsw: 0.82, r_alpha: 1.25}; break;} case ("Fly(>15%, <=30%) - Super(>5%)"): {multiplier = {T_cem: 0.5, Eps_au: 0.8, r_epsw: 0.8, r_alpha: 2.81}; break;} case ("Fly(>30%) - Super(<=5%)"): {multiplier = {T_cem: 0.63, Eps_au: 1.38, r_epsw: 0.0, r_alpha: 1.2}; break;} case ("Fly(>30%) - Super(>5%)"): {multiplier = {T_cem: 0.63, Eps_au: 0.95, r_epsw: 0.76, r_alpha: 3.11}; break;} case ("Super(<=5%) - Silica(<=8%)"): {multiplier = {T_cem: 6.0, Eps_au: 2.8, r_epsw: 0.29, r_alpha: 0.21}; break;} case ("Super(<=5%) - Silica(>8%)"): {multiplier = {T_cem: 3.0, Eps_au: 0.96, r_epsw: 0.26, r_alpha: 0.71}; break;} case ("Super(>5%) - Silica(<=8%)"): {multiplier = {T_cem: 8.0, Eps_au: 1.95, r_epsw: 0.0, r_alpha: 1.0}; break;} case ("Silica(<=8%)"): {multiplier = {T_cem: 1.90, Eps_au: 0.47, r_epsw: 0.0, r_alpha: 1.20}; break;} case ("Silica(>8%, <=18%)"): {multiplier = {T_cem: 2.60, Eps_au: 0.82, r_epsw: 0.0, r_alpha: 1.20}; break;} case ("Silica(>18%)"): {multiplier = {T_cem: 1.0, Eps_au: 1.5, r_epsw: 5.0, r_alpha: 1.0}; break;} case ("AEA(<=0.05%)"): {multiplier = {T_cem: 2.3, Eps_au: 1.1, r_epsw: 0.28, r_alpha: 0.35}; break;} case ("AEA(>0.05%)"): {multiplier = {T_cem: 0.44, Eps_au: 4.28, r_epsw: 0.0, r_alpha: 0.36}; break;} case ("WR(<=2%)"): {multiplier = {T_cem: 0.5, Eps_au: 0.38, r_epsw: 0.0, r_alpha: 1.9}; break;} case ("WR(>2%, <=3%)"): {multiplier = {T_cem: 6.0, Eps_au: 0.45, r_epsw: 1.51, r_alpha: 0.3}; break;} case ("WR(>3%)"): {multiplier = {T_cem: 2.40, Eps_au: 0.4, r_epsw: 0.68, r_alpha: 1.40}; break;} } return multiplier; }48:T4db,BAZANT_B4_AdmixtureModificationForCreep = function(material) // Table 5 { let multiplier = {p2: 1, p3: 1, p4: 1, p5: 1}; // Check especially Silica & Super cases. The maximum values are taken for the cases including both of them. switch (material.admixtureClass_Creep) { case ("Re(<=0.5%) - Fly(<=15%)"): {multiplier = {p2: 0.31, p3: 7.14, p4: 1.35, p5: 0.48}; break;} case ("Re(>0.5%- Fly(<=15%)"): {multiplier = {p2: 1.43, p3: 0.58, p4: 0.9, p5: 0.46}; break;} case ("Fly(>=15%)"): {multiplier = {p2: 0.37, p3: 2.33, p4: 0.63, p5: 1.6}; break;} case ("Super(>=0%)"): {multiplier = {p2: 0.72, p3: 2.19, p4: 1.72, p5: 0.48}; break;} case ("Silica(>=0%)"): {multiplier = {p2: 1.12, p3: 3.11, p4: 0.51, p5: 0.61}; break;} case ("AEA(>=0%)"): {multiplier = {p2: 0.9, p3: 3.17, p4: 1.0, p5: 0.1}; break;} case ("WR(<=2%)"): {multiplier = {p2: 1.0, p3: 2.1, p4: 1.68, p5: 0.45}; break;} case ("WR(>2%, <=3%)"): {multiplier = {p2: 1.41, p3: 0.72, p4: 1.76, p5: 0.6}; break;} case ("WR(>3%)"): {multiplier = {p2: 1.28, p3: 2.58, p4: 0.73, p5: 1.1}; break;} } return multiplier; }49:T7ba,AS3600_2009_Eps_cc = function(material,t){ let msg = ""; // holds the warning messages let f_c = material.f_cm - 8; // characteristic compressive strength let k_4 = material.environmentVariable; let t_h = 2 * material.V_S; // notional thickness let t_0 = material.t_0; // age of loading let phi_cbb = material.basicCreepCoef; if (phi_cbb == 0) // for "basicCreepCoef: 0", default values are used based on Table 3.1.8.2 { if (f_c<20) phi_cbb = 5.2; else if (f_c<25) phi_cbb = 5.2 + ((f_c-20)*(-1))/5; else if (f_c<32) phi_cbb = 4.2 + ((f_c-25)*(-0.8))/7; else if (f_c<40) phi_cbb = 3.4 + ((f_c-32)*(-0.6))/8; else if (f_c<50) phi_cbb = 2.8 + ((f_c-40)*(-0.4))/10; else if (f_c<65) phi_cbb = 2.4 + ((f_c-50)*(-0.4))/15; else if (f_c<80) phi_cbb = 2.0 + ((f_c-65)*(-0.3))/15; else if (f_c<100) phi_cbb = 1.7 + ((f_c-80)*(-0.2))/20; else phi_cbb = 1.5; } let t_1 = t - t_0; // time after loading let alpha_2 = 1 + 1.12*Math.exp(-0.008*t_h); // Figure 3.1.8.3(A) let k_2 = (alpha_2*(t_1**0.8))/((t_1**0.8)+0.15*t_h); // Figure 3.1.8.3(A) let k_3; // Figure 3.1.8.3(B) if (t_0<=28) k_3 = 1.75 + ((t_0-7)*(1.1-1.75)/(28-7)); else if (t_0>28 && t_0<=365) k_3 = 1.1 + ((t_0-28)*(0.9-1.1)/(365-28)); else k_3 = 0.9; let alpha_3 = 0.7/(k_4*alpha_2); let k_5; // modification factor for high strength concrete if (f_c<= 50) k_5 = 1; else if (f_c <= 100) k_5 = (2-alpha_3)-0.02*(1-alpha_3)*f_c; else return({value:"-", message:"Modification factor for high strength concrete(k_5) cannot be specified for fc' greater than 100 MPa"}); // LARSA engine doesn't give an error when f_c > 100 MPa and uses k_5 formula for 50 MPa < f_c <= 100 MPa let phi_cc = k_2*k_3*k_4*k_5*phi_cbb; //eq. 3.1.8.3 let AS3600_2009_Eps_cc = phi_cc * material.Sigma / material.E_cm; let disp = AS3600_2009_Eps_cc * material.L; return ({value:disp, message:msg}); }4a:Tdf3,IRC_112_2020_Eps_sh = function(material,t,t_s){ let msg = "-"; // holds the warning messages let dbgOutput = "IRC_112_2020 Shrinkage"; let f_cm = material.f_cm; // mean compressive strength let f_ck = f_cm - 10; let RH = material.RH; // relative humidity let h_0 = 2 * material.V_S; // notional thickness, should be in mm let cement_hardtype = material.cement_hardtype; dbgOutput = Utility_Add(dbgOutput, "f_cm",f_cm); dbgOutput = Utility_Add(dbgOutput, "f_ck",f_ck); dbgOutput = Utility_Add(dbgOutput, "h_0",h_0); dbgOutput = Utility_Add(dbgOutput, "RH",RH); dbgOutput = Utility_Add(dbgOutput, "t",t); dbgOutput = Utility_Add(dbgOutput, "ts", t_s); let alpha_ds1; let alpha_ds2; switch (cement_hardtype){ case "N": {alpha_ds1 = 4; alpha_ds2 =0.12;} break; case"SL": {alpha_ds1 = 3; alpha_ds2 =0.13;} break; case "R": case "RS": {alpha_ds1 = 6; alpha_ds2 =0.11;} break; default: return msg += " Undefined Cement Hardening Type "; } dbgOutput = Utility_Add(dbgOutput, "alpha_ds1",alpha_ds1); dbgOutput = Utility_Add(dbgOutput, "alpha_ds2",alpha_ds2); let beta_RH = 1.55*(1-(RH/100)**3); dbgOutput = Utility_Add(dbgOutput, "beta_RH",beta_RH); let epsilon_cd0 = 0.85* ((220+110*alpha_ds1)*Math.exp(-alpha_ds2*(f_cm/12.5)))*10**(-6)*beta_RH; //f_cm in MPa dbgOutput = Utility_Add(dbgOutput, "epsilon_cd0",epsilon_cd0); //Table 6.6 Autogenous Shrinkage Strain of Concrete (epsilon_ca), In absence of accurate field/laboratory data, the values given in Table 6.6 may be considered. //This table could be default values, user defined input can be used.....(Idea) let epsilon_ca; if (f_ck<30) epsilon_ca = 35/(10**6); else if (f_ck < 35) epsilon_ca = Utility_Interpolation(30, f_ck, 35, 35, 45)/(10**6); else if (f_ck < 45) epsilon_ca = Utility_Interpolation(35, f_ck, 45, 45, 65)/(10**6); else if (f_ck < 50) epsilon_ca = Utility_Interpolation(45, f_ck, 50, 65, 75)/(10**6); else if (f_ck < 60) epsilon_ca = Utility_Interpolation(50, f_ck, 60, 75, 95)/(10**6); else if (f_ck < 65) epsilon_ca = Utility_Interpolation(60, f_ck, 65, 95, 105)/(10**6); else epsilon_ca = 105/(10**6); dbgOutput = Utility_Add(dbgOutput, "epsilon_ca",epsilon_ca); //Table 6.7 for k_h let k_h; if (h_0 < 100) k_h = 1; else if (h_0 < 200 ) k_h = Utility_Interpolation(100, h_0, 200, 1, 0.85); else if (h_0 < 300 ) k_h = Utility_Interpolation(200, h_0, 300, 0.85, 0.75); else if (h_0 < 500 ) k_h = Utility_Interpolation(300, h_0, 500, 0.75, 0.70); else k_h = 0.7; dbgOutput = Utility_Add(dbgOutput, "k_h",k_h); // The development of autogenous shrinkage with time: let beta_as = 1-Math.exp(-0.2*(t**(0.5))); let epsilon_ca_t = beta_as*epsilon_ca; dbgOutput = Utility_Add(dbgOutput, "beta_as",beta_as); dbgOutput = Utility_Add(dbgOutput, "epsilon_ca_t",epsilon_ca_t); //The development of the drying shrinkage strain in time: let epsilon_cd_t = 0.0; if (t-t_s > 0) { let beta_ds = (t-t_s)/((t-t_s)+0.04*((h_0**3)**0.5)); dbgOutput = Utility_Add(dbgOutput, "beta_ds",beta_ds); epsilon_cd_t = beta_ds*k_h*epsilon_cd0; } dbgOutput = Utility_Add(dbgOutput, "epsilon_cd_t",epsilon_cd_t); let IRC_112_2020_Eps_sh = epsilon_cd_t+epsilon_ca_t; dbgOutput = Utility_Add(dbgOutput,"IRC_112_2020_Eps_sh",IRC_112_2020_Eps_sh); let disp = -IRC_112_2020_Eps_sh *material.L; dbgOutput = Utility_Add(dbgOutput,"disp",disp); return ({value:disp, message:msg, debug: dbgOutput}); }4b:Td2b,IRC_112_2020_Eps_cc = function(material,t){ let msg = ""; // holds the warning messages let dbgOutput = "IRC_112_2020 Creep" let f_cm = material.f_cm; // mean compressive strength at age of 28 days !!! fcm=fck+10 in IRC !!! let h_0 = 2 * material.V_S; // notional thickness, should be in mm let t_0_adj = material.t_0; // age of loading if(material.Consider_Temperature_Adjusted_Age_of_Concrete == "Yes") { t_0_adj = (Math.exp(-(4000/(273+material.T)-13.65)))*t_0_adj; // eq(B.10) dbgOutput = Utility_Add(dbgOutput, "Temp_Adj_T0",t_0_adj); } let a; // taken from explanation of (B.9) if (material.cement_hardtype == "SL") a = -1; else if (material.cement_hardtype == "N") a = 0; else if (material.cement_hardtype == "R" || material.cement_hardtype == "RS") a =1; else return ({value:0.0, mesage:"Undefined Cement Type - Alpha parameter", debug:dbgOutput}); t_0_adj = t_0_adj*(9/(2+t_0_adj**1.2)+1)**a; // eq(B.9) if (t_0_adj < 0.5) t_0_adj = 0.5; dbgOutput = Utility_Add(dbgOutput, "t_0",t_0_adj); let RH = material.RH; // relative humidity let sigma = material.sigma; //MPa let E_cm= 35000; // Elastic Modulus at 28th day (MPa) dbgOutput = Utility_Add(dbgOutput, "f_cm",f_cm); dbgOutput = Utility_Add(dbgOutput, "h_0",h_0); dbgOutput = Utility_Add(dbgOutput, "RH",RH); let beta_f_cm = 18.78/ (f_cm**(0.5)); dbgOutput = Utility_Add(dbgOutput, "beta_f_cm",beta_f_cm); let beta_t_0 = 1/(0.1+(t_0_adj**(0.2))); dbgOutput = Utility_Add(dbgOutput, "beta_t_0",beta_t_0); let alpha_1 = (43.75/f_cm)**(0.7); dbgOutput = Utility_Add(dbgOutput, "alpha_1",alpha_1); let alpha_2 = (43.75/f_cm)**(0.2); dbgOutput = Utility_Add(dbgOutput, "alpha_2",alpha_2); let alpha_3 = (43.75/f_cm)**(0.5); // Where 45 in numerator and fcm in denominator has units of MPa dbgOutput = Utility_Add(dbgOutput, "alpha_3",alpha_3); let beta_H; if (f_cm <= 45 && 1.5 * (1 + (0.012*RH)**18) * h_0 + 250 <= 1500) { beta_H = 1.5 * (1 + (0.012*RH)**18) * h_0 + 250; //<=1500 for f_cm <= 45 MPa } else if (f_cm <= 45 && 1.5 * (1 + (0.012*RH)**18) * h_0 + 250 > 1500) beta_H =1500; else if (f_cm>45 && 1.5 * (1 + (0.012*RH)** 18) * h_0 + 250 * alpha_3<= 1500*alpha_3) { beta_H = 1.5 * (1 + (0.012*RH)** 18) * h_0 + 250 * alpha_3; //<=1500*alpha_3 for f_cm >= 45 MPa } else if (f_cm>45 && 1.5 * (1 + (0.012*RH)** 18) * h_0 + 250 * alpha_3> 1500*alpha_3) beta_H = 1500*alpha_3; dbgOutput = Utility_Add(dbgOutput, "beta_H",beta_H); let phi_RH; if (f_cm <= 45) phi_RH = 1+ ((1-RH/100)/(0.1*(h_0**(1/3)))); else phi_RH = (1+ ((1-RH/100)/(0.1*(h_0**(1/3))))*alpha_1)*alpha_2; dbgOutput = Utility_Add(dbgOutput, "phi_RH",phi_RH); let phi_0 = phi_RH*beta_f_cm*beta_t_0; dbgOutput = Utility_Add(dbgOutput, "phi_0",phi_0); let beta_c = ((t - material.t_0) / (beta_H + (t - material.t_0)))** 0.3; dbgOutput = Utility_Add(dbgOutput, "beta_c",beta_c); let phi = phi_0*beta_c; dbgOutput = Utility_Add(dbgOutput, "phi",phi); let IRC_112_2020_Eps_cc = phi* material.Sigma / material.E_cm; dbgOutput = Utility_Add(dbgOutput, "IRC_112_2020_Eps_cc",IRC_112_2020_Eps_cc); let disp = IRC_112_2020_Eps_cc * material.L; dbgOutput = Utility_Add(dbgOutput, "disp",disp); return ({value:disp, message:msg, debug:dbgOutput}); }4c:[] 2f:{"title":"Creep and Shrinkage Code Comparison","cells":[{"id":196,"value":"md`# Creep and Shrinkage Code Comparison `","pinned":false,"hidden":false,"mode":"ojs"},{"id":2734,"value":"md `In this notebook creep and shrinkage displacements calculated according to different codes for a wide column using a beam element with dimensions 1.0 m x 1.2 m x 0.4 m. (A similar verification problem is described in the LARSA 4D manual as S08: Time dependent Material Properties, in the Sample and Verification Problems - Samples for Staged Construction Analysis section.) ` ","pinned":false,"hidden":false,"mode":"ojs"},{"id":4523,"value":"$31","pinned":true,"hidden":false,"mode":"ojs"},{"id":1703,"value":"md` # Creep`","pinned":false,"hidden":false,"mode":"ojs"},{"id":4266,"value":"chart({\n xAxis: {\n title: \"Days\",\n min: 16,\n max: 120\n },\n yAxis: {\n title: \"Creep Displacement (mm)\",\n min: 0,\n max: 1.4\n },\n series: CreepExample(100).map((series,i) => {\n return { title: series.Code, points: x => -CreepExample(x)[i]['Creep Displacement'] };\n })\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":1667,"value":"viewof data = table(CreepExample(100))","pinned":false,"hidden":false,"mode":"ojs"},{"id":4274,"value":"$32","pinned":false,"hidden":false,"mode":"ojs"},{"id":2742,"value":"md` Creep displacements are calculated at the age of 100 days for an external sustained point load P which is 10,000 kN. The age when the load is applied (t₀) is chosen as 16 days.\n\nFor the Bažant and Baweja Model B3 (Model B3) and the Wendner and Bažant Model B4 (Model B4), additional parameters are used which are not used in the other code models. The age when drying begins (t_c) is considered as 15 days to calculate additional drying creep value. Models B3 and B4's additional parameters relate to concrete composition are water-cement ratio (w/c), aggregate cement ratio (a/c), water content (w), and cement content (c), and geometry of the structural element. These are assumed as w/c = 0.5, a/c = 6, w = 175 kg/m³, c = 350 kg/m³ and infinite square prism.\n\nNo effort was made to choose the additional B3 and B4 parameters to match the assumptions of the other design codes.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":5077,"value":"md `Long Term Response:`","pinned":false,"hidden":false,"mode":"ojs"},{"id":5081,"value":"chart({\n xAxis: {\n title: \"Days\",\n min: 16,\n max: 25000\n },\n yAxis: {\n title: \"Creep Displacement\",\n min: 0,\n max: 3\n },\n series: CreepExample(100).map((series,i) => {\n return { title: series.Code, points: x => -CreepExample(x)[i]['Creep Displacement'] };\n })\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":5069,"value":"viewof data3 = table(CreepExample(25000))","pinned":false,"hidden":false,"mode":"ojs"},{"id":1707,"value":"md`# Shrinkage (Case A)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":4352,"value":"$33","pinned":false,"hidden":false,"mode":"ojs"},{"id":4358,"value":"chart({\n xAxis: {\n title: \"Days\",\n min: 2,\n max: 120\n },\n yAxis: {\n title: \"Shrinkage Displacement\",\n min: 0,\n max: .5\n },\n series: ShrinkageExampleA(100).map((series,i) => {\n return { title: series.Code, points: x => -ShrinkageExampleA(x)[i]['Shrinkage Displacement'] };\n })\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":1700,"value":"viewof data1 = table(ShrinkageExampleA(100))\n","pinned":false,"hidden":false,"mode":"ojs"},{"id":2769,"value":"md` Case A is a cast-in place model in other words concrete stiffness is taken into account from the beginning at the age of 1. Shrinkage displacements in the first column (Shrinkage Displacement at 100th day) are calculated for the concrete age of 100 days by considering the same input parameters such as the shrinkage starts at the end of the first day (i.e. t_s = 1), etc. Larsa4D assumptions and Larsa4D results based on these assumptions are presented in second (Larsa4D Assumptions) and third (Larsa4D Shrinkage Displacement at 100th day) columns, respectively.` ","pinned":false,"hidden":false,"mode":"ojs"},{"id":1726,"value":"md` # Shrinkage (Case B)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":4875,"value":"$34","pinned":false,"hidden":false,"mode":"ojs"},{"id":1731,"value":"viewof data2 = table(ShrinkageExampleB(100))","pinned":false,"hidden":false,"mode":"ojs"},{"id":2709,"value":"md `Case B is a pre-cast model and the elements are constructed on the 15th day in other words concrete stiffness taken into account from the beginning of the age of 15. In this way, the shrinkage deformation at the age of 85 days for concrete is considered. Shrinkage displacements in the first column (Shrinkage Displacement at 85th day) are calculated for the concrete age of 85 days by considering the same input parameters such as the shrinkage starts at the end of the first day (i.e. t_s = 1), etc. Larsa4D assumptions and Larsa4D results based on these assumptions are presented in second (Larsa4D Assumptions) and third (Larsa4D Shrinkage Displacement at 85th day) columns, respectively.` ","pinned":false,"hidden":false,"mode":"ojs"},{"id":2699,"value":"md`For Models B3 and B4, w/c = 0.5, a/c = 5, w = 175 kg/m3, c = 350 kg/m3 and an infinite square prism is assumed.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":571,"value":"md `# CEB-FIP 78`","pinned":false,"hidden":false,"mode":"ojs"},{"id":580,"value":"tex` SHRINKAGE`","pinned":false,"hidden":false,"mode":"ojs"},{"id":600,"value":"tex `\\epsilon_{s} (t,t_0) = \\epsilon_{so} \\cdot [\\beta_s(t)-\\beta_s(t_0)]`","pinned":false,"hidden":false,"mode":"ojs"},{"id":606,"value":"tex` \\beta_s(t) = [\\frac{t}{t+K_3(h_0)}]^{K_4(h_0)} `","pinned":false,"hidden":false,"mode":"ojs"},{"id":611,"value":"tex` K_3(h_0) = 11.8h_0+16`","pinned":false,"hidden":false,"mode":"ojs"},{"id":618,"value":"tex` K_4(h_0) = e^{[-0.00257h_0+\\frac{0.32}{h_0}+ln(0.22h_0^{0.4})]} `","pinned":false,"hidden":false,"mode":"ojs"},{"id":626,"value":"tex ` \\epsilon_{so} = \\epsilon_{s1} \\cdot \\epsilon_{s2}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":629,"value":"tex` \\epsilon_{s1}= (0.000775(RH)^3-0.1565(RH)^2 +11.0325(RH)-303.25) \\cdot 10^{-5}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":632,"value":"tex`\\epsilon_{s2} = e^{[0.00174h_0-\\frac{0.32}{h_0}-ln(\\frac{h_0^{0.251}}{1.9})]}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":592,"value":"$35","pinned":false,"hidden":false,"mode":"ojs"},{"id":780,"value":"tex` CREEP `","pinned":false,"hidden":false,"mode":"ojs"},{"id":801,"value":"tex` \\epsilon_{cc}(t,t_0)=\\frac{\\sigma_0}{E{c28}} \\cdot \\phi(t,t_0)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":806,"value":"tex`\\phi(t,t_0)=\\beta_a(t_0)+\\phi_d \\cdot \\beta_d(t-t_0)+\\phi_f[\\beta_f(t)-\\beta_f(t_0)]`","pinned":false,"hidden":false,"mode":"ojs"},{"id":809,"value":"tex`\\beta_a(t_0) = 0.8 \\cdot (1-[\\frac{t_o}{t_o+47}]^{\\frac{1}{2.45}})`","pinned":false,"hidden":false,"mode":"ojs"},{"id":812,"value":"tex`\\phi_d =0.4` ","pinned":false,"hidden":false,"mode":"ojs"},{"id":822,"value":"tex`\\phi_f = \\phi_{f1} \\cdot \\phi_{f2}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":824,"value":"tex`\\phi_{f1}=4.45-0.035RH`","pinned":false,"hidden":false,"mode":"ojs"},{"id":831,"value":"tex`\\phi_{f2}=e^{[4.4*10^{-5} h_0-\\frac{0.35}{h_o}-ln(\\frac{h_o^{0.1667}}{2.6})]}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":842,"value":"tex`\\beta_d(t-t_0)=[\\frac{t-t_0}{t+328}]^{1/4.2}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":854,"value":"tex`\\beta_f(t)=[\\frac{t}{t+K_1(h_o)}]^{K_2(h_o)}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":855,"value":"tex`K_1(h_o)=e^{[\\frac{5.02}{h_o}+ln(6.95h_o^{1.25})]}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":858,"value":"tex`K_2(h_o)=e^{[0.00144h_o-\\frac{1.1}{h_o}-ln(1.005h_o^{0.2954})]}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":799,"value":"$36","pinned":true,"hidden":false,"mode":"ojs"},{"id":656,"value":"md` # CEB-FIP 90 updated knowledge `","pinned":false,"hidden":false,"mode":"ojs"},{"id":4073,"value":"md`\"CEB-FIP 90 updated knowledge\" was published by ___ on ____. This update to CEB-FIP 90 is not implemented in LARSA 4D.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":657,"value":"tex` SHRINKAGE`","pinned":false,"hidden":false,"mode":"ojs"},{"id":660,"value":"tex` \\epsilon_{cs} (t,t_s) = \\epsilon_{cas}(t)+\\epsilon_{cds}(t,t_s)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":667,"value":"tex` \\epsilon_{cas} = \\epsilon_{caso}(f_{cm}) \\cdot \\beta_{as}(t-t_s)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":668,"value":"tex` \\epsilon_{cds} (t,t_s)=\\epsilon_{cdso}(f_{cm}) \\cdot \\beta_{RH}(RH) \\cdot \\beta_{ds}(t-t_s)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":675,"value":"tex` \\epsilon_{caso}(f_{cm})= -\\alpha_{as}(\\frac{f_{cm}/f_{cmo}}{6+f_{cm}/f_{cmo}})^{2.5} \\cdot 10^{-6}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":677,"value":"tex`\\beta_{as} = 1- exp(-0.2 \\cdot (\\frac{t}{t_1})^{0.5})`","pinned":false,"hidden":false,"mode":"ojs"},{"id":680,"value":"tex` \\epsilon_{cdso}(f_{cm})= [(220+110 \\cdot \\alpha_{ds1}) \\cdot exp(-\\alpha_{ds2} \\cdot \\frac{f_{cm}}{f{cmo}})] \\cdot 10^{-6}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":690,"value":"tex` \\beta_{RH}(RH)= -1.55 \\cdot [1-(\\frac{RH}{RH_o})^3] \\text{ for } RH<0.99 \\cdot \\beta_{s1}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":701,"value":"tex` \\beta_{RH}(RH)= 0.25 \\text{ for } RH \\ge 0.99 \\cdot \\beta_{s1}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":716,"value":"tex`\\beta_{s1} = (\\frac{3.5f_{cmo}}{f_{cm}})^{0.1}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":717,"value":"tex` \\beta_{ds} (t-t_s) = [\\frac{(t-t_s)/t_1}{350(h/h_0)^2+(t-t_s)/t_1})^{0.5}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":725,"value":"$37","pinned":true,"hidden":false,"mode":"ojs"},{"id":4079,"value":"tex` CREEP`","pinned":false,"hidden":false,"mode":"ojs"},{"id":4084,"value":"md`We have not yet reviewed the CEB-FIP 90 updated knowledge creep model.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":896,"value":"md` # CEB-FIP Model Code 90 `","pinned":false,"hidden":false,"mode":"ojs"},{"id":909,"value":"tex`SHRINKAGE`","pinned":false,"hidden":false,"mode":"ojs"},{"id":919,"value":"tex`\\epsilon_{cs}(t,t_s)=\\epsilon_{cso} \\cdot \\beta_s(t-t_s)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":921,"value":"tex`\\epsilon_{cso}=\\epsilon_s(f_{cm})*\\beta_{RH}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":928,"value":"tex`\\epsilon_s(f_{cm})=[160+10\\beta_{sc}(9-f_{cm}/f_{cmo})] \\cdot 10^{-6}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":929,"value":"tex`\\beta_{RH} = -1.55\\beta_{srh} \\text{ for } 0.4 \\le RH<0.99`","pinned":false,"hidden":false,"mode":"ojs"},{"id":932,"value":"tex`\\beta_{RH} = 0.25 \\text{ for } RH\\ge0.99`","pinned":false,"hidden":false,"mode":"ojs"},{"id":940,"value":"tex`\\beta_{sRH}= 1- (\\frac{RH}{RH_o})^3`","pinned":false,"hidden":false,"mode":"ojs"},{"id":945,"value":"tex`\\beta_s(t-t_s)=[\\frac{(t-t_s)/t_1}{350(h/h_o)^2+(t-t_s)/t_1}]{0.5}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":951,"value":"$38","pinned":false,"hidden":false,"mode":"ojs"},{"id":976,"value":"tex`CREEP`","pinned":false,"hidden":false,"mode":"ojs"},{"id":989,"value":"tex`\\epsilon_{cc}(t,t_0)=\\frac{\\sigma_c(t_0)}{E_{ci}}\\phi(t,t_0)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":993,"value":"tex`\\phi(t,t_0)=\\phi_0 \\cdot \\beta_c(t-t_0) `","pinned":false,"hidden":false,"mode":"ojs"},{"id":1001,"value":"tex`\\phi_0=\\phi_{RH} \\cdot \\beta(f_{cm}) \\cdot \\beta(t_0)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1002,"value":"tex`\\phi_{RH}= 1+\\frac{1-RH/RH_o}{0.46(h/h_o)^{1/3}}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1010,"value":"tex`\\beta(f_{cm}) = \\frac{5.3}{(f_{cm}/f_{cmo})^{0.5}}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1011,"value":"tex`\\beta(t_0)=\\frac{1}{0.1+(t_0/t_1)^{0.2}}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1018,"value":"tex`\\beta_c(t-t_0)=[\\frac{(t-t_0)/t_1}{\\beta_H+(t-t_0)/t_1}]^{0.3}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1021,"value":"tex`\\beta_H = 150[1+(1.2\\frac{RH}{RH_o})^{18}]\\frac{h}{h_o}+250 \\le 1500`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1027,"value":"$39","pinned":true,"hidden":false,"mode":"ojs"},{"id":1037,"value":"md` # fib Model Code 2010 / CEB-FIP 2010`","pinned":false,"hidden":false,"mode":"ojs"},{"id":4100,"value":"md`The model below is from fib Bulletin 70. The model implemented in LARSA 4D may be from an earlier bulletin --- this page will be updated when we determine which bulletin is implemented in LARSA 4D.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1040,"value":"tex`SHRINKAGE`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1048,"value":"tex`\\epsilon_{cs}(t,t_s)=\\epsilon_{cbs}(t)+\\epsilon_{cds}(t,t_s)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1051,"value":"tex`\\epsilon_{cbs}(t)=\\epsilon_{cbso}(f_{cm}) \\cdot \\beta_{bs}(t)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1054,"value":"tex` \\epsilon_{cds}(t,t_s)=\\epsilon_{cdso}(f_{cm}) \\cdot \\beta_{RH}(RH) \\cdot \\beta_{ds}(t-t_s)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1055,"value":"tex`\\epsilon_{cbso}(f_{cm})=-\\alpha_{bs}(\\frac{f_{cm}/10}{6+f_{cm}/10})^{2.5} \\cdot 10^{-6}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1059,"value":"tex`\\beta_{ds}(t)=1-exp(-0.2\\sqrt{t})`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1064,"value":"tex`\\epsilon_{cdso}(f_{cm})=[(220+110 \\cdot \\alpha_{ds1}) \\cdot exp(-\\alpha_{ds2} \\cdot f_{cm})] \\cdot 10^{-6}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1067,"value":"tex`\\beta_{RH}=-1.55*(1-(\\frac{RH}{100})^3) \\text{ for } 40 \\le RH<99 \\cdot \\beta_{s1}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1075,"value":"tex`\\beta_{RH}=0.25 \\text{ for } RH \\ge99 \\cdot \\beta_{s1}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1078,"value":"tex`\\beta_{s1}=(\\frac{35}{f_{cm}})^{0.1}\\le1.0`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1094,"value":"$3a","pinned":true,"hidden":false,"mode":"ojs"},{"id":1124,"value":"tex`CREEP`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1127,"value":"tex`\\epsilon_{cc}(t,t_0)=\\frac{\\sigma_c(t_0)}{E_{ci}}\\phi(t,t_0)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1131,"value":"tex`\\phi(t,t_0)= \\phi_{bc}(t,t_0)+\\phi_{dc}(t,t_0)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1134,"value":"tex`\\phi_{bc}(t,t_0)=\\beta_{bc}(f_{cm}) \\cdot \\beta_{bc}(t,t_0)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1137,"value":"tex`\\beta_{bc}(f_{cm}) = \\frac{1.8}{(f_{cm}){0.7}}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1140,"value":"tex`\\beta_{bc}(t,t_0)=ln((\\frac{30}{t0,adj}+0.035)^2 \\cdot (t-t_0)+1)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1143,"value":"tex`\\phi_{dc}(t,t_0) =\\beta_{dc}(f_{cm}) \\cdot \\beta(RH) \\cdot \\beta_{dc}(t_0) \\cdot \\beta_{dc}(t,t_0)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1262,"value":"tex`\\beta_{dc}(f_{cm})=\\frac{412}{(f_{cm})^{1.4}}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1265,"value":"tex`\\beta(RH) = \\frac{1-\\frac{RH}{100}}{(0.1\\frac{h}{100})^{1/3}}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1268,"value":"tex`\\beta_{dc}(t_0)=\\frac{1}{0.1+t_{0,adj}^{0.2}}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1270,"value":"tex`\\beta_{dc}(t,t_0)=[\\frac{(t-t_0)}{*beta_h+(t-t_0)}]^{\\gamma(t_0)}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1275,"value":"tex`\\gamma(t_0)=\\frac{1}{2.3+\\frac{3.5}{\\sqrt{t_{0,adj}}}}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1278,"value":"tex`\\beta_h=1.5h+250\\alpha_{f_{cm}} \\text{ up to } 1500 \\cdot \\alpha_{f_{cm}}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1281,"value":"tex`\\alpha_{f_{cm}}=(\\frac{35}{f_{cm}})^{0.5}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1287,"value":"tex`t_{0,adj}=t_{0,T}*(\\frac{9}{2+t_{0,T}^{1.2}}+1)^{\\alpha}\\ge0.5days`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1294,"value":"$3b","pinned":false,"hidden":false,"mode":"ojs"},{"id":1326,"value":"md` # EN1992/EUROCODE 2004`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1329,"value":"tex`SHRINKAGE`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1332,"value":"tex`\\epsilon_{cs} = \\epsilon_{cd}+\\epsilon_{ca}`\n","pinned":false,"hidden":false,"mode":"ojs"},{"id":1335,"value":"tex`\\epsilon_{cd}(t)=\\beta_{ds}(t,t_s) \\cdot k_h \\cdot \\epsilon_{cd,0}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1339,"value":"tex` \\beta_{ds}(t,t_s)=\\frac{t-t_s}{(t-t_s)+0.04\\sqrt{h_0^3}}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1370,"value":"tex`\\epsilon_{cd,0}= 0.85[(220+110 \\cdot \\alpha_{ds1}) \\cdot exp(-\\alpha_{ds2}\\frac{f_{cm}}{f_{cmo}})] \\cdot 10^{-6} \\cdot \\beta_{RH}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":5921,"value":"tex` f_{cmo} = 10 \\space MPa `","pinned":false,"hidden":false,"mode":"ojs"},{"id":1374,"value":"tex`\\beta_{RH}=1.55[1-(\\frac{RH}{RH_0})^3]`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1342,"value":"tex`\\epsilon_{ca}(t)=\\beta_{as}(t) \\cdot \\epsilon_{ca}(∞)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1345,"value":"tex`\\epsilon_{ca}(∞) = 2.5(f_{ck}-10) \\cdot 10^{-6}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1348,"value":"tex` \\beta_{as}(t)=1-exp(-0.2t^{0.5})`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1363,"value":"$3c","pinned":false,"hidden":false,"mode":"ojs"},{"id":1462,"value":"tex`CREEP`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1473,"value":"tex`\\epsilon_{cc}(t,t_0) = \\phi(t,t_0) \\cdot \\frac{\\sigma_c}{E_c}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1481,"value":"tex`\\phi(t,t_0)=\\phi_0 \\cdot \\beta_c(t,t_0)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1483,"value":"tex`\\phi_0 =\\phi_{RH} \\cdot \\beta(f_{cm}) \\cdot \\beta(t_0)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1496,"value":"tex`\\phi_{RH}= 1+\\frac{1-RH/100}{0.1h_0^{1/3}} (for f_{cm} \\le 35MPa)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1487,"value":"tex`\\phi_{RH}= [1+\\frac{1-RH/100}{0.1h_0^{1/3}} \\cdot \\alpha_1] \\cdot \\alpha_2(for f_{cm}>35MPa) `","pinned":false,"hidden":false,"mode":"ojs"},{"id":1501,"value":"tex`\\beta(f_{cm})=\\frac{16.8}{\\sqrt{f_{cm}}}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1505,"value":"tex`\\beta(t_0)=\\frac{1}{0.1+t_0^{0.20}}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1516,"value":"tex`\\beta_c(t,t_0) = [\\frac{(t-t_0)}{(\\beta_H+t-t_0)}]^{0.3}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1521,"value":"tex`\\beta_H =1.5*[1+(0.012RH)^{18}]h_0+250 \\le 1500 (for f_{cm} \\le 35)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1523,"value":"tex`\\beta_H =1.5*[1+(0.012RH)^{18}]h_0+250 \\cdot \\alpha_3 \\le 1500*\\alpha_3 (for f_{cm}>35)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":5916,"value":"tex`\\alpha_1 =[\\frac{35}{f_{cm}}]^{0.7} \\space\\space\\space\\space\\space\\space \\alpha_2 =[\\frac{35}{f_{cm}}]^{0.2} \\space\\space\\space\\space\\space\\space \\alpha_3 =[\\frac{35}{f_{cm}}]^{0.5}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":5915,"value":"md `Temperature Adjusted Age of Concrete`","pinned":false,"hidden":false,"mode":"ojs"},{"id":5914,"value":"tex ` t_T = \\displaystyle\\sum_{i=1}^n \\Delta t_i \\cdot exp[13.65-\\frac{4000}{273+T_{(\\Delta t_i)}/t_0}]`","pinned":false,"hidden":false,"mode":"ojs"},{"id":5913,"value":"tex `t_0 = t_{0,T} \\cdot [\\frac{9}{2+t_{0,T} 1.2} + 1]^a \\space \\ge \\space 0.5`","pinned":false,"hidden":false,"mode":"ojs"},{"id":5912,"value":"md`Effect of High Stress`","pinned":false,"hidden":false,"mode":"ojs"},{"id":5911,"value":"tex`\\phi_k(t,t_0)= \\phi(t,t_0) \\cdot exp(1.5(k_{\\sigma}-0.45)) \\space \\space where \\space k_{\\sigma} = \\sigma_c / f_{cm}(t_0)` //Not implemented in LARSA","pinned":false,"hidden":false,"mode":"ojs"},{"id":1467,"value":"$3d","pinned":false,"hidden":false,"mode":"ojs"},{"id":0,"value":"md`# AASHTO LRFD v7/8`","pinned":false,"hidden":false,"mode":"ojs"},{"id":4108,"value":"md`The creep and shrinkage models in AASHTO LRFD v7 and v8 are identical. This model is not yet implemented in LARSA 4D.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":7,"value":"tex` SHRINKAGE`","pinned":false,"hidden":false,"mode":"ojs"},{"id":8,"value":"tex`\\epsilon_{sh}=k_s \\cdot k_{hs} \\cdot k_f \\cdot k_{td} \\cdot 0.48 \\cdot 10^-3`","pinned":false,"hidden":false,"mode":"ojs"},{"id":165,"value":"tex`k_{s} = 1.45-0.13(V/S) \\ge 1`","pinned":false,"hidden":false,"mode":"ojs"},{"id":166,"value":"tex`k_{hs} = (2.00-0.014H)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":169,"value":"tex`k_f = \\frac{5}{(1+f_ci)}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":174,"value":"tex`k_{td} = \\frac{t}{12(\\frac{100-4f'_ci}{f'_ci+20})+t}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":94,"value":"AASHTO_v7_v8_Eps_sh = function(material,t) {\n \n let msg = \"\"; // holds the warning messages\n \n let V_S = material.V_S/25.4;\n \n let k_s; // eq(5.4.2.3.2-1)\n if (1.45 - 0.13 * V_S >= 1) \n k_s = 1.45 - 0.13 * V_S;\n else \n k_s = 1;\n\n let k_hs = 2 - 0.014 * material.RH; // eq(5.4.2.3.3-2)\n \n let f_ci = 0.8*((material.f_cm-8)/6.89475908677537); // converting unit of f_ci form Mpa into ksi\n\n let k_f = 5/(1+f_ci); // eq(5.4.3.3.2-4)\n \n\n let k_td = t/(12*((100-4*0.8*f_ci)/(f_ci + 20))+t); // eq(5.4.2.3.2-5)\n\n let AASHTO_v7_v8_Eps_sh = -k_s * k_hs * k_f * k_td * 0.48 * 10 ** -3; // eq(5.4.2.3.3-1)\n\n let disp = AASHTO_v7_v8_Eps_sh*material.L;\n\n return {value: disp, message: msg};\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":117,"value":"tex` CREEP`","pinned":false,"hidden":false,"mode":"ojs"},{"id":122,"value":"tex`\\epsilon_{cc}= \\frac {\\sigma}{E_{ci}}\\phi`","pinned":false,"hidden":false,"mode":"ojs"},{"id":185,"value":"tex`\\phi=1.9 \\cdot k_s \\cdot k_{hc} \\cdot k_f \\cdot k{td} \\cdot t_i^{-0.118}` //creep coefficient","pinned":false,"hidden":false,"mode":"ojs"},{"id":191,"value":"tex`k_{hc}=1.56-0.008 \\cdot H`","pinned":false,"hidden":false,"mode":"ojs"},{"id":136,"value":"AASHTO_v7_v8_Eps_cc = function(material, t) {\n let msg = \"\";\n \n let V_S = material.V_S/25.4; // converting mm to inch\n \n let k_s; // eq(5.4.2.3.2-1)\n if (1.45-0.13*V_S >= 1)\n k_s = 1.45-0.13*V_S;\n else\n k_s = 1;\n \n let k_hc = 1.56-0.008*material.RH; // eq(5.4.2.3.2-3)\n \n let f_ci = 0.8*((material.f_cm-8)/6.89475908677537); // converting unit of f_cm form Mpa into ksi\n \n let k_f = 5/(1+f_ci); // eq(5.4.2.3.2-4)\n \n let k_td = (t-material.t_0)/(12*(100-4*f_ci)/(20+f_ci)+(t-material.t_0)); // eq(5.4.2.3.2-5)\n \n let phi = 1.9*k_s*k_hc*k_f*k_td*material.t_0**(-0.118); // eq(5.4.2.3.2-1)\n \n let AASHTO_v7_v8_Eps_cc = phi*material.Sigma/material.E_cm; \n \n let disp = AASHTO_v7_v8_Eps_cc *material.L;\n\n return ({value:disp, message:msg});\n\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":203,"value":"md`# AASHTO LRFD v6`","pinned":false,"hidden":false,"mode":"ojs"},{"id":209,"value":"tex` SHRINKAGE`","pinned":false,"hidden":false,"mode":"ojs"},{"id":215,"value":"tex`\\epsilon_{sh}=k_s \\cdot k_{hs} \\cdot k_f \\cdot k_{td} \\cdot 0.48 \\cdot 10^-3`","pinned":false,"hidden":false,"mode":"ojs"},{"id":221,"value":"tex`k_{s} = 1.45-0.13(V/S) \\ge 1`","pinned":false,"hidden":false,"mode":"ojs"},{"id":226,"value":"tex`k_{hs} = (2.00-0.014H)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":231,"value":"tex`k_f = \\frac{5}{(1+f_ci)}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":235,"value":"tex`k_{td} = \\frac{t}{61-4f'_{ci}+t}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":259,"value":"AASHTO_v6_Eps_sh = function(material,t) {\n\n let msg = \"\"; // holds the warning messages\n \n let V_S = material.V_S/25.4;\n \n let k_s; // eq(5.4.2.3.2-2)\n if (1.45-0.13*V_S >= 1) \n k_s = 1.45-0.13*V_S;\n else \n k_s = 1;\n\n let k_hs = (2-0.014*material.RH); // eq(5.4.2.3.3-1)\n \n let f_ci = 0.8*((material.f_cm-8)/6.89475908677537); // converting unit of f_ci form Mpa into ksi\n \n let k_f = (5/(1+f_ci)); // eq(5.4.2.3.2-4)\n\n let k_td= (t/(61-4*f_ci+t)); // eq(5.4.2.3.2-5)\n \n let AASHTO_v6_Eps_sh = -k_s*k_hs*k_f*k_td*0.48*10**(-3); // eq(5.4.2.3.3-1)\n \n let disp = AASHTO_v6_Eps_sh*material.L;\n\n return {value: disp, message: msg};\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":274,"value":"tex` CREEP`","pinned":false,"hidden":false,"mode":"ojs"},{"id":277,"value":"tex`\\epsilon_{cc}= \\frac {\\sigma}{E_{ci}}\\phi`","pinned":false,"hidden":false,"mode":"ojs"},{"id":279,"value":"tex`\\phi=1.9k_s \\cdot k_{hc} \\cdot k_f \\cdot k_{td} \\cdot t_i^{-0.118}` //creep coefficient","pinned":false,"hidden":false,"mode":"ojs"},{"id":281,"value":"tex`k_{hc}=1.56-0.008\\cdot H`","pinned":false,"hidden":false,"mode":"ojs"},{"id":292,"value":"AASHTO_v6_Eps_cc = function(material, t) {\n \n let msg = \"\";\n \n let V_S = material.VS/25.4; //converting mm to inch\n \n let k_s; // eq(5.4.2.3.2-2)\n if (1.45 - 0.13 * V_S >= 1) \n k_s = 1.45 - 0.13 * V_S;\n else \n k_s = 1;\n\n let k_hc = 1.56 - 0.008 * material.RH; // eq(5.4.2.3.2-3)\n \n let f_ci = 0.8*((material.f_cm-8)/6.89475908677537); // converting unit of f_ci form Mpa into ksi\n\n let k_f = 5 / (1 + f_ci); // eq(5.4.2.3.2-4)\n\n let k_td =(t - material.t_0) /(61 - 4 * f_ci + (t - material.t_0)); // eq(5.4.2.3.2-5)\n\n let phi = 1.9 * k_s * k_hc * k_f * k_td * material.t_0 ** -0.118; // eq(5.4.2.3.2-1)\n\n let AASHTO_v6_Eps_cc = (phi * material.Sigma) / material.E_cm;\n\n let disp = AASHTO_v6_Eps_cc*material.L;\n\n return ({value:disp, message:msg});\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":297,"value":"md ` # Bažant and Baweja Model B3 (Model B3)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":3116,"value":"md `This model is defined in Zdenek P. Bazant and Sandeep Baweja (1995). \"Creep and Shrinkage Prediction Model for Analysis and Design of Concrete Structures: Model B3.\" This model is not yet implemented in LARSA 4D.\n\nFor verification, the example prepared by A. Al-Manaseer and T. Monawar, Department of Civil\nEngineering and Construction, Bradley University (Zdenek P. Bazant and Sandeep Baweja, 1995) was used. The formulation on this page is compared to the values presented in the paper in the following table:\n\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":5986,"value":"$3e","pinned":false,"hidden":false,"mode":"ojs"},{"id":3091,"value":"$3f","pinned":false,"hidden":false,"mode":"ojs"},{"id":305,"value":"tex` SHRINKAGE`","pinned":false,"hidden":false,"mode":"ojs"},{"id":426,"value":"tex`\\epsilon_{sh}(t,t_0)=-\\epsilon_{sh,∞} \\cdot k_h \\cdot S(t)` // k_h is humidity dependence (1.10)","pinned":false,"hidden":false,"mode":"ojs"},{"id":435,"value":"tex`S(t) =tanh\\sqrt{\\frac{t-t_0}{T_sh}}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":439,"value":"tex` T_{sh} = k_t(k_sD)^2` // k_s is shape factor can be taken as 1 for simlified analysis (1.12)","pinned":false,"hidden":false,"mode":"ojs"},{"id":442,"value":"tex`k_t =8.5t_0^{-0.08}f_c^{-1/4}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":454,"value":"tex`\\epsilon_{sh,∞}=\\epsilon_{s,∞}\\frac{E(607)}{E(t_0+T_{sh})}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":455,"value":"tex`\\epsilon_{s,∞}=-\\alpha1 \\cdot \\alpha2 \\cdot [1.9\\cdot10^{-2}w^{2.1}f_c^{-0.28}+270]`","pinned":false,"hidden":false,"mode":"ojs"},{"id":477,"value":"$40","pinned":false,"hidden":false,"mode":"ojs"},{"id":325,"value":"tex` CREEP`","pinned":false,"hidden":false,"mode":"ojs"},{"id":428,"value":"tex`\\epsilon_{cc} =J(t,t')\\cdot sigma`","pinned":false,"hidden":false,"mode":"ojs"},{"id":330,"value":"tex`J(t,t')=q_1+C_0(t,t')+C_d(t,t',t_0)` // here C_d is additional creep due to drying, however we aimed to compute basic creep for this reason we will not consider it, the equation returns that => J = q1+C0.","pinned":false,"hidden":false,"mode":"ojs"},{"id":320,"value":"tex`C_0(t,t')=q_2Q(t,t')+q_3 \\cdot ln[1+(t-t')^n]+q_4 \\cdot ln(\\frac{t}{t'})` //the total basic creep compliance obtained by integrating its time rate","pinned":false,"hidden":false,"mode":"ojs"},{"id":1610,"value":"tex`C_d(t,t',t_0) =q_5[exp(-8H(t))-exp(-8H(t_0'))]^{1/2}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1614,"value":"tex`H(t)=1-(1-h)S(t)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":338,"value":"tex`q_1= 0.6 \\cdot 10^6/E_{28} ` // for SI Unit system","pinned":false,"hidden":false,"mode":"ojs"},{"id":344,"value":"tex`q_2 = 185.4c^{0.5}f_c^{-0.9}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":348,"value":"tex`q_3=0.29(w/c)^4q_2 `","pinned":false,"hidden":false,"mode":"ojs"},{"id":351,"value":"tex`q_4= 20.3(a/c)^{-0.7}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1605,"value":"tex ` q_5= 7.57 \\cdot 10^5f_{cm}^{-1}|Eps_{sh,infinity}|^{-0.6}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":354,"value":"tex` Q(t,t')=Q_f(t')[1+(\\frac{Q_f(t')}{Z(t,t')})^{r(t')}]^{-1/r(t2)}` // it can be also obtained by numerical interpolation by using table 1.1.","pinned":false,"hidden":false,"mode":"ojs"},{"id":370,"value":"tex` where`","pinned":false,"hidden":false,"mode":"ojs"},{"id":358,"value":"tex`r(t') =1.7 \\cdot (t')^{0.12}+8`","pinned":false,"hidden":false,"mode":"ojs"},{"id":359,"value":"tex`Z(t,t')=(t')^{-m}ln[1+(t-t')^n]` // where m=0.5 and n=0.1","pinned":false,"hidden":false,"mode":"ojs"},{"id":365,"value":"tex`Q_f(t')=[0.086(t')^{2/9}+1.21(t')^{4/9}]^{-1}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":388,"value":"$41","pinned":false,"hidden":false,"mode":"ojs"},{"id":6037,"value":"$42","pinned":false,"hidden":false,"mode":"ojs"},{"id":3186,"value":"tex `Bazant B3 Ecm28: eq(1.16)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":3180,"value":"BAZANT_B3_Ecm28 = function(f_cm_28) { return 4734 * f_cm_28**0.5;}","pinned":false,"hidden":false,"mode":"ojs"},{"id":2103,"value":"md `# Wendner and Bažant Model B4 (Model B4)`\n","pinned":false,"hidden":false,"mode":"ojs"},{"id":3270,"value":"md `This model is not yet implemented in LARSA 4D.\n\nThe verification that follows is based on RILEM draft recommendation: TC-242-MDC multi-decade creep and shrinkage of concrete: material model and structural analysis*. Mater Struct 48, 753–770 (2015). https://doi.org/10.1617/s11527-014-0485-2 We believe the discrepancies between the formulation implemented on this page and the reference values are due to a computation error in the reference document, but we are still investigating.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":3272,"value":"$43","pinned":false,"hidden":false,"mode":"ojs"},{"id":2106,"value":"tex` Shrinkage`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2120,"value":"tex`t_{0,corrected}=t_0 \\cdot \\beta_{TH}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2124,"value":"tex`t_{corrected}= (t-t_0) \\cdot \\beta_{TS}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2182,"value":"tex`\\beta_{TH}=exp[\\frac{U_h}{R}(\\frac{1}{293}-\\frac{1}{T_{cur}+273})]`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2185,"value":"tex`\\beta_{TS}=exp[\\frac{U_s}{R}(\\frac{1}{293}-\\frac{1}{T_{cur}+273})]`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2110,"value":"tex` \\epsilon_{sh,total} =\\epsilon_{sh}(t_{corrected}, t_{0,corrected})+\\epsilon_{au}(t_{corrected},t_{0,corrected})`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2115,"value":"tex` \\epsilon_{sh}(t_{corrected},t_{0,corrected})= \\epsilon_{sh,∞}(t_{0,corrected}) \\cdot k_h \\cdot S(t_{corrected})`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2119,"value":"tex`\\epsilon_{sh,∞}(t_{0,corrected})= -\\epsilon_0k_{\\epsilon a}\\frac{E(7\\cdot \\beta_{Th}+600\\cdot \\beta_{Ts})}{E(t_{0,corrected}+\\tau_{sh} \\cdot \\beta_{TS})}`\n","pinned":false,"hidden":false,"mode":"ojs"},{"id":2143,"value":"tex`\\epsilon_0= \\epsilon_{cem}(\\frac{a/c}{6})^{P_{\\epsilon a}}(\\frac{w/c}{0.38})^{P_{\\epsilon w}}(\\frac{6.5c}{\\rho})^{P_{\\epsilon c}}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2149,"value":"tex`E(t)=E_{28}\\sqrt{\\frac{1}{4+(6/7)t}}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2154,"value":"tex`\\tau_{sh}=\\tau_0 \\cdot k_{\\tau a}(k_s\\frac{D}{1mm})^2`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2157,"value":"tex`\\tau_0= \\tau_{cem}(\\frac{a/c}{6})^{P_{\\tau a}}(\\frac{w/c}{0.38})^{P_{\\tau w}}(\\frac{6.5c}{\\rho})^{P_{\\tau c}}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2161,"value":"tex`\\epsilon_{au}(t_{corrected},t_{0,corrected})=\\epsilon_{au,∞}[1+(\\frac{\\tau_{au}}{t_{corrected}+t_{0,corrected}})^{\\alpha})]^{r_t}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2168,"value":"tex`\\alpha=r_{\\alpha}(\\frac{w/c}{0.38})`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2172,"value":"tex`\\epsilon_{au,∞} =-\\epsilon_{au,cem}(\\frac{a/c}{6})^{r_{\\epsilon a}}(\\frac{w/c}{0.38})^{r_{\\epsilon w}}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2175,"value":"tex`\\tau_{au}=\\tau_{au,cem}(\\frac{w/c}{0.38})^{r_{\\tau w}}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":4037,"value":"tex `Bazant B3 Ecm28: eq(29)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":4150,"value":"BAZANT_B4_Ecm28 = function(f_cm_28) { return 4734 * f_cm_28**0.5;}","pinned":false,"hidden":false,"mode":"ojs"},{"id":2195,"value":"$44","pinned":false,"hidden":false,"mode":"ojs"},{"id":2516,"value":"tex` Creep`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2517,"value":"tex` \\epsilon_{cc} (t) = J( t, t') \\cdot \\sigma`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2522,"value":"tex` J(t,t') = q_1+ R_TC_0(t,t')+C_d(t,t2,t_0)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2526,"value":"tex` q_1 = \\frac{p_1}{E_{28}}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2529,"value":"tex` E_{28}= 4734MPa\\sqrt{f_c/MPa}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2533,"value":"tex ` C_0(t,t') = q_2Q(t,t')+q_3ln[1+(\\frac{t-t'}{1 day})^{0.1}]+q_4ln[\\frac{t}{t'}] `","pinned":false,"hidden":false,"mode":"ojs"},{"id":2539,"value":"tex` Q_(t,t') = Q_f(t') (1+(\\frac{Q_f(t')}{Z(t,t')})^{r(t')})^{-\\frac{1}{r(t')}}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2543,"value":"tex` Q_f(t') = [0.086(\\frac{t'}{1day})^{2/9}+1.21(\\frac{t'}{1day})^{4/9}]^{-1}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2546,"value":"tex` Z(t') =(\\frac{t'}{1day})^{-0.5}ln[1+ (\\frac{t-t'}{1day})^{0.1}]`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2553,"value":"tex` r(t') = 1.7(\\frac{t'}{1day})^{0.12}+8`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2556,"value":"tex` q_2 = \\frac{p_2}{1GPa}(\\frac{w/c}{0.38})^{p_{2w}}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2559,"value":"tex` q_3 = p_3q_2 (\\frac{a/c}{6})^{p_{3a}}(\\frac{w/c}{0.38})^{p_{3a}}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2563,"value":"tex` q_4 = \\frac{p_4}{1GPa}(\\frac{a/c}{6})^{p_{4a}}(\\frac{w/c}{0.38})^{p_{4w}}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2566,"value":"tex` C_d (t,t't_0) = q_5[exp[-p_{5H}H(t,t_0)]-exp[-p_{5H}H_c(t_0',t_0)]]^{0.5}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2570,"value":"tex` H(t,t_0) = 1-(1-h)tanh\\sqrt{\\frac{t-t_0}{T_{sh}}}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2575,"value":"tex` H_c(t,t_0) = 1-(1-h)tanh\\sqrt{\\frac{t_0'-t_0}{T_{sh}}}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2578,"value":"tex` q_5 =\\frac{p_5}{1GPa}(\\frac{a/c}{6})^{p_{5a}}(\\frac{w/c}{0.38})^{p_{5w}}|k_h\\epsilon_{sh,∞}(t_0)|^{p_{5\\epsilon}}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2585,"value":"tex` R_T = exp[\\frac{U_c'}{R}(\\frac{1}{293}-\\frac{1}{T+273})]`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2591,"value":"$45","pinned":false,"hidden":false,"mode":"ojs"},{"id":6066,"value":"$46","pinned":false,"hidden":false,"mode":"ojs"},{"id":3639,"value":"{\n let specimen = {admixtureClass: \"Fly(>15%, <=30%) - Super(<=5%)\"};\n return BAZANT_B4_AdmixtureModificationForShrinkage (specimen);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":3558,"value":"$47","pinned":false,"hidden":false,"mode":"ojs"},{"id":3659,"value":"$48","pinned":false,"hidden":false,"mode":"ojs"},{"id":5838,"value":"md `# AS 3600-2009`","pinned":false,"hidden":false,"mode":"ojs"},{"id":5837,"value":"tex` SHRINKAGE`","pinned":false,"hidden":false,"mode":"ojs"},{"id":5836,"value":"tex` \\alpha_1 = 0.8+1.2 \\cdot e^{-0.005 \\cdot t_h} ` //Figure 3.1.7.2","pinned":false,"hidden":false,"mode":"ojs"},{"id":5835,"value":"tex` k_1 = \\frac{\\alpha_1 \\cdot t^{0.8}}{t^{0.8}+0.15 \\cdot t_h} ` //Figure 3.1.7.2","pinned":false,"hidden":false,"mode":"ojs"},{"id":5834,"value":"tex`\\epsilon_{csd.b} = (1 - 0.008f_c') \\cdot \\epsilon_{csd.b}^*`","pinned":false,"hidden":false,"mode":"ojs"},{"id":5833,"value":"tex ` \\epsilon_{csd} = k_1 \\cdot k_4 \\cdot \\epsilon_{csd.b} `","pinned":false,"hidden":false,"mode":"ojs"},{"id":5832,"value":"tex`\\epsilon_{cse}^* = (0.06 f_c' - 1.0) \\cdot 50 \\cdot 10^{-6} `","pinned":false,"hidden":false,"mode":"ojs"},{"id":5831,"value":"tex`\\epsilon_{cse} = \\epsilon_{cse}^* (1.0 - e^{-0.1 \\cdot t})`","pinned":false,"hidden":false,"mode":"ojs"},{"id":5830,"value":"tex`\\epsilon_{cs} = \\epsilon_{cse} + \\epsilon_{csd}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":5829,"value":"AS3600_2009_Eps_sh = function(material,t,t_s){\n let msg = \"-\"; // holds the warning messages\n let f_c = material.f_cm - 8; // characteristic compressive strength \n let k_4 = material.environmentVariable;\n let epsilon_csdb_star = material.basicDryingShrinkageStrain;\n let t_h = 2 * material.V_S; // notional thickness\n \n let t_1 = t - t_s; // time since begining of drying\n let alpha_1 = 0.8 + 1.2*Math.exp(-0.005*t_h);\n let k_1 = (alpha_1*(t_1**0.8))/((t_1**0.8)+0.15*t_h);\n \n let epsilon_csdb = (1-0.008*f_c)*epsilon_csdb_star;\n let epsilon_csd = k_1*k_4*epsilon_csdb; // eq 3.1.7.2(4)\n let epsilon_cse_star = (((0.06*f_c)-1)*50)*0.000001; //eq 3.1.7.2(3)\n let epsilon_cse = epsilon_cse_star*(1-Math.exp(-0.1*t)); // eq 3.1.7.2(2)\n \n let AS3600_2009_Eps_sh = -(epsilon_cse+epsilon_csd);\n let disp = AS3600_2009_Eps_sh*material.L;\n return {value: disp, message: msg};\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":5828,"value":"tex` CREEP`","pinned":false,"hidden":false,"mode":"ojs"},{"id":5827,"value":"tex`\\alpha_2 = 1.0 + 1.12 \\cdot e^{-0.008 \\cdot t_h}` ","pinned":false,"hidden":false,"mode":"ojs"},{"id":5826,"value":"tex`k_2 =\\frac{\\alpha_2 \\cdot t^{0.8}}{t^{0.8}+0.15 \\cdot t_h}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":5825,"value":"tex`k_3 = 1.75 + \\frac{(t_0 - 7)(1.1 -1.75)}{(28-7)} \\space\\space\\space\\space\\space for \\space(t_0 \\le 28)` //t_0 is age of loading, Figure 3.1.8.3(B)","pinned":false,"hidden":false,"mode":"ojs"},{"id":5824,"value":"tex`k_3 =1.1+ \\frac{(t_0-28)(0.9-1.1)}{(365-28)} \\space\\space\\space\\space\\space for \\space(28 \\lt t_0 \\le 365 )`","pinned":false,"hidden":false,"mode":"ojs"},{"id":5823,"value":"md`(for t₀ > 365, k₃ = 0.9) ` ","pinned":false,"hidden":false,"mode":"ojs"},{"id":5822,"value":"tex`\\alpha_3 = \\frac{0.7}{k_4 \\cdot \\alpha_2}` ","pinned":false,"hidden":false,"mode":"ojs"},{"id":5821,"value":"tex`k_5= (2.0 - \\alpha_3 ) - 0.02 \\cdot (1.0 - \\alpha_3 ) \\cdot f'_c`","pinned":false,"hidden":false,"mode":"ojs"},{"id":5820,"value":"md`(for f_c' ≤ 50 MPa, k₅ = 1)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":5819,"value":"tex`\\phi_{cc}=k_2 \\cdot k_3 \\cdot k_4 \\cdot k_5 \\cdot \\phi_{cc.b}` //design creep coefficient at time (t) ","pinned":false,"hidden":false,"mode":"ojs"},{"id":5818,"value":"tex`\\epsilon_{cc}= \\phi_{cc} \\cdot \\frac{\\sigma}{E_{c}}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":5817,"value":"$49","pinned":false,"hidden":false,"mode":"ojs"},{"id":5897,"value":"md `# IRC 112 2020`","pinned":false,"hidden":false,"mode":"ojs"},{"id":5936,"value":"//TESTS: \n{\n let tol = 1e-5;\n let output = \"TEST: IRC 112 2020\\n\\n\";\n \n // SI units\n let t = 100; // age of concrete\n let t_s = 3;\n let spec = _.clone(specimen);\n \n // Shrinkage\n let shrinkageOutput = IRC_112_2020_Eps_sh(spec,t, t_s)\n let shrinkage_disp_current = shrinkageOutput.value;\n output += \"SHRINKAGE: \";\n output += shrinkage_disp_current\n output += \"\\n\\nMessages: \" + shrinkageOutput.message;\n output += \"\\n\\nDebug: \" + shrinkageOutput.debug;\n\n // Creep\n //let creep_disp_current = IRC_112_2020_Eps_cc(spec,t).value;\n //output +=\" CREEP: \";\n //output += Utility_CompareResults(creep_disp_expected, creep_disp_current, tol);\n \n return output\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":5896,"value":"tex ` SHRINKAGE `","pinned":false,"hidden":false,"mode":"ojs"},{"id":5895,"value":"tex`\\epsilon_{cs} = \\epsilon_{cd} + \\epsilon_{ca}` // Eq. 6.11","pinned":false,"hidden":false,"mode":"ojs"},{"id":5894,"value":"tex`\\epsilon_{ca}(t) = \\beta_{as}(t) \\cdot \\epsilon_{ca}` // Eq. 6.12","pinned":false,"hidden":false,"mode":"ojs"},{"id":5893,"value":"tex`\\beta_{as}(t) = 1 - e^{-0.2 \\cdot \\sqrt{t}}` //Eq. 6.13","pinned":false,"hidden":false,"mode":"ojs"},{"id":5892,"value":"tex`(\\epsilon_{ca}:\\space Autogenous \\space Shrinkage \\space Strain \\space\\space from \\space Table \\space 6.6)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":5891,"value":"viewof table6_6 = table([{\"Grade of Concrete\": \"Autogenous Shrinkage Strain x 10^6\", \"M30\": 35, \"M35\":45,\"M45\":65,\"M50\":75,\"M60\":95,\"M65\":105}, {x: 12, y: 99}]) //Table 6.6","pinned":false,"hidden":false,"mode":"ojs"},{"id":5890,"value":"tex`\\epsilon_{cd}(t) = \\beta_{ds}(t,t_s) \\cdot k_h \\cdot \\epsilon_{cd}` // Eq. 6.14","pinned":false,"hidden":false,"mode":"ojs"},{"id":5889,"value":"tex`\\beta_{ds}(t,t_s) = \\frac{(t-t_s)}{(t-t_s)+0.04 \\cdot \\sqrt{h_0^3} }` // Eq. 6.15","pinned":false,"hidden":false,"mode":"ojs"},{"id":5888,"value":"tex`\\epsilon_{cd} = 0.85((220+110 \\cdot \\alpha_{ds1}) \\cdot exp(- \\alpha_{ds2} \\cdot \\frac{f_{cm}}{f_{cmo}})) \\cdot10^{-6} \\cdot \\beta_{RH}` // Eq. 6.14","pinned":false,"hidden":false,"mode":"ojs"},{"id":5887,"value":"tex` f_{cmo} = 12.5 \\space MPa ` //Eq.A2-26","pinned":false,"hidden":false,"mode":"ojs"},{"id":5886,"value":"tex`\\beta_{RH} = 1.55(1-(\\frac{RH}{RH_0})^3)` //Eq. A2-27","pinned":false,"hidden":false,"mode":"ojs"},{"id":5885,"value":"tex`RH_0=100 \\space\\%`","pinned":false,"hidden":false,"mode":"ojs"},{"id":5884,"value":"$4a","pinned":false,"hidden":false,"mode":"ojs"},{"id":5883,"value":"tex`CREEP`","pinned":false,"hidden":false,"mode":"ojs"},{"id":5882,"value":"tex`\\epsilon_{cc}(t,t_0)= \\phi(t,t_0) \\cdot \\frac{\\sigma_c}{E_c} `","pinned":false,"hidden":false,"mode":"ojs"},{"id":5881,"value":"tex`\\phi(t,t_0) = \\phi_0 \\cdot \\beta_c(t,t_0) ` //Eq. A2-14","pinned":false,"hidden":false,"mode":"ojs"},{"id":5880,"value":"tex`\\phi_0 = \\phi_{RH} \\cdot \\beta(f_{cm}) \\cdot \\beta(t_0)` //Eq. A2-15","pinned":false,"hidden":false,"mode":"ojs"},{"id":5879,"value":"tex` \\phi_{RH} = 1+ \\frac{1-RH/100}{0.1 \\cdot \\sqrt[3]{h_0}} \\space\\space\\space\\space for \\space f_{cm} \\le 45 \\space MPa` //Eq. A2-16","pinned":false,"hidden":false,"mode":"ojs"},{"id":5878,"value":"tex` \\phi_{RH} = [1+ \\frac{1-RH/100}{0.1 \\cdot \\sqrt[3]{h_0}} \\cdot \\alpha_1] \\cdot \\alpha_2 \\space\\space\\space\\space for \\space f_{cm} > 45 \\space MPa` //Eq. A2-17","pinned":false,"hidden":false,"mode":"ojs"},{"id":5877,"value":"tex`\\beta(f_{cm}) = \\frac{18.78}{\\sqrt{f_{cm}}}` //Eq. A2-18","pinned":false,"hidden":false,"mode":"ojs"},{"id":5876,"value":"tex`\\beta(t_0) = \\frac{1}{0.1+t_0^{0.20}}` //Eq. A2.19","pinned":false,"hidden":false,"mode":"ojs"},{"id":5875,"value":"tex`\\beta_c(t,t_0) = [\\frac{(t-t_0)}{\\beta_H+t-t_0}]^{0.3}` // Eq. A2-21","pinned":false,"hidden":false,"mode":"ojs"},{"id":5874,"value":"tex`\\beta_H = 1.5 \\cdot(1+(0.012 \\cdot RH)^{18}) \\cdot h_0 + 250 \\le 1500 \\space\\space\\space for \\space\\space f_{cm} \\le45 \\space MPa` //Eq. A2-22","pinned":false,"hidden":false,"mode":"ojs"},{"id":5873,"value":"tex`\\beta_H = 1.5 \\cdot(1+(0.012 \\cdot RH)^{18}) \\cdot h_0 + 250 \\cdot \\alpha_3 \\le 1500 \\cdot \\alpha_3 \\space\\space\\space for \\space\\space f_{cm} > 45 \\space MPa` //Eq. A2-23","pinned":false,"hidden":false,"mode":"ojs"},{"id":5872,"value":"tex`\\alpha_1 =[\\frac{43.75}{f_{cm}}]^{0.7} \\space\\space\\space\\space\\space\\space \\alpha_2 =[\\frac{43.75}{f_{cm}}]^{0.2} \\space\\space\\space\\space\\space\\space \\alpha_3 =[\\frac{43.75}{f_{cm}}]^{0.5}` //Eq. A2-24","pinned":false,"hidden":false,"mode":"ojs"},{"id":5871,"value":"md `Temperature Adjusted Age of Concrete`","pinned":false,"hidden":false,"mode":"ojs"},{"id":5870,"value":"tex ` t_T = \\displaystyle\\sum_{i=1}^n \\Delta t_i \\cdot exp[13.65-\\frac{4000}{273+T_{(\\Delta t_i)}/t_0}]`","pinned":false,"hidden":false,"mode":"ojs"},{"id":5869,"value":"tex `t_0 = t_{0,T} \\cdot [\\frac{9}{2+t_{0,T} 1.2} + 1] \\space \\ge \\space 0.5`","pinned":false,"hidden":false,"mode":"ojs"},{"id":5868,"value":"$4b","pinned":true,"hidden":false,"mode":"ojs"},{"id":3226,"value":"md `# Utility Functions`","pinned":true,"hidden":false,"mode":"ojs"},{"id":3225,"value":"Utility_CompareResults = function(expectedValue, currentValue, tol)\n{\n let output = \" LARSA: \" + currentValue.toLocaleString (undefined, {minimumFractionDigits: 6}) + \", Reference: \" + expectedValue.toLocaleString (undefined, {minimumFractionDigits: 6}) + \"\\n\"; \n \n //if (Math.abs(expectedValue-currentValue) < tol) output += \" Passed\\n\";\n //else output += \" Failed\\n\";\n \n return output;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":3950,"value":"Utility_Interpolation = function(x1, x2, x3, y1, y3)\n{ \n // This function is a general linear interpolation function which uses x and y values of two points such that (x1, y1) and (x3, y3) to find corresponding y2 value for a known x2 value of a point (x2, y2). \n // Where x1 <= x2 <= x3 and y1 <= y2 <= y3\n \n let y2 = y1-((x1-x2)*(y1-y3)/(x1-x3))\n\n return y2;\n \n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":5394,"value":"Utility_Add = function(dbgMsg, str, val)\n{\n return dbgMsg + \"\\n\" + str + \": \" + val;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1764,"value":"import {table} with { data as data }\nfrom \"@anandthakker/editable-table\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":4268,"value":"import {chart} from \"@joshdata/simple-line-chart\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":5595,"value":"_ = require('lodash')","pinned":true,"hidden":false,"mode":"ojs"}],"files":"$W4c","stdlib":"1","titling":"auto"}