2c:null 2d:["$","title",null,{"children":"Creep and Shrinkage Code Comparison | ualbostan | Observable"}] 32:T9b3,viewof data = table([{Code: "CEB-FIP 78", "Creep Displacement": CEB_FIP_78_Eps_cc({t: 100, t0: 16, RH: 60, h: 300, coeff: 1.5, P: -(10 ** 7), b: 1200, d: 400, E_c28: 35000, L: 1000 }) .toLocaleString (undefined, {minimumFractionDigits: 3}) }, {Code: "CEB-FIP 90 ", "Creep Displacement": CEB_FIP_90_Eps_cc ({RH: 0.6, h: 300, cement_hardtype: "N", RH_0: 1, f_cmo: 10,f_cm: 40, P:-(10**7), b:400, d:1200, t: 100, t_cons: 1, t0: 16, h_0: 100, E_c28: 35000, L:1000}) .toLocaleString (undefined, {minimumFractionDigits: 3})}, {Code: "CEB-FIP 2010 Bulletin 70 ", "Creep Displacement": CEB_FIP_2010_Eps_cc ({RH: 0.6, h: 300, cement_type: "32.5R", RH_0: 1, f_cmo: 10,f_cm: 40, P:-(10**7), b:1200, d:400, t: 100, t_cons: 1, t0: 16, h_0: 100, E_c28: 35000, L:1000, T:20}) .toLocaleString (undefined, {minimumFractionDigits: 3})}, {Code: "EN1992/Eurocode 2004 ", "Creep Displacement": EN_1992_1_1_2004_Eps_cc ({RH: 60, h_0: 300, f_cm: 40, P:-(10**7), cement_hardtype: "N", t: 100, t0: 16, E_c28: 35000, b:1200, d:400, L:1000, T:20}) .toLocaleString (undefined, {minimumFractionDigits: 3})}, {Code: "AASHTO v6 ", "Creep Displacement": AASHTO_v6_Eps_cc ({ V_S: 5.905512, RH: 60, f_cm: 40, t: 100, t0: 16, P: -(10 ** 7), b: 1200, d: 400, E_c28: 35000, L:1000}) .toLocaleString (undefined, {minimumFractionDigits: 3})}, {Code: "AASHTO v7/v8 ", "Creep Displacement": AASHTO_v7_v8_Eps_cc ({ V_S: 5.905512, RH: 60, f_cm: 40, t: 100, t0: 16, P: -(10 ** 7), b: 1200, d: 400, E_c28: 35000, L:1000}) .toLocaleString (undefined, {minimumFractionDigits: 3}) }, {Code: "BAZANT B3 ", "Creep Displacement": BAZANT_B3_Eps_cc ({V_S: 15, RH:0.6, c:200, a_c:5, w_c:0.5, f_cm: 40, t: 100, t0: 16, t_0:15, cement_type: "I", curing: "normalcuring", specimen_geometry: "infinite square prism", P:-(10**7), w: 130, b: 1200, d: 400, E_c28: 35000, L:1000 }) .toLocaleString (undefined, {minimumFractionDigits: 3}) }, {Code: "BAZANT B4" , "Creep Displacement": BAZANT_B4_Eps_cc({V_S: 120, cement_type:"R", curing: "normalcuring", RH: 0.6, f_cm: 40, t: 100, t0:16, t_0: 15, w: 240, c:350, a_c:5, w_c:0.5, aggregate_type: "Unknown", specimen_geometry: "infinite square prism", E_28: 35000, L:1000, density: 2350, UH_R: 4000, US_R: 4000, UC_R: 4000, T_cur:20, T: 20, b: 1200, d: 400, P:-(10**7) }) .toLocaleString (undefined, {minimumFractionDigits: 3}) } ])33:Tf5c,viewof data1 = table([{Code: "CEB-FIP 78", "Shrinkage Displacement": CEB_FIP_78_Eps_sha ({ t: 100, t_cons: 1, t_s: 1, RH: 60, h: 300, coeff: 1.5, L:1000 }) .toLocaleString (undefined, {minimumFractionDigits: 3}), "Larsa Assumptions" : "t_s >0 " , " Larsa Shrinkage Displacement": CEB_FIP_78_Eps_sha ({ t: 100, t_cons: 1, t_s: 1, RH: 60, h: 300, coeff: 1.5, L:1000 }) .toLocaleString (undefined, {minimumFractionDigits: 3}) }, {Code: "CEB-FIP 90 updated knowledge ", "Shrinkage Displacement":CEB_FIP_90_upd_Eps_sha({RH: 0.6, h: 300, cement_hardtype: "N", RH_0: 1, f_cmo: 10,f_cm: 40, t: 100, t_cons:1, t_s: 1 ,h_0: 100, L: 1000}) .toLocaleString (undefined, {minimumFractionDigits: 3}), "Larsa Assumptions" : "- " , " Larsa Shrinkage Displacement": "-"}, {Code: "CEB-FIP 90 ", "Shrinkage Displacement": CEB_FIP_90_Eps_sha({RH: 0.6, h: 300, cement_hardtype: "N", RH_0: 1, f_cmo: 10,f_cm: 40, t: 100, t_cons: 1, t_s: 1,h_0: 100, L: 1000}) .toLocaleString (undefined, {minimumFractionDigits: 3}), "Larsa Assumptions" : "t_s =3 " , " Larsa Shrinkage Displacement": CEB_FIP_90_Eps_sha({RH: 0.6, h: 300, cement_hardtype: "N", RH_0: 1, f_cmo: 10,f_cm: 40, t: 100, t_cons: 1, t_s: 3,h_0: 100, L: 1000}) .toLocaleString (undefined, {minimumFractionDigits: 3}) }, {Code: "CEB-FIP 2010 Bulletin 70 ", "Shrinkage Displacement": CEB_FIP_2010_Eps_sha ({RH: 60, h: 300, cement_type: "32.5R", f_cm: 40, t: 100, t_cons: 1, t_s: 1, h_0: 100, L:1000}) .toLocaleString (undefined, {minimumFractionDigits: 3}), "Larsa Assumptions" : "t_s =3 ", " Larsa Shrinkage Displacement": CEB_FIP_2010_Eps_sha ({RH: 60, h: 300, cement_type: "32.5R", f_cm: 40, t: 100, t_cons: 1, t_s: 1, h_0: 100, L:1000}) .toLocaleString (undefined, {minimumFractionDigits: 3}) }, {Code: "EN1992/Eurocode 2004 ", "Shrinkage Displacement": EN_1992_1_1_2004_Eps_sha ({RH: 60, h_0:300, cement_hardtype: "N", f_cm: 40, t: 100, t_cons: 1, t_s: 1, f_cmo:10, RH_0:100 , L:1000}) .toLocaleString (undefined, {minimumFractionDigits: 3}), "Larsa Assumptions" : "t_s =14 ", " Larsa Shrinkage Displacement": EN_1992_1_1_2004_Eps_sha ({RH: 60, h_0:300, cement_hardtype: "N", f_cm: 40, t: 100, t_cons: 1, t_s: 14, f_cmo:10, RH_0:100 , L:1000}) .toLocaleString (undefined, {minimumFractionDigits: 3}) }, {Code: "AASHTO v6 ", "Shrinkage Displacement": AASHTO_v6_Eps_sha ({V_S: 5.905512, RH: 60, f_cm: 40, t: 100, t0:1, L:1000}) .toLocaleString (undefined, {minimumFractionDigits: 3}), "Larsa Assumptions" : "t_s =0 ", " Larsa Shrinkage Displacement": AASHTO_v6_Eps_sha ({V_S: 5.905512, RH: 60, f_cm: 40, t: 100, t0:1, L:1000}) .toLocaleString (undefined, {minimumFractionDigits: 3}) }, {Code: "AASHTO v7/v8 ", "Shrinkage Displacement": AASHTO_v7_v8_Eps_sha ({V_S: 5.905512, RH: 60, f_cm: 40, t: 100, t_cons:1, L:1000}) .toLocaleString (undefined, {minimumFractionDigits: 3}), "Larsa Assumptions" : "- ", " Larsa Shrinkage Displacement": "- " }, {Code: "BAZANT B3 ", "Shrinkage Displacement": BAZANT_B3_Eps_sha ({V_S: 15, cement_type:"I", curing: "normalcuring", specimen_geometry: "infinite square prism", RH: 0.6, f_cm: 40, t: 100, t_s:1, t_cons:1, w: 200, E_28: 35000, L:1000 }) .toLocaleString (undefined, {minimumFractionDigits: 3}), "Larsa Assumptions" : "- ", " Larsa Shrinkage Displacement": "- " } , {Code: "BAZANT B4 ", "Shrinkage Displacement": BAZANT_B4_Eps_sha ({V_S: 120, cement_type:"R", curing: "normalcuring", RH: 0.6, f_cm: 40, t: 100, t_s:1, t_cons:1, w: 240, c:350, a_c:5, w_c:0.5, aggregate_type: "Unknown", specimen_geometry: "infinite square prism", E_28: 35000, L:1000, density: 2350, UH_R: 4000, US_R: 4000, T_cur:20 }) .toLocaleString (undefined, {minimumFractionDigits: 3}), "Larsa Assumptions" : "- ", " Larsa Shrinkage Displacement": "- " } ]) 34:T22a4, viewof data2 = table([{Code: "CEB-FIP 78", "Shrinkage Displacement b1":CEB_FIP_78_Eps_shb1 ({ t: 100, t_cons: 1, t_s: 1, RH: 60, h: 300, coeff: 1.5, L:1000 }) .toLocaleString (undefined, {minimumFractionDigits: 3}), "Shrinkage Displacement b2": CEB_FIP_78_Eps_shb2 ({ t: 15, t_cons: 1, t_s: 1, RH: 60, h: 300, coeff: 1.5, L:1000 }).toLocaleString (undefined, {minimumFractionDigits: 3}), "Shrinkage Displacement b": [CEB_FIP_78_Eps_shb1 ({ t: 100, t_cons: 1, t_s: 1, RH: 60, h: 300, coeff: 1.5, L:1000 })- CEB_FIP_78_Eps_shb2 ({ t: 15, t_cons: 1, t_s: 1, RH: 60, h: 300, coeff: 1.5, L:1000 }) ] .toLocaleString (undefined, {minimumFractionDigits: 3}), "Larsa4D Assumptions" : "t_s >0 " , " Larsa4D Shrinkage Displacement at 85 (100-15) days": [CEB_FIP_78_Eps_shb1 ({ t: 100, t_cons: 1, t_s: 1, RH: 60, h: 300, coeff: 1.5, L:1000 })- CEB_FIP_78_Eps_shb2 ({ t: 15, t_cons: 1, t_s: 1, RH: 60, h: 300, coeff: 1.5, L:1000 }) ] .toLocaleString (undefined, {minimumFractionDigits: 3}) }, {Code: "CEB-FIP 90 ", "Shrinkage Displacement b1": CEB_FIP_90_Eps_shb1({RH: 0.6, h: 300, cement_hardtype: "N", RH_0: 1, f_cmo: 10,f_cm: 40, t: 100, t_cons: 1, t_s: 1,h_0: 100, L:1000}) .toLocaleString (undefined, {minimumFractionDigits: 3}), "Shrinkage Displacement b2": CEB_FIP_90_Eps_shb2({RH: 0.6, h: 300, cement_hardtype: "N", RH_0: 1, f_cmo: 10,f_cm: 40, t: 15, t_cons: 1, t_s: 1,h_0: 100, L:1000}) .toLocaleString (undefined, {minimumFractionDigits: 3}), "Shrinkage Displacement b": [CEB_FIP_90_Eps_shb1({RH: 0.6, h: 300, cement_hardtype: "N", RH_0: 1, f_cmo: 10,f_cm: 40, t: 100, t_cons: 1, t_s: 1,h_0: 100, L:1000})- CEB_FIP_90_Eps_shb2({RH: 0.6, h: 300, cement_hardtype: "N", RH_0: 1, f_cmo: 10,f_cm: 40, t: 15, t_cons: 1, t_s: 1,h_0: 100, L:1000})] .toLocaleString (undefined, {minimumFractionDigits: 3}), "Larsa4D Assumptions" : "t_s =3 " , " Larsa4D Shrinkage Displacement at 85 (100-15) days": [CEB_FIP_90_Eps_shb1({RH: 0.6, h: 300, cement_hardtype: "N", RH_0: 1, f_cmo: 10,f_cm: 40, t: 100, t_cons: 1, t_s: 3,h_0: 100, L:1000})- CEB_FIP_90_Eps_shb2({RH: 0.6, h: 300, cement_hardtype: "N", RH_0: 1, f_cmo: 10,f_cm: 40, t: 15, t_cons: 1, t_s: 3,h_0: 100, L:1000})] .toLocaleString (undefined, {minimumFractionDigits: 3}) }, {Code: "CEB-FIP 2010 Bulletin 70 ", "Shrinkage Displacement b1": CEB_FIP_2010_Eps_shb1({RH: 60, h: 300, cement_type: "32.5R", f_cm: 40, t: 100, t_s: 1,h_0: 100, L:1000}) .toLocaleString (undefined, {minimumFractionDigits: 3}), "Shrinkage Displacement b2": CEB_FIP_2010_Eps_shb2({RH: 60, h: 300, cement_type: "32.5R", f_cm: 40, t: 15, t_s: 1,h_0: 100, L:1000}) .toLocaleString (undefined, {minimumFractionDigits: 3}), "Shrinkage Displacement b": [CEB_FIP_2010_Eps_shb1({RH: 60, h: 300, cement_type: "32.5R", f_cm: 40, t: 100, t_cons: 1, t_s: 1,h_0: 100, L:1000})- CEB_FIP_2010_Eps_shb2({RH: 60, h: 300, cement_type: "32.5R", f_cm: 40, t: 15, t_cons: 1, t_s: 1,h_0: 100, L:1000})] .toLocaleString (undefined, {minimumFractionDigits: 3}), "Larsa4D Assumptions" : "t_s =3 " , " Larsa4D Shrinkage Displacement at 85 (100-15) days": [CEB_FIP_2010_Eps_shb1({RH: 60, h: 300, cement_type: "32.5R", f_cm: 40, t: 100, t_cons: 1, t_s: 3,h_0: 100, L:1000})- CEB_FIP_2010_Eps_shb2({RH: 60, h: 300, cement_type: "32.5R", f_cm: 40, t: 15, t_cons: 1, t_s: 3,h_0: 100, L:1000})] .toLocaleString (undefined, {minimumFractionDigits: 3}) }, {Code: "EN1992/Eurocode 2004 ", "Shrinkage Displacement b1": EN_1992_1_1_2004_Eps_shb1 ({RH: 60, h_0:300, cement_hardtype: "N", f_cm: 40, t: 100, t_s: 1, f_cmo:10, RH_0:100 , L:1000}) .toLocaleString (undefined, {minimumFractionDigits: 3}), "Shrinkage Displacement b2": EN_1992_1_1_2004_Eps_shb2 ({RH: 60, h_0:300, cement_hardtype: "N", f_cm: 40, t: 15, t_s: 1, f_cmo:10, RH_0:100 , L:1000}) .toLocaleString (undefined, {minimumFractionDigits: 3}), "Shrinkage Displacement b" : [EN_1992_1_1_2004_Eps_shb1 ({RH: 60, h_0:300, cement_hardtype: "N", f_cm: 40, t: 100, t_s: 1, f_cmo:10, RH_0:100 , L:1000})- EN_1992_1_1_2004_Eps_shb2 ({RH: 60, h_0:300, cement_hardtype: "N", f_cm: 40, t: 15, t_s: 1, f_cmo:10, RH_0:100 , L:1000})] .toLocaleString (undefined, {minimumFractionDigits: 3}), "Larsa4D Assumptions" : "t_s = 14 " , " Larsa4D Shrinkage Displacement at 85 (100-15) days": [EN_1992_1_1_2004_Eps_shb1 ({RH: 60, h_0:300, cement_hardtype: "N", f_cm: 40, t: 100, t_s: 14, f_cmo:10, RH_0:100 , L:1000})- EN_1992_1_1_2004_Eps_shb2 ({RH: 60, h_0:300, cement_hardtype: "N", f_cm: 40, t: 15, t_s: 14, f_cmo:10, RH_0:100 , L:1000})] .toLocaleString (undefined, {minimumFractionDigits: 3}) }, {Code: "AASHTO v6 ", "Shrinkage Displacement b1":AASHTO_v6_Eps_shb1 ({V_S: 5.905512, RH: 60, f_cm: 40, t: 100, L:1000}) .toLocaleString (undefined, {minimumFractionDigits: 3}), "Shrinkage Displacement b2": AASHTO_v6_Eps_shb2 ({V_S: 5.905512, RH: 60, f_cm:40, t: 15, L:1000}) .toLocaleString (undefined, {minimumFractionDigits: 3}), "Shrinkage Displacement b": [AASHTO_v6_Eps_shb1 ({V_S: 5.905512, RH: 60, f_cm: 40, t: 100, L:1000})- AASHTO_v6_Eps_shb2 ({V_S: 5.905512, RH: 60, f_cm:40, t: 15, L:1000})] .toLocaleString (undefined, {minimumFractionDigits: 3}), "Larsa4D Assumptions" : "t_s = 0 " , " Larsa4D Shrinkage Displacement at 85 (100-15) days": [AASHTO_v6_Eps_shb1 ({V_S: 5.905512, RH: 60, f_cm: 40, t: 100, L:1000})- AASHTO_v6_Eps_shb2 ({V_S: 5.905512, RH: 60, f_cm:40, t: 15, L:1000})] .toLocaleString (undefined, {minimumFractionDigits: 3}) }, {Code: "AASHTO v7/v8 ", "Shrinkage Displacement b1": AASHTO_v7_v8_Eps_shb1 ({V_S: 5.905512, RH: 60, f_cm: 40, t: 100, L:1000}) .toLocaleString (undefined, {minimumFractionDigits: 3}), "Shrinkage Displacement b2": AASHTO_v7_v8_Eps_shb2 ({V_S: 5.905512, RH: 60, f_cm: 40, t: 15, L:1000}) .toLocaleString (undefined, {minimumFractionDigits: 3}), "Shrinkage Displacement b": [AASHTO_v7_v8_Eps_shb1 ({V_S: 5.905512, RH: 60, f_cm: 40, t: 100, L:1000})-AASHTO_v7_v8_Eps_shb2 ({V_S: 5.905512, RH: 60, f_cm: 40, t: 15, L:1000})] .toLocaleString (undefined, {minimumFractionDigits: 3}), "Larsa4D Assumptions" : "- " , " Larsa4D Shrinkage Displacement at 85 (100-15) days": "- " }, {Code: "BAZANT B3 ", "Shrinkage Displacement b1": BAZANT_B3_Eps_shb1 ({V_S: 15, cement_type:"I", curing: "normalcuring", specimen_geometry: "infinite square prism", RH: 0.6, f_cm: 40, t: 100, t_s:1, w: 200, E_28: 35000, L:1000 }) .toLocaleString (undefined, {minimumFractionDigits: 3}), "Shrinkage Displacement b2": BAZANT_B3_Eps_shb2 ({V_S: 15, cement_type:"I", curing: "normalcuring", specimen_geometry: "infinite square prism", RH: 0.6, f_cm: 40, t: 15, t_s:1, w: 200, E_28: 35000, L:1000 }) .toLocaleString (undefined, {minimumFractionDigits: 3}), "Shrinkage Displacement b": [BAZANT_B3_Eps_shb1 ({V_S: 15, cement_type:"I", curing: "normalcuring", specimen_geometry: "infinite square prism", RH: 0.6, f_cm: 40, t: 100, t_s:1, w: 200, E_28: 35000, L:1000 })- BAZANT_B3_Eps_shb2 ({V_S: 15, cement_type:"I", curing: "normalcuring", specimen_geometry: "infinite square prism", RH: 0.6, f_cm: 40, t: 15, t_s:1, w: 200, E_28: 35000, L:1000 }) ] .toLocaleString (undefined, {minimumFractionDigits: 3}), "Larsa4D Assumptions" : "- " , " Larsa4D Shrinkage Displacement at 85 (100-15) days": "- " }, {Code: "BAZANT B4", "Shrinkage Displacement b1": BAZANT_B4_Eps_shb1({V_S: 120, cement_type:"R", curing: "normalcuring", RH: 0.6, f_cm: 40, t: 100, t_s:1, w: 240, c:350, a_c:5, w_c:0.5, aggregate_type: "Unknown", specimen_geometry: "infinite square prism", E_28: 35000, L:1000, density: 2350, UH_R: 4000, US_R: 4000, T_cur:20 }) .toLocaleString (undefined, {minimumFractionDigits: 3}), "Shrinkage Displacement b2": BAZANT_B4_Eps_shb2({V_S: 120, cement_type:"R", curing: "normalcuring", RH: 0.6, f_cm: 40, t: 15, t_s:1, w: 240, c:350, a_c:5, w_c:0.5, aggregate_type: "Unknown", specimen_geometry: "infinite square prism", E_28: 35000, L:1000, density: 2350, UH_R: 4000, US_R: 4000, T_cur:20 }) .toLocaleString (undefined, {minimumFractionDigits: 3}), "Shrinkage Displacement b": [ BAZANT_B4_Eps_shb1({V_S: 120, cement_type:"R", curing: "normalcuring", RH: 0.6, f_cm: 40, t: 100, t_s:1, w: 240, c:350, a_c:5, w_c:0.5, aggregate_type: "Unknown", specimen_geometry: "infinite square prism", E_28: 35000, L:1000, density: 2350, UH_R: 4000, US_R: 4000, T_cur:20 }) - BAZANT_B4_Eps_shb2({V_S: 120, cement_type:"R", curing: "normalcuring", RH: 0.6, f_cm: 40, t: 15, t_s:1, w: 240, c:350, a_c:5, w_c:0.5, aggregate_type: "Unknown", specimen_geometry: "infinite square prism", E_28: 35000, L:1000, density: 2350, UH_R: 4000, US_R: 4000, T_cur:20 })] .toLocaleString (undefined, {minimumFractionDigits: 3}), "Larsa4D Assumptions" : "- " , " Larsa4D Shrinkage Displacement at 85 (100-15) days": "- " } ]) 35:T4c0,CEB_FIP_78_Eps_sha = function(material) { let h_0 = (material.h * material.coeff) / 10; //[e.9] 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; //(D-8.1) if (material.t_cons - material.t_s > 0) Beta_s_t = (material.t / (material.t + K_3)) ** K_4 - ((material.t_cons - material.t_s) / (material.tcons - material.t_s+K_3)) ** K_4; else Beta_s_t = (material.t / (material.t + K_3)) ** K_4; let Beta_s_t0; //(D-8.1) if (material.t_cons - material.t_s > 0) Beta_s_t0 =(material.t_s/(material.t_s + K_3))**K_4+((material.t_cons - material.t_s)/(material.t_cons-material.t_s+ K_3))**K_4; else Beta_s_t0 = (material.t_s / (material.t_s + K_3)) ** K_4; let CEB_FIP_78_Eps_sha = Eps_s0 * (Beta_s_t - Beta_s_t0); //[e.7] let disp = CEB_FIP_78_Eps_sha*material.L; return disp; }36:T4aa,CEB_FIP_78_Eps_cc = function(material) { let h_0 = (material.h * material.coeff) / 10; // [e.9] let K_1 = Math.exp(5.02 / h_0 + Math.log(6.95 * h_0 ** 1.25)); // (D-5.2) let K_2 = Math.exp(0.00144 * h_0 - 1.1 / h_0 - Math.log(1.005 * h_0 ** 0.2954)); // (D-5.3) let Beta_f_t = (material.t / (material.t + K_1)) ** K_2; // (D-5.1) let Beta_f_t0 = (material.t0 / (material.t0 + K_1)) ** K_2; // (D-5.1) let Beta_d = ((material.t - material.t0) / (material.t + K_1)) ** K_2; //(D-4) let Beta_a = 0.8 * (1 - (material.t0 / (material.t0 + 47)) ** (1 / 2.45)); // [e.4] let Phi_f1 = 4.45 - 0.035 * material.RH; //(D-6) 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) let Phi_f = Phi_f1 + Phi_f2; // taken form expalantion of [e.4] let Phi_d = 0.4; //denotes delayed modulus of elasticity, taken form expalantion of [e.4] let Phi_t_t0 = Beta_a + Phi_d * Beta_d + Phi_f * (Beta_f_t - Beta_f_t0); // [e.4] let Sigma = material.P / (material.b * material.d); let CEB_FIP_78_Eps_cc = (Sigma * Phi_t_t0) / material.E_c28; // [e.1] let disp = CEB_FIP_78_Eps_cc*material.L; return disp; }37:T609,CEB_FIP_90_upd_Eps_sha = function(material) { let Alpha_as; // talen from explanation of eq (3.1-16 b) if (material.cement_hardtype == "S") Alpha_as = 800; else Alpha_as = 700; let Beta_as = 1-Math.exp(-0.2*(material.t/material.t_cons)**0.5); // eq(3.1-16 b) let Eps_caso = -Alpha_as*(material.f_cm/material.f_cmo/(6+material.f_cm/material.f_cmo))**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_hardtype == "S") alpha_ds1 = 3; else alpha_ds1 = 4; let alpha_ds2; // taken from explanation of eq(3.1-17 d) if (material.cement_hardtype == "S") alpha_ds2 = 0.13; else alpha_ds2 = 0.11; let Eps_cdso = (220+110*alpha_ds1)*Math.exp((-alpha_ds2*material.f_cm)/material.f_cmo)*0.000001; // eq(3.1-17 a) let Beta_s1 = ((3.5 * material.f_cmo) / material.f_cm) ** 0.1; // eq(3.1-17 d) let Beta_RH; // eq(3.1-17 b) if (material.RH < 0.99 * Beta_s1) Beta_RH = -1.55 * (1 - (material.RH / material.RH_0) ** 3); else Beta_RH = 0.25; let Beta_ds =((material.t-material.t_s)/material.t_cons/(350*(material.h/material.h_0)**2+(material.t-material.t_s)/ material.t_cons))**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_sha = Eps_cas + Eps_cds; // eq(3.1-15 a) let disp = CEB_FIP_90_upd_Eps_sha*material.L; return disp; }38:T944,CEB_FIP_2010_Eps_sha = function(material) { 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; let Beta_ds; // eq(9-15) if (material.t_cons- material.t_s > 0) Beta_ds = ((material.t-material.t_s)/(0.035*material.h ** 2+(material.t - material.t_s)))**0.5-((material.t_cons - material.t_s)/(0.035 * material.h ** 2 + (material.t_cons - material.t_s)))**0.5; else Beta_ds =((material.t - material.t_s) /(0.035 * material.h ** 2 + (material.t - material.t_s))) ** 0.5; let Alpha_ds1; // Table(9-2) if (material.cement_type == "32.5N") Alpha_ds1 = 3; else if (material.cement_type == "32.5R" || material.cement_type == "42.5N") Alpha_ds1 = 4; else if (material.cement_type == "42.5R" ||material.cement_type == "52.5N" ||material.cement_type == "52.5R") Alpha_ds1 = 6; let Alpha_ds2; // Table(9-2) if (material.cement_type == "32.5N") Alpha_ds2 = 0.013; else if (material.cement_type == "32.5R" || material.cement_type == "42.5N") Alpha_ds2 = 0.012; else if (material.cement_type == "42.5R" ||material.cement_type == "52.5N" ||material.cement_type == "52.5R") Alpha_ds2 = 0.012; 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_type == "32.5N") Alpha_bs = 800; else if (material.cement_type == "32.5R" || material.cement_type == "42.5N") Alpha_bs = 700; else if (material.cement_type == "42.5R" ||material.cement_type == "52.5N" ||material.cement_type == "52.5R") Alpha_bs = 600; 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(material.t)))-(1-Math.exp(-0.2 *Math.sqrt(material.t_cons))); // eq(9.12) let Eps_cbs = Eps_cbs0 * Beta_bs; // basic shrinkage at time t. eq(9-10 b) let CEB_FIP_2010_Eps_sha = Eps_cbs + Eps_cds; // eq(9-10 a) let disp = CEB_FIP_2010_Eps_sha*material.L; return disp; }39:T788,CEB_FIP_2010_Eps_shb1 = function(material) { let Beta_s1; if ((35 / material.f_cm) ** 0.1 <= 1) Beta_s1 = (35 / material.f_cm) ** 0.1; else Beta_s1 = 1; let Beta_RH; 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; let Beta_ds =((material.t - material.t_s) / (0.035 * material.h ** 2 + (material.t - material.t_s))) ** 0.5; let Alpha_ds1; if (material.cement_type == "32.5N") Alpha_ds1 = 3; else if (material.cement_type == "32.5R" || material.cement_type == "42.5N") Alpha_ds1 = 4; else if ( material.cement_type == "42.5R" || material.cement_type == "52.5N" || material.cement_type == "52.5R" ) Alpha_ds1 = 6; let Alpha_ds2; if (material.cement_type == "32.5N") Alpha_ds2 = 0.013; else if (material.cement_type == "32.5R" || material.cement_type == "42.5N") Alpha_ds2 = 0.012; else if ( material.cement_type == "42.5R" || material.cement_type == "52.5N" || material.cement_type == "52.5R") Alpha_ds2 = 0.012; let Eps_cds0 = (220 + 110 * Alpha_ds1) * Math.exp(-Alpha_ds2 * material.f_cm) * 0.000001; let Eps_cds = Eps_cds0 * Beta_RH * Beta_ds; //drying shrinkage at time t let Alpha_bs; if (material.cement_type == "32.5N") Alpha_bs = 800; else if (material.cement_type == "32.5R" || material.cement_type == "42.5N") Alpha_bs = 700; else if ( material.cement_type == "42.5R" || material.cement_type == "52.5N" || material.cement_type == "52.5R" ) Alpha_bs = 600; let Eps_cbs0 = -Alpha_bs * (((material.f_cm / 10 )/ (6 + material.f_cm / 10))**2.5) * 0.000001; let Beta_bs = 1 - Math.exp(-0.2 *Math.sqrt(material.t) ); let Eps_cbs = Eps_cbs0 * Beta_bs; // basic shrinkage at time t let CEB_FIP_2010_Eps_shb1 = Eps_cbs + Eps_cds; let disp =CEB_FIP_2010_Eps_shb1*material.L; return disp; }3a:T782,CEB_FIP_2010_Eps_shb2 = function(material) { let Beta_s1; if ((35 / material.f_cm) ** 0.1 <= 1) Beta_s1 = (35 / material.f_cm) ** 0.1; else Beta_s1 = 1; let Beta_RH; 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; let Beta_ds =((material.t - material.t_s) /(0.035 * material.h ** 2 + (material.t - material.t_s))) **0.5; let Alpha_ds1; if (material.cement_type == "32.5N") Alpha_ds1 = 3; else if (material.cement_type == "32.5R" || material.cement_type == "42.5N") Alpha_ds1 = 4; else if ( material.cement_type == "42.5R" ||material.cement_type == "52.5N" || material.cement_type == "52.5R") Alpha_ds1 = 6; let Alpha_ds2; if (material.cement_type == "32.5N") Alpha_ds2 = 0.013; else if (material.cement_type == "32.5R" || material.cement_type == "42.5N") Alpha_ds2 = 0.012; else if (material.cement_type == "42.5R" || material.cement_type == "52.5N" || material.cement_type == "52.5R") Alpha_ds2 = 0.012; let Eps_cds0 = (220 + 110 * Alpha_ds1) * Math.exp(-Alpha_ds2 * material.f_cm) * 0.000001; let Eps_cds = Eps_cds0 * Beta_RH * Beta_ds; //drying shrinkage at time t let Alpha_bs; if (material.cement_type == "32.5N") Alpha_bs = 800; else if (material.cement_type == "32.5R" || material.cement_type == "42.5N") Alpha_bs = 700; else if (material.cement_type == "42.5R" || material.cement_type == "52.5N" || material.cement_type == "52.5R") Alpha_bs = 600; let Eps_cbs0 = -Alpha_bs * (((material.f_cm / 10 )/ (6 + material.f_cm / 10))**2.5) * 0.000001; let Beta_bs = 1 - Math.exp(-0.2 *Math.sqrt(material.t) ); let Eps_cbs = Eps_cbs0 * Beta_bs; // basic shrinkage at time t let CEB_FIP_2010_Eps_shb2 = Eps_cbs + Eps_cds; let disp = CEB_FIP_2010_Eps_shb2*material.L; return disp; }3b:T622,CEB_FIP_2010_Eps_cc =function(material) { let Alpha; // taken from explanation of eq(9-40) if (material.cement_type =="32.5N") Alpha = -1; else if (material.cement_type == "32.5R" || material.cement_type == "42.5N") Alpha = 0; else if (material.cement_type == "42.R" || material.cement_type == "52.5N" || material.cement_type == "52.5R") Alpha = 1; let t_0_adj = material.t0*((9/(2+material.t0**(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 Beta_h; // eq(9-38) if (1.5*material.h+250*Alpha_fcm<=1500*Alpha_fcm) Beta_h= 1.5*material.h+250*Alpha_fcm; else Beta_h= 1500*Alpha_fcm; let Beta_dc_tt0 = ((material.t-material.t0)/(Beta_h+(material.t-material.t0)))**Gamma_t0; // eq(9.36) let Beta_RH = (1-material.RH)/(0.1*material.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*(material.t-material.t0)+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) let sigma = material.P/(material.d*material.b); let CEB_FIP_2010_Eps_cc = Phi*sigma/material.E_c28; // eq(9-20) let disp = CEB_FIP_2010_Eps_cc*material.L; return disp; } 3c:T6d5,EN_1992_1_1_2004_Eps_sha =function(material) { let Beta_ds; // eq(3.10) if (material.t_cons-material.t_s>0) Beta_ds =(material.t-material.t_s)/((material.t-material.t_s)+0.04*Math.sqrt(material.h_0**3))-(material.t_cons-material.t_s)/((material.t_cons-material.t_s)+0.04*Math.sqrt(material.h_0**3)); else Beta_ds = (material.t-material.t_s)/((material.t-material.t_s)+0.04*Math.sqrt(material.h_0**3)); let k_h; // Table(3.3) if (material.h_0==100) k_h= 1; else if (material.h_0 ==200) k_h = 0.85; else if (material.h_0 == 300) k_h= 0.75; else if (material.h_0 >= 500) k_h =0.7; let Alpha_ds1; // taken from explanation of eq.(B11) if (material.cement_hardtype == "S") Alpha_ds1 = 3; else if (material.cement_hardtype == "N") Alpha_ds1 = 4; else if (material.cement_hardtype == "R") Alpha_ds1 =6; let Alpha_ds2; // taken from explanation of eq.(B11) if (material.cement_hardtype == "S") Alpha_ds2 = 0.13; else if (material.cement_hardtype == "N") Alpha_ds2 = 0.12; else if (material.cement_hardtype == "R") Alpha_ds2 = 0.11; let Beta_RH = 1.55*(1-(material.RH/material.RH_0)**3); // eq(B.12) let Eps_cd0 = 0.85*((220+110*Alpha_ds1)*Math.exp(-Alpha_ds2*material.f_cm/material.f_cmo))*0.000001*Beta_RH; // eq(B11) let Eps_cd = Eps_cd0*Beta_ds*k_h; // eq(3.9) let Beta_as = (1-Math.exp(-0.2*material.t**0.5))-(1-Math.exp(-0.2*material.t_cons**0.5)); // eq(3.13) let f_ck= material.f_cm-8; // Table (3.1) let Eps_ca_inf = 0.0000025*(f_ck-10); // eq(3.12) let Eps_ca = Beta_as*Eps_ca_inf; // eq(3.11) let EN_1992_1_1_2004_Eps_sha = Eps_cd+Eps_ca; // eq(3.8) let disp = -EN_1992_1_1_2004_Eps_sha *material.L; return disp; } 3d:T502,EN_1992_1_1_2004_Eps_shb1 =function(material) { let Beta_ds =(material.t-material.t_s)/((material.t-material.t_s)+0.04*Math.sqrt(material.h_0**3)); let k_h; if (material.h_0==100) k_h= 1; else if (material.h_0 ==200) k_h = 0.85; else if (material.h_0 == 300) k_h= 0.75; else if (material.h_0 >= 500) k_h =0.7; let Alpha_ds1; if (material.cement_hardtype == "S") Alpha_ds1 = 3; else if (material.cement_hardtype == "N") Alpha_ds1 = 4; else if (material.cement_hardtype == "R") Alpha_ds1 =6; let Alpha_ds2; if (material.cement_hardtype == "S") Alpha_ds2 = 0.13; else if (material.cement_hardtype == "N") Alpha_ds2 = 0.12; else if (material.cement_hardtype == "R") Alpha_ds2 = 0.11; let Beta_RH = 1.55*(1-(material.RH/material.RH_0)**3); let Eps_cd0 = 0.85*((220+110*Alpha_ds1)*Math.exp(-Alpha_ds2*material.f_cm/material.f_cmo))*0.000001*Beta_RH; let Eps_cd = Eps_cd0*Beta_ds*k_h; let Beta_as = (1-Math.exp(-0.2*material.t**0.5)); let f_ck= material.f_cm-8; let Eps_ca_inf = 0.0000025*(f_ck-10); let Eps_ca = Beta_as*Eps_ca_inf; let EN_1992_1_1_2004_Eps_shb1= Eps_cd+Eps_ca; let disp = -EN_1992_1_1_2004_Eps_shb1*material.L; return disp; }3e:T4d1,EN_1992_1_1_2004_Eps_shb2 =function(material) { let Beta_ds =(material.t-material.t_s)/((material.t-material.t_s)+0.04*Math.sqrt(material.h_0**3)); let k_h; if (material.h_0==100) k_h= 1; else if (material.h_0 ==200) k_h = 0.85; else if (material.h_0 == 300) k_h= 0.75; else if (material.h_0 >= 500) k_h =0.7; let Alpha_ds1; if (material.cement_hardtype == "S") Alpha_ds1 = 3; else if (material.cement_hardtype == "N") Alpha_ds1 = 4; else if (material.cement_hardtype == "R") Alpha_ds1 =6; let Alpha_ds2; if (material.cement_hardtype == "S") Alpha_ds2 = 0.13; else if (material.cement_hardtype == "N") Alpha_ds2 = 0.12; else if (material.cement_hardtype == "R") Alpha_ds2 = 0.11; let Beta_RH = 1.55*(1-(material.RH/material.RH_0)**3); let Eps_cd0 = 0.85*((220+110*Alpha_ds1)*Math.exp(-Alpha_ds2*material.f_cm/material.f_cmo))*0.000001*Beta_RH; let Eps_cd = Eps_cd0*Beta_ds*k_h; let Beta_as = (1-Math.exp(-0.2*material.t**0.5)); let f_ck= material.f_cm-8; let Eps_ca_inf = 0.0000025*(f_ck-10); let Eps_ca = Beta_as*Eps_ca_inf; let EN_1992_1_1_2004_Eps_shb2 = Eps_cd+Eps_ca; let disp = -EN_1992_1_1_2004_Eps_shb2*material.L; return disp; }3f:T7e9,EN_1992_1_1_2004_Eps_cc =function(material) { 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 Phi_RH; // eq(B.3a) & eq(B.3b) if (material.f_cm <= 35) Phi_RH = 1+(1-material.RH/100)/(0.1*material.h_0**(1/3)); else Phi_RH = (1+((1-material.RH/100)/(0.1*material.h_0**(1/3)))*Alpha_1)*Alpha_2; let Beta_fcm = 16.8/material.f_cm**0.5; // eq(B.4) let t0_T = (Math.exp(-(4000/(273+material.T)-13.65)))*material.t0; // eq(B.10) let Alpha; // taken from explanation of (B.9) if (material.cement_hardtype == "S") Alpha = -1; else if (material.cement_hardtype == "N") Alpha = 0; else if (material.cement_hardtype == "R") Alpha =1; let t_0_adj; // eq(B.9) if (t0_T*(9/(2+t0_T**1.2)+1)**Alpha >= 0.5) t_0_adj = t0_T*(9/(2+t0_T**1.2)+1)**Alpha; else t_0_adj = 0.5; let Beta_t0 = 1/(0.1+t0_T**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 && 1.5*(1+(0.012*material.RH)**18)*material.h_0+250<=1500) Beta_H=1.5*(1+(0.012*material.RH)**18)*material.h_0+250; else if (material.f_cm<=35 && 1.5*(1+(0.012*material.RH)**18)*material.h_0+250>1500) Beta_H =1500; else if (material.f_cm>35 && 1.5*(1+(0.012*material.RH)**18)*material.h_0+250*Alpha_3<=1500*Alpha_3) Beta_H = 1.5*(1+(0.012*material.RH)**18)*material.h_0+250*Alpha_3; else if (material.f_cm>35 && 1.5*(1+(0.012*material.RH)**18)*material.h_0+250*Alpha_3>1500*Alpha_3) Beta_H =1500*Alpha_3; let Beta_c = ((material.t-material.t0)/(Beta_H+material.t-material.t0))**0.3; // eq(B.7) let Phi = Phi_0*Beta_c; // eq(B.1) let Sigma = material.P/(material.b*material.d); let EN_1992_1_1_2004_Eps_cc = Phi*Sigma/material.E_c28; // eq(3.6) let disp = EN_1992_1_1_2004_Eps_cc *material.L; return disp; } 40:T812,BAZANT_B3_Eps_sha = function(material) { let alfa1; // eq(1.21) if (material.cement_type == "I") alfa1 = 1; else if (material.cement_type == "II") alfa1 = 0.85; else alfa1 = 1.1; let alfa2; // eq(1.22) if (material.curing == "steamcuring") alfa2 = 0.75; else if (material.curing == "normalcuring") alfa2 = 1.2; else alfa2 = 1.0; let k_t; // eq(1.20) if (material.t_s-material.t_cons>0) k_t = 8.5*material.t_s**(-0.08)*material.f_cm**(-1/4)-8.5*material.t_cons**(-0.08)*material.f_cm**(-1/4); else k_t = 8.5*material.t_s**(-0.08)*material.f_cm**(-1/4) let D = 2*material.V_S; // taken from explanation of eq(1.11) 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; let T_sh = k_t*(k_s*D)**2; // eq(1.11) let Eps_s_inf = (-alfa1*alfa2*(1.9*10**(-2)*material.w**(2.1)*material.f_cm**(-0.28)+270))*10**(-6); // eq(1.19) let E_607 = material.E_28*(607/(4+0.85*607))**(1/2); // eq(1.13) let E = material.E_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) let Eps_sh_inf = Eps_s_inf*E_607/E; // eq(1.13) let k_h; // eq(1.10) if (material.RH <=0.98) k_h = 1-(material.RH)**3; else if (material.RH == 1) k_h = -0.2; else k_h = 0.2-0.141192*(material.RH)/0.02; let S; // eq(1.9) if (material.t_cons-material.t_s>0) S = Math.tanh(((material.t-material.t_s)/T_sh)**(0.5))- Math.tanh(((material.t_cons-material.t_s)/T_sh)**0.5); else S = Math.tanh(((material.t-material.t_s)/T_sh)**(0.5)); let BAZANT_B3_Eps_sha = Eps_sh_inf*k_h*S; // eq(1.8) let disp = BAZANT_B3_Eps_sha*material.L; return disp; } 41:T61b,BAZANT_B3_Eps_shb1 = function(material) { let alfa1; if (material.cement_type == "I") alfa1 = 1; else if (material.cement_type == "II") alfa1 = 0.85; else alfa1 = 1.1; let alfa2; if (material.curing == "steamcuring") alfa2 = 0.75; else if (material.curing == "normalcuring") alfa2 = 1.2; else alfa2 = 1.0; let k_t = 8.5*material.t_s**(-0.08)*material.f_cm**(-1/4); let D = 2*material.V_S; let k_s; 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; let T_sh = k_t*(k_s*D)**2; let Eps_s_inf = (-alfa1*alfa2*(1.9*10**(-2)*material.w**(2.1)*material.f_cm**(-0.28)+270))*10**(-6); let E_607 = material.E_28*(607/(4+0.85*607))**(1/2); let E = material.E_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) let Eps_sh_inf = Eps_s_inf*E_607/E; let k_h; if (material.RH <=0.98) k_h = 1-(material.RH)**3; else if (material.RH == 1) k_h = -0.2; else k_h = 0.2-0.141192*(material.RH)/0.02; let S = Math.tanh(((material.t-material.t_s)/T_sh)**(0.5)); let BAZANT_B3_Eps_shb1 = Eps_sh_inf*k_h*S; let disp = BAZANT_B3_Eps_shb1 *material.L; return disp; } 42:T60a,BAZANT_B3_Eps_shb2 = function(material) { let alfa1; if (material.cement_type == "I") alfa1 = 1; else if (material.cement_type == "II") alfa1 = 0.85; else alfa1 = 1.1; let alfa2; if (material.curing == "steamcuring") alfa2 = 0.75; else if (material.curing == "normalcuring") alfa2 = 1.2; else alfa2 = 1.0; let k_t = 8.5*material.t_s**(-0.08)*material.f_cm**(-1/4); let D = 2*material.V_S; let k_s; 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; let T_sh = k_t*(k_s*D)**2; let Eps_s_inf = (-alfa1*alfa2*(1.9*10**(-2)*material.w**(2.1)*material.f_cm**(-0.28)+270))*10**(-6); let E_607 = material.E_28*(607/(4+0.85*607))**(1/2); let E = material.E_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) let Eps_sh_inf = Eps_s_inf*E_607/E; let k_h; if (material.RH <=0.98) k_h = 1-(material.RH)**3; else if (material.RH == 1) k_h = -0.2; else k_h = 0.2-0.141192*(material.RH)/0.02; let S = Math.tanh(((material.t-material.t_s)/T_sh)**(0.5)); let BAZANT_B3_Eps_shb2 = Eps_sh_inf*k_h*S; let disp = BAZANT_B3_Eps_shb2*material.L; return disp; } 43:Tb9b,BAZANT_B3_Eps_cc = function(material) { let a_c; // eq(1.1) if (material.a_c>=2.5 && material.a_c <=13.5) a_c= material.a_c; else return "a_c is out of limit"; let w_c; // eq(1.1) if (material.w_c>=0.35 && material.w_c<=0.85) w_c= material.w_c; else return "w_c is out of limit"; let c; // eq(1.2) if (material.c>=160 && material.c<=720) c= material.c; else return "c is out of limit"; //Basic Creep let Q_f = (0.086*(material.t0)**(2/9)+1.21*(material.t0)**(4/9))**(-1); // eq(1.35) let Z = (material.t0)**(-0.5)*(Math.log(1+(material.t-material.t0)**(0.1))); // eq(1.36) let r = 1.7*(material.t0)**(0.12)+8; // eq(1.36) let Q = Q_f*(1+(Q_f/Z)**r)**(-1/r); // eq(1.36) let E_c = 4734*material.f_cm**0.5; // eq(1.16) let q_1 = 0.6*10**(6)/E_c; // eq(1.16) let q_2 = 185.4*c**(0.5)*material.f_cm**(-0.9); // eq(1.17) let q_3 = 0.29*(w_c)**4*q_2; // eq(1.18 let q_4 = 20.3*(a_c)**(-0.7); // eq(1.17) let C_0 = q_2*Q+q_3*(Math.log(1+(material.t-material.t0)**(0.1)))+q_4*(Math.log(material.t/material.t0)); // eq(1.7) // Additional drying creep let alfa1; // (eq1.21) if (material.cement_type == "I") alfa1 = 1; else if (material.cement_type == "II") alfa1 = 0.85; else alfa1 = 1.1; let alfa2; // eq(1.22) if (material.curing == "steamcuring") alfa2 = 0.75; else if (material.curing == "normalcuring") alfa2 = 1.2; else alfa2 = 1.0; let k_t = 8.5*material.t_0**(-0.08)*material.f_cm**(-1/4); // eq(1.20) let D = 2*material.V_S; // taken from explanation of eq(1.11) 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; let T_sh = k_t*(k_s*D)**2; // eq(1.11) let Eps_s_inf = -alfa1*alfa2*(0.019*material.w**(2.1)*material.f_cm**(-0.28)+270); // eq(1.19) Eps_s_inf is used istead of Eps_sh_inf since both is almost equal let q_5 = 7.57*100000*material.f_cm**(-1)*(Math.abs(Eps_s_inf))**(-0.6); // eq(1.23) let t__0 = Math.max(material.t0, material.t_0); // eq(1.14) let S_t = Math.tanh(((material.t-material.t_0)/T_sh)**(0.5)); // eq(1.9) let S_t0 = Math.tanh(((t__0-material.t_0)/T_sh)**(0.5)); // eq(1.9) let H_t = 1-(1-material.RH)*S_t; // eq(1.15) let H_t_0 = 1-(1-material.RH)*S_t0; // eq(1.15) let C_d; // eq(1.14) if (material.t>t__0) C_d = q_5*(Math.exp(-8*H_t)-Math.exp(-8*H_t_0))**(0.5); else C_d = 0; let J = (q_1+C_0+C_d)*0.000001; // eq(1.4) let sigma = material.P/(material.b*material.d); let BAZANT_B3_Eps_cc = J*sigma; // eq(1.3) let disp = BAZANT_B3_Eps_cc*material.L return disp ; }44:T15e1,BAZANT_B4_Eps_sha= function(material) { // equations are taken from J020A_2014_MASS_BAZ let V_S; // (6) if (material.V_S >= 12 && material.V_S <=120) V_S = material.V_S; else return "V_S is out of limit"; let w_c; // (1) if (material.w_c<= 0.87 && material.w_c >= 0.22) w_c = material.w_c; else return "w_c is out of limit"; let a_c; // (1) if (material.a_c>=1 && material.a_c <= 13.2) a_c = material.a_c; else return "a_c is out of limit"; let c; // (3) if (material.c>=200 && material.c <= 1500) c = material.c; else return "c is out of limit"; let T_cur; // (5) if (material.T_cur>=20 && material.T_cur <= 30) T_cur = material.T_cur; else return " T_cur is out of limit"; let Beta_TH = Math.exp(material.UH_R*(1/293-1/(T_cur+273))); // eq(8) let Beta_TS = Math.exp(material.US_R*(1/293-1/(T_cur+273))); // eq(9) let t_s_corrected = material.t_s*Beta_TH; //eq(8) let t_corrected = (material.t-material.t_s)*Beta_TS; // eq(9) let t_cons_corrected; // eq(9) if (material.t_cons>material.t_s) t_cons_corrected = (material.t_cons-material.t_s)*Beta_TS; else t_cons_corrected = 0; // Drying Shrinkage let T_cem; // Table 1 if (material.cement_type == "R") T_cem = 0.016; else if (material.cement_type == "RS") T_cem = 0.080; else if (material.cement_type == "SL") T_cem = 0.010; let P_Ta = -0.33; // Table 1 let P_Tw; // Table 1 if (material.cement_type == "R") P_Tw = -0.06; else if (material.cement_type == "RS") P_Tw = -2.40; else if (material.cement_type == "SL") P_Tw = 3.55; let P_Tc; // Table 1 if (material.cement_type == "R") P_Tc = -0.10; else if (material.cement_type == "RS") P_Tc = -2.70; else if (material.cement_type == "SL") P_Tc = 3.80; let T_0 = T_cem*(a_c/6)**P_Ta*(w_c/0.38)**P_Tw*(6.5*c/material.density)**P_Tc; // eq(22) let D = 2*V_S; // taken from explanation of eq(21) 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; 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; let T_sh = T_0*k_Ta*(k_s*D)**2; // eq(21) let Eps_cem; // Table 1 if (material.cement_type == "R") Eps_cem = 0.00036; else if (material.cement_type == "RS") Eps_cem = 0.00086; else if (material.cement_type == "SL") Eps_cem = 0.00041; let P_Epsa = -0.80; // Table 1 let P_Epsw; // Table 1 if (material.cement_type == "R") P_Epsw = 1.10; else if (material.cement_type == "RS") P_Epsw = -0.27; else if (material.cement_type == "SL") P_Epsw = 1.00; let P_Epsc = 0.11; // Table 1 let Eps_0 = Eps_cem*(a_c/6)**P_Epsa*(w_c/0.38)**P_Epsw*(6.5*c/material.density)**P_Epsc; // eq(16) 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; let E_7TH_600TS = material.E_28*(1/(4+(6/7)*(Beta_TH*7+Beta_TS*600)))**0.5; // eq(19) let E_t_Tsh_TS = material.E_28*(1/(4+(6/7)*(t_s_corrected+Beta_TS*T_sh)))**0.5; // eq(19) let Eps_sh_inf = -(Eps_0*k_Epsa*E_7TH_600TS)/E_t_Tsh_TS; // eq(17) let k_h; // eq(20) if (material.RH <=0.98) k_h = 1- material.RH**3; else k_h = 12.94*(1-material.RH)-0.2; let S_t = Math.tanh(Math.sqrt(t_corrected/T_sh)) - Math.tanh(Math.sqrt(t_cons_corrected/T_sh)); // eq(15) let Eps_sh = Eps_sh_inf*k_h*S_t; // eq(14) //Autogenous Shrinkage let T_au_cem; // Table 2 if (material.cement_type == "R") T_au_cem = 1.00; else if (material.cement_type == "RS") T_au_cem = 41.0; else if (material.cement_type == "SL") T_au_cem =1.00; let r_Tw = 3.0; // Table 2 let T_au = T_au_cem*(w_c/0.38)**r_Tw; // eq(26) let Eps_au_cem; // Table 2 if (material.cement_type == "R") Eps_au_cem = 0.00021; else if (material.cement_type == "RS") Eps_au_cem = -0.000084; else if (material.cement_type == "SL") Eps_au_cem = 0; let r_Epsa = -0.75; // Table 2 let r_Epsw = -3.5; // Table 2 let Eps_au_inf = -Eps_au_cem*(a_c/6)**r_Epsa*(w_c/0.38)**r_Epsw; // eq(25) let r_alpha; // Table 2 if (material.cement_type == "R") r_alpha = 1.00; else if (material.cement_type == "RS") r_alpha = 1.40; else if (material.cement_type == "SL") r_alpha =1.00; let Alpha = r_alpha*(w_c/0.38); // eq(24) let r_t = -4.5; // Table 2 let Eps_au = Eps_au_inf*(1+(T_au/(t_corrected+t_s_corrected)**Alpha))**r_t; // eq(24) let BAZANT_B4_Eps_sha = Eps_sh + Eps_au; // eq(13) let disp = BAZANT_B4_Eps_sha*material.L; return disp; } 45:T1506,BAZANT_B4_Eps_shb1= function(material) { // equations are taken from J020A_2014_MASS_BAZ let V_S; // (6) if (material.V_S >= 12 && material.V_S <=120) V_S = material.V_S; else return "V_S is out of limit"; let w_c; // (1) if (material.w_c<= 0.87 && material.w_c >= 0.22) w_c = material.w_c; else return "w_c is out of limit"; let a_c; // (1) if (material.a_c>=1 && material.a_c <= 13.2) a_c = material.a_c; else return "a_c is out of limit"; let c; // (3) if (material.c>=200 && material.c <= 1500) c = material.c; else return "c is out of limit"; let T_cur; // (5) if (material.T_cur>=20 && material.T_cur <= 30) T_cur = material.T_cur; else return " T_cur is out of limit"; let Beta_TH = Math.exp(material.UH_R*(1/293-1/(T_cur+273))); // eq(8) let Beta_TS = Math.exp(material.US_R*(1/293-1/(T_cur+273))); // eq(9) let t_s_corrected = material.t_s*Beta_TH; //eq(8) let t_corrected = (material.t-material.t_s)*Beta_TS; // eq(9) // Drying Shrinkage let T_cem; // Table 1 if (material.cement_type == "R") T_cem = 0.016; else if (material.cement_type == "RS") T_cem = 0.080; else if (material.cement_type == "SL") T_cem = 0.010; let P_Ta = -0.33; // Table 1 let P_Tw; // Table 1 if (material.cement_type == "R") P_Tw = -0.06; else if (material.cement_type == "RS") P_Tw = -2.40; else if (material.cement_type == "SL") P_Tw = 3.55; let P_Tc; // Table 1 if (material.cement_type == "R") P_Tc = -0.10; else if (material.cement_type == "RS") P_Tc = -2.70; else if (material.cement_type == "SL") P_Tc = 3.80; let T_0 = T_cem*(a_c/6)**P_Ta*(w_c/0.38)**P_Tw*(6.5*c/material.density)**P_Tc; // eq(22) let D = 2*V_S; // taken from explanation of eq(21) 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; 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; let T_sh = T_0*k_Ta*(k_s*D)**2; // eq(21) let Eps_cem; // Table 1 if (material.cement_type == "R") Eps_cem = 0.00036; else if (material.cement_type == "RS") Eps_cem = 0.00086; else if (material.cement_type == "SL") Eps_cem = 0.00041; let P_Epsa = -0.80; // Table 1 let P_Epsw; // Table 1 if (material.cement_type == "R") P_Epsw = 1.10; else if (material.cement_type == "RS") P_Epsw = -0.27; else if (material.cement_type == "SL") P_Epsw = 1.00; let P_Epsc = 0.11; // Table 1 let Eps_0 = Eps_cem*(a_c/6)**P_Epsa*(w_c/0.38)**P_Epsw*(6.5*c/material.density)**P_Epsc; // eq(16) 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; let E_7TH_600TS = material.E_28*(1/(4+(6/7)*(Beta_TH*7+Beta_TS*600)))**0.5; // eq(19) let E_t_Tsh_TS = material.E_28*(1/(4+(6/7)*(t_s_corrected+Beta_TS*T_sh)))**0.5; // eq(19) let Eps_sh_inf = -(Eps_0*k_Epsa*E_7TH_600TS)/E_t_Tsh_TS; // eq(17) let k_h; // eq(20) if (material.RH <=0.98) k_h = 1- material.RH**3; else k_h = 12.94*(1-material.RH)-0.2; let S_t = Math.tanh(Math.sqrt(t_corrected/T_sh)) // eq(15) let Eps_sh = Eps_sh_inf*k_h*S_t; // eq(14) //Autogenous Shrinkage let T_au_cem; // Table 2 if (material.cement_type == "R") T_au_cem = 1.00; else if (material.cement_type == "RS") T_au_cem = 41.0; else if (material.cement_type == "SL") T_au_cem =1.00; let r_Tw = 3.0; // Table 2 let T_au = T_au_cem*(w_c/0.38)**r_Tw; // eq(26) let Eps_au_cem; // Table 2 if (material.cement_type == "R") Eps_au_cem = 0.00021; else if (material.cement_type == "RS") Eps_au_cem = -0.000084; else if (material.cement_type == "SL") Eps_au_cem = 0; let r_Epsa = -0.75; // Table 2 let r_Epsw = -3.5; // Table 2 let Eps_au_inf = -Eps_au_cem*(a_c/6)**r_Epsa*(w_c/0.38)**r_Epsw; // eq(25) let r_alpha; // Table 2 if (material.cement_type == "R") r_alpha = 1.00; else if (material.cement_type == "RS") r_alpha = 1.40; else if (material.cement_type == "SL") r_alpha =1.00; let Alpha = r_alpha*(w_c/0.38); // eq(24) let r_t = -4.5; // Table 2 let Eps_au = Eps_au_inf*(1+(T_au/(t_corrected+t_s_corrected)**Alpha))**r_t; // eq(24) let BAZANT_B4_Eps_shb1 = Eps_sh + Eps_au; // eq(13) let disp = BAZANT_B4_Eps_shb1*material.L; return disp; }46:T1506,BAZANT_B4_Eps_shb2= function(material) { // equations are taken from J020A_2014_MASS_BAZ let V_S; // (6) if (material.V_S >= 12 && material.V_S <=120) V_S = material.V_S; else return "V_S is out of limit"; let w_c; // (1) if (material.w_c<= 0.87 && material.w_c >= 0.22) w_c = material.w_c; else return "w_c is out of limit"; let a_c; // (1) if (material.a_c>=1 && material.a_c <= 13.2) a_c = material.a_c; else return "a_c is out of limit"; let c; // (3) if (material.c>=200 && material.c <= 1500) c = material.c; else return "c is out of limit"; let T_cur; // (5) if (material.T_cur>=20 && material.T_cur <= 30) T_cur = material.T_cur; else return " T_cur is out of limit"; let Beta_TH = Math.exp(material.UH_R*(1/293-1/(T_cur+273))); // eq(8) let Beta_TS = Math.exp(material.US_R*(1/293-1/(T_cur+273))); // eq(9) let t_s_corrected = material.t_s*Beta_TH; //eq(8) let t_corrected = (material.t-material.t_s)*Beta_TS; // eq(9) // Drying Shrinkage let T_cem; // Table 1 if (material.cement_type == "R") T_cem = 0.016; else if (material.cement_type == "RS") T_cem = 0.080; else if (material.cement_type == "SL") T_cem = 0.010; let P_Ta = -0.33; // Table 1 let P_Tw; // Table 1 if (material.cement_type == "R") P_Tw = -0.06; else if (material.cement_type == "RS") P_Tw = -2.40; else if (material.cement_type == "SL") P_Tw = 3.55; let P_Tc; // Table 1 if (material.cement_type == "R") P_Tc = -0.10; else if (material.cement_type == "RS") P_Tc = -2.70; else if (material.cement_type == "SL") P_Tc = 3.80; let T_0 = T_cem*(a_c/6)**P_Ta*(w_c/0.38)**P_Tw*(6.5*c/material.density)**P_Tc; // eq(22) let D = 2*V_S; // taken from explanation of eq(21) 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; 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; let T_sh = T_0*k_Ta*(k_s*D)**2; // eq(21) let Eps_cem; // Table 1 if (material.cement_type == "R") Eps_cem = 0.00036; else if (material.cement_type == "RS") Eps_cem = 0.00086; else if (material.cement_type == "SL") Eps_cem = 0.00041; let P_Epsa = -0.80; // Table 1 let P_Epsw; // Table 1 if (material.cement_type == "R") P_Epsw = 1.10; else if (material.cement_type == "RS") P_Epsw = -0.27; else if (material.cement_type == "SL") P_Epsw = 1.00; let P_Epsc = 0.11; // Table 1 let Eps_0 = Eps_cem*(a_c/6)**P_Epsa*(w_c/0.38)**P_Epsw*(6.5*c/material.density)**P_Epsc; // eq(16) 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; let E_7TH_600TS = material.E_28*(1/(4+(6/7)*(Beta_TH*7+Beta_TS*600)))**0.5; // eq(19) let E_t_Tsh_TS = material.E_28*(1/(4+(6/7)*(t_s_corrected+Beta_TS*T_sh)))**0.5; // eq(19) let Eps_sh_inf = -(Eps_0*k_Epsa*E_7TH_600TS)/E_t_Tsh_TS; // eq(17) let k_h; // eq(20) if (material.RH <=0.98) k_h = 1- material.RH**3; else k_h = 12.94*(1-material.RH)-0.2; let S_t = Math.tanh(Math.sqrt(t_corrected/T_sh)) // eq(15) let Eps_sh = Eps_sh_inf*k_h*S_t; // eq(14) //Autogenous Shrinkage let T_au_cem; // Table 2 if (material.cement_type == "R") T_au_cem = 1.00; else if (material.cement_type == "RS") T_au_cem = 41.0; else if (material.cement_type == "SL") T_au_cem =1.00; let r_Tw = 3.0; // Table 2 let T_au = T_au_cem*(w_c/0.38)**r_Tw; // eq(26) let Eps_au_cem; // Table 2 if (material.cement_type == "R") Eps_au_cem = 0.00021; else if (material.cement_type == "RS") Eps_au_cem = -0.000084; else if (material.cement_type == "SL") Eps_au_cem = 0; let r_Epsa = -0.75; // Table 2 let r_Epsw = -3.5; // Table 2 let Eps_au_inf = -Eps_au_cem*(a_c/6)**r_Epsa*(w_c/0.38)**r_Epsw; // eq(25) let r_alpha; // Table 2 if (material.cement_type == "R") r_alpha = 1.00; else if (material.cement_type == "RS") r_alpha = 1.40; else if (material.cement_type == "SL") r_alpha =1.00; let Alpha = r_alpha*(w_c/0.38); // eq(24) let r_t = -4.5; // Table 2 let Eps_au = Eps_au_inf*(1+(T_au/(t_corrected+t_s_corrected)**Alpha))**r_t; // eq(24) let BAZANT_B4_Eps_shb2 = Eps_sh + Eps_au; // eq(13) let disp = BAZANT_B4_Eps_shb2*material.L; return disp; }47:T19e6,BAZANT_B4_Eps_cc = function(material) { let V_S; // (6) if (material.V_S >= 12 && material.V_S <=120) V_S = material.V_S; else return "V_S is out of limit"; let w_c; // (1) if (material.w_c<= 0.87 && material.w_c >= 0.22) w_c = material.w_c; else return "w_c is out of limit"; let a_c; // (1) if (material.a_c>=1 && material.a_c <= 13.2) a_c = material.a_c; else return "a_c is out of limit"; let c; // (3) if (material.c>=200 && material.c <= 1500) c = material.c; else return "c is out of limit"; let Beta_TH = Math.exp(material.UH_R*(1/293-1/(material.T_cur+273))); // eq(8) let Beta_TS = Math.exp(material.US_R*(1/293-1/(material.T_cur+273))); // eq(9) let t_0_corrected = material.t_0*Beta_TH; //eq(8) let t_corrected = (material.t-material.t0)*Beta_TS; // eq(9) let t0_corrected = material.t0*Beta_TH // eq(8) let p_1; // Table(3) if (material.cement_type == "R") p_1 = 0.70; else if (material.cement_type == "RS") p_1 = 0.60; else if (material.cement_type == "SL") p_1 = 0.80; let p_2; // Table(3) if (material.cement_type == "R") p_2 = 0.0586; else if (material.cement_type == "RS") p_2 = 0.0174; else if (material.cement_type == "SL") p_2 = 0.0405; let p_3 = 0.0393; // Table(3) let p_4 = 0.0034; // Table(3) let p_5; // Table(3) if (material.cement_type == "R") p_5 = 0.00077 ; else if (material.cement_type == "RS") p_2 = 0.000946; else if (material.cement_type == "SL") p_2 = 0.000496; let p_5H; // Table(3) if (material.cement_type == "R" || material.cement_type == "SL") p_5H = 8.00; else if (material.cement_type == "RS") p_5H = 1.00; 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) // Instantaneous Compliance let E_28 = 4734*(material.f_cm)**0.5*0.001; // Eq.29 let q_1 = (p_1/E_28*1000)*0.000001; // Eq.28 //Basic Creep let q_2 = (p_2*((w_c/0.38)**p_2w)*1000)*0.000001; // eq(40) let q_3 = (p_3*q_2*((a_c/6)**p_3a)*((w_c/0.38)**p_3w)); // eq(41) let q_4 = (p_4*((a_c/6)**p_4a)*((w_c/0.38)**p_4w)*1000)*0.000001; // eq(42) let r_t = 1.7*(t0_corrected)**0.12+8; // eq(35) let Z_t = t0_corrected**(-0.5)*Math.log(1+(t_corrected-t0_corrected)**0.1); // eq(34) let Q_f = (0.086*t0_corrected**(2/9)+1.21*t0_corrected**(4/9))**(-1); // eq(33) let Q_t = Q_f*(1+(Q_f/Z_t)**r_t)**(-1/r_t); // eq(32) let C_0 = q_2*Q_t + q_3*Math.log(1+(t_corrected-t0_corrected)**(0.1)) + q_4*Math.log(t_corrected/t0_corrected); // eq(31) // Drying Creep let k_h; // eq(20) if (material.RH <=0.98) k_h = 1- material.RH**3; else k_h = 12.94*(1-material.RH)-0.2; let T_cem; // Table 1 if (material.cement_type == "R") T_cem = 0.016; else if (material.cement_type == "RS") T_cem = 0.080; else if (material.cement_type == "SL") T_cem = 0.010; let P_Ta = -0.33; // Table 1 let P_Tw; // Table 1 if (material.cement_type == "R") P_Tw = -0.06; else if (material.cement_type == "RS") P_Tw = -2.40; else if (material.cement_type == "SL") P_Tw = 3.55; let P_Tc; // Table 1 if (material.cement_type == "R") P_Tc = -0.10; else if (material.cement_type == "RS") P_Tc = -2.70; else if (material.cement_type == "SL") P_Tc = 3.80; let T_0 = T_cem*(a_c/6)**P_Ta*(w_c/0.38)**P_Tw*(6.5*c/material.density)**P_Tc; // eq(22) let D = 2*V_S; // taken from explanation of eq(21) 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; 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; let T_sh = T_0*k_Ta*(k_s*D)**2; // eq(21) let Eps_cem; // Table 1 if (material.cement_type == "R") Eps_cem = 0.00036; else if (material.cement_type == "RS") Eps_cem = 0.00086; else if (material.cement_type == "SL") Eps_cem = 0.00041; let P_Epsa = -0.80; // Table 1 let P_Epsw; // Table 1 if (material.cement_type == "R") P_Epsw = 1.10; else if (material.cement_type == "RS") P_Epsw = -0.27; else if (material.cement_type == "SL") P_Epsw = 1.00; let P_Epsc = 0.11; // Table 1 let Eps_0 = Eps_cem*(a_c/6)**P_Epsa*(w_c/0.38)**P_Epsw*(6.5*c/material.density)**P_Epsc; // eq(16) 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; let E_7TH_600TS = material.E_28*(1/(4+(6/7)*(Beta_TH*7+Beta_TS*600)))**0.5; // eq(19) let E_t_Tsh_TS = material.E_28*(1/(4+(6/7)*(t_0_corrected+Beta_TS*T_sh)))**0.5; // eq(19) let Eps_sh_inf = -(Eps_0*k_Epsa*E_7TH_600TS)/E_t_Tsh_TS; // eq(17) let q_5 = (p_5*((a_c/6)**p_5a)*((w_c/0.38)**p_5w)*(Math.abs(k_h*Eps_sh_inf))**p_5Eps*1000)*0.000001; let H = 1-(1-material.RH)*Math.tanh(((t_corrected-t0_corrected)/T_sh)**0.5); // eq(37) let t__0 = Math.max(t0_corrected, t_0_corrected); let H_c = 1-(1-material.RH)*Math.tanh(((t__0-t0_corrected)/T_sh)**0.5); // eq(38) 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; let J_t = (q_1+ C_0+C_d); // eq(27) let Sigma = material.P/(material.b*material.d); let BAZANT_B4_Eps_cc = J_t*Sigma; // eq(12) let disp = BAZANT_B4_Eps_cc*material.L; return disp; }48:[] 30:{"id":"10b56bc91b1c2eb2","slug":"creep-and-shrinkage-code-comparison","title":"Creep and Shrinkage Code Comparison","thumbnail":"e286474e34322e72b2d36ed063f0e2c32210005d7ed447d7845dd568bc1b5cde","access_level":"public","create_time":"$D2020-05-28T12:20:11.696Z","update_time":"$D2020-05-28T12:20:11.696Z","view_time":null,"first_public_time":"$D2020-05-28T12:20:57.751Z","has_unpublished_edits":null,"fork":{"id":"b976705b76a1796c","slug":"creep-and-shrinkage-code-comparison","title":"Creep and Shrinkage Code Comparison","owner":{"id":"ead0a69180b9c7fc","login":"larsa4d","name":"LARSA, 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Displacement b1 is the shrinkage displacment at age of concrete at the moment considered, for this case 100 days and Shrinkage Displacement b2 is the shrinkage displacement at the day of construction for this case 15 days. Resultant shrinkage displacement is named as Shrinkage Displacement b and calculated by substracting b2 from b1. `","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":571,"value":"md `# CEB-FIP 78`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":580,"value":"tex` SHRINKAGE`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":585,"value":"tex`CaseA`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":600,"value":"tex `Eps_{s} (t,t_0) = Eps_{so}*[Beta_s(t)-Beta_s(t_0)]`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":606,"value":"tex` Beta_s(t) = [\\frac{t}{t+K_3(h_0)}]^{K_4(h_0)} `","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":611,"value":"tex` K_3(h_0) = 11.8h_0+16`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":618,"value":"tex` K_4(h_0) = e^{[-0.00257h_0+\\frac{0.32}{h_0}+ln(0.22h_0^{0.4})]} `","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":626,"value":"tex ` Eps_{so} = Eps_{s1}*Eps_{s2}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":629,"value":"tex` Eps_{s1}= (0.000775(RH)^3-0.1565(RH)^2 +11.0325(RH)-303.25)*10^{-5}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":632,"value":"tex`Eps_{s2} = e^{[0.00174h_0-\\frac{0.32}{h_0}-ln(\\frac{h_0^{0.251}}{1.9})]}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":590,"value":"CEB_FIP_78_Eps_sha ({ t: 100, t_cons: 1, t_s: 1, RH: 60, h: 300, coeff: 1.5, L:1000 }) // coeff is notional thickness coefficient, h_0 given above formulas is notinal thickness (in cm)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":592,"value":"$35","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":784,"value":"tex`CaseB`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":790,"value":"CEB_FIP_78_Eps_shb1 ({ t: 100, t_cons: 1, t_s: 1, RH: 60, h: 300, coeff: 1.5, L:1000 }) // coeff is notional thickness coefficient, h_0 placed in above formulas is notinal thickness (in cm), t0 is consturction day","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":794,"value":"CEB_FIP_78_Eps_shb1 = function(material) {\n let h_0 = (material.h * material.coeff) / 10;\n\n let Eps_s1 = (0.000775 * material.RH ** 3 - 0.1565 * material.RH **2 +11.0325 * material.RH-303.25)*0.00001;\n\n let Eps_s2 = Math.exp(0.00174 * h_0 - 0.32 / h_0 - Math.log(h_0 ** 0.251 / 1.9));\n\n let Eps_s0 = Eps_s1 * Eps_s2;\n\n let K_3 = 11.8 * h_0 + 16;\n\n let K_4 = Math.exp(-0.00257 * h_0 + 0.32 / h_0 + Math.log(0.22 * h_0 ** 0.4));\n\n let Beta_s_t = (material.t / (material.t + K_3)) ** K_4;\n\n let Beta_s_t0;\n \n if (material.t_cons - material.t_s > 0)\n Beta_s_t0 = (material.t_s/(material.t_s+K_3))**K_4+((material.t_cons - material.t_s)/(material.t_cons - material.t_s+ K_3))**K_4;\n else \n Beta_s_t0 = (material.t_s / (material.t_s + K_3)) ** K_4;\n\n let CEB_FIP_78_Eps_shb1 = Eps_s0 * (Beta_s_t - Beta_s_t0);\n\n let disp = CEB_FIP_78_Eps_shb1*material.L;\n\n return disp;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1183,"value":"CEB_FIP_78_Eps_shb2 ({ t: 15, t_cons: 1, t_s: 1, RH: 60, h: 300, coeff: 1.5, L:1000 }) // coeff is notional thickness coefficient, h_0 placed in above formulas is notinal thickness (in cm), t0 is consturction day","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1185,"value":"CEB_FIP_78_Eps_shb2 = function(material) {\n let h_0 = (material.h * material.coeff) / 10;\n\n let Eps_s1 =\n (0.000775 * material.RH ** 3 -\n 0.1565 * material.RH ** 2 +\n 11.0325 * material.RH -\n 303.25) *\n 0.00001;\n\n let Eps_s2 = Math.exp(\n 0.00174 * h_0 - 0.32 / h_0 - Math.log(h_0 ** 0.251 / 1.9)\n );\n\n let Eps_s0 = Eps_s1 * Eps_s2;\n\n let K_3 = 11.8 * h_0 + 16;\n\n let K_4 = Math.exp(-0.00257 * h_0 + 0.32 / h_0 + Math.log(0.22 * h_0 ** 0.4));\n\n let Beta_s_t = (material.t / (material.t + K_3)) ** K_4;\n\n let Beta_s_t0;\n\n if (material.t_cons - material.t_s > 0)\n Beta_s_t0 =\n (material.t_s / (material.t_s + K_3)) ** K_4 +\n ((material.t_cons - material.t_s) / (material.t_cons - material.t_s + K_3)) **\n K_4;\n else Beta_s_t0 = (material.t_s / (material.t_s + K_3)) ** K_4;\n\n let CEB_FIP_78_Eps_shb2= Eps_s0 * (Beta_s_t - Beta_s_t0);\n\n let disp = CEB_FIP_78_Eps_shb2*material.L;\n\n return disp;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":780,"value":"tex` CREEP `","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":801,"value":"tex` Eps_{cc}(t,t_0)=\\frac{Sigma_0}{E{c28}}*Phi(t,t_0)`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":806,"value":"tex`Phi(t,t_0)=Beta_a(t_0)+phi_d*Beta_d(t-t_0)+Phi_f[Beta_f(t)-Beta_f(t_0)]`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":809,"value":"tex`Beta_a(t_0) = 0.8*(1-[\\frac{t_o}{t_o+47}]^{\\frac{1}{2.45}})`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":812,"value":"tex`Phi_d =0.4` ","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":822,"value":"tex`Phi_f = Phi_{f1}+Phi_{f2}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":824,"value":"tex`Phi_{f1}=4.45-0.035RH`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"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","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":842,"value":"tex`Beta_d(t-t_0)=[\\frac{t-t_0}{t+K_1(h_o)}]^{K_2(h_o)}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":854,"value":"tex`Beta_f(t)=[\\frac{t}{t+K_1(h_o)}]^{K_2(h_o)}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":855,"value":"tex`K_1(h_o)=e^{[\\frac{5.02}{h_o}+ln(6.95h_o^{1.25})]}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"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","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":797,"value":"CEB_FIP_78_Eps_cc({t: 100, t0: 16, RH: 60, h: 300, coeff: 1.5, P: -(10 ** 7), b: 1200, d: 400, E_c28: 35000, L: 1000 })","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":799,"value":"$36","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":656,"value":"md` # CEB-FIP 90 updated knowledge `","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":657,"value":"tex` SHRINKAGE`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":660,"value":"tex` Eps_{cs} (t,t_s) = Eps_{cas}(t)+Eps_{cds}(t,t_s)`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":667,"value":"tex` Eps_{cas} = Eps_{caso}(f_{cm})*Beta_{as}(t-t_s)`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":668,"value":"tex` Eps_{cds} (t,t_s)=Eps_{cdso}(f_{cm})*Beta_{RH}(RH)*Beta_{ds}(t-t_s)`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":675,"value":"tex` Eps_{caso}(f_{cm})= -alpha_{as}(\\frac{f_{cm}/f_{cmo}}{6+f_{cm}/f_{cmo}})^{2.5}*10^{-6}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":677,"value":"tex`Beta_{as} = 1- exp(-0.2*(\\frac{t}{t_1})^{0.5})`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":680,"value":"tex` Eps_{cdso}(f_{cm})= [(220+110*Alpha_{ds1})*exp(-Apha_{ds2}*\\frac{f_{cm}}{f{cmo}})]*10^{-6}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":690,"value":"tex` Beta_{RH}(RH)= -1.55*[1-(\\frac{RH}{RH_o})^3] for RH<0.99*Beta_{s1}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":701,"value":"tex` Beta_{RH}(RH)= 0.25 for RH>=0.99*Beta_{s1}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":716,"value":"tex`Beta_{s1} = (\\frac{3.5f_{cmo}}{f_{cm}})^{0.1}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":717,"value":"tex` Beta_{ds} (t-t_s) = [\\frac{(t-t_s)/t_1}{350(h/h_0)^2+(t-t_s)/t_1})^{0.5}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":723,"value":"CEB_FIP_90_upd_Eps_sha({RH: 0.6, h: 300, cement_hardtype: \"N\", RH_0: 1, f_cmo: 10,f_cm: 40, t: 100, t_cons:1, t_s: 1,h_0: 100, L: 1000})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":725,"value":"$37","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":896,"value":"md` # CEB-FIP 90 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= -1.55Beta_{srh} for 0.4<=RH<0.99`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":932,"value":"tex`Beta_{RH} = 0.25 for RH>=0.99`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":940,"value":"tex`Beta{sRH}= 1- (\\frac{RH}{RH_o})^3`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":945,"value":"tex`Beta_s(t-t_s)=[\\frac{(t-t_s)/t_1}{350(h/h_o)^2+(t-t_s)/t_1}]{0.5}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":950,"value":"CEB_FIP_90_Eps_sha({RH: 0.6, h: 300, cement_hardtype: \"N\", RH_0: 1, f_cmo: 10,f_cm: 40, t: 100, t_cons: 1, t_s: 3,h_0: 100, L: 1000})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":951,"value":"CEB_FIP_90_Eps_sha = function(material) {\n \n let Beta_sRH = 1 - (material.RH / material.RH_0) ** 3; // eq(2.1-79)\n\n let Beta_RH; // eq(2.1-78)\n if (material.RH >= 0.4 && material.RH < 0.99) Beta_RH = -1.55 * Beta_sRH;\n else if (material.RH >= 0.99) Beta_RH = 0.25;\n\n let Beta_sc; // taken from explanation of eq(2.1-76)\n if (material.cement_hardtype == \"SL\") Beta_sc = 4;\n else if (material.cement_hardtype == \"N\" || material.cement_hardtype == \"R\")\n Beta_sc = 5;\n else if (material.cement_hardtype == \"RS\") Beta_sc = 8;\n\n let Eps_s = (160 + 10 * Beta_sc * (9 - material.f_cm / material.f_cmo)) * 0.000001; // eq(2.1-76)\n\n let Eps_cso = Eps_s * Beta_RH; // eq(2.1-75)\n\n let Beta_s =((material.t-material.t_s)/material.t_cons/(350*(material.h/material.h_0)**2+(material.t-material.t_s) / material.t_cons))**0.5; // eq(2.1-79)\n\n let CEB_FIP_90_Eps_sha = Eps_cso * Beta_s; //eq(2.1-74)\n\n let disp = CEB_FIP_90_Eps_sha*material.L;\n\n return disp;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":966,"value":"tex`CaseB`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":971,"value":"CEB_FIP_90_Eps_shb1({RH: 0.6, h: 300, cement_hardtype: \"N\", RH_0: 1, f_cmo: 10,f_cm: 40, t: 100, t_cons: 1, t_s: 3,h_0: 100, L:1000})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":975,"value":"CEB_FIP_90_Eps_shb1 = function(material) {\n let Beta_sRH = 1 - (material.RH / material.RH_0) ** 3;\n\n let Beta_RH;\n if (material.RH >= 0.4 && material.RH < 0.99) Beta_RH = -1.55 * Beta_sRH;\n else if (material.RH >= 0.99) Beta_RH = 0.25;\n\n let Beta_sc;\n if (material.cement_hardtype == \"SL\") Beta_sc = 4;\n else if (material.cement_hardtype == \"N\" || material.cement_hardtype == \"R\")\n Beta_sc = 5;\n else if (material.cement_hardtype == \"RS\") Beta_sc = 8;\n\n let Eps_s =\n (160 + 10 * Beta_sc * (9 - material.f_cm / material.f_cmo)) * 0.000001;\n\n let Eps_cso = Eps_s * Beta_RH;\n\n let Beta_s = ((material.t-material.t_s)/material.t_cons/(350*(material.h/material.h_0)**2+(material.t-material.t_s) / material.t_cons))**0.5;\n\n let CEB_FIP_90_Eps_shb1 = Eps_cso * Beta_s;\n\n let disp = CEB_FIP_90_Eps_shb1*material.L;\n\n return disp;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1197,"value":"CEB_FIP_90_Eps_shb2({RH: 0.6, h: 300, cement_hardtype: \"N\", RH_0: 1, f_cmo: 10,f_cm: 40, t: 15, t_cons: 1, t_s: 3,h_0: 100, L:1000})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1199,"value":"CEB_FIP_90_Eps_shb2 = function(material) {\n \n let Beta_sRH = 1 - (material.RH / material.RH_0) ** 3;\n\n let Beta_RH;\n if (material.RH >= 0.4 && material.RH < 0.99) Beta_RH = -1.55 * Beta_sRH;\n else if (material.RH >= 0.99) Beta_RH = 0.25;\n\n let Beta_sc;\n if (material.cement_hardtype == \"SL\") Beta_sc = 4;\n else if (material.cement_hardtype == \"N\" || material.cement_hardtype == \"R\")\n Beta_sc = 5;\n else if (material.cement_hardtype == \"RS\") Beta_sc = 8;\n\n let Eps_s =\n (160 + 10 * Beta_sc * (9 - material.f_cm / material.f_cmo)) * 0.000001;\n\n let Eps_cso = Eps_s * Beta_RH;\n\n let Beta_s = ((material.t - material.t_s) /material.t_cons /(350 * (material.h / material.h_0) ** 2 +(material.t - material.t_s) / material.t_cons))**0.5;\n\n let CEB_FIP_90_Eps_shb2 = Eps_cso * Beta_s;\n\n let disp = CEB_FIP_90_Eps_shb2*material.L;\n\n return disp;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":976,"value":"tex`CREEP`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":989,"value":"tex`Eps_{cc}(t,t_0)=\\frac{Sigma_c(t_0)}{E_{ci}}Phi(t,t_0)`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":993,"value":"tex`Phi(t,t_0)=Phi_0*Beta_c(t-t_0) 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20))+material.t)-material.t_cons/(12*((100-4*f_ci)/(f_ci+20)) +material.t_cons); // eq(5.4.2.3.2-5)\n\n let AASHTO_v7_v8_Eps_sha = -k_s * k_hs * k_f * k_td * 0.48 * 10 ** -3; // eq(5.4.2.3.3-1)\n\n let disp = AASHTO_v7_v8_Eps_sha*material.L;\n\n return disp;\n\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":68,"value":"tex`CaseB` ","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":15,"value":"AASHTO_v7_v8_Eps_shb1 ({V_S: 5.905512, RH: 60, f_cm: 40, t: 100, 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(1.45-0.13*material.V_S >= 1)\n k_s = 1.45-0.13*material.V_S;\n else\n k_s = 1;\n \n let k_hc = 1.56-0.008*material.RH; // eq(5.4.2.3.2-3)\n \n let f_ci = 0.8*((material.f_cm-8)/6.89475908677537); // converting unit of f_cm form Mpa into ksi\n \n let k_f = 5/(1+f_ci); // eq(5.4.2.3.2-4)\n \n let k_td = (material.t-material.t0)/(12*(100-4*f_ci)/(20+f_ci)+(material.t-material.t0)); // eq(5.4.2.3.2-5)\n \n let phi = 1.9*k_s*k_hc*k_f*k_td*material.t0**(-0.118); // eq(5.4.2.3.2-1)\n \n let sigma = (material.P)/(material.b*material.d);\n \n let AASHTO_v7_v8_Eps_cc = phi*sigma/material.E_c28; \n \n let disp = AASHTO_v7_v8_Eps_cc *material.L;\n\n return disp;\n\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":203,"value":"md`# AASHTO LRFD 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k_s = 1.45-0.13*material.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= (material.t/(61-4*f_ci+material.t))- (material.t0/(61-4*f_ci+material.t0)); // eq(5.4.2.3.2-5)\n \n let AASHTO_v6_Eps_sha = -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_sha*material.L;\n\n return disp;\n\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":263,"value":"tex`CaseB` 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({V_S: 15, cement_type:\"I\", curing: \"normalcuring\", specimen_geometry: \"infinite square prism\", RH: 0.6, f_cm: 40, t: 100, t_s:1, w: 130, E_28: 35000, L:1000 });","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1594,"value":"$41","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1600,"value":"BAZANT_B3_Eps_shb2 ({V_S: 15, cement_type:\"I\", curing: \"normalcuring\", specimen_geometry: \"infinite square prism\", RH: 0.6, f_cm: 40, t: 15, t_s:1, w: 130, E_28: 35000, L:1000 });","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1602,"value":"$42","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":325,"value":"tex` CREEP`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":428,"value":"tex`Eps_{cc} 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Eps_{cem}(\\frac{a/c}{6})^{P_{Epsa}}(\\frac{w/c}{0.38})^{P_{Epsw}}(\\frac{6.5c}{Density})^{P_{Epsc}}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2149,"value":"tex`E(t)=E_{28}\\sqrt{\\frac{1}{4+(6/7)t}}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2154,"value":"tex`T_{sh}=T_0*k_{Ta}(k_s\\frac{D}{1mm})^2`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2157,"value":"tex`T_0= 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T_cur is temperature of the environment during curing and density is set to 2350 kg/m^3 as indicated in eq(16)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2507,"value":"$46","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2516,"value":"tex` Creep`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2517,"value":"tex` Eps_{cc} (t) = J( t, 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4734MPa\\sqrt{f_c/MPa}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"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","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2539,"value":"tex` Q_(t,t') = Q_f(t') (1+(\\frac{Q_f(t')}{Z(t,t')})^{r(t')})^{-\\frac{1}{r(t')}}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"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","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2546,"value":"tex` Z(t') =(\\frac{t'}{1day})^{-0.5}ln[1+ (\\frac{t-t'}{1day})^{0.1}]`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2553,"value":"tex` r(t') = 1.7(\\frac{t'}{1day})^{0.12}+8`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2556,"value":"tex` q_2 = \\frac{p_2}{1GPa}(\\frac{w/c}{0.38})^{p_{2w}}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"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","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2563,"value":"tex` q_4 = \\frac{p_4}{1GPa}(\\frac{a/c}{6})^{p_{4a}}(\\frac{w/c}{0.38})^{p_{4w}}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"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","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2570,"value":"tex` H(t,t_0) = 1-(1-h)tanh\\sqrt{t-t_0}{T_{sh}}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2575,"value":"tex` H_c(t,t_0) = 1-(1-h)tanh\\sqrt{t_0'-t_0}{T_{sh}}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2578,"value":"tex` q_5 =\\frac{p_5}{1GPa}(\\frac{a/c}{6})^{p_{5a}}(\\frac{w/c}{0.38})^{p_{5w}}|k_hEps_{sh,inf}(t_0)|^{p_{5Eps}}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2585,"value":"tex` R_T = exp[\\frac{U_c'}{R}(\\frac{1}{293}-\\frac{1}{T+273})]`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2590,"value":"BAZANT_B4_Eps_cc({V_S: 120, cement_type:\"R\", curing: \"normalcuring\", RH: 0.6, f_cm: 40, t: 100, t0:16, t_0: 15, w: 240, c:350, a_c:5, w_c:0.5, aggregate_type: \"Unknown\", specimen_geometry: \"infinite square prism\", E_28: 35000, L:1000, density: 2350, UH_R: 4000, US_R: 4000, UC_R: 4000, T_cur:20, T: 20, b: 1200, d: 400, P:-(10**7) }); // t0 : age of 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