f'c ≔ 280 b ≔ 80 fy ≔ 4200 Es ≔ 2 ⋅ 10 h ≔ 130 rec ≔ 8 l ≔ 20 d ≔ h − rec = 122 Ø ≔ 0.9 Es n ≔ ― = 7.968 Ec 5 Ec ≔ 15000 ⋅ ‾‾‾ f'c = 2.51 ⋅ 10 6 CM ＝ PPV + CP CM ≔ 0.80 ⋅ 1.3 ⋅ 2.400 + 6.800 = 9.296 CV ≔ 3.200 wu ≔ 1.4 ⋅ CM + 1.7 ⋅ CV = 18.454 wS ≔ CM + CV = 12.496 CARGA ÚLTIMA CARGA SERVICIO 2 w⋅l MA ＝ MB ＝ ―― 12 2 w⋅l Mmax ＝ ―― 24 ESTADO LÍMITE ÚLTIMO Apoyos: Centro: 2 wu ⋅ l MAu ≔ ――― = 615.147 12 2 wu ⋅ l MABu ≔ ――― = 307.573 24 ESTADO LÍMITE SERVICIO 2 wS ⋅ l MAs ≔ ――― = 416.533 12 2 wS ⋅ l MABs ≔ ――― = 208.267 24 MOMENTO NEGATIVO ⎛ ‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾ 2 ⋅ MAu ⋅ 100000 ⎞ a ≔ ⎜1 − 1 − ―――――― ⎟ ⋅ d = 34.225 2 Ø ⋅ 0.85 ⋅ f'c ⋅ b ⋅ d ⎠ ⎝ cb ≔ 0.6 ⋅ d = 73.2 f'c As ≔ 0.85 ⋅ ― ⋅ b ⋅ a = 155.154 fy 30Ø1" cmax ≔ 0.75 ⋅ cb = 54.9 MOMENTO POSITIVO a > c ≔ ―― = 40.265 0.85 ⎛ ‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾ 2 ⋅ MABu ⋅ 100000 ⎞ a ≔ ⎜1 − 1 − ―――――― ⎟ ⋅ d = 15.726 2 Ø ⋅ 0.85 ⋅ f'c ⋅ b ⋅ d ⎠ ⎝ cb ≔ 0.6 ⋅ d = 73.2 Falla dúcil f'c As ≔ 0.85 ⋅ ― ⋅ b ⋅ a = 71.29 fy 15Ø1" a > c ≔ ―― = 18.501 0.85 cmax ≔ 0.75 ⋅ cb = 54.9 Falla dúcil ACERO MÍNIMO ‾‾‾ f'c Asmin ≔ 0.7 ⋅ ――⋅ b ⋅ d = 27.219 fy Ascol ≔ 3 ⋅ 2.85 = 8.55 Asmin ρmin ≔ ――⋅ 100 = 0.279 b⋅d b = 80 d = 122 ACERO MÁXIMO f'c Asmax ≔ 0.75 ⋅ 0.85 ⋅ ― ⋅ b ⋅ ab = 211.548 fy ab ≔ 0.85 ⋅ cb = 62.22 ⎛ b ⋅ h2 ⎞ 1 Mcr ≔ fr ⋅ ⎜――⎟ ⋅ ――― = 75.411 ⎝ 6 ⎠ 100000 fr ≔ 2 ⋅ ‾‾‾ f'c = 33.466 MAs = 416.533 > Mcr = 75.411 Luego Ief.neg ＝ Icrneg MABs = 208.267 > Mcr = 75.411 Luego Ief.pos ＝ Icrpos M O M EN TO N EG A TIV O Asneg ≔ 30 ⋅ 5.07 = 152.1 n = 7.968 3 b⋅h Ig ≔ ――= 14646666.667 12 ‾‾‾‾‾‾‾‾‾ Asneg ⎛ 2⋅b⋅d ⎞ cfisneg ≔ n ⋅ ――⋅ ⎜−1 + 1 + ――― ⎟ ⋅ d = 47.508 b⋅d ⎝ n ⋅ Asneg ⎠ 3 2 b ⋅ cfisneg Icrneg ≔ ―――― + n ⋅ Asneg ⋅ ⎛⎝d − cfisneg⎞⎠ = 9584607.364 3 Icrneg ――= 0.654 Ig M O M EN TO PO SITIV O Aspos ≔ 15 ⋅ 5.07 = 76.05 n = 7.968 ‾‾‾‾‾‾‾‾‾ Aspos ⎛ 2⋅b⋅d ⎞ cfispos ≔ n ⋅ ――⋅ ⎜−1 + 1 + ――― ⎟ ⋅ d = 36.079 b⋅d ⎝ n ⋅ Aspos ⎠ 3 2 b ⋅ cfispos Icrpos ≔ ――― + n ⋅ Aspos ⋅ ⎛⎝d − cfispos⎞⎠ = 5725973.193 3 Icrpos ――= 0.391 Ig IN ERCIA EFEC TIV A 2 ⋅ Icrneg + 2 ⋅ Icrpos Ief ≔ ―――――― = 7655290.278 4 CV = 3.2 l = 20 4 CV ⋅ l ⋅ 1000000000 ΔiL ≔ ――――――― = 0.694 384 ⋅ Ec ⋅ Ief l ⋅ 100 ――= 2882.194 ΔiL Limite normativo (en caso la viga no estuviera ligada a elementos estructurales): l ⋅ 100 ――= 5.556 360 PP ≔ 0.8 ⋅ 1.3 ⋅ 2.4 = 2.496 l = 20 4 PP ⋅ l ⋅ 1000000000 ΔiPP ≔ ――――――― = 0.541 384 ⋅ Ec ⋅ Ief CP ≔ CM − PP = 6.8 l = 20 4 CP ⋅ l ⋅ 1000000000 ΔiCP ≔ ――――――― = 1.475 384 ⋅ Ec ⋅ Ief A's ≔ 10 ⋅ 5.07 = 50.7 A's ρ' ≔ ―― = 0.005 b⋅d 2.0 λ ≔ ―――= 1.588 1 + 50 ⋅ ρ' ΔdL ≔ λ ⋅ ΔiL = 1.102 ΔdD ≔ λ ⋅ ΔiCP + λ ⋅ ΔiPP = 3.2 Δt ≔ ΔiL + λ ⋅ ΔiL + ΔiCP + λ ⋅ ΔiCP + λ ⋅ ΔiPP = 6.471 Limite normativo: l ⋅ 100 ――= 8.333 240 Δt ≔ ΔiPP + ΔiL + λ ⋅ ΔiL + ΔiCP + λ ⋅ ΔiCP + λ ⋅ ΔiPP = 7.012