Vista previa del material en texto
E1 45 60 2.3 4.5 2.2 2.8 6.2 2.1 Mf -119.025 75.9375 -75.9375 135.1452 -126.2748 144.15 -144.15 99.225 ΔB 10 mm ΔC 12 mm Viga de concreto f'c 21 Mpa 3000 psi E 21538 Mpa b h Viga 250 450 I 1898437500 mm4 EI 40889 KN/m2 ƟA ƟB ƟC ƟD Carga puntual EI 0.889 0.444 0.000 0.000 ƟA = 43.0875 0.444 1.689 0.400 0.000 ƟB -59.2077 0.000 0.400 1.445 0.323 ƟC -17.8752 0.000 0.000 0.323 0.645 ƟD 44.925 1/EI 1.3112830754 -0.3725661508 0.1160758862 -0.0580379431 43.0875 = ƟA -0.3725661508 0.7451323015 -0.2321517723 0.1160758862 -59.2077 ƟB 0.1160758862 -0.2321517723 0.8512231653 -0.4256115826 -17.8752 ƟC -0.0580379431 0.1160758862 -0.4256115826 1.7628057913 44.925 ƟD 73.88 = ƟA -50.81 ƟB -15.59 ƟC 77.43 ƟD ELEMENTO AB ELEMENTO BC EI/L 4 2 Ɵi + Mfij = Mij EI/L 4 2 Ɵi + Mfij = Mij 2 4 Ɵj Mfij Mji 2 4 Ɵj Mfij Mji EI 0.8889 0.4444 73.88 + 75.9375 = MAB EI 0.8000 0.4000 -50.81 + 135.1452 = MAB 0.4444 0.8889 -50.81 -75.9375 MBA 0.4000 0.8000 -15.59 -126.2748 MBA 43.09 + 75.9375 = MAB -46.88 + 135.1452 = MAB -12.33 -75.9375 MBA -32.79 -126.2748 MBA 119.03 = MAB 88.26 = MAB -88.26 MBA -159.07 MBA 45 kN/m A B C D 60 kN E2 Empotrada 45 60 2.3 4.5 2.2 2.8 6.2 2.1 Mf -119.025 75.9375 -75.9375 135.1452 -126.2748 144.15 -144.15 Carga ΔB 10 mm ΔC 12 mm Viga de concreto f'c 21 Mpa 3000 psi E 21538 Mpa b h Viga 250 450 I 1898437500 mm4 EI 40889 KN/m2 ƟA ƟB ƟC Carga puntual EI 0.889 0.444 0.000 ƟA = 43.0875 0.444 1.689 0.400 ƟB -59.2077 0.000 0.400 1.445 ƟC -17.8752 1/EI 1.3093722564 -0.3687445127 0.1020632133 43.0875 = ƟA -0.3687445127 0.7374890255 -0.2041264267 -59.2077 ƟB 0.1020632133 -0.2041264267 0.7484635645 -17.8752 ƟC 76.43 = ƟA -55.90 ƟB 3.10 ƟC ELEMENTO AB ELEMENTO BC ELEMENTO CD EI/L 4 2 Ɵi + Mfij = Mij EI/L 4 2 Ɵi + Mfij = Mij EI/L 4 2 Ɵi + Mfij = Mij 2 4 Ɵj Mfij Mji 2 4 Ɵj Mfij Mji 2 4 Ɵj Mfij Mji EI 0.8889 0.4444 76.43 + 75.9375 = MAB EI 0.8000 0.4000 -55.90 + 135.1452 = MBC EI 0.6452 0.3226 3.10 + 144.15 = MCD 0.4444 0.8889 -55.90 -75.9375 MBA 0.4000 0.8000 3.10 -126.2748 MCB 0.3226 0.6452 0.00 -144.15 MCD 43.09 + 75.9375 = MAB -43.48 + 135.1452 = MBC 2.00 + 144.15 = MCD -15.73 -75.9375 MBA -19.88 -126.2748 MCB 1.00 -144.15 MCD 119.03 = MAB 91.66 = MBC 146.15 = MCD -91.66 MBA -146.15 MCB -143.15 MCD 45 kN/m A B C D 60 kN E3 45 60 2.3 4.5 2.2 2.8 6.2 2.1 Mf -119.025 75.9375 -75.9375 135.1452 -126.2748 144.15 -144.15 99.225 121.152 121.152 19.627 19.627 -76.587 -76.587 Δ ΔB 10 mm ΔC 12 mm Viga de concreto f'c 21 Mpa 3000 psi E 21538 Mpa b h Viga 250 450 I 1898437500 mm4 EI 40889 KN/m2 ƟA ƟB ƟC ƟD Carga puntual EI 0.889 0.444 0.000 0.000 ƟA = -78.064 0.444 1.689 0.400 0.000 ƟB -199.986 0.000 0.400 1.445 0.323 ƟC 39.085 0.000 0.000 0.323 0.645 ƟD 121.512 1/EI 1.3112830754 -0.3725661508 0.1160758862 -0.0580379431 -78.064 = ƟA -0.3725661508 0.7451323015 -0.2321517723 0.1160758862 -199.986 ƟB 0.1160758862 -0.2321517723 0.8512231653 -0.4256115826 39.085 ƟC -0.0580379431 0.1160758862 -0.4256115826 1.7628057913 121.512 ƟD -30.37 = ƟA -114.90 ƟB 18.92 ƟC 178.88 ƟD ELEMENTO AB ELEMENTO BC EI/L 4 2 Ɵi + Mfij = Mij EI/L 4 2 Ɵi + Mfij = Mij 2 4 Ɵj Mfij Mji 2 4 Ɵj Mfij Mji EI 0.8889 0.4444 -30.37 + 197.089 = MAB EI 0.8000 0.4000 -114.90 + 154.772 = MBC 0.4444 0.8889 -114.90 45.214 MBA 0.4000 0.8000 18.92 -106.648 MCB -78.06 + 197.0893449354 = MAB -84.35 + 154.7717988795 = MBC -115.63 45.2143449354 MBA -30.83 -106.6482011205 MCB 119.03 = MAB 70.42 = MBC -70.42 MBA -137.47 MCB 45 kN/m A B C D 60 kN E4 30 KN/m 45 KN 20 KN/m 20 KN 6.1 4.5 2.4 2.4 5 3 Mf 0.00 0.00 50.63 -50.63 27.00 -27.00 16.67 -25.00 60.00 Mgiro -1.90E+00 -9.49E-01 Masent 2.673E+01 2.67E+01 -49.1260490351 -49.1260490351 b h ƟA = -0.005 ° Viga 250 400 -8.726646E-05 Rad ΔB 5 mm 0.005 m F'c 28 Mpa Ec 24870 Mpa I(viga) 1333333333.33333 mm4 EI 33160 KN/m2 ƟB ƟC ƟD ƟE EI 1.54 0.44 0.00 0.00 ƟB = -2.73E+01 0.44 1.72 0.42 0.00 ƟC 72.75 0.00 0.42 1.63 0.40 ƟD 10.33 0.00 0.00 0.40 0.80 ƟE -35.00 1/EI 0.7036037615 -0.1953114335 0.0567765795 -0.0283882898 -2.73E+01 = ƟB -0.1953114335 0.6787872771 -0.1973218829 0.0986609414 72.75 ƟC 0.0567765795 -0.1973218829 0.7550354311 -0.3775177155 10.33 ƟD -0.0283882898 0.0986609414 -0.3775177155 1.4387588578 -35.00 ƟE -31.8266531339 = ƟB 49.2194316169 ƟC 5.1106303439 ƟD -46.305315172 ƟE ELEMENTO AB ELEMENTO BC EI/L 4 2 Ɵi + Mfij = Mij EI/L 4 2 Ɵi + Mfij = Mij 2 4 Ɵj Mfij Mji 2 4 Ɵj Mfij Mji EI 0.6557 0.3279 0.00 + 24.837 = MAB EI 0.8889 0.4444 -31.83 + 1.499 = MBC 0.3279 0.6557 -31.83 25.786 MBA 0.4444 0.8889 49.22 -99.751 MCB -10.43 + 24.8372661129 = MAB -6.42 + 1.4989509649 = MBC -20.87 25.7860409167 MBA 29.61 -99.7510490351 MCB 14.40 = MAB -4.92 = MBC 4.92 MBA -70.15 MCB A B C D E
