analisis modal espectral, Esquemas y mapas conceptuales de Ingeniería

¡Descarga analisis modal espectral y más Esquemas y mapas conceptuales en PDF de Ingeniería solo en Docsity! Instituto Tecnologico de Santo Domingo Maestria en Ingenieria Estructural MIS-507 "Ingenieria Sismica" Ing. Francisco Alfredo Díaz Manzano ID: 1068251 ANALISIS ESPECTRAL MODAL 1. Propiedades de la estructura Gravedad ≔g 981 Pisos ≔P 1 2 3 4 5 6 7 8 9[ ] ≔P T P Altura ≔h ⋅4 1 1 1 1 1 1 1 1 1[ ] Rigidez ≔k ⋅303 1 1 1 1 1 1 1 1 1[ ] Pesos ≔W 816.44 1 1 1 1 1 1 1 1 1[ ] 2. Ensamblaje de la matriz de masa. ≔i ‥1 cols (W) ≔M ,i i ―― W ,1 i g =M ⋅832.2528 10 −3 0 0 0 0 0 0 0 ⋅832.2528 10 −3 0 0 0 0 0 0 0 ⋅832.2528 10 −3 0 0 0 0 0 0 0 ⋅832.2528 10 −3 0 0 0 0 0 0 0 ⋅832.2528 10 −3 0 0 0 0 0 0 0 ⋅832.2528 10 −3 0 0 0 0 0 0 0 ⋅832.2528 10 −3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 … ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣ ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦ 3. Ensamblaje de la matriz de rigidez. ≔K ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ for ∊i ‥1 cols (k) ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ if else ≤i −cols (k) 1 ‖ ‖ ‖ ‖ ‖ ‖ ←K ,i i +k ,1 i k ,1 +i 1 ←K ,i +i 1 ⋅−1 k ,1 +i 1 ←K ,+i 1 i K ,i +i 1 ‖ ‖‖ ←K ,i i k ,1 i K =K 606 −303 0 0 0 0 0 0 0 −303 606 −303 0 0 0 0 0 0 0 −303 606 −303 0 0 0 0 0 0 0 −303 606 −303 0 0 0 0 0 0 0 −303 606 −303 0 0 0 0 0 0 0 −303 606 −303 0 0 0 0 0 0 0 −303 606 −303 0 0 0 0 0 0 0 −303 606 −303 0 0 0 0 0 0 0 −303 303 ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ Página 1 de 10 Instituto Tecnologico de Santo Domingo Maestria en Ingenieria Estructural MIS-507 "Ingenieria Sismica" Ing. Francisco Alfredo Díaz Manzano ID: 1068251 4. Calculo de formas modales y periodos de vibración. ≔A ⋅M −1 K ≔ω2 sort (eigenvals (A)) Frecuencia circular ≔ω =‾‾‾ω2 3.1513 9.3681 15.3292 20.8723 25.846 30.1147 33.5619 36.0937 37.6409 ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ Periodo natural ≔T =―― ⋅2 π ω 1.9938 0.6707 0.4099 0.301 0.2431 0.2086 0.1872 0.1741 0.1669 ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ Formas modales ≔ϕ ‖ ‖ ‖ ‖ ‖‖ for ∊i ‥1 rows (T) ‖ ‖ ‖ ←ϕ ⟨i⟩ eigenvec ⎛ ⎝ ,A ω2 ,i 1 ⎞ ⎠ ϕ =ϕ 0.0755 0.2184 −0.3376 −0.4202 −0.4573 0.4448 −0.3841 −0.2818 0.149 0.149 0.3841 −0.4573 −0.3376 −0.0755 −0.2184 0.4202 0.4448 −0.2818 0.2184 0.4573 −0.2818 0.149 0.4448 −0.3376 −0.0755 −0.4202 0.3841 0.2818 0.4202 0.0755 0.4573 0.149 0.3841 −0.3376 0.2184 −0.4448 0.3376 0.2818 0.3841 0.2184 −0.4202 0.149 0.4448 0.0755 0.4573 0.3841 0.0755 0.4448 −0.2818 −0.2184 −0.4573 −0.149 −0.3376 −0.4202 0.4202 −0.149 0.2184 −0.4448 0.3841 0.0755 −0.2818 0.4573 0.3376 0.4448 −0.3376 −0.149 −0.0755 0.2818 0.4202 0.4573 −0.3841 −0.2184 0.4573 −0.4448 −0.4202 0.3841 −0.3376 −0.2818 −0.2184 0.149 0.0755 ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ 1.8 2.7 3.6 4.5 5.4 6.3 7.2 8.1 0 0.9 9 0.09.1350.180.2250.270.3150.360.405.450.045 0.495 ϕ1 ⟨1⟩ P1 1.8 2.7 3.6 4.5 5.4 6.3 7.2 8.1 0 0.9 9 -0.27-0.18-0.0900.090.180.270.360.45-0.45-0.36 0.54 ϕ1 ⟨2⟩ P1 1.8 2.7 3.6 4.5 5.4 6.3 7.2 8.1 0 0.9 9 -0.36-0.27-0.18-0.0900.09.180.270.36-0.54-0.45 0.45 ϕ1 ⟨3⟩ P1 1.8 2.7 3.6 4.5 5.4 6.3 7.2 8.1 0 0.9 9 -0.27-0.18-0.0900.090.180.270.360.45-0.45-0.36 0.54 ϕ1 ⟨4⟩ P1 1.8 2.7 3.6 4.5 5.4 6.3 7.2 8.1 0 0.9 9 -0.36-0.27-0.18-0.0900.09.180.270.36-0.54-0.45 0.45 ϕ1 ⟨5⟩ P1 1° Modo 2° Modo 3° Modo 4° Modo 5° Modo Página 2 de 10 Instituto Tecnologico de Santo Domingo Maestria en Ingenieria Estructural MIS-507 "Ingenieria Sismica" Ing. Francisco Alfredo Díaz Manzano ID: 1068251 Coeficientes sismicos para cada periodo de vibración. ≔Csm ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ for ∊i ‥1 rows (T) ‖ ‖ ‖ ‖ ‖ ←Csm ,i 1 ――――――― linterp ⎛ ⎝ ,,t Sa T ,i 1 ⎞ ⎠ ⋅g ⎛ ⎜⎝ ― R Ie ⎞ ⎟⎠ Csm =Csm 0.1075 0.1704 0.194 0.2508 0.153 ⋮ ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ Calculo de fuerzas modales laterales ＝fmodal ⋅⋅⋅Γn ϕjn mj Cj ≔fmodal ‖ ‖ ‖ ‖ ‖ ‖ ‖ for ∊i ‥1 5 ‖ ‖ ‖ ‖ ‖‖ for ∊ii ‥1 rows (ϕ) ‖ ‖‖ ←fmodal ,ii i ⋅⋅⋅Γ ,i 1 ϕ ,ii i W ,1 ii Csm ,i 1 fmodal =fmodal 18.3582 27.5192 27.969 30.2161 14.2378 36.2156 48.4048 37.8858 24.2753 2.3515 53.0851 57.6223 23.3497 −10.7135 −13.8494 68.5066 52.9498 −6.2572 −32.8824 −4.6388 82.0594 35.5136 −31.8254 −15.704 13.0833 93.3739 9.5168 −36.8523 20.266 6.7997 102.1414 −18.774 −18.0934 31.9855 −11.9602 108.1227 −42.5394 12.3436 5.4308 −8.775 111.1547 −56.0505 34.8137 −27.6224 10.511 ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ Cortante basal. ≔Vmodal ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ for ∊i ‥1 cols ⎛⎝fmodal⎞⎠ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖‖ ←a 0 for ∊ii ‥1 rows ⎛⎝fmodal⎞⎠ ‖ ‖ ‖ ‖‖ ←a +fmodal ,ii i a ←Vmodal ,1 i a Vmodal ≔VSRSS ‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾ ∑ =n 1 cols ⎛⎝Vmodal⎞⎠ ⎛ ⎝ Vmodal ,1 n ⎞ ⎠ 2 ≔Vnom ―――― VSRSS ∑ =n 1 cols (W) W ,1 n =VSRSS 684.5154 =Vnom 0.0932 =Vmodal 673.0175 114.1626 43.3334 25.2514 7.7597[ ] Página 5 de 10 Instituto Tecnologico de Santo Domingo Maestria en Ingenieria Estructural MIS-507 "Ingenieria Sismica" Ing. Francisco Alfredo Díaz Manzano ID: 1068251 Calculo de fuerzas laterales en entrepiso ≔fSRSS ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ for ∊i ‥1 rows ⎛⎝fmodal⎞⎠ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ←a 0 for ∊ii ‥1 5 ‖ ‖ ‖ ←a +fmodal ,i ii 2 a ←fSRSS ,i 1 ‾‾a fSRSS =P 1 2 3 4 5 6 7 8 9 ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ =fSRSS 54.7021 75.3972 83.6071 92.9449 97.0856 103.0742 110.8098 117.2987 132.599 ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ 1.8 2.7 3.6 4.5 5.4 6.3 7.2 8.1 0 0.9 9 30 45 60 75 90 105 1200 15 135 fSRSS. P. Fuerzas laterales por piso Calculo de fuerzas cortantes en entrepiso ≔VEmodal ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ for ∊i ‥1 5 ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖‖ ←a 0 for ∊ii ‥rows (ϕ) 1 ‖ ‖ ‖ ‖‖ ←a +fmodal ,ii i a ←VEmodal ,ii i a VEmodal Página 6 de 10 Instituto Tecnologico de Santo Domingo Maestria en Ingenieria Estructural MIS-507 "Ingenieria Sismica" Ing. Francisco Alfredo Díaz Manzano ID: 1068251 =VEmodal 673.0175 114.1626 43.3334 25.2514 7.7597 654.6594 86.6434 15.3644 −4.9647 −6.4781 618.4438 38.2386 −22.5213 −29.24 −8.8296 565.3587 −19.3837 −45.871 −18.5265 5.0198 496.8521 −72.3335 −39.6138 14.356 9.6587 414.7926 −107.8471 −7.7884 30.0599 −3.4246 321.4187 −117.3639 29.0639 9.7939 −10.2243 219.2774 −98.5899 47.1573 −22.1916 1.736 111.1547 −56.0505 34.8137 −27.6224 10.511 ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ≔VESRSS ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ for ∊i ‥1 rows ⎛⎝VEmodal⎞⎠ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ←a 0 for ∊ii ‥1 5 ‖ ‖ ‖ ←a +VEmodal ,i ii 2 a ←VESRSS ,i 1 ‾‾a VESRSS =P 1 2 3 4 5 6 7 8 9 ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ =VESRSS 684.5154 660.5972 620.7858 567.8721 503.9472 429.7207 343.6997 246.0118 132.599 ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ 1.8 2.7 3.6 4.5 5.4 6.3 7.2 8.1 0 0.9 9 140 210 280 350 420 490 560 6300 70 700 VESRSS. T P_ Fuerzas cortantes por entrepiso. T 2 Página 7 de 10