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Diseño columna seccion t
- 1. Ing. Marco Saravia Clavo ANÁLISISY DISEÑO DE COLUMNASDE SECCIÓN "T" DE C°A° 1.- DATOSDE ENTRADA COLUMNA T-1 1.1 Esfuerzo de Fluencia, ≔ fy 4200 ―― kgf cm2 1.2 Esfuerzo de Compresión, ≔ f'c 210 ―― kgf cm2 1.3 Carga Axial Ultima de Diseño, ≔ Pu 65.00 tonnef 1.4 Momento Ultimo de Diseño, ≔ Mux ⋅ 31.00 tonnef m 1.5 Momento Ultimo de Diseño, ≔ Muy ⋅ 31.72 tonnef m 1.6 Módulo de Elasticidad del Acero, ≔ Es ⋅ 2 106 ―― kgf cm2 ≔ εs = ―― fy Es 0.0021 2.- GEOMETRIA DE LA SECCIÓN ≔ bf1 25 cm ≔ hf1 25 cm ≔ bw 30 cm ≔ hf2 40 cm ≔ bf2 25 cm ≔ Hf = + hf1 hf2 65 cm ≔ Bf = + + bf1 bw bf2 80 cm 3.- RESULTADOSGENERALES 3.1 Centro de Gravedad X-X ≔ A1 = ⋅ Bf hf1 2000 cm2 ≔ X1 = ―― hf1 2 12.5 cm = ⋅ A1 X1 25000 ⋅ cm2 cm ≔ A2 = ⋅ bw hf2 1200 cm2 ≔ X2 = + hf1 ―― hf2 2 45 cm = ⋅ A2 X2 54000 ⋅ cm2 cm ≔ Ag = + A1 A2 3200 cm2 ≔ SUMA1 = + ( ( ⋅ A1 X1) ) ( ( ⋅ A2 X2) ) 79000 ⋅ cm2 cm ≔ CGx = ――― SUMA1 Ag 24.688 cm 3.2 Centro de Gravedad Y-Y ≔ A1 = ⋅ Bf hf1 2000 cm2 ≔ Y1 = ―― Bf 2 40 cm = ⋅ A1 Y1 80000 ⋅ cm2 cm ≔ A2 = ⋅ bw hf2 1200 cm2 ≔ Y2 = + bf2 ―― bw 2 40 cm = ⋅ A2 Y2 48000 ⋅ cm2 cm ≔ Ag = + A1 A2 3200 cm2 ≔ SUMA2 = + ( ( ⋅ A1 Y1) ) ( ( ⋅ A2 Y2) ) 128000 ⋅ cm2 cm ≔ CGy = ――― SUMA2 Ag 40 cm
- 2. Ing. Marco Saravia Clavo 3.3 Momento de Inercia X-X ≔ Jx + + + ―――― ⎛ ⎝ ⋅ hf1 Bf3 ⎞ ⎠ 12 ⋅ ( ( ⋅ hf1 Bf) ) ⎛ ⎜ ⎝ - CGy ―― Bf 2 ⎞ ⎟ ⎠ 2 ―――― ⎛ ⎝ ⋅ hf2 bw3 ⎞ ⎠ 12 ⋅ ( ( ⋅ hf2 bw) ) ⎛ ⎜ ⎝ - CGy ⎛ ⎜ ⎝ + bf2 ―― bw 2 ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ 2 = Jx 1156666.667 cm4 3.4 Momento de Inercia Y-Y ≔ Jy + + + ―――― ⎛ ⎝ ⋅ Bf hf13 ⎞ ⎠ 12 ⋅ ( ( ⋅ hf1 Bf) ) ⎛ ⎜ ⎝ - CGx ―― hf1 2 ⎞ ⎟ ⎠ 2 ―――― ⎛ ⎝ ⋅ bw hf23 ⎞ ⎠ 12 ⋅ ( ( ⋅ hf2 bw) ) ⎛ ⎜ ⎝ - CGx ⎛ ⎜ ⎝ + hf1 ―― hf2 2 ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ 2 = Jy 1056354.167 cm4 3.4 Radio de Giro ≔ Rx = ‾‾‾ ―― Jx Ag 19.012 cm ≔ Ry = ‾‾‾ ―― Jy Ag 18.169 cm 3.5 Verificación de Esbeltez ≔ kx 1 ≔ ky 1 ≔ lu 300 cm ≔ esbx if ⎛ ⎜ ⎝ , , < ――― ( ( ⋅ kx lu) ) Rx 22 “No presenta problemas de esbeltez” “Presenta problemas de esbeltez” ⎞ ⎟ ⎠ = esbx “No presenta problemas de esbeltez” ≔ esby if ⎛ ⎜ ⎝ , , < ――― ( ( ⋅ ky lu) ) Ry 22 “No presenta problemas de esbeltez” “Presenta problemas de esbeltez” ⎞ ⎟ ⎠ = esby “No presenta problemas de esbeltez” 4.- ACERO DE REFUERZO ≔ barras = ― 5 8 ― 1 2 ― 5 8 0 0 0 ― 1 2 0 ― 1 2 0 0 0 ― 1 2 0 ― 1 2 ― 1 2 ― 1 2 ― 5 8 ― 1 2 0 0 0 0 ― 1 2 ― 1 2 0 ― 1 2 ― 1 2 ― 1 2 ― 5 8 ― 1 2 0 ― 1 2 0 0 0 ― 5 8 ― 1 2 ― 5 8 0 0 0 ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ in 1.588 1.27 1.588 0 0 0 1.27 0 1.27 0 0 0 1.27 0 1.27 1.27 1.27 1.588 1.27 0 0 0 0 1.27 1.27 0 1.27 1.27 1.27 1.588 1.27 0 1.27 0 0 0 1.588 1.27 1.588 0 0 0 ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ cm
- 3. Ing. Marco Saravia Clavo ≔ ORIGIN 1 ≔ k = cols( (barras) ) 6 ≔ n = rows( (barras) ) 7 ≔ As = → ― ― ― ―――― ⋅ π barras2 4 1.979 1.267 1.979 0 0 0 1.267 0 1.267 0 0 0 1.267 0 1.267 1.267 1.267 1.979 1.267 0 0 0 0 1.267 1.267 0 1.267 1.267 1.267 1.979 1.267 0 1.267 0 0 0 1.979 1.267 1.979 0 0 0 ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ cm2 ≔ rec 4 cm ≔ ϕestr = ― 3 8 in 0.953 cm 5.- CÁLCULOSPARA EL EJE X-X 5.1 Areas de acero y distancia "d" para el eje X-X ≔ Asx ∑ = i 1 k As ⟨ ⟨i⟩ ⟩ ≔ d 1 = + + rec ――― barras , 5 k 2 ϕestr 5.746 cm ≔ sep1 = ―― bf1 2 12.5 cm ≔ Ast = ∑ = i 1 n Asx , i 1 32.144 cm2 ≔ sep2 = ―――― ⎛ ⎝ - bw ⋅ 2 d 1 ⎞ ⎠ 2 9.254 cm ≔ ρ = ⋅ ―― Ast Ag 100 1.005 ≔ sep3 = ―― bf2 2 12.5 cm ≔ j ‥ 2 n ≔ d j ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ if else > ⎛ ⎝ + d - j 1 sep1 ⎞ ⎠ ⎛ ⎝ + bf1 d 1 ⎞ ⎠ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ + d - j 1 sep2 if > ⎛ ⎝ + d - j 1 sep2 ⎞ ⎠ ( ( + bf1 bw) ) ‖ ‖ ‖ + d - j 1 sep3 ‖ ‖ ‖ + d - j 1 sep1 = Asx 5.225 2.534 7.046 2.534 7.046 2.534 5.225 ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ cm2 = d 5.746 18.246 30.746 40 49.254 61.754 74.254 ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ cm 5.2 Compresión Pura ≔ P0 = + ⋅ ⋅ 0.85 f'c ( ( - Ag Ast) ) ⋅ fy Ast 700.468 tonnef ≔ Pnmax = ⋅ 0.8 P0 560.374 tonnef ≔ ϕP0 = ⋅ 0.65 P0 455.304 tonnef ≔ ϕPnmax = ⋅ ⋅ 0.65 0.8 P0 364.243 tonnef 5.3 Cálculo de "Cy", Area (Ay) y Centro de Gravedad (CGY) del Bloque Comprimido ≔ β1 ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ if else ≤ f'c 280 ―― kgf cm2 ‖ ‖ 0.85 ‖ ‖ ‖ ‖ ‖ ‖ - 0.85 ―――――――― ⎛ ⎜ ⎝ ⋅ 0.5 ⎛ ⎜ ⎝ - f'c 280 ―― kgf cm2 ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ 70 ≔ Ay ⎛ ⎝ay ⎞ ⎠ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ if else if else > ay ( ( + bf2 bw) ) ‖ ‖ ‖ + + ( ( ⋅ bf2 hf1) ) ( ( ⋅ bw Hf) ) ⎛ ⎝ ⋅ ⎛ ⎝ - ay ( ( + bf2 bw) )⎞ ⎠ hf1⎞ ⎠ < < bf2 ay ( ( + bf2 bw) ) ‖ ‖ ‖ + ( ( ⋅ bf2 hf1) ) ⎛ ⎝ ⋅ ⎛ ⎝ - ay bf2⎞ ⎠ Hf⎞ ⎠ ‖ ‖ ‖ ⎛ ⎝ ⋅ ay hf1⎞ ⎠ = β1 0.85 ≔ cy ⎛ ⎝ay ⎞ ⎠ ― ay β1
- 4. Ing. Marco Saravia Clavo ≔ CGY10 ⎛ ⎝ay ⎞ ⎠ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ if else if else > ay ( ( + bf2 bw) ) ‖ ‖ ‖ ‖ ‖ ‖ ―――――――――――――――――――――――――――――― + + ⎛ ⎜ ⎝ ⋅ ⋅ ―― bf2 2 bf2 hf1 ⎞ ⎟ ⎠ ⎛ ⎜ ⎝ ⋅ ⋅ ⎛ ⎜ ⎝ + bf2 ―― bw 2 ⎞ ⎟ ⎠ Hf bw ⎞ ⎟ ⎠ ⎛ ⎜ ⎝ ⋅ ⋅ ⎛ ⎝ - ay ( ( + bf2 bw) )⎞ ⎠ hf1 ⎛ ⎜ ⎝ + + bf2 bw ――――― - ay ( ( + bf2 bw) ) 2 ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ Ay ⎛ ⎝ay ⎞ ⎠ < < bf2 ay ( ( + bf2 bw) ) ‖ ‖ ‖ ‖ ‖ ‖ ――――――――――――――――― + ⎛ ⎜ ⎝ ⋅ ⋅ bf2 hf1 ―― bf2 2 ⎞ ⎟ ⎠ ⎛ ⎜ ⎝ ⋅ ⋅ ⎛ ⎝ - ay bf2⎞ ⎠ Hf ⎛ ⎜ ⎝ + bf2 ――― - ay bf2 2 ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ Ay ⎛ ⎝ay ⎞ ⎠ ‖ ‖ ‖ ‖ ‖ ‖ ――――― ⎛ ⎜ ⎝ ⋅ ⋅ ay hf1 ― ay 2 ⎞ ⎟ ⎠ Ay ⎛ ⎝ay ⎞ ⎠ 5.4 Esfuerzos presentes en el Acero de refuerzo ≔ fsy ⎛ ⎝ , i ay ⎞ ⎠ ‖ ‖ ‖ ‖ ‖ ‖ ← εyy ⋅ 0.003 ―――― - cy ⎛ ⎝ay ⎞ ⎠ d i cy ⎛ ⎝ay ⎞ ⎠ ⋅ sign⎛ ⎝εyy ⎞ ⎠ min⎛ ⎝ , ⋅ Es | |εyy | | fy⎞ ⎠ 5.5 Cálculo de Factor de Minoración "“ϕ” ≔ dty = max( (d) ) 74.254 cm ≔ ϕy ⎛ ⎝ay ⎞ ⎠ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ← εty ⋅ 0.003 ―――― - cy ⎛ ⎝ay ⎞ ⎠ dty cy ⎛ ⎝ay ⎞ ⎠ ← ϕy max ⎛ ⎜ ⎝ , min ⎛ ⎜ ⎝ , 0.9 + 0.65 ⋅ 0.25 ―――― - | |εty | | εs - 0.005 εs ⎞ ⎟ ⎠ 0.65 ⎞ ⎟ ⎠ 5.6 Cálculo de Capacidad Axial minorada de la columna "“ϕPn” ≔ Pnx ⎛ ⎝ay ⎞ ⎠ min ⎛ ⎜ ⎝ , ⎛ ⎜ ⎝ + ⋅ ⋅ 0.85 f'c Ay ⎛ ⎝ay ⎞ ⎠ ∑ = i 1 n ⎛ ⎝ ⋅ Asx i fsy ⎛ ⎝ , i ay ⎞ ⎠⎞ ⎠ ⎞ ⎟ ⎠ Pnmax ⎞ ⎟ ⎠ ≔ ϕPnx ⎛ ⎝ay ⎞ ⎠ min ⎛ ⎜ ⎝ , ⋅ ϕy ⎛ ⎝ay ⎞ ⎠ ⎛ ⎜ ⎝ + ⋅ ⋅ 0.85 f'c Ay ⎛ ⎝ay ⎞ ⎠ ∑ = i 1 n ⎛ ⎝ ⋅ Asx i fsy ⎛ ⎝ , i ay ⎞ ⎠⎞ ⎠ ⎞ ⎟ ⎠ ϕPnmax ⎞ ⎟ ⎠ 5.7 Cálculo de Momento Resistente minorado "“ϕMn” ≔ Mnx ⎛ ⎝ay ⎞ ⎠ ⎛ ⎜ ⎝ + ⋅ ⋅ ⋅ 0.85 f'c Ay ⎛ ⎝ay ⎞ ⎠ ⎛ ⎝ - CGy CGY10 ⎛ ⎝ay ⎞ ⎠⎞ ⎠ ∑ = i 1 n ⎛ ⎝ ⋅ ⋅ Asx i fsy ⎛ ⎝ , i ay ⎞ ⎠ ⎛ ⎝ - CGy d i ⎞ ⎠ ⎞ ⎠ ⎞ ⎟ ⎠ ≔ ϕMnx ⎛ ⎝ay ⎞ ⎠ ⋅ ϕy ⎛ ⎝ay ⎞ ⎠ ⎛ ⎜ ⎝ + ⋅ ⋅ ⋅ 0.85 f'c Ay ⎛ ⎝ay ⎞ ⎠ ⎛ ⎝ - CGy CGY10 ⎛ ⎝ay ⎞ ⎠⎞ ⎠ ∑ = i 1 n ⎛ ⎝ ⋅ ⋅ Asx i fsy ⎛ ⎝ , i ay ⎞ ⎠ ⎛ ⎝ - CGy d i ⎞ ⎠ ⎞ ⎠ ⎞ ⎟ ⎠ 5.8 Rango valores del Bloque de Compresiones "ay" ≔ ay , ‥ 0 ―― Bf 150 Bf
- 5. Ing. Marco Saravia Clavo 0 70 140 210 280 350 420 490 560 -140 -70 630 12.5 18.5 24.5 30.5 36.5 42.5 48.5 54.5 60.5 0.5 6.5 66.5 44.847 ϕMnx ⎛ ⎝ay ⎞ ⎠ ( ( ⋅ tonnef m) ) Mux ( ( ⋅ tonnef m) ) Mnx ⎛ ⎝ay ⎞ ⎠ ( ( ⋅ tonnef m) ) ϕPnx ⎛ ⎝ay ⎞ ⎠ ( (tonnef) ) Pu ( (tonnef) ) Pnx ⎛ ⎝ay ⎞ ⎠ ( (tonnef) ) Pu ( (tonnef) ) 6.- CÁLCULOSPARA EL EJE Y-Y 6.1 Areas de acero y distancia "d" para el eje Y-Y ≔ ORIGIN 1 ≔ Asy ∑ = i 1 n As i ≔ k = cols( (barras) ) 6 ≔ n = rows( (barras) ) 7 ≔ rec 4 cm ≔ Ast = ∑ = i 1 k Asy , 1 i 32.144 cm2 ≔ ϕestr = ― 3 8 in 0.953 cm ≔ ρ = ⋅ ―― Ast Ag 100 1.005 = Asy 10.292 2.534 9.026 2.534 2.534 5.225 [ [ ] ] cm2 ≔ l 1 = + + rec ――― barras , 1 1 2 ϕestr 5.746 cm ≔ sep4 = ―――― ⎛ ⎝ - hf1 ⋅ 2 l 1 ⎞ ⎠ 2 6.754 cm ≔ sep5 = ―― hf2 3 13.333 cm
- 6. Ing. Marco Saravia Clavo ≔ q ‥ 2 k ≔ l q ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ if else > ⎛ ⎝ + l - q 1 sep4 ⎞ ⎠ ( (hf1) ) ‖ ‖ ‖ + l - q 1 sep5 ‖ ‖ ‖ + l - q 1 sep4 = l 5.746 12.5 19.254 32.587 45.92 59.254 ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ cm 6.2 Cálculo de "Cx", Area (Ax) y Centro de Gravedad (CGX) del Bloque Comprimido ≔ β1 ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ if else ≤ f'c 280 ―― kgf cm2 ‖ ‖ 0.85 ‖ ‖ ‖ ‖ ‖ ‖ - 0.85 ―――――――― ⎛ ⎜ ⎝ ⋅ 0.5 ⎛ ⎜ ⎝ - f'c 280 ―― kgf cm2 ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ 70 ≔ Ax ⎛ ⎝ax ⎞ ⎠ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ if else > ax hf1 ‖ ‖ ‖ + ( ( ⋅ hf1 Bf) ) ⎛ ⎝ ⋅ ⎛ ⎝ - ax hf1⎞ ⎠ bw⎞ ⎠ ‖ ‖ ‖ ⎛ ⎝ ⋅ ax Bf⎞ ⎠ = β1 0.85 ≔ cx ⎛ ⎝ax ⎞ ⎠ ― ax β1 ≔ CGX10 ⎛ ⎝ax ⎞ ⎠ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ if else > ax hf1 ‖ ‖ ‖ ‖ ‖ ‖ ――――――――――――――――― + ⎛ ⎜ ⎝ ⋅ ⋅ ―― hf1 2 hf1 Bf ⎞ ⎟ ⎠ ⎛ ⎜ ⎝ ⋅ ⋅ ⎛ ⎝ - ax hf1⎞ ⎠ bw ⎛ ⎜ ⎝ + hf1 ――― - ax hf1 2 ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ Ax ⎛ ⎝ax ⎞ ⎠ ‖ ‖ ‖ ‖ ‖ ‖ ――――― ⎛ ⎜ ⎝ ⋅ ⋅ ax Bf ― ax 2 ⎞ ⎟ ⎠ Ax ⎛ ⎝ax ⎞ ⎠ 6.3 Esfuerzos presentes en el Acero de refuerzo ≔ fsx ⎛ ⎝ , i ax ⎞ ⎠ ‖ ‖ ‖ ‖ ‖ ‖ ← εxx ⋅ 0.003 ―――― - cx ⎛ ⎝ax ⎞ ⎠ l i cx ⎛ ⎝ax ⎞ ⎠ ⋅ sign⎛ ⎝εxx ⎞ ⎠ min⎛ ⎝ , ⋅ Es | |εxx | | fy⎞ ⎠ 6.4 Cálculo de Factor de Minoración "“ϕ” ≔ ltx = max( (l) ) 59.254 cm ≔ ϕx ⎛ ⎝ax ⎞ ⎠ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ← εtx ⋅ 0.003 ―――― - cx ⎛ ⎝ax ⎞ ⎠ ltx cx ⎛ ⎝ax ⎞ ⎠ ← ϕx max ⎛ ⎜ ⎝ , min ⎛ ⎜ ⎝ , 0.9 + 0.65 ⋅ 0.25 ―――― - | |εtx | | εs - 0.005 εs ⎞ ⎟ ⎠ 0.65 ⎞ ⎟ ⎠
- 7. Ing. Marco Saravia Clavo 6.5 Cálculo de Capacidad Axial minorada de la columna "“ϕPn” ≔ Pny ⎛ ⎝ax ⎞ ⎠ min ⎛ ⎜ ⎝ , ⎛ ⎜ ⎝ + ⋅ ⋅ 0.85 f'c Ax ⎛ ⎝ax ⎞ ⎠ ∑ = i 1 k ⎛ ⎝ ⋅ Asy , 1 i fsx ⎛ ⎝ , i ax ⎞ ⎠⎞ ⎠ ⎞ ⎟ ⎠ Pnmax ⎞ ⎟ ⎠ ≔ ϕPny ⎛ ⎝ax ⎞ ⎠ min ⎛ ⎜ ⎝ , ⋅ ϕx ⎛ ⎝ax ⎞ ⎠ ⎛ ⎜ ⎝ + ⋅ ⋅ 0.85 f'c Ax ⎛ ⎝ax ⎞ ⎠ ∑ = i 1 k ⎛ ⎝ ⋅ Asy , 1 i fsx ⎛ ⎝ , i ax ⎞ ⎠⎞ ⎠ ⎞ ⎟ ⎠ ϕPnmax ⎞ ⎟ ⎠ 6.6 Cálculo de Momento Resistente minorado "“ϕMn” ≔ Mny ⎛ ⎝ax ⎞ ⎠ ⎛ ⎜ ⎝ + ⋅ ⋅ ⋅ 0.85 f'c Ax ⎛ ⎝ax ⎞ ⎠ ⎛ ⎝ - CGx CGX10 ⎛ ⎝ax ⎞ ⎠⎞ ⎠ ∑ = i 1 k ⎛ ⎝ ⋅ ⋅ Asy , 1 i fsx ⎛ ⎝ , i ax ⎞ ⎠ ⎛ ⎝ - CGx l i ⎞ ⎠ ⎞ ⎠ ⎞ ⎟ ⎠ ≔ ϕMny ⎛ ⎝ax ⎞ ⎠ ⋅ ϕx ⎛ ⎝ax ⎞ ⎠ ⎛ ⎜ ⎝ + ⋅ ⋅ ⋅ 0.85 f'c Ax ⎛ ⎝ax ⎞ ⎠ ⎛ ⎝ - CGx CGX10 ⎛ ⎝ax ⎞ ⎠⎞ ⎠ ∑ = i 1 k ⎛ ⎝ ⋅ ⋅ Asy , 1 i fsx ⎛ ⎝ , i ax ⎞ ⎠ ⎛ ⎝ - CGx l i ⎞ ⎠ ⎞ ⎠ ⎞ ⎟ ⎠ 6.7 Rango valores del Bloque de Compresiones "ax" ≔ ax , ‥ 0 ―― Hf 150 Hf 0 70 140 210 280 350 420 490 560 -140 -70 630 13.5 20 26.5 33 39.5 46 52.5 59 0.5 7 65.5 35.487 ϕMny ⎛ ⎝ax ⎞ ⎠ ( ( ⋅ tonnef m) ) Muy ( ( ⋅ tonnef m) ) Mny ⎛ ⎝ax ⎞ ⎠ ( ( ⋅ tonnef m) ) ϕPny ⎛ ⎝ax ⎞ ⎠ ( (tonnef) ) Pu ( (tonnef) ) Pny ⎛ ⎝ax ⎞ ⎠ ( (tonnef) ) Pu ( (tonnef) ) 7.- CÁLCULOSPARA FLEXOCOMPRESIÓN BIAXIAL 7.1 Cálculo de Mnx, Mny, Mnox y Mnoy
- 8. Ing. Marco Saravia Clavo Una vez construido los DI considerando Flexo-compresión Recta, se obtendrán los valores de Muox y Muoy para la carga de cálculo Pu, esto nos permitira conocer los valores de Mnox y Mnoy. ≔ Muox ⋅ 44.847 tonnef m ≔ Muoy ⋅ 35.487 tonnef m ≔ ϕx 0.875 ≔ ϕy 0.90 ≔ Mnox = ――― Muox ϕx 51.254 ⋅ tonnef m ≔ Mnoy = ――― Muoy ϕy 39.43 ⋅ tonnef m ≔ Mnx = ―― Mux ϕx 35.429 ⋅ tonnef m ≔ Mny = ―― Muy ϕy 35.244 ⋅ tonnef m 7.2 Cálculo de por medio del Nomograma del PCA β ≔ dato1 = ――― Mnx Mnox 0.691 ≔ dato2 = ――― Mny Mnoy 0.894 ≔ f1 ( (x) ) ⎛ ⎜ ⎝ - 1 x ―――― log ( (0.5) ) log ( (0.50) ) ⎞ ⎟ ⎠ ≔ f2 ( (x) ) ⎛ ⎜ ⎝ - 1 x ―――― log ( (0.5) ) log ( (0.55) ) ⎞ ⎟ ⎠ ≔ f3 ( (x) ) ⎛ ⎜ ⎝ - 1 x ―――― log ( (0.5) ) log ( (0.60) ) ⎞ ⎟ ⎠ ≔ f4 ( (x) ) ⎛ ⎜ ⎝ - 1 x ―――― log ( (0.5) ) log ( (0.65) ) ⎞ ⎟ ⎠ ≔ f5 ( (x) ) ⎛ ⎜ ⎝ - 1 x ―――― log ( (0.5) ) log ( (0.70) ) ⎞ ⎟ ⎠ ≔ f6 ( (x) ) ⎛ ⎜ ⎝ - 1 x ―――― log ( (0.5) ) log ( (0.75) ) ⎞ ⎟ ⎠ ≔ f7 ( (x) ) ⎛ ⎜ ⎝ - 1 x ―――― log ( (0.5) ) log ( (0.80) ) ⎞ ⎟ ⎠ ≔ f8 ( (x) ) ⎛ ⎜ ⎝ - 1 x ―――― log ( (0.5) ) log ( (0.85) ) ⎞ ⎟ ⎠ ≔ f9 ( (x) ) ⎛ ⎜ ⎝ - 1 x ―――― log ( (0.5) ) log ( (0.90) ) ⎞ ⎟ ⎠ ≔ x , ‥ 0 0.1 1 Nomograma de la PCA 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0.1 1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0.1 1 0.894 0.691 x f1( (x) ) f2( (x) ) f3( (x) ) f4( (x) ) f5( (x) ) f6( (x) ) f7( (x) ) f8( (x) ) f9( (x) )
- 9. Ing. Marco Saravia Clavo Luego de ingresar los valores de "dato1" y "dato2" al Nomograma de la PCA, podremos obtener el valor de β ≔ β 0.88 7.3 Comprobación por el Método de Contorno de Carga del PCA ≔ Conclusión ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ if else < ⎛ ⎜ ⎜ ⎝ + ⎛ ⎜ ⎝ ――― Mux Muox ⎞ ⎟ ⎠ ―――― log ( (0.5) ) log ( (β) ) ⎛ ⎜ ⎝ ――― Muy Muoy ⎞ ⎟ ⎠ ―――― log ( (0.5) ) log ( (β) ) ⎞ ⎟ ⎟ ⎠ 1 ‖ ‖ “La Sección Sí es capaz de Resistir las Cargas de Diseño” ‖ ‖ “La Sección No es capaz de Resistir las Cargas de Diseño” = Conclusión “La Sección Sí es capaz de Resistir las Cargas de Diseño”