DESARROLLO PRIMER EXAMEN PARCIAL - DESARROLLO PRIMER EXAMEN PARCIAL 1 Calcule las reacciones en los apoyos Ay B para la viga cargada Desarrollo F2 F1 d1

DESARROLLO PRIMER EXAMEN PARCIAL - DESARROLLO PRIMER EXAMEN...

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DESARROLLO PRIMER EXAMEN PARCIAL 1.- Calcule las reacciones en los apoyos Ay B para la viga cargada. Desarrollo: F 1 = (w 0 x l/3)/2 = w 0 l/6 d 1 = (l/3)/3 = l/9 F 2 = (w 0 x 2l/3)/2 = w 0 l/3 d 2 = l/3 + 2(2l/3)3 = 7l/9 Fy = 0 ∑Fy =R A + R B - F 1 - F 2 = 0 R A + R B = F 1 + F 2 R A + R B = w 0 l/2 M A = 0 ∑M A = R B (l)- F 1 (d 1 ) - F 2 (d 2 ) R B (l)= F 1 (d 1 ) + F 2 (d 2 ) Reemplazando: R B (l)= ( w 0 l/6)( l/9 ) + (w 0 l/3)( 7l/9 ) R B = 5w 0 l/18 = 0.277778 w 0 l =0.28 w 0 l R A = 13w0l/18= 0.72 w 0 l F 1 F 2 R B R A d 1 d 2
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F 1 2.- La placa homogénea de 48lb esta soldada al eje vertical AB de peso despreciable. El conjunto esta soportado por un cojinete deslizante en A y uno de empuje en B. Determine la fuerza en el cable CD y la magnitud de la reacción en el cojinete en A. Desarrollo: Puntos: A= (0; 0; 6.1) B= (0; 0; 0) C= (0; 4.8; 1.8) D= (3.6; 0; 0) E= (0; 4.8; 5.3) F= (0; 2.4; 3.55) Datos obtenidos: F 1 = 48k F 2 = 60i Cable ´ CD = (3.6 -4.8 -1.8) µ CD =(0.5747 -0.7662 -0.2873) r 0 = (0: 4.8; 1.8) r 1 = (0:0; 2.4) r 2 = (0: 4.8; 5.3) µ BA =(0; 0; 1) M eje BA = 0 ((F CD . µ CD ) x r 0 . µ BA ) + (F 1 x r 1 . µ BA ) + (F 2 x r 2 . µ BA ) = 0 2.75856F CD k + 0 + 288k =0 F CD =104.40229 F CD F. F 2 Eje BA A y A x
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Reacciones en A: M B =(( 7.1 k )( A x i + A y j )+( 134.4 j )+( 288 k – 315 j )+( 108 j – 288 k )) A x (6.1)= -315+108 A x =-33.9344 lb. A y (6.1)=134.4 A y =22.03 Magnitud del a reacción en A =40.454 lb
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3.- Encuentre los momentos de inercia principales y las direcciones principales en el cantroide para la región sombreada. Desarrollo: Datos obtenidos: Figura Base(B) Altura(H) ´ I x ´ I y Área x y Ix Iy ´ xy A I 160 40 853333.3333 13653333.3 6400 -80 60 41813333.3 36693333.3 -30720000 II 40 120 5760000 640000 4800 0 0 5760000 640000 0 III 160 40 853333.3333 13653333.3 6400 80 -60 41813333.3 36693333.3 -30720000 89386666.7 74026666.7 -61440000 Dato: El producto de inercia por cada uno de los rectángulos, con respecto a los ejes centroidales
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