MECANICA E RESISTENCIA DOS MATERIAIS - EA1_Abcdeiver Barbosa Conde

Prévia do material em texto

NOME: Abcdeiver Barbosa Condé 
1- 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
C1 = ( x1 , y1) 
C1 = 55/2 , 15/2 = 27,5 cm ; 7,5 cm 
 
C2 = ( x2 , y2) 
C2 = 15/2 , 85/2 = 7,5 cm ; 42,5 cm 
 
C3 = ( x3 , y3) 
C3 = 85/2 , 15/2 = 42,5 cm ; 77,5 cm 
 
 
 
 
REC 1 
R
EC
 2
 
REC 3 
FIGURA Xi (cm) Yi (cm) Ai (cm²) Xi*Ai (cm³) Yi*Ai (cm³) 
REC1 27,5 7,5 55 * 15 = 825 (27,5 * 825) = 22687,5 (7,5 * 825) = 6187,5 
REC2 7,5 42,5 55 * 15 = 825 (7,5 * 825) = 6187,5 (42,5 * 825) = 35062,5 
REC3 42,5 77,5 85 * 15 = 1275 (42,5 * 1.275) = 54187,5 (77,5 * 1.275) = 98812,5 
∑ 2925 83062,5 140062,5 
 
Coordenada x = ∑ Xi*Ai / ∑Ai 
= 83062,5 / 2925 = 28,4 cm 
Coordenada y = ∑ Yi*Ai / ∑Ai 
= 140062,5 / 2925 = 47,885 cm 
C (27,4 ; 47,885) 
 
2 
Ix (b h^3)/12+A.dy^2 
F1) Ix1=(55 (15)^3)/12+825.(40,38)^2=1361001,0356 cm^4 
F2) Ix2=(15 (55)^3)/12+825.(5,4)^2=232025,75 cm^4 
F3) Ix3=(85 (15)^3)/12+1275.(-29,615)^2=1142142,737 cm^4 
Ix=Ix1+Ix2+ Ix3 
Ix=1361001,0356 + 232025,75 + 1142142,737 
Ix= 2735169,522 cm^4 
Iy (h b^3)/12+A.dx^2 
F1) Iy1=(15 (55)^3)/12+825.(0,9)^2=208637 cm^4 
F2) Iy2=(55 (15)^3)/12+825.(20,9)^2=375837 cm^4 
F3) Iy3=(15 (85)^3)/12+1275.(-14,1)^2=1021139 cm^4 
Iy=Iy1+Iy2+ Iy3 
Iy=208637 + 375837+1021139 
Iy= 1605613cm^4