formula-I - V M FORMUL FOR ME 211 INTRODUCTION TO SOLID...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: V M FORMUL FOR ME 211 INTRODUCTION TO SOLID MECHANICS Vectors, forces and moments: F = iFx + jFy + kFz = {Fx , Fy , Fz } = e|F | ; e= Fx Fy Fz , , |F | |F | |F | |F | = 2 2 Fx + Fy + Fz2 M V = {cos x , cos y , cos z } T i j k M = r F = x y z Fx Fy Fz T = (yFz -zFy )i+ (zFx -xFz )j + (xFy -yFx )k . p q = px qx + py qy + pz qz = |p||q| cos , where is the angle between the vectors p and q. N Properties of areas: Coordinates of the centroid are x, y where A= dA ; A = x xdA ; A = y ydA ; Ix = y 2dA ; Iy = x2 dA . N In Cartesian coordinates, dA = dxdy. In polar coordinates, dA = rdrd. A= Ai ; A = x Ai xi ; A = y Ai yi . Trigonometric identities and integrals: sin2 x + cos2 x = 1 ; cos2 x = 1 + cos(2x) ; 2 sin2 x = 1 - cos(2x) ; 2 sin(2x) = 2 sin x cos x ; n/2 0 cos(2x) = cos2 x - sin2 x . n , where n is any integer . 4 cos2 xdx = 0 n/2 sin2 xdx = ...
View Full Document

Ask a homework question - tutors are online