handige statica formuleblad/samenvatting

Fundamental Equations of Statics

Cartesian Vector Equilibrium SI Prefixes
A = Axi + Ay j + Azk Particle Multiple Expon
Magnitude ©Fx = 0, ©Fy = 0, ©Fz = 0 1 000 000 000
A = 2Ax2 + Ay2 + A 2z Rigid Body-Two Dimensions 1 000 000
1 000
Directions ©Fx = 0, ©Fy = 0, ©MO = 0
A Ax Ay Az Rigid Body-Three Dimensions Submultiple
uA = = i + j + k
A A A A ©Fx = 0, ©Fy = 0, ©Fz = 0 0.001
= cos ai + cos bj + cos gk 0.000 001
©Mx¿ = 0, ©My¿ = 0, ©Mz¿ = 0
cos2 a + cos2 b + cos2 g = 1 0.000 000 001

Dot Product Friction
A # B = AB cos u Static (maximum) Fs = ms N
= A x Bx + A y By + A z Bz Kinetic Fk = mk N
Cross Product
Center of Gravity
i j k
Particles or Discrete Parts
C = A  B = Ax Ay Az '
Bx By Bz ©r W
r =
©W Conversion Factors (FPS) to (SI)
Cartesian Position Vector Body Unit of
Quantity Measurement (
r = 1x2 - x12i + 1y2 - y12j + 1z2 - z12k '
r dW Force lb
L
Cartesian Force Vector r = Mass slug
r dW Length ft
F = Fu = F a b L
r
Moment of a Force Area and Mass Moments of Inertia
Mo = Fd i j k
M o = r : F = rx ry rz I = r 2 dA I = r 2 dm
L L
Fx Fy Fz
Parallel-Axis Theorem
Moment of a Force About a Specified Axis
I = I + Ad 2 I = I + md 2
ux uy uz
#
Ma = u r  F = rx ry rz Radius of Gyration Conversion Factors (FPS)
Fx Fy Fz I I
k = k =
B A B m 1 mi
Simplification of a Force and Couple System 1 kip (kilo
FR = ©F Virtual Work