Chapter 3- Equilibrium of a Particle 3.1 Condition for the Equilibrium of a Particle -Newton First Law Must be Satisfied Resultant Force Acting on a Particle Must be Zero F = 0 Necessary and Sufficient Condition In component form: Fx = 0 Fy = 0
3.2 The Fr

2.5 Cartesian vectors
Right hand coordinate system
y
j
i
x
k
z
3-dimensional vectors
y
Fy
F
y
Fz
x
z
Fx
x
z
F = Fx + Fy + Fz
F = Fx i + Fy + Fz k
j
2
Note:
2
F = Fx + Fy + Fz
Fx = F cos x
2
Fy = cos y
Fz = F cos z
F
= uF
F
F Fx Fy Fz
uF = =
i+
j+
k
F
F
F

2.8 Force vector directed along a line
In many cases, a force is defined by its magnitude and two points along its line of action.
y
B (x 2, y 2, z2)
F
uF
A (x 2, y 2, z2)
x
z
F = F uF
need
given
rAB
F = F
rAB
rAB = ( x 2 x1 ) i + ( y 2 y1 ) + ( z 2 z1

4.7-4.9 Force Couple Systems Let us look at the following F
r O
A
We want for one reason or another, to have F act at point 0. How do we do this? We can move F along its line of action, but we cannot just move it to 0 because if we do so we will modify th

Composite plates and wires
In most cases a flat plate can be divided up into common shapes. We can use this fact to
find the center of gravity and/or the centroid.
z
z
y
y
W3
X
Y
W1
W
x
W2 x
Equating moments
M y : X W = X (W1 + W2 + .Wn ) = x1W1 + x 2W2 +

Chapter 6 - Analysis of Structures
Now we are going to consider internal forces.
In the force analysis of structures it is necessary to dismember the structure and to
analyze separate FBD of individual members in order to determine the forces internal to

Frames and Machines
Trusses
1). Consists of pins
2). Straight 2-force members
3). Forces directed along the member
Frames
- Structures that have at least one multi-force member
3 or more forces
- Forces usually will not be directed along the member
Thus