5.4 Two and Three Force Members The solution to some problems can be made easier if you recognize members that are subjected to only 2 forces. Two force members - only 2 forces applied at 2 points on the member. - no moments. - line of action of both forc
Chapter 10: Moments of Inertia
Chapter Objectives
To develop a method for determining the moment of inertia and product of inertia
for an area with respect to given x- and y-axes.
To develop a method for determining the polar moment of inertia for an are
Chapter 2: Force Vectors
Chapter Objectives
To show how to add forces and resolve them into components using the
Parallelogram Law.
To express force and position in Cartesian vector form and explain how to
determine the vectors magnitude and direction.
T
Chapter 5: Equilibrium of a Rigid Body
Chapter Objectives
To develop the equations of equilibrium for a rigid body.
To introduce the concept of a free-body diagram for a rigid body.
To show how to solve rigid body equilibrium problems using the equations
Chapter 9: Center of Gravity and Centroid
Chapter Objectives
To discuss the concept of the center of gravity, center of mass, and the centroid.
To show how to determine the location of the centroid for a body of arbitrary
shape.
To use the Theorems of Pa
Chapter 3: Equilibrium of a Particle
Chapter Objectives
To introduce the concept of the free-body diagram for a particle.
To show how to solve particle equilibrium problems using the equations of
equilibrium.
In this chapter, we shall discuss forces in m
Chapter 7: Internal Forces
Chapter Objectives
To show how to use the method of sections for determining the internal
loadings in a member.
To generalize this procedure by formulating equations that can be plotted so
that they describe the internal shear
Chapter 6: Structural Analysis
Chapter Objectives
To show how to determine the forces in the members of a truss using the method
of joints and the method of sections.
To analyze the forces acting on the members of frames and machines composed of
pin-conn
Chapter 1: Introduction
Chapter Objectives
To provide an introduction to the basic quantities and idealizations of mechanics.
To give a statement of Newtons Laws of Motion and Gravitation.
To review the principles for applying the SI system of units.
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
4.4 Principle of Moments Also known as Varigon's Theorem Let's say we have several concurrent forces. We can determine its resultant R = F1 + F2 . The moment of R about 0, where r is the position vector from 0 to a point on the line of action of R . MO =
Chapter 8 - Friction 8.1 Characteristics of dry friction Friction - a resistive force that prevents or retards the slipping of one body with respect to another. 2 types of friction 1). Dry (coulomb)- non-lubricated 2). fluid Coefficients of friction
W P F
2.5 Cartesian vectors Right hand coordinate system y j i k z 3-dimensional vectors
y
x
Fy
y x
F
x
Fz
z
Fx
z
F = Fx + Fy + Fz F = Fx i + Fy + Fz k j F = uF F uF =
Note:
F = Fx + Fy + Fz Fx = F cos x
2
2
2
Fy = cos y
Fz = F cos z
F Fx Fy Fz = i+ j+ k F F F
Chapter 5- Equilibrium of a rigid body 5.1 Conditions for rigid-body equilibrium Previously we found that a system of forces can be reduced to a force-couple system. When the force and couple are equal to zero, the body is said to be in equilibrium. The n
Chapter 9 Center of Gravity and Centroid Center of gravity- the point at which the weight of the body can be concentrated. CG of 2-D body z y ( x 1 y 1 ) weight x y ( x 2 y 2 ) weight = dW = dW
1 2
W Fz
x
W = dW1 + dW2 + . + dWn M y : x W = x1 dW1 + x 2 d
Method of Sections Method of joints works well when you want to know the forces in all the members. If we want to know a force in a particular member, the method of sections is more efficient. Look at the following truss:
F A
1
F
2
F B
3
D
G
C
E
To solve
Addition of a System of Coplanar Forces Vector Notation In many problems it will be necessary to resolve a force into 2 components that are perpendicular to each other. y j i x
O 2 vectors, i and that have the direction shown and magnitude 1 - unit j vect
Chapter 4: Force System Resultants
Chapter Objectives
To discuss the concept of the moment of a force and show how to calculate it in
two and three dimensions.
To provide a method for finding the moment of a force about a specified axis.
To define the mo