Post on 10-Apr-2018
8/8/2019 ENGR221 Lecture 2
1/34
Concurrent Force SystemsConcurrent Force Systems
ENGR 221
January 15, 2003
8/8/2019 ENGR221 Lecture 2
2/34
Lecture Goals
Lecture Goals
2.1 Introduction
2.2 Forces and their Characteristics 2.4 Resultant of Three or more concurrent Forces
2.5 Resolution of a Force into Components
8/8/2019 ENGR221 Lecture 2
3/34
IntroductionIntroduction -- DefinitionDefinition
Concurrent Force Systems:
A concurrent force system contains forces whose
lines-of action meet at some one point.
Forces may be tensile (pulling)
8/8/2019 ENGR221 Lecture 2
4/34
IntroductionI
ntroduction -- DefinitionDefinitionConcurrent Force Systems:A concurrent force system contains forces whose
lines-of action meet at some one point.
Forces may be compressive (pushing)
8/8/2019 ENGR221 Lecture 2
5/34
IntroductionI
ntroduction -- DefinitionDefinitionForce exerted on a body has two effects:
The external effect, which is tendency to
change the motion of the body or to develop
resisting forces in the body
The internal effect, which is the tendency to
deform the body.
8/8/2019 ENGR221 Lecture 2
6/34
IntroductionI
ntroduction -- DefinitionDefinitionIf the force system acting on a body produces
no external effect, the forces are said to be in
balance and the body experience no change inmotion is said to be in equilibrium.
The process of reducing a force system to a simpler
equivalent stem is called a reduction. The processof expanding a force or a force system into a less
simple equivalent system is called a resolution.
8/8/2019 ENGR221 Lecture 2
7/34
IntroductionI
ntroduction -- DefinitionDefinitionAforce is a vector quantity that, when applied to
some rigid body, has a tendency to produce translation
(movement in a straight line) or translation androtation of body. When problems are given, a force
may also be referred to as a load or weight.
Characteristics of force are the magnitude,
direction(orientation) andpoint of application.
8/8/2019 ENGR221 Lecture 2
8/34
IntroductionI
ntroduction -- DefinitionDefinitionScalar Quantity has magnitude only (not direction)
and can be indicated by a point on a scale. Examples
are temperature, mass, time and dollars.
Vector Quantities have magnitude and direction.
Examples are wind velocity, distance between to
points on a map and forces.
8/8/2019 ENGR221 Lecture 2
9/34
IntroductionI
ntroduction -- DefinitionDefinitionCollinear: If several forces lie along the same line-of
action, they are said to be collinear.
CoplanarWhen all forces acting on a body are in the
same plane, the forces are coplanar.
8/8/2019 ENGR221 Lecture 2
10/34
IntroductionI
ntroduction -- DefinitionDefinitionType of Vectors
Free Vector- is vector which may be freely moved
creating couples in space.
Sliding Vector- forces action on a rigid body are
represented by vectors which may move or slid along
their line of action.
Bound Vector or Fixed Vector- can not be moved
without modifying the conditions of the problem.
8/8/2019 ENGR221 Lecture 2
11/34
IntroductionI
ntroduction -- DefinitionDefinitionPrinciple of Transmissibility
The principle of transmissibility states that the
condition of equilibrium or of motion of a rigid body
will remain unchanged if aforce Faction at a given
point of the rigid body is replace by aforce Fof the
same magnitude and the same direction, but acting at
a different point, provided that the two forces have the
same line of action.
8/8/2019 ENGR221 Lecture 2
12/34
IntroductionI
ntroduction -- DefinitionDefinitionPrinciple of Transmissibility
Line of action
8/8/2019 ENGR221 Lecture 2
13/34
IntroductionI
ntroduction -- DefinitionsDefinitions
1. Point loads - concentratedforces exerted at point or
location
2. Distributed loads - a force
applied along a length or
over an area. The
distribution can be uniform
or non-uniform.
Types of Forces(Loads)
8/8/2019 ENGR221 Lecture 2
14/34
IntroductionI
ntroduction -- DefinitionsDefinitions
Resultant Forces
If two forcesP
and Q acting ona particleA may be replaced by
a single forceR, which has the
same effect on the particle.
8/8/2019 ENGR221 Lecture 2
15/34
IntroductionI
ntroduction -- DefinitionsDefinitions
Resultant Forces
This force is called the resultantof the forces P and Q and may be
obtained by constructing a
parallelogram, using P and Q as
two sides of the parallelogram.The diagonal that pass through A
represents the resultant.
8/8/2019 ENGR221 Lecture 2
16/34
IntroductionI
ntroduction -- DefinitionsDefinitions
Resultant Forces
This is known as theparallelogram law for the
addition of two forces. This law
is based on experimental
evidence,; it can not be provedor derived mathematically.
8/8/2019 ENGR221 Lecture 2
17/34
IntroductionI
ntroduction -- DefinitionsDefinitions
Resultant Forces
For multiple forces action on a point, the forces canbe broken into the components of x and y.
8/8/2019 ENGR221 Lecture 2
18/34
VectorsVectorsThe vectors can be solved by
1. Law of sine and law of cosines (two forces)
2. Graphically
3. Equilibrium
a) Table
b) Sum of values
0F !
8/8/2019 ENGR221 Lecture 2
19/34
Homework (Due 1/22/03)
Homework (Due 1/22/03)
Problems:
2-3, 2-5, 2-8, 2-14, 2-15, 2-29,2-37
8/8/2019 ENGR221 Lecture 2
20/34
Example
Problems
Example
Problems
1. Determine the magnitude and
direction of the resultant of the twoforces.
8/8/2019 ENGR221 Lecture 2
21/34
Example
Problems
Example
Problems
2. Two structural members B and C are
riveted to the bracketA
. Knowingthat the tension in member B is 6 kN
and the tension in C is 10 kN,
determine the magnitude and
direction of the resultant force acting
on the bracket.
8/8/2019 ENGR221 Lecture 2
22/34
Example ProblemsExample Problems3. Determine the magnitude and direction ofP
so that the resultant ofP and the 900-N force
is a vertical force of 2700-N directed
downward.
8/8/2019 ENGR221 Lecture 2
23/34
Example ProblemsExample Problems4. A cylinder is to be lifted by two cables. Knowing
that the tension in one cable is 600 N, determine
the magnitude and direction of the force so that the
resultant of the vertical force of 900 N.
8/8/2019 ENGR221 Lecture 2
24/34
Example ProblemsExample Problems5. Determine the force in each supporting wire.
8/8/2019 ENGR221 Lecture 2
25/34
Example ProblemsExample Problems6. The stoplight is supported by two wires. The light
weighs 75-lb and the wires make an angle of 10o with
the horizontal. What is the force in each wire?
8/8/2019 ENGR221 Lecture 2
26/34
Example ProblemsExample Problems7. In a ship-unloading operation, a
3500-lb automobile is supported by
a cable. A rope is tied to the cable
at A and pulled in order to center the
automobile over its intendedposition. The angle between the
cable and the vertical is 2o, while
the angle between the rope and the
horizontal is 30o. What is the
tension in the rope?
8/8/2019 ENGR221 Lecture 2
27/34
Example ProblemsExample Problems8. The barge B is pulled by two tugboatsA and C. At a given
instant the tension in cable AB is 4500-lb and the tension in
cable BC is 2000-lb. Determine the magnitude and direction
of the resultant of the two forces applied at B at that instant.
8/8/2019 ENGR221 Lecture 2
28/34
Example ProblemsExample Problems9. Determine the resultant of the forces on the bolt.
8/8/2019 ENGR221 Lecture 2
29/34
Example ProblemsExample Problems10. Determine which set of force system is in equilibrium. For
those force systems that are not in equilibrium, determine
the balancing force required to place the body in
equilibrium.
8/8/2019 ENGR221 Lecture 2
30/34
Example ProblemsExample Problems11. Two forces P and Q of magnitude P=1000-lb and
Q=1200-lb are applied to the aircraft connection.
Knowing that the connection is in equilibrium,
determine the tensions T1 and T2.
8/8/2019 ENGR221 Lecture 2
31/34
Example ProblemsExample Problems
12. Determine the forces in each of the four wires.
8/8/2019 ENGR221 Lecture 2
32/34
Example ProblemsExample Problems
13. The blocks are at rest on a frictionless incline. Solve for
the forces F1 and F2 required for equilibrium.
8/8/2019 ENGR221 Lecture 2
33/34
Example ProblemsExample Problems
14. LengthA= 5 ft, and length B =10 ft and angle E = 30o.
Determine the angle F of the incline in order to maintain
equilibrium.
8/8/2019 ENGR221 Lecture 2
34/34
Example ProblemsExample Problems
15. Solve for the resisting force at pinA to maintain equilibrium.