工程力学全英文Engineering Mechanics (2)
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Fundamental Concepts and Principles of Statics
Fundamental Concepts and Principles of Statics
Fundamental Concepts of Statics
Force is the mechanical interaction between bodies that changes or tends to change the motion state or the shape of the body on which it acts.
opposite senses. Fifth Principle (Principle of Solidification)
C
The system will
move.
F If a freely deformable body (or body system)
subjected to the action of a force system is in M
without
changing
its
external
effect
on
a
rigid
body.
(Forces
are
sliding
vectors)
F
F F' F F
F
A
B
A
=
B
=
A
B
Fundamental Concepts and Principles of Statics
Third Principle (Principle of Force Parallelogram)
Fundamental Concepts and Principles of Statics
A force system means a few forces acting on the bodies.
Coplanar
Concurrent Parallel
Force system
General case Concurrent
ogram constructed by the vectors F1 and F2 .
R is called the resultant of the two forces
F1
and
F2 .
F1and F2are called components of the force R .
A C F1 R O B
1. Effect of forces: to affect the motion of bodies (external effect of forces) to affect the deformation of bodies (internal effect of forces)
2. Three elements of a force:
changed
Q
if
we
add P
or subtract
Q' Q
any
other
equilibrium
force
system.
F
The new force system is equivalent to the old one.
Principle of transmissibility: A force is allowed to move along its line of action
Point of application, Direction, Magnitude
Байду номын сангаас
Force is a vector.
F
3. Unit of force: Newton (N) 1N=1kg•m/s2 1KN=103N
1MN=106N
line of action
Fundamental Concepts and Principles of Statics
Three nonparallel, coplanar forces that hold a rigid body in equilibrium must be
concurrent.
Proof:
F1
Suppose a rigid body is subjected to three
nonparallel, coplanar forces F1 , F2 and F3 . Two of them, F1 and F2 must intersect at some
Equilibrium implies a body is at rest or moving with constant velocity along a straight line.
Fundamental Concepts and Principles of Statics
Fundamental Principles of Statics
F2
An equivalent statement of the third principle is the Principle of Force Triangle
C
R
O
F1
B
F1
A
F2 R
C
F2
O
Fundamental Concepts and Principles of Statics
Three-Force Principle
A rigid body is defined as one, which does not deform at all under the action of applied forces.
1. Physical bodies like engineering structures and machine parts are never absolutely rigid and will deform slightly under the action of forces.
equilibrium, the state of equilibrium will not be disturbed if the body (or body system) solidifies.
A
B
If M and F make the system in equilibrium state, the combination of bars AC and BC can be considered as a rigid body.
A FA
FA FB
B
FB
When a body (or a member) in equilibrium is subjected to no couple moments and forces are applied at only two points on the body (or member), the body (or member) is called a two-force body (or two-force member).
Two forces F1 and F2 are applied on a body at pointO.
Their action is equivalent to the action of one force R .
R can be represented by the diagonal of theparallel-
2. However, such deformation is usually very small and can be completely ignored. Rigid body assumption is used in Theoretical Mechanics.
3. Deformable bodies, in which the effect of small deformation must be taken into account, are treated in Mechanics of Materials.
First Principle (Principle of Two Force Equilibrium)
If a rigid body is held in equilibrium by two forces only, the two forces must
have the same magnitude, the same line of action and opposite senses.
Noncoplanar
Parallel
General case A force system is concurrent if the action lines of all forces intersect at a common point.
Two force systems that produce the same external effects on a rigid body are said to be equivalent.
Fourth Principle (Principle of Action and Reaction)
There are mutual actions between any two bodies such that the action and
reaction forces have the same magnitude, the same line of action and
Fundamental Concepts and Principles of Statics
Second Principle (Principle of Plus or Minus an Equilibrium Force System)
The action of a given force system acting on a rigid body will in no way be
point O and have a resultant F12 passing through
A
F1
F12
O
F2
B
F2
point O.
C
Based on two-force equilibrium principle, F3 must also pass through point O.
F3
Fundamental Concepts and Principles of Statics
Fundamental Concepts and Principles of Statics
Fundamental Concepts of Statics
Force is the mechanical interaction between bodies that changes or tends to change the motion state or the shape of the body on which it acts.
opposite senses. Fifth Principle (Principle of Solidification)
C
The system will
move.
F If a freely deformable body (or body system)
subjected to the action of a force system is in M
without
changing
its
external
effect
on
a
rigid
body.
(Forces
are
sliding
vectors)
F
F F' F F
F
A
B
A
=
B
=
A
B
Fundamental Concepts and Principles of Statics
Third Principle (Principle of Force Parallelogram)
Fundamental Concepts and Principles of Statics
A force system means a few forces acting on the bodies.
Coplanar
Concurrent Parallel
Force system
General case Concurrent
ogram constructed by the vectors F1 and F2 .
R is called the resultant of the two forces
F1
and
F2 .
F1and F2are called components of the force R .
A C F1 R O B
1. Effect of forces: to affect the motion of bodies (external effect of forces) to affect the deformation of bodies (internal effect of forces)
2. Three elements of a force:
changed
Q
if
we
add P
or subtract
Q' Q
any
other
equilibrium
force
system.
F
The new force system is equivalent to the old one.
Principle of transmissibility: A force is allowed to move along its line of action
Point of application, Direction, Magnitude
Байду номын сангаас
Force is a vector.
F
3. Unit of force: Newton (N) 1N=1kg•m/s2 1KN=103N
1MN=106N
line of action
Fundamental Concepts and Principles of Statics
Three nonparallel, coplanar forces that hold a rigid body in equilibrium must be
concurrent.
Proof:
F1
Suppose a rigid body is subjected to three
nonparallel, coplanar forces F1 , F2 and F3 . Two of them, F1 and F2 must intersect at some
Equilibrium implies a body is at rest or moving with constant velocity along a straight line.
Fundamental Concepts and Principles of Statics
Fundamental Principles of Statics
F2
An equivalent statement of the third principle is the Principle of Force Triangle
C
R
O
F1
B
F1
A
F2 R
C
F2
O
Fundamental Concepts and Principles of Statics
Three-Force Principle
A rigid body is defined as one, which does not deform at all under the action of applied forces.
1. Physical bodies like engineering structures and machine parts are never absolutely rigid and will deform slightly under the action of forces.
equilibrium, the state of equilibrium will not be disturbed if the body (or body system) solidifies.
A
B
If M and F make the system in equilibrium state, the combination of bars AC and BC can be considered as a rigid body.
A FA
FA FB
B
FB
When a body (or a member) in equilibrium is subjected to no couple moments and forces are applied at only two points on the body (or member), the body (or member) is called a two-force body (or two-force member).
Two forces F1 and F2 are applied on a body at pointO.
Their action is equivalent to the action of one force R .
R can be represented by the diagonal of theparallel-
2. However, such deformation is usually very small and can be completely ignored. Rigid body assumption is used in Theoretical Mechanics.
3. Deformable bodies, in which the effect of small deformation must be taken into account, are treated in Mechanics of Materials.
First Principle (Principle of Two Force Equilibrium)
If a rigid body is held in equilibrium by two forces only, the two forces must
have the same magnitude, the same line of action and opposite senses.
Noncoplanar
Parallel
General case A force system is concurrent if the action lines of all forces intersect at a common point.
Two force systems that produce the same external effects on a rigid body are said to be equivalent.
Fourth Principle (Principle of Action and Reaction)
There are mutual actions between any two bodies such that the action and
reaction forces have the same magnitude, the same line of action and
Fundamental Concepts and Principles of Statics
Second Principle (Principle of Plus or Minus an Equilibrium Force System)
The action of a given force system acting on a rigid body will in no way be
point O and have a resultant F12 passing through
A
F1
F12
O
F2
B
F2
point O.
C
Based on two-force equilibrium principle, F3 must also pass through point O.
F3
Fundamental Concepts and Principles of Statics