statics of rigid bodies chapter 1

7/27/2019 Statics of Rigid Bodies Chapter 1

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Statics of Rigid Bodies

Gevelyn Bontilao Itao, MOE

Mindanao State UniversityIligan Institute of Technology

College of Engineering


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MECHANICS

Mechanics

-a branch of physical sciences which describes and

predicts the condition of ret or motion of bodies that

are subjected to the action of forces.

MECHANICS

Rigid-BodyMechanics

Statics Dynamics

Deformable-BodyMechanics

FluidMechanics


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Statics

deals with equilibrium of bodies, i.e., those that

are either at rest or move with constant velocity

Dynamics

deals with accelerated motion of bodies

Two Areas of Rigid-Body Mechanics


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Particle

has a mass, but a size that can be neglected.

Rigid-body a combination of a large number of a particles in

which all the particles remain at a fixed distance from

one another, both before and after applying a load..

Definition of Terms

Concentrated Force

represents the effect of a loading which is assumed

to act at a point on a body.

Idealizations:


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1. The Parallelogram Law for the Addition of Forces

States that the two forces acting on a particle may

be replaced by a single force which is called the

RESULTANT FORCE.

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Six Fundamental Principles


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2. The Principle of Transmissibility

States that the condition of equilibrium or of motion

of a rigid body will remain unchanged if a force, F,

acting at a given point of rigid body is replaced by a

force F of the same magnitude and same direction,bur acting at a different point, provided that the

forces have the same line of action.

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3. The First Law

If the resultant force acting on a particle is zero, the

particle will remain at rest (if originally at rest) or will

move with constant speed in a straight line (if

originally in motion), provided that the particle is not

subjected to an unbalanced force.

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Newtons Three Laws of Motion:


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4. The Second Law

If the resultant force acting on a particle is not equal

to zero (subjected to an unbalanced force), the

particle will have an acceleration proportional to the

magnitude of the resultant and in the direction of this

resultant force.

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5. The Third Law

The mutual forces of action and reaction between

two bodies in contact have the same magnitude,

same line of action and opposite sense.

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6. The Third Law States that two particles of mass m1 and m2 are

mutually attracted with equal and opposite forces, F

andF of magnitude F given by the formula

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SI Units

Base Units:

Length - meter

Time - secondMass - kilogram

Derived Unit:

Force - Newton

1N = 1 kg m/sec2

US Customary

Base Units:

Length - feet

Time - secondMass - pounds

Derived Unit:

Force - Slug

slug= 1 lb sec2 / ft

Systems of Units


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Conversion Factor


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Prefixes of Units


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1. Read the problem carefully and try to correlate theactual physical situation with the concepts.

Methods of Problem Solving

2. Draw any necessary diagrams and tabulate the

problem data.

3. Apply the relevant principles, generally inmathematical form.

4. Solve the necessary equations algebraically as far as

practical, making sure they are dimensionally

homogeneous. Use a consistent set of units andcomplete the solution numerically.

5. Study the answer with technical judgment and

common sense to determine whether or not it seems

reasonable.


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Numerical Accuracy

The accuracy of the solutions of the problem depends

upon

1. The accuracy of the given data.

2. The accuracy of the computations performed.


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FORCE VECTORS

What is a FORCE?

We cannot measure force, only it effects:

deformation of structures, acceleration.

Instead we hypothesize:

A force applied to a particle is a vector.

Motion is determined by vector sum.

A particle remains at rest only if total forceacting on it is zero.


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Scalar

a quantity characterized by a positive or negative

number

have magnitude but no direction, represented by

plain numbers.

FORCE VECTORS

Vector

represented by a letter with an arrow over it (A).

Graphically,

the length of an arrow (magnitude)

the angle between a reference axis and arrows

line of action (direction)

indicated by the arrow head (sense)


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1. Vector Addition: A + B = R (Resultant Force)

Methods of Vector Addition:

a. Parallelogram Method

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Vector Operations


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1. Vector Addition: A + B = R (Resultant Force)


b. Head-to-Tail Method

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Vector Operations


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2. Vector Subtraction: A - B = R (Resultant Force)


a. Parallelogram Method

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Vector Operations


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3. Multiplication and Division of Vector by a Scalar:

a x A = a A (Vector)

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Vector Operations

Ifa is positive: the sense is the same as A

Ifa is negative: the sense is opposite to A

Example: A = 2

a. Ifa = 2

b. Ifa = -1


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4. Resolution of Vector

- A vector maybe resolved into two components

having known line of action using the

parallelogram method.

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Vector Operations


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Law of SINE and COSINE:

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Vector Operations


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Vector Addition of Forces in Coplanar System

Example 1:

The screw eye is subjected to two forces F1 and F2.

Determine the magnitude and direction of the

resultant force.


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Vector Addition of Forces in Coplanar System

Example 2:The forces F acting on the frame has a magnitude of

500N and is to be resolved into two components

acting along members AB and AC. Determine the

angle , measured below the horizontal, so that the

component FAC is directed from A towards C and has a

magnitude of 400N. Determine also FAB .


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Addition of a System of Coplanar System

Cartesian Unit Vectors

- Used to designate the direction of the known axes in

coplanar system


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Scalar Notation

- The scalar component of F with respect to , can be

express as

Fx = F cos Fy = F sin

- And the direction of the force F can be obtained by

tan = Fy /Fx- The magnitude of the force is then

F2 = Fx2 + Fy

2


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- For two or more forces

R = F1 + F2 + F3+ Fn

= (Fx1i+Fy1j)+(Fx2i+Fy2j)+(Fx3i+Fy3j)++(Fxni+Fynj)

R = Fx i+ Fy j

- And the direction of the resultant force R is then

tan = Fy

/Fx

- The magnitude of the resultant force R is then

R2 = (Fx)2 + (Fy)

2


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Example 1:

The screw eye is subjected to two forces F1 and F2.

Determine the magnitude and direction of the

resultant force.


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Example 2:

Determine the magnitude of the component force F

and the magnitude of the resultant force FR if FR is

directed along the positive yaxis.

statics of rigid bodies chapter 1

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