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MAE 241 - Statics

Summer 2009

Dr. Konstantinos A. Sierros

Office Hours: M and W 10:30 11:30 (263 ESB new add)

[email protected]

Teaching Blog: http://wvumechanicsonline.blogspot.com

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Textbook

R. C. Hibbeler, STATICS, 12th Edition, Pearson Prentice Hall, NewJersey USA, 2004, ISBN 0-13-607790-0

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Schedule

Week Day Lecture/Class Topic Assignments/Problems

M General introduction, Units, Methodology, Introduction to force vectors (1.1-2.1) Ch 1T Vector operations, Cartesian Vectors, Addit ion of Cartesian vectors (2.1-2.6) 2.1-2.6

1 W Position vectors, Dot product, Condition for particle equillibrium (2.7-3.1) 2.7-3.1

R Free body diagrams, Coplanar force systems, 3D force systems (3.2-3.4) 3.2-3.4

M Moment of a force, Cross product, Vector formulation, Principle of moments (4.1-4.4)4.1-4.4

T Moment of a couple, Simplification of force-couple systems (4.5-4.9) 4.5-4.9

2 W Rigid body equill ibrium, Free body diagrams, Equations of equill ibrium (5.1-5.3) 5.1-5.3

R Force members, Free body diagrams, Equillibrium, Constraints (5.4-5.7) 5.4-5.7

M Exam 1 and Simple trusses (6.1)T Method of joints, sections (6.1-6.4) 6.1-6.4

3 W Space trusses, frames and machines (6.5-6.6) 6.5-6.6

R Internal forces, Shear and moment equations (7.1-7.2) 7.1-7.2

M Distributed loads, shear and moment relations, cables (7.3-7.4) 7.3-7.4

T Dry friction, Wedges, Frictional forces on screws (8.1-8.4) 8.1-8.4

4 W Frictional forces on flat belts, bearing, disks, rolling resistance (8.5-8.8) 8.5-8.8

R Review 1 Revice Ch 1-8

M Exam 2 and Center of gravity, mass centroid (9.1) 9.1

T Composite bodies, Pappus and Guldinus (9.1-9.3) 9.1-9.3

5 W Distributed loading, fluid pressure (9.4-9.5) 9.4-9.5

R Moments of inertia, Parallel ax is theorem, Radius of gyration (10.1-10.3) 10.1-10.3

M Composite areas, product of inertia,inclined axes (10.4-10.6) 10.4-10.6

T Mohr's circle and start of final review (10.7) 10.7 (Revice Ch 1-10)

6 W Review 2 Revice Ch 1-10

R Final exam

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Chapter 1: General principles

Objectives

Intro to the basic quantities and

idealizations of mechanicsNewtons laws

SI unit system

Numerical calculations procedure

General guide for problem solving

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1.1 Mechanics

Mechanics is a branch of physics that is concerned with the state of

rest or motion of bodies that are subjected to the action of forces

Mechanics

Rigid-body

Deformable-body

Fluid

Rigid-body mechanics

Statics Dynamics

Statics deals with the equilibrium of bodies that are either at rest

or move with constant velocity. Dynamics is dealing with bodies

in accelerated motion

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History

Archimedes

(287-212 B.C.)

Lever principle

Galileo Galilei

(1564-1642.)Pendulums, falling

bodies

Newton

(1642-1727)

3 Fundamental laws

Euler

DAlembert

Langrange

and others

The subjects of statics developed very early in history because its

principles can be formulated simply from measurements of geometryand force

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1.2 Fundamental concepts

Basic quantities Length is used to locate the position of a point in

space and describe the size of a physical system

Time is conceived as a succession of events

Mass is a measure of a quantity of matter that is

used to compare the action of one body with that

of another

Force is considered as push or pull exerted by

one body or another.

- Direct contact (eg. A person pushing a wall)- Distant action (gravitational, electrical, magnetic

forces)

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1.2 Fundamental concepts

Idealizations

We use some idealizations in order to simplify the

application of theory

Particle: It has a mass, but its size can be neglected

(eg size of earth is insignificant as compared to the size

of its orbit)

When a body is modelled as a particle, mechanics

become simpler since the geometry of the body is not

involved in the analysis of the problem

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1.2 Fundamental concepts

Idealizations

A Rigid body can be considered as a combination of a large number of

particles in which all the particles remain at a fixed distance from one

another, both before and after applying a load

A Concentratedforce represents the effect of a loading which is assumed

to act at a point on a body. (eg. Contact force between wheel and ground)

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Newtons three laws of motion

The basis of engineering mechanics is formed by Newtons three laws

of motion. These laws, based on experimental observation, apply to

the motion of a particle as measured from a nonacceleratingreference

frame.

1st LawA particle originally at rest, or moving in

a straight line with constant velocity, tends to

remain in this state provided the particle is notSubjected to an unbalanced force

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Newtons three laws of motion

2nd LawA particle acted upon by an unbalancedforce F experiences an

acceleration a that has the same direction as the force and a magnitude

directly proportional to the force

F = ma

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Newtons three laws of motion

3rd LawThe mutual forces of action and reaction between two particles

are equal, opposite, and collinear

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Newtons law of gravitational attraction

F is force of gravitation between two particles

G is constant of gravitation measured

experimentally, G=66.73*10-12 m3/(kg s2)

m1,m2 represent the mass of each particle

r is the distance between the two particles

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Newtons law of gravitational attraction

Weight

According to the equation described, any two particleshave a mutual attractive (gravitational) force acting between them

For a particle located at the surface of the earth (or close enough) the

only gravitational force, of significant magnitude, is that between the

earth and the particle. This force is termed weight.

If we put m1 = m and m2 =Me (mass of earth) and r is distance between

the particle and the earths center

Letting g=GMe/r2, then W = mg

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Units of measurement

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Conversion of units

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The International System of units

SI is used throughout

Rules for use

(please read carefully page 10)

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Numerical calculations

Dimensional homogeneity: Each term in an equation must be expressed

in the same unitsSignificant figures:Number of significant figures determines accuracy of

the number. Use engineering notation.

Rounding off numbers: Any numerical figure ending in five or greater is

rounded up and a number less less than five is rounded downCalculations: Do not round off calculations until expressing the final

result. Round off the answer to three significant figures

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General procedure for analysis

Read the problem carefully and correlate physical situation with

theory

Tabulate the problem data and draw diagrams

Apply the relevant principles, generally

with equations

Solve the equations and report the answer

Judge the answer in technical terms and

common sense to determine whether the

answer seems reasonable

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Chapter 2:Force vectors

Objectives

To show how to add forces and

resolve them into components

using the Parallelogram Law

Cartesian vectors

Introduce dot product

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2.1 Scalars and vectors

Ascalaris any positive or negative physical quantity that can becompletely specified by its magnitude (eg. length, mass, time)

A vectoris any physical quantity that requires both a magnitude

and a direction for its complete description (eg. force, moment)