Download MECHANICS OF MATERIALS

MSE 221
MECHANICS OF
MATERIALS
Ass. Prof. Dr. Yahya K. Tür
Things to Know
Course hours:
Monday: 15:00-16:50
Friday 11:00 -11:50
Office hours: Wednesday 16:00-17:00
Room :
MLZ 221,
Phone:
605 2640
Course Book : Statics and Mechanics of Materials, R. C. Hibbeler, SI edition,
Sources:
Statik ve Mukavemet, Mehmet H. Omurtag, Nobel
Statics and Mechanics of Materials, Beer and Johnston, Mc Graw Hill
Grading :
2 Midterms (30% + 30 %) + Final (40 %)
In the exams sharing a calculator is strictly forbidden.
Chapter Objectives
 To provide an introduction to the basic quantities and
idealizations of mechanics.
 To state Newton’s Laws of Motion and Gravitation.
 To review the principles for applying the SI system of
units.
 To examine the standard procedures for performing
numerical calculations.
 To present a general guide for solving problems.
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In-Class Activities
1.
2.
3.
4.
5.
6.
7.
8.
9.
Reading Quiz
Applications
Mechanics
Fundamental Concepts
Units of Measurement
The International System of Units
Numerical Calculations
General Procedure for Analysis
Concept Quiz
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READING QUIZ
1.
The subject of mechanics deals with what
happens to a body when ______ is/are applied to it.
a)
Magnetic field
b)
Heat
c)
Forces
d)
Neutrons
e)
Lasers
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READING QUIZ
2.
________________ still remains the basis of most of
today’s engineering sciences.
a)
Newtonian Mechanics
b)
Relativistic Mechanics
c)
Greek Mechanics
d)
Euclidean Mechanics
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APPLICATIONS
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MECHANICS
• Mechanics can be divided into 3 branches:
- Rigid-body Mechanics (MSE 221)
- Deformable-body Mechanics (MSE 321)
- Fluid Mechanics
• Rigid-body Mechanics deals with
- Statics – Equilibrium of bodies
 At rest
 Moving with a constant velocity
- Dynamics – Accelerated motion of bodies
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FUNDAMENTAL CONCEPTS
Basic Quantities
1. Length
- locate the position of a point in space
- describe the size of a physical system
2. Time
- succession of events
3. Mass
- measure of a quantity of matter
- used to compare the action of one body with that of
another
4. Force
- a “push” or “pull” exerted by one body on another
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FUNDAMENTAL CONCEPTS (cont)
Idealizations
1. Particle
- has a mass, but size can be neglected
2. Rigid Body
- a combination of a large number of particles
3. Concentrated Force
- the effect of a loading assumed to act at a point
on a body
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FUNDAMENTAL CONCEPTS (cont)
Newton’s Three Laws of Motion
•
First Law
“A particle originally at rest, or
moving in a straight line with
constant velocity, will remain in
this state provided that the
particle is not subjected to an
unbalanced force”
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FUNDAMENTAL CONCEPTS (cont)
•
Second Law
“A particle acted upon by an unbalanced force F
experiences an acceleration a that has the same
direction as the force and a magnitude that is
directly proportional to the force”
F  ma
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FUNDAMENTAL CONCEPTS (cont)
•
Third Law
“The mutual forces of action and reaction
between two particles are equal and, opposite
and collinear”
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FUNDAMENTAL CONCEPTS (cont)
Newton’s Law of Gravitational Attraction
F G
m1 m 2
r2
F = force of gravitation between two particles
G = universal constant of gravitation
m1,m2 = mass of each of the two particles
r = distance between the two particles
mM e
Weight: W  G 2
r
2
Letting g  GM e / r yields W  mg
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UNITS OF MEASUREMENT
SI Units
•
•
Stands for Système International d’Unités
SI system specifies length in meters (m), time in
seconds (s) and mass in kilograms (kg)
* Force unit, Newton (N), is derived from the others
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UNITS OF MEASUREMENT (cont)
•
•
•
At the standard location,
g = 9.806 65 m/s2
For calculations, we use
g = 9.81 m/s2
Thus,
W = mg (g = 9.81 m/s2)
•
Hence, a body of mass 1 kg has a weight of 9.81 N, a
2 kg body weighs 19.62 N
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THE INTERNATIONAL SYSTEM OF UNITS
Prefixes
•
For a very large or small numerical quantity, units can
be modified by using a prefix
•
Each represent a multiple or sub-multiple of a unit
Eg: 4,000,000 N = 4000 kN (kilonewton)
= 4 MN (meganewton)
0.005 m = 5 mm (millimeter)
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THE INTERNATIONAL SYSTEM OF UNITS
(cont)
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NUMERICAL CALCULATIONS
Dimensional Homogeneity
•
•
•
Each term must be expressed in the same units
Regardless of how the equation is evaluated, it
maintains its dimensional homogeneity
All terms can be replaced by a consistent set of units
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NUMERICAL CALCULATIONS (cont)
Significant Figures
•
•
•
Accuracy of a number is specified by the number of
significant figures it contains
A significant figure is any digit including zero
e.g. 5604 and 34.52 have four significant numbers
When numbers begin or end with zero, we make use
of prefixes to clarify the number of significant figures
e.g. 400 as one significant figure would be 0.4(103)
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NUMERICAL CALCULATIONS (cont)
Rounding Off Numbers
•
•
•
Accuracy obtained would never be better than the
accuracy of the problem data
Calculators or computers involve more figures in the
answer than the number of significant figures in the
data
Calculated results should always be “rounded off” to
an appropriate number of significant figures
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NUMERICAL CALCULATIONS (cont)
Calculations
•
•
Retain a greater number of digits for accuracy
Round off final answers to three significant figures
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GENERAL PROCEDURE FOR ANALYSIS
To solve problems, it is important to present work in a
logical and orderly way as suggested:
1. Correlate actual physical situation with theory
2. Draw any diagrams and tabulate the problem data
3. Apply principles in mathematics forms
4. Solve equations which are
dimensionally homogenous
5. Report the answer with correct
UNITS and significant figures
6. Use technical judgment
and common sense
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EXAMPLE 1
Convert 2 km/h to m/s.
Solution
2 km  1000 m  1 h 
2 km/h 


  0.556 m/s
h  km  3600 s 
Remember to round off the final answer to three significant figures.
Copyright © 2011 Pearson Education South Asia Pte Ltd
Copyright © 2011 Pearson Education South Asia Pte Ltd
CONCEPT QUIZ (cont)
1)
Give the most appropriate reason for using three
significant figures in reporting results of typical
engineering calculations.
a)
Historically slide rules could not handle more than three
significant figures.
b)
Three significant figures gives better than one-percent accuracy.
c)
Telephone systems designed by engineers have area codes
consisting of three figures.
d)
Most of the original data used in engineering calculations do not
have accuracy better than one percent.
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CONCEPT QUIZ (cont)
2)
For a statics problem, calculations show
the final answer as 12345.6 N. What will
you write as your final answer?
a)
12345.6 N
b)
12.3456 kN
c)
12 kN
d)
12.3 kN
e)
123 kN
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