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MSE 221

MECHANICS OF

MATERIALS

Ass. Prof. Dr. Yahya K. Tür

Things to Know

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 %)

Tentative exam dates: November 9, Friday; December 14, Friday

Office hours: Wednesday 13:00-14:00

Room : MLZ 208,

Phone: 605 2640

In the exams sharing a calculator is strictly forbidden.

Copyright © 2011 Pearson Education South Asia Pte Ltd

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.


1. Reading Quiz

2. Applications

3. Mechanics

4. Fundamental Concepts

5. Units of Measurement

6. The International System of Units

7. Numerical Calculations

8. General Procedure for Analysis

9. Concept Quiz

In-Class Activities


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


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


APPLICATIONS


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


FUNDAMENTAL CONCEPTS

Basic Quantities1. 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


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


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”



• 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”

maF



• Third Law

“The mutual forces of action and reaction

between two particles are equal and, opposite

and collinear”



Newton’s Law of Gravitational Attraction

Weight:

Letting yields

2

21

r

mmGF

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

2r

mMGW e

2/ rGMg e mgW



SI Units

• Stands for Système International d’Unités

• SI system specifies length in meters (m), time in

seconds (s) and mass in kilograms (kg)

UNITS OF MEASUREMENT

* Force unit, Newton (N), is derived from the others


• 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

UNITS OF MEASUREMENT (cont)


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)

THE INTERNATIONAL SYSTEM OF UNITS


THE INTERNATIONAL SYSTEM OF UNITS

(cont)


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

NUMERICAL CALCULATIONS


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)

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



Calculations• Retain a greater number of digits for accuracy

• Round off final answers to three significant figures



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

GENERAL PROCEDURE FOR ANALYSIS


EXAMPLE 1

Convert 2 km/h to m/s.


m/s 556.0s 3600

h 1

km

m 1000

h

km 2 km/h 2

Remember to round off the final answer to three significant figures.

Solution


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.


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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