MECHANICS OF MATERIALS

MSE 221

MECHANICS OF MATERIALS Ass. Prof. Dr. Yahya K. Tür

Things to Know Course hours: Friday 9:00 -12:00 Office hours: Wednesday 13:00-14:00 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. Copyright © 2011 Pearson Education South Asia Pte Ltd

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

Copyright © 2011 Pearson Education South Asia Pte Ltd

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 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


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 Copyright © 2011 Pearson Education South Asia Pte Ltd

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”


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


FUNDAMENTAL CONCEPTS (cont) •

Third Law “The mutual forces of action and reaction between two particles are equal and, opposite and collinear”


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


UNITS OF MEASUREMENT

SI Units • •

•

Stands for Système International d’Unités F = ma is maintained only if – 3 of the units, called base units, are defined – 4th unit is derived from the equation SI system specifies length in meters (m), time in seconds (s) and mass in kilograms (kg)


UNITS OF MEASUREMENT (cont)

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


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


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)


THE INTERNATIONAL SYSTEM OF UNITS (cont)


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


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)



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


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 Copyright © 2011 Pearson Education South Asia Pte Ltd

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.



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. Copyright © 2011 Pearson Education South Asia Pte Ltd

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 Copyright © 2011 Pearson Education South Asia Pte Ltd