1 / 19

MEGR 2144 Introduction to Solid Mechanics

- Instructor Qiuming Wei
- Grader Matt Bolen
- Office DCH 362
- Phone 704 687 8213
- Office Hours M, W, F 300-430pm
- Other times by appointment

Course Objectives

- Apply the principles of equilibrium to the

problems of solid mechanics to determine external

and internal forces and moments, distinguish

between statically determinate and indeterminate

systems - Explain the concepts of stress, strain, material

behavior and distinguish between linear and

nonlinear material behavior (elastic and

inelastic) - Formulate and solve mechanical and structural

problems involving tension and torsion - Formulate and solve mechanical and structural

problems involving pure bending and transverse

loading - Formulate and solve mechanical problems involving

pressure vessels - Determine various modes of buckling and determine

the critical loads of buckling for various

boundary conditions - Analyze the stress-state at a point and determine

principal stresses and maximum shear-stress at

any point in a simple structural problem - Select, design and analyze a mechanical part

based on stress-based and maximum

deflection-based design criteria.

Syllabus

- Textbook James M. Gere Mechanics of Materials,

6th Edition, 2004, Thomson ISBN0-534-41793-0 - 22 Lectures
- 3 reviews classes (for the 3 tests)
- 1 comprehensive review for final exam
- 3 exams
- 1 comprehensive close book final
- BlackBoard Vista Domain available for this

section. - Course materials also available on Dr. Weis

personal website http//www.coe.uncc.edu/qwei/

Course Materials

- All lecture notes (ppt files) will be posted on

my personal website, and Blackboard Vista - http//www.mees.uncc.edu/Qwei.htm
- All homework solutions will be posted on my

personal website, and Blackboard Vista. - All exam problem solutions will be posted on my

personal website, and Blackboard Vista .

Rules of Classroom, Exams, Homework, and Grading

Policy

- Standard Grading Policy A, B, C, D, F.
- Homework/Quizzes 10 Quiz will be given at the

end of each class except for the first. - 3 Exams (total 60, 20 for each exam)
- Comprehensive Final 30.
- Cell phone use in classroom is prohibited.
- Homework
- is typically due at the beginning of class on the

second class from the assignment date. - may not be accepted late except for instances of

sickness or death in the family (in the case of

sickness or personal emergency, notify me via

email and place your paper in my mailbox as soon

as possible). - must have your full name printed legibly on the

top right corner. - must be done on straight-cut paper (points may be

deducted for uneven or frilly edges). - must be stapled (for multiple pages) (or points

may be deducted). - must NOT be copied from another person or any

other source (submitting copied work is a

violation of the code of academic integrity,

policy 105). - must show coherent solution methods (writing the

answer down will not earn credit). - must have proper units on all answers, and all

answers should be boxed. - must have three or four significant figures for

answers (and engineering notation is

recommended). - must be neat and legible.
- Course Attendance Policy
- Students are expected to punctually attend all

scheduled lectures. - Absences from class may be excused by the

instructor for personal illness, religious

holidays, or participation as an authorized

University representative in an out-of-town

event. Wherever possible, students are expected

to seek permission of the instructor prior to

absences.

Chapter 01 Tension, Compression and Shear

- What is Mechanics of Materials? Or what is Solid

Mechanics? - Study of the behavior of solid bodies under

different kinds of mechanical loading. - Important concepts in Mechanics of Materials
- Stress force/area
- SI Unit is Pascal, or Pa, after the French

scientist and philosopher Pascal (1623-1662) - 1 Pa1Newton/1m2 1kPa103Pa 1MPa106Pa,

1GPa109 Pa - US Unit is PSI Pound per square inch.
- 1PSI6894.76 Pa.
- Strain (change in length/original length)
- Dimensionless (no unit)
- Displacements unit is meter (SI) or inch (US)

1.1 Why Solid Mechanics?

- Upper Left A ship breaks from the middle. Why

did this happen? - Low Left A bridge is collapsed. Design problem?
- Right montage The twin towers collapsed about 2

hours after the 911 terrorist attack. Why?

1.2 Normal stress and strain examples

- In the tug-of-war game, the rope is pulled by two

(groups) of people. - An axial force is applied to the rope by the

players. - The rope is said to have a normal stress stress

along the axis of the rope that tends to elongate

the rope.

1.2 Normal Stress and strain definition

- A prismatic member a straight structural member

with a constant cross sections thru-out its

length. - If a prismatic member with cross-sectional area A

is subjected to a normal force F, then we say

that a normal stress, s is applied to this

prismatic member, and we have - sF/A (PaN/m2 , or psilb/in2 )
- We also say that the normal force is an axial

force applied along the axial direction of the

prismatic member. - If the initial length of the member is l0, and

under the normal force it is elongated to the

final length l, we say that the normal strain of

this prismatic member is - e (l-l0)/l0 d/l0
- d l-l0

1.3 Mechanical Properties of Materials

- With special mechanical testing equipment, we can

measure how a solid responds to mechanical

loading. - The responses of a solid to mechanical loading

are called the mechanical properties , or

mechanical behavior of the solid (material). - Generally speaking, mechanical testing is

performed on standardized specimens ASTM

(American Society for Testing and Materials).

Types and Equipment for Mechanical Testing

What do we measure in a mechanical testing?

- During a mechanical testing, we measure the force

applied to the specimen, and use a strain gage or

an extensometer to measure the elongation of the

specimen. - From the force and the cross-section area of the

specimen, we calculate the stress of the

specimen. - From the elongation of the specimen and the

original length of the specimen, we calculate

the strain of the specimen. - We then plot the stress vs. strain we obtain the

stress-strain curve of the specimen. - The stress-strain curve reflects the mechanical

properties of the solid. - If the specimen recovers its original dimension

when the mechanical load (force) is removed, we

say the deformation is elastic. - If the specimen can not recover its original

dimension when the force is removed, we say the

specimen has gone through plastic deformation,

and the strain that remains after the load is

removed is called plastic strain. - Important parameters in a tensile stress-strain

curve of metal - Proportional limit the stress beyond which the

stress-strain relation is no longer linear. - Elastic limit the stress beyond which plastic

deformation begins. - Yield point the stress beyond which material

starts to yield (to have permanent deformation ). - Quite often the elastic limit and the yield point

are hard to differentiate. - Fracture point the point at which the specimen

breaks. - Tensile strength the maximum stress on the

stress-strain curve. - Percent elongation El (L1-L0)/L0 x (100),

where L0 is the original gage length, and L1 is

the distance between the gage marks at fracture.

Definition of s0.2

- In practice, it is hard to determine the exact

yield strength (yield point). - We use the offset method to define a point on the

stress-strain curve, and use the stress at that

point to represent the yield strength for

engineering design. - The most common way is to draw a straight line on

the stress-strain curve parallel to the elastic

part (initial linear part), but offset by a

strain of 0.002 (or 0.2). - The stress at the intersection of the offset line

and the stress-strain curve define the yield

strength s0.2.

- Offset method to define the yield strength.
- Please note that the offset strain 0.002 is

plastic (permanent strain) - The 0.2 offset yield strength of a material is

extremely important for engineering design.

Two types of elasticity

- If the specimen recovers its original dimension

upon unloading, we say the deformation is

elastic. - If during elastic deformation, the stress is

proportional to the strain, we say the material

is linearly elastic, and Hookes law applies - s E e
- E is a materials constant, called the elastic

modulus, or Youngs modulus. - The unit of E is Pa. For most solids, E is from a

few GPa to 1000 GPa (diamond) - If during elastic deformation, the stress is not

proportional to the strain, we say the material

has non-linear elasticity.

Typical values of Youngs modulus

- Aluminum 70 GPa
- Steels 210 GPa
- Copper 130 GPa
- Plastics 100 MPa10 GPa
- Tungsten 400 GPa.
- Ceramics 300-600 GPa
- Diamond 1000 GPa.

- Note
- The Youngs modulus, or any elastic constant of a

solid, does not depend on the heat-treatment

history, microstructure, etc. of the solid. - It only depends on the inter-atomic bonds of the

solid. - The stronger the bond, the greater the Youngs

modulus.

Poissons Ratio of a Solid

- When a round bar (or any prismatic member) is

pulled by a force F, it gets longer (normal

strain (or axial strain) ezgt 0), and thinner

(lateral strain (or transverse strain) ex lt0) - The ratio of the lateral strain to the normal

strain is a material constant, and - n -(ez /ex) Poissons ratio (After Poisson,

the French scientist, 1781-1840) - Most metals n is 0.3
- Diamond n 0.17
- Some ceramics n 0.2
- Can n be negative?
- When the round bar is compressed by a force F, it

gets shorter (normal strain ezlt 0) and thicker

(lateral strain ex gt0), and the definition of

Poissons ratio stays the same, and is positive.

General mechanical behavior of solid materials

- Ductile materials
- If the specimen undergoes significant amount of

plastic deformation before it breaks (fractures),

we call the material ductile. - The blue stress-strain curve represents that of a

ductile material. - Most metals (Cu, Ag, Ni, Al, etc.), some steels,

some alloys, are typical ductile metals. - Brittle materials
- If the specimen undergoes little or no plastic

deformation before it breaks (fractures), we call

the material brittle . - The red stress-strain curve represents that of a

brittle material. - Most ceramics, some hardened steels, metal-metal

compounds (intermetallic compounds) are brittle.

Summary of Lecture 01

- Prismatic member structural member with constant

cross-sectional area - Normal stress s (Pa, KPa, MPa, GPa, or PSI) F

(N or lb)/A (m2 or in2) - Normal strain e (m/m or in/in) d (m or in)/L0

(m or in) - Mechanical behavior of solids
- Stress-strain curves
- Elastic and inelastic deformation
- Plastic (permanent) deformation
- Hookes law for linear elasticity
- Youngs modulus (E, GPa) Poissons ratio (n)
- Yield strength elastic limit proportional

limit - Ductile and brittle materials.

Homework Problems

- 1.2-4
- 1.3-6
- 1.4-4
- 1.5-4.
- Homework due on Thursday, August 23, 2007.