Mechanics of Materials
–
MAE 243 (Section 002)
Spring 2008
Dr. Konstantinos A. Sierros
General info
•
M, W, F
8:00

8:50 A.M. at Room G

83 ESB
•
Office: Room G

19 ESB
•
E

mail: kostas.sierros@mail.wvu.edu
•
Tel: 304

293

3111 ext.2310
•
Course notes: http://www.mae.wvu.edu/~cairns/teaching.html
USER NAME: cairns PASSWORD: materials
•
Facebook : Konstantinos Sierros (using courses: Mechanics of
Materials)
•
Office hours:
M, W
9:00

10:30 A.M. or by appointment
Course textbook
Mechanics of Materials, 6
th
edition,
James M. Gere, Thomson,
Brooks/Cole, 2006
1.1: Introduction to Mechanics of Materials
Definition
:
Mechanics of materials
is a branch of applied
mechanics that deals with the behaviour of solid bodies
subjected to various types of loading
Compression
Tension (stretched)
Bending
Torsion (twisted)
Shearing
1.1: Introduction to Mechanics of Materials
Fundamental concepts
•
stress and strain
•
deformation and
displacement
•
elasticity and
inelasticity
•
load

carrying
capacity
Design and analysis of mechanical
and structural systems
1.2: Normal stress and strain
•
Most fundamental concepts in
Mechanics of Materials are
stress
and
strain
•
Prismatic bar:
Straight structural
member with the
same
cross

section throughout its length
•
Axial force:
Load directed along
the axis of the member
•
Axial force can be
tensile
or
compressive
•
Type of loading for landing gear
strut and for tow bar?
Examples
A truss bridge is a type of beam
bridge with a skeletal structure. The
forces of
tension
, or pulling, are
represented by red lines and the
forces of
compression
, or squeezing,
are represented by green lines.
The Howe Truss was originally
designed to combine diagonal
timber compression members and
vertical iron rod tension members
Normal stress
•
Continuously distributed
stresses
acting over the entire cross

section.
Axial force P is the resultant of those
stresses
•
Stress
(σ) has units of force per
unit area
•
If
stresses
acting on cross

section
are uniformly distributed then:
Units of stress in USCS: pounds per square inch (psi) or
kilopounds per square inch (ksi)
SI units: newtons per square meter (N/m
2
) which is equal to Pa
Limitations
The loads P are transmitted to the bar by pins that pass through
the holes
High localized stresses are produced
around the holes !!
Stress concentrations
Normal strain
A prismatic bar will change in length when under a uniaxial tensile
force…and obviously it will become longer…
•
Definition of elongation per unit
length or
strain (ε)
•
If bar is in tension, strain is
tensile and if in compression the
strain is compressive
•
Strain is a dimensionless
quantity (i.e. no units!!)
Line of action of the axial forces for a uniform stress
distribution
It can be demonstrated that in
order to have uniform tension
or compression in a prismatic
bar, the axial force must act
through the centroid of the
cross

sectional area.
*In geometry, the
centroid
or
barycenter
of an object
X
in
n

dimensional
space is the intersection of all hyperplanes that divide
X
into two parts of
equal moment about the hyperplane. Informally, it is the "average" of all
points of
X
.
*The geometric centroid of a physical object coincides with its center of mass if the object has
uniform density, or if the object's shape and density have a symmetry which fully determines the
centroid. These conditions are sufficient but not necessary.
Problem 1.2

4
A circular aluminum tube of length
L
=
400 mm is loaded in compression by
forces
P
(see figure). The outside and inside diameters are 60 mm and 50 mm,
respectively. A strain gage is placed on the outside of the bar to measure
normal strains in the longitudinal direction.
(a) If the measured strain is
550
x
10

6
, what is the shortening
of the bar?
(b) If the compressive stress in the bar is intended to be 40 MPa, what should
be the load
P
?
Problem 1.2

7
Two steel wires,
AB
and
BC
, support a lamp weighing 18 lb (see figure). Wire
AB
is at an angle α = 34
°
to the horizontal and wire
BC
is at an angle β = 48
°
.
Both wires have diameter 30 mils. (Wire diameters are often expressed in mils;
one mil equals 0.001 in.) Determine the tensile stresses
AB
and
BC
in the two
wires.
Problem 1.2

11
A reinforced concrete slab 8.0 ft square and 9.0 in. thick is lifted by four cables
attached to the corners, as shown in the figure. The cables are attached to a
hook at a point 5.0 ft above the top of the slab. Each cable has an effective
cross

sectional area
A
0.12 in2.
Determine the tensile stress σ
t
in the cables due to the weight of the concrete
slab. (See Table H

1, Appendix H, for the weight density of reinforced concrete.)
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