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, 6th 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 crosssection 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?
Structural members subjected
to axial loads
FIG. 1-1
Copyright 2005 by Nelson, a division of Thomson Canada Limited
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:
FIG. 1-2
Prismatic bar in
tension:
(a) free-body
diagram of a
segment of the bar,
(b) segment of the
bar before loading,
(c) segment of the
bar after loading,
and (d) normal
stresses in the bar
Copyright 2005 by Nelson, a division of Thomson Canada Limited
Units of stress in USCS: pounds per square inch (psi) or kilopounds per square inch (ksi)
SI units: newtons per square meter (N/m2) 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
Steel eyebar subjected
to tensile loads P
FIG. 1-3
Copyright 2005 by Nelson, a division of Thomson Canada Limited
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)
FIG. 1-2
• If bar is in tension, strain is
tensile and if in compression the
strain is compressive
Prismatic bar in
tension:
(a) free-body
diagram of a
segment of the bar,
(b) segment of the
bar before loading,
(c) segment of the
bar after loading,
and (d) normal
stresses in the bar
Copyright 2005 by Nelson, a division of Thomson Canada Limited
• 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.
FIG. 1-4
Uniform stress distribution
in a prismatic bar:
(a) axial forces P, and
(b) cross section of the bar
Copyright 2005 by Nelson, a division of Thomson Canada Limited
*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 σt in the cables due to the weight of the concrete
slab. (See Table H-1, Appendix H, for the weight density of reinforced concrete.)