Centroid
Centroid or center of gravity is the point within an object from which the force
of gravity appears to act.
Centroid of 3D objects often (but not always) lies somewhere along the lines
of symmetry.
Centroidal axis
or Neutral axis
Centroid of Area

Torsion
Torsion is the twisting of a straight bar when it is loaded
by twisting moments or torques that tend to produce
rotation about the longitudinal axes of the bar.
For instance, when we turn a screw driver to produce
torsion our hand applies torque T

Shear Forces and Bending Moments
Planar (2-D) Structures:
All loads act in the same plane and all deflections
occurs in the same plane (x-y plane)
Associated with the shear forces and bending
moments are normal stresses and shear stresses.
Types of Beams,

3D Stress Components
The most general state of stress at a point may
be represented by 6 components
Normal Stresses
x
y
z
Shear Stresses
From equilibrium principles:
xy = yx , xz = zx , zy = yz
xy
yz
xz
Normal stress () : the subscript identifies the f

Constitutive Equations (Linear Elasticity)
Equations that characterize the physical properties of the
material of a system are called constitutive equations. It is
possible to find the applied stresses knowing the strains and
viceversa.
x =
Poissons rati

MECHANICS OF MATERIALS II
(INGE 4012)
Pablo G. Caceres (B.Sc., Ph.D. U.K.)
GENERAL INFORMATION
Course Number
INGE 4012 (GEEG 4012)
Course Title
Mechanics of Materials II
Credit Hours
3
Instructor
Dr. Pablo G. Caceres
Office
Terrat T-205 Phone Ext. 3498
Of

COURSE POLICIES AND GENERAL INFORMATION
Course Number
Course Title
Credit Hours
Instructor
Office
Office Hours
e-mail
Web-site
INGE 4012 (GEEG 4012)
Mechanics of Materials II
3
Dr. Pablo G. Caceres
Terrat T-205. Phone Ext: 3498
Tu-Th from 9:15am to 12:15p

* 11.4. ECCENTRIC LOADING; THE SEGANT FORMULA
In this section we shall approach the problem of column buckling in a
different way, by observing that the load P applied to a column is never
perfectly centric. Denoting by e the ecentricity of the load, i.e.

LECTURE
Third Edition
ADVANCED TOPICS IN
MECHANICS-I
A. J. Clark School of Engineering Department of Civil and Environmental Engineering
28
by
Dr. Ibrahim A. Assakkaf
SPRING 2003
ENES 220 Mechanics of Materials
Department of Civil and Environmental Engin

Mechanical Eng. Dept.
Machine Design I (Lecture 6&7)
Third Class-All Branches
1. Maximum normal stresses: Principle stresses, [Ref.1]:
The combination of the applied normal and shear stresses that produce the
maximum normal stresses is called the max. & m