MECH 320 Solid Mechanics II
Lecture 14
Lecture 14
Stresses Due to Concentrated Loads:
St. Venants principle states: the actual forces acting on a body
can be replaced with an average system of forces, to determine the
internal stress distribution (field)
MECH 320 Solid Mechanics II
Lecture 8
Lecture 8
2D-Strain Transformation:
Consider the case of plane strain (2-D). Given the values of xx ,
yy and xy , we would like to find the state of strain of a line element
at any orientation on the xy plane.
Addit
MECH 320 Solid Mechanics II
Lectrue 2
Lecture 2
In the previous lecture, a solid body with externally applied loads
was considered. To analyze the internal forces, we considered a small
area A, and considered the force Fi that acts through it.
By splitt
MECH 320 Solid Mechanics II
Lecture 17
Lecture 17
4.7 Maximum Distortion Energy Theory (For Ductile Failure)
This theory is also called the von Mises Theory
THEORY DEFINTION:
The material will fail (yield) when the distortion energy per unit volume
at an
MECH 320 Solid Mechanics II
Lecture 6
Lecture 6
Special Cases of Normal and Shear Stress on a 3D Oblique Plane
There are some special cases, where we wish to determine the
normal and shear stress on an oblique plane, with respect to known
principal stres
MECH 320 Solid Mechanics II
Lecture 7
Lecture 7
Chapter 2: Strain and Stress Relations
Review:
When a set of loads are applied to a body, its shape will change,
and we can say that the body deforms.
Consider the following 2D body, under load:
When the b
MECH 320 Solid Mechanics II
Lecture 3
Lecture 3
Review of 2D-Stress Transformation Equations:
In the previous lecture, we considered the stress transformation
equations as it applies to uniaxial stress.
We now consider 2D stress transformation.
Consider
MECH 320 Solid Mechanics II
Lecture 21
Lecture 21
Pure Bending of Beams of Asymmetrical Cross-Section
Consider the general problem of bending of beams, which have a
non-symmetrical cross section.
Or, alternatively, the bending of beams about an arbitrar
MECH 320 Solid Mechanics II
Lecture 19
Lecture 19
4.16 Impact or Dynamic Loads
An impact is a load that results from the collision of two solid
bodies. For example a bowling ball dropped onto the floor, or a hammer
striking a plate.
A shock is a load th
MECH 320 Solid Mechanics II
Lecture 10
Lecture 10
St. Venants Principle
This principal is concerned with the distribution of internal stresses
and strains (internal stress field and strain field) that arise when loads are
applied to a body.
The principl
MECH 320 Solid Mechanics II
Lecture 1
Lecture 1
The study of Solid Mechanics explores the internal forces that
occur within solid bodies, when they are subjected to a set of externally
applied loads.
Solid mechanics analysis can be used to determine:
Li
MECH 320 Solid Mechanics II
Lecture 24
Lecture 24
Prandtls Membrane Analogy
The Prandtl Stress function , can be conceptualized by
considering the deformation of a thin membrane, subjected to pressure.
This analogy is possible, because the equation gove
MECH 320 Solid Mechanics II
Lecture 5
Lecture 5
3D Principal Stress
Given the stress transformation equations of Lecture 4, and given
an infinitesimal cube under an arbitrary state of stress, we would like to
find the maximum/minimum values for x' , y' a
MECH 320 Solid Mechanics II
Lectures 13
Lecture 13
Stress and Strain, in Polar Coordinates:
Cylindrical or semi-cylindrical bodies, or some stress
concentrations, are better modeled using polar coordinates, as opposed
to Cartesian coordinates.
This incl
MECH 320 Solid Mechanics II
Lecture 20
Lecture 20
Chapter 5: Beam Theory
There are a number of methods for beam analysis. In Mech220
you learned the familiar mechanics of materials approach.
In most cases, the mechanics of materials approach yields solu
MECH 320 Solid Mechanics II
Lecture 12
Lecture 12
Examples of 2D Elasticity Problems:
Example #1 (Prob. 3.10):
Consider a rectangular plate with sides a and b of thickness t, as
shown below:
We are given Airys stress function, which takes the form of:
x,
MECH 320 Solid Mechanics II
Lecture 15
Lecture 15
In the previous lecture, we observed that concentrated loads can
cause a localized area of high stress in a solid body.
Another phenomenon that can cause a localized area of high stress,
is an abrupt cha
MECH 320 — Solid Mechanics II Lecture 32
Lecture 32 ‘ '
Finite Element Method
Coordinate Transformations of Vectors in 2-D
> In order to assemble the ‘global system stiffness matrix’, we must
transform each of the ‘local element stiffness matrices’ into
c
MECH 320 - Solid Mechanics II Lecture 31
Lecture 31
Finite Element Method
FEM of Truss Structures
> Truss structures consist of ‘a set of 1-D bar elements’, arranged in
2-D space.
> Here, the bar elements (circled numbers) are oriented-at an angle 6,
wi
MECH 320 - Solid Mechanics 1] Lecture 33
Lecture 33
Finite Element Method
Solution of a Plane Truss {Using Bar Elements)
> A Plane Truss is a structure composed of ‘bar elements’ that all lie
in a common plane, and are connected together by frictionless .
MECH 320 Solid Mechanics II
Lecture 23
Lecture 23
Review of: Torsion of Circular Bars
Torsion of circular bars is based upon elementary theory, which
accurately models the behavior of these members.
The assumptions are:
(a) All sections initially planar
MECH 320 Solid Mechanics II
Lecture 16
Lecture 16
Chapter 4: Failure Criteria
We can define the Failure of a solid material, as the point at
which the material ceases to function in the manner intended.
For example, failure could be:
We will examine the
MECH 320 Solid Mechanics II
Lecture 18
Lecture 18
4.13 Introductory Fracture Mechanics
The study of fracture mechanics generally deals with the fracture
of brittle materials in a state of tension.
The primary assumption for this analysis is the existenc
MECH 320 Solid Mechanics II
Lecture 9
Lecture 9
Review of Past Concepts:
*
For Homework, please read textbook sections:
Section 2.6: Engineering Materials
Section 2.7: Stress-Strain Diagrams
Review of Hookes Law:
Quite simply, Hookes Law is the mathemati
MECH 320 Solid Mechanics II
Lecture 4
Lecture 4
3D-Stress Transformation Equations
The derivation of the 3D stress transformation equations is now
presented. These equations allow for the determination of the stress for
any direction with respect to the