5.1, 5.2
Mechanics of Materials I
Torsion
TOPICS
Effect of torsional loading (torsional moment or torque)
Long straight circular shaft or tube
Stress distribution, strain distribution, angle of twist
Linear elastic regime
Statically determinate and indete
5.3, 5.4
Mechanics of Materials I
Power transmission
Shafts and tubes of circular cross section are often used to
transmit power developed by a machine
Circular cross-sections are easy to manufacture and
straightforward to support through bearings
Rela
4.4, 4.3, 4.5, 4.6
Mechanics of Materials I
Recall: Statically indeterminate systems
The first equation comes from equilibrium:
The second equation (comes from compatibility constraint):
Two equations now enable us to
determine the two unknowns
Applicatio
3.1 3.7
Mechanics of Materials I
The tension test
The tension test (ductile material)
Ductile and brittle behavior
Ductile materials: Type 1
Upper and lower yield points
Ductile materials: Type 2
Aluminum alloy
Yield stress by the offset
method
True stres
4.1, 4.2, 4.4
Mechanics of Materials I
Saint-Venants Principle
Recall
Validity?
Statically Equivalent Loading
For
practical
purposes, the region
of
uniform
deformation
and
stress can be taken
to start at the largest
dimension of the
loaded cross-sectio
5.5
Mechanics of Materials I
Statically Indeterminacy
Recall similarity of form and concept with the axial loading
indeterminate problems
Application
Application
Meaning of negative sign
Application
Do the same problem using:
Assuming opposite direction
2.1, 2.2
Mechanics of Materials I
Deformation
The load changes the length and/or orientation (angle) of line
segments in the rubber member shown
These changes are referred to as deformation
In rubber it is visible but deformation (small or large) is th
1.5 1.7
Mechanics of Materials I
Average shear stress
Approximately!
Simple or direct shear
Direction is the same as
Distribution not accurate
Average shear stress
Much higher stresses actually develop on the cross section
Still, acceptable for many
1.3, 1.4
Mechanics of Materials I
Looking back: by scalar equations
Resultant internal loading at
Pipe mass 2 kg/m
Looking back
Relationship between external loads and internal effects
External loads include applied and reactive forces and
moments
Int
Stress
Stress
Its important to determine actual distribution of loading acting over
the sectioned area
Sectioned area to be subdivided into
small areas, such as
Material Assumptions
Material to be continuous, that is, to
consist of a continuum or uniform
Shear Stress
Average Shear Stress
Shear stress is the stress component that acts in
the plane of the sectioned area
Consider the effect of applying a force F to the
bar
The supports are considered rigid
F is large enough, it will cause the material of
the
Stress Problems
Problem Set
Lecture 1
Problem 1-1 to 1-20
Lecture 2, 3
Problem 1-50 to 1-68
Lecture 4, 5
Problem 1-100 to 1-108
Problem
Problem
Problem
Problem
Problem
Problem
Problem
Problem
Problem
Problem
Strain
Deformation
When a force is applied to a body, it will tend to change the bodys
shape and size
These changes are referred to as deformation
May be either highly visible or practically unnoticeable
Deformation of a body can also occur when the tempe
Mechanical Properties
of Materials
Experimental Stress-Strain Diagram
Which one to use
in engineering
design?
Engineering
stress-strain
True stress-strain
Hookes Law
Stressstrain diagrams exhibit a linear relationship between stress and
strain within the
Axial Loads
Saint-Venants Principle
Consider a rectangular bar deforming elastically when subjected to
a force P applied along its centroidal axis
Bar is fixed connected at one end
Force is applied through a hole at its
other end
Deformation is shown usin
Mechanical Properties
of Materials
The Tension or Compression Test
Strength of a material depends on its ability to sustain a load without
undue deformation or failure
Strength is material property and must be determined by experiment
One of the most impo
Allowable Stress
Allowable Stress
To design a structural member, the stress in the material
should be restricted to a safe level
Choose an allowable stress that restricts the applied load to
less than the load the member can fully support
Allowable Stress
Mechanics of Materials - I
ME 211
Introduction
Dr Aamir Mubashar
PhD, Mechanical Engineering, Loughborough University,
Loughborough, UK
MSc, Advanced Manufacturing Technology and Systems
Management, The University of Manchester, Manchester, UK
Reference T
Moments and Couples
Equilibrium of a
Particle
Dr Muhammad Ali Khan
1/10
Engineering Mechanics (ME-121) Lecture 1/10
Mechanical Engineering Department
Moments and Couples Equilibrium of a Particle
Will study in
dynamics part
Dr Muhammad Ali Khan
Engineeri
Fundamental Concepts and Principles of Mechanics
Fundamental Concepts
Of Scalars and Vectors
Dr Muhammad Ali Khan
1/6
Engineering Mechanics (ME-121) Lecture 1/6
Mechanical Engineering Department
Fundamental Concepts and Principles of Mechanics
Scalars a
Moments and Couples
Equilibrium of a
Particle
Dr Muhammad Ali Khan
1/10
Engineering Mechanics (ME-121) Lecture 1/10
Mechanical Engineering Department
Moments and Couples Equilibrium of a Particle
Will study in
dynamics part
Dr Muhammad Ali Khan
Engineeri
Structural Analysis
Simple trusses
Dr Muhammad Ali Khan
1/3
Engineering Mechanics (ME-121) Lecture 1/3
Mechanical Engineering Department
Structural Analysis
Dr Muhammad Ali Khan
Engineering Mechanics (ME-121) Lecture 1/3
Mechanical Engineering Department
Kinematics of a particle
Introduction
Dr Muhammad Ali Khan
1/7
Engineering Mechanics (ME-121) Lecture 1/7
Mechanical Engineering Department
Kinematics of a particle
Dr Muhammad Ali Khan
Engineering Mechanics (ME-121) Lecture 1/7
Mechanical Engineering De
Equilibrium of a rigid body
Conditions and
Equations of the
Equilibrium
Dr Muhammad Ali Khan
1/5
Engineering Mechanics (ME-121) Lecture 1/5
Mechanical Engineering Department
Equilibrium of a rigid body Conditions and Equations
Dr Muhammad Ali Khan
Engine
Introduction to Engineering Mechanics Course
Class Introduction
0
Course Details
Dr Muhammad Ali Khan
Engineering Mechanics (ME-121) Lecture - 0
Mechanical Engineering Department
Introduction to Engineering Mechanics Course
Class Introduction
- Names an
Richard Kass
Winter 2004
A Physics 416 Fortran Tutorial
(based on the information at: http:/macams1.bo.infn.it/tutorial/)
1. What is Fortran?
2. Fortran basics
3. Variables, declarations, and types
4. Expressions and assignment
5. Logical expressions
6. T