Course Description
In this elementary study on the strength
of materials the response of some simple structural components is
analyzed in a consistent manner using i) equilibrium equations, ii)
material law equations, and iii) the geometry of deformation. The
components analyzed include rods subjected to axial loading, shafts
loaded in torsion, slender beams in bending, thin-walled pressure
vessels, slender columns susceptible to buckling, as well as some more
complex structures and loads where stress transformations are used to
determine principal stresses and the maximum shear stress. The free body
diagram is indispensable in each of these applications for relating the
applied loads to the internal forces and moments and plotting internal
force diagrams. Material behavior is restricted to be that of materials
in the linear elastic range. A description of the geometry of
deformation is necessary to determine internal forces and moments in
statically indeterminate problems
Mechanics of materials, also
called strength of materials, is a subject which deals with the behavior
of solid objects subject to stresses and strains. The complete theory
began with the consideration of the behavior of one and two dimensional
members of structures, whose states of stress can be approximated as two
dimensional, and was then generalized to three dimensions to develop a
more complete theory of the elastic and plastic behavior of materials
The
study of strength of materials often refers to various methods of
calculating the stresses and strains in structural members, such as
beams, columns, and shafts. The methods employed to predict the response
of a structure under loading and its susceptibility to various failure
modes takes into account the properties of the materials such as its
yield strength, ultimate strength, Young's modulus, and Poisson's ratio;
in addition the mechanical element's macroscopic properties (geometric
properties), such as it length, width, thickness, boundary constraints
and abrupt changes in geometry such as holes are considered
So in
materials science, the strength of a material is its ability to
withstand an applied load without failure. The field of strength of
materials deals with forces and deformations that result from their
acting on a material. A load applied to a mechanical member will induce
internal forces within the member called stresses when those forces are
expressed on a unit basis. The stresses acting on the material cause
deformation of the material in various manner. Deformation of the
material is called strain when those deformations too are placed on a
unit basis. The applied loads may be axial (tensile or compressive), or
shear. The stresses and strains that develop within a mechanical member
must be calculated in order to assess the load capacity of that member.
This requires a complete description of the geometry of the member, its
constraints, the loads applied to the member and the properties of the
material of which the member is composed. With a complete description of
the loading and the geometry of the member, the state of stress and of
state of strain at any point within the member can be calculated. Once
the state of stress and strain within the member is known, the strength
(load carrying capacity) of that member, its deformations (stiffness
qualities), and its stability (ability to maintain its original
configuration) can be calculated. The calculated stresses may then be
compared to some measure of the strength of the member such as its
material yield or ultimate strength. The calculated deflection of the
member may be compared to deflection criteria that is based on the
member's use. The calculated buckling load of the member may be compared
to the applied load. The calculated stiffness and mass distribution of
the member may be used to calculate the member's dynamic response and
then compared to the acoustic environment in which it will be used
We
are going to focus on stress and strain concepts, axial load,
statically indeterminate axially loaded members, thermal stress,
torsion, angle of twist, statically indeterminate torque-loaded members,
bending, eccentric axial loading of beams, transverse shear, shear flow
in build-up members, combined loadings, stress and strain
transformation, deflection of beams and shafts, statically indeterminate
beams and shafts
Curriculum
Concept of Stress
Determining decrease in diameter
Determining Volumetric strength
Direct or Normal Stress
Elastic Constants- important Formulae
Finding value of k
Hooke's Law
Important Formulas
Introduction to mechanical properties
Introduction to Strength of Material
Malleability and Impact Strength
Mechanics of Material
Numerical- Bulk Modulus
Numerical- Diameter of Steel Rod
Numerical- Finding Deformation of the Rod
Numerical for Practice
Numerical- Poisson's ratio
Numerical- Poisson's ratio & Modules of elasticity
Problem Solving
Revision of Concepts
Revision on numericals
Section 1: Introduction to Strength of Materials
Section 2: Important Concepts in Strength of Materials
Section 3: Mechanical Properties
Section 4: Numericals
Stress Types
Understanding Creep property
Understanding Ductility
Understanding Hardness property
Understanding Plasticity
What is an Elastic Material??
What is Strength of Material?
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