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PCC-CE205 |
Introduction to Solid Mechanics |
3L:0T:0P |
3 credits |
The objective of this course is to introduce to continuum mechanics and material
modelling of engineering materials based on first energy principles:
deformation and strain; momentum balance, stress and stress states;
elasticity and elasticity bounds; plasticity and yield design.
The overarching theme is a unified mechanistic language using
thermodynamics, which allows understanding, modelling and design of a large
range of engineering materials. The subject of mechanics of materials involves
analytical methods for determining the strength, stiffness (deformation
characteristics), and stability of the various members in a structural system.
The behaviour of a member depends
not only on the fundamental laws that govern
the equilibrium of forces, but also on the mechanical characteristics of the material. These
mechanical characteristics
come from the laboratory, where materials are tested under accurately known
forces and their behaviour is carefully observed and measured. For this reason,
mechanics of materials is a blended science of experiment and Newtonian postulates of analytical mechanics.
Proposed Syllabus
Module1: Simple Stresses
and Strains- Concept of stress and strain, St. Venant’s principle, stress and strain diagram,
Elasticity and plasticity – Types of stresses and strains, Hooke’s
law – stress – strain diagram
for mild steel
– Working stress
– Factor of safety – Lateral strain,
Poisson’s ratio and volumetric strain – Elastic
moduli and the relationship between
them – Bars of varying
section – composite bars – Temperature stresses. Strain Energy
– Resilience – Gradual, sudden,
impact and shock loadings
– simple applications.
Module 2: Compound Stresses and Strains- Two dimensional system,
stress at a point on a plane, principal stresses and principal planes, Mohr circle
of stress, ellipse
of stress and their applications. Two dimensional stress-strain system,
principal strains and principal axis of strain,
circle of strain and ellipse of strain.
Relationship between elastic
constants.
Module 3: Bending moment and Shear Force Diagrams- Bending
moment (BM) and shear force (SF)
diagrams.BM and SF diagrams for cantilevers simply
supported and fixed beams with or without overhangs. Calculation of maximum
BM and SF and the point of contra flexure
under concentrated loads, uniformly
distributed loads over the whole span or part of span, combination of
concentrated
loads (two or three) and uniformly distributed loads, uniformly varying loads,
application of moments.
Module 4: Flexural Stresses-Theory of simple bending – Assumptions
– Derivation of bending equation: M/I = f/y = E/R - Neutral axis – Determination of bending stresses
– Section modulus
of rectangular and circular
sections (Solid and Hollow), I,T, Angle and Channel sections
– Design of simple beam sections.
Module 5: Shear Stresses- Derivation of formula – Shear stress
distribution across various
beam sections like rectangular, circular, triangular, I, T angle sections.
Module 6:Slope and deflection- Relationship between moment,
slope and deflection, Moment area method,
Macaulay’s method. Use of these methods to calculate slope and deflection for
determinant beams.
Module 7:Torsion- Derivation of torsion equation and its assumptions. Applications of the equation
of the hollow and solid circular shafts,
torsional rigidity, Combined
torsion and bending
of circular shafts, principal
stress and maximum shear stresses under combined loading of bending and
torsion. Analysis of close-coiled-helical springs.
Module 8: Thin
Cylinders and Spheres- Derivation of formulae and calculations of hoop stress, longitudinal stress
in a cylinder, and sphere subjected to internal pressures.
List of
Experiments:
Ø Tension test
Ø Bending tests
on simply supported beam and Cantilever beam.
Ø Compression test on concrete
Ø Impact test
Ø Shear test
Ø Investigation of Hook’s law that is the proportional relation between force and stretching in elastic deformation,
Ø Determination of torsion and deflection,
Ø Measurement of forces on supports in statically determinate beam,
Ø Determination of shear forces
in beams,
Ø Determination of bending moments
in beams,
Ø Measurement of deflections in statically determinate beam,
Ø Measurement of strain in a bar
Ø Bend test steel bar;
Ø Yield/tensile strength
of steel bar;
Text/Reference Books:
1. Timoshenko, S. and Young,
D. H., “Elements of Strength of Materials”, DVNC,
New York, USA.
2.
Kazmi, S. M. A., “Solid
Mechanics” TMH, Delhi,
India.
3. Hibbeler, R. C. Mechanics of Materials. 6th ed. East Rutherford, NJ: Pearson Prentice Hall, 2004
4. Crandall, S. H., N. C. Dahl,
and T. J. Lardner. An Introduction to the Mechanics of Solids. 2nd ed. New York, NY: McGraw Hill, 1979
5.
Laboratory Manual of Testing Materials - William Kendrick
Hall
6. Mechanics of Materials
- Ferdinand P. Beer, E. Russel Jhonston
Jr., John T. DEwolf – TMH
2002.
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