UNIVERSITY OF KERALA - College of Engineering, Trivandrum

03.705.1 Elective III THEORY OF ELASTICITY
L T P/D Cr
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Module I
Analysis of stress and strain in three dimensions –stress at a point, transformation, principal stress, surface force
and body forces, equations of equilibrium. Homogeneous deformation, strain at a point, principal axes of strain,
compatibility equations. Invarients of stress and strain. Equation of theory of elasticity, Generalised Hook’s lawreduction
in number of elastic constants for orthotropic, transversely isotropic and isotropic media. Stress strain
relations.
Module II
Equations of equilibrium in terms of displacements conditions of compatibility in terms of stresses. Method of
solution of the elasticity problems. Stress displacement and mixed methods. The principle of superposition. St.
Venant’s principle.
Two-dimensional problems in rectangular coordinates Generalized plane stress and plane strain, Basic
equations, stress functions, solutions by polynomials, Bending of a cantilever loaded at free end and bending of
a beam by uniform load. Solution in the form of Fourier series for a simply supported beam subjected to
continuous loads.
Module III
Two-dimensional problems in polar co ordinates, Basic equations in polar co ordinates, Axi-symmetric stress
distribution curved beams, thick cylinders, rotating disc. General solution bending of a curved bar by a force at
the end, effect of circular holes on stress distribution in plates. Concentrated force at a point of a straight
boundary, circular disc subjected to diametrical compression.
Torsion of prismatic members, circular cross section, non-circular rectangular and elliptic section, membrane
analogy.
References:
1 S. P. Timoshenko and J.N. Goodier,“Theory of elasticity”-, McGraw-Hill
2 I.N. Sokolnikoff, “ Mathematical theory of elasticity”,McGraw-Hill Inc.,US
3 Ernest E Sechler, “Elasticity in Engineering” - Wiley: Chapman & Hall, New York
Question Paper: Duration: 3 hours
The question paper consists of Part A and Part B.
Part A is for 40 marks. There will be 8 compulsory short answer questions covering entire syllabus.
Part B is for 60 marks. There will two questions from each module. The candidate has to answer one question
of 20 marks from each module.
Note: No charts, tables, codes are permitted in the Examination hall .If necessary relevant data shall be given
along with the question paper by the question paper setter.
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