In this course, the following topics will be covered which are applicable to various University Exams, MPSC, ESE &amp; GATE.
sppu aktu batu&nbsp;
Unit I: Simple Stresses and Strains
a) Materials used in construction and their nature, Hook&rsquo;s Law, Stress-Strain Diagram for elastic, plastic materials and brittle material, Idealized stress-strain diagram , Concept of axial stresses (compression, tension), strains(linear, lateral, shear and volumetric), Elastic constants and their relations. Stresses and strains due to change in temperature.
b) Stresses, strains and deformations in determinate and indeterminate structures for homogeneous and composite structures under concentrated loads and temperature changes.
Unit II: Shear Force and Bending Moment Diagram&nbsp;
Concept of shear force and bending moment. Relation between shear force, bending moment and intensity of loading. Shear force and bending moment diagrams for determinate beams due to concentrated, uniformly distributed, uniformly varying loads and couples. Bending moment and loading diagram from given shear force diagram.
Unit III: Shear and Bending Stresses:
a) Shear stresses in beams: the concept of shear, complimentary shear, derivation of shear stress formula, shear stress distribution for various cross sections, maximum and average shear stress for circular and rectangular sections.
b) Bending stresses in beams: theory of simple or pure bending, assumptions, derivation of flexure formula, bending stress distribution diagrams, Moment of Resistance of cross-section.
Unit IV: Torsion of Circular Shaftsand Principal Stresses and Strains:
a) Torsion of circular shafts: theory of torsion, assumptions, derivation of torsion formula. Stresses, strains, and deformations in determinate and indeterminate shafts of hollow, solid, homogeneous cross-sections subjected to twisting moments. Power is transmitted by shafts.
b) Principal stresses and strains: the concept of principal planes and principal stresses, normal and shear stresses on an oblique plane, magnitude, and orientation of principal stresses and maximum shear stress.
Unit V: Axially and Eccentrically Loaded Columns.&nbsp;
a) Axially loaded columns: the concept of critical load and buckling, Euler&rsquo;s formula for buckling load with hinged ends, the concept of equivalent length for various end conditions, Rankine&rsquo;s formula, safe load on the column, and limitations of Euler&rsquo;s formula.
b) Direct and bending stresses for eccentrically loaded short columns and other structural components such as retaining walls, dams, chimneys, etc. Effect of lateral force and self-weight. Resultant stress diagrams due to axial loads, uni-axial, and bi-axial bending. Concept of the core of section for solid and hollow rectangular and circular sections.
Unit VI: Slope and Deflection of Beams and Trusses
a) Slope and deflection of determinate beams by Macaulay&rsquo;s method and Strain energy method, Castigliano&rsquo;s first theorem. Joint displacement of determinate trusses by Unit load method

In this course following point will be discussed&nbsp;
<h2>Unit I: Differential Calculus: (08 Hrs.) Rolle&rsquo;s Theorem, Mean Value Theorems, Taylor&#39;s Series and Maclaurin&#39;s Series, Expansion of functions using standard expansions, Indeterminate Forms, L&#39; Hospital&#39;s Rule, Evaluation of Limits and Applications. </h2>
<h2>Unit II: Fourier Series (08 Hrs.) Definition, Dirichlet&rsquo;s conditions, Full range Fourier series, Half range Fourier series, Harmonic analysis, Parseval&rsquo;s identity and Applications to problems in Engineering. </h2>
<h2>Unit III: Partial Differentiation (08Hrs.) Introduction to functions of several variables, Partial Derivatives, Euler&#39;s Theorem on Homogeneous functions, Partial derivative of Composite Function, Total Derivative, Change of Independent variables </h2>
<h2>Unit IV: Applications of Partial Differentiation (08 Hrs.) Jacobian and its applications, Errors and Approximations, Maxima and Minima of functions of two variables, Lagrange&#39;s method of undetermined multipliers. </h2>
<h2>Unit V: Linear Algebra-Matrices, System of Linear Equations (08 Hrs.) Rank of a Matrix, System of Linear Equations, Linear Dependence and Independence, Linear and Orthogonal Transformations, Application to problems in Engineering.</h2>
<h2>Unit VI: Linear Algebra-Eigen Values and Eigen Vectors, Diagonaliztion (08 Hrs.) Eigen Values and Eigen Vectors, Cayley Hamilton theorem, Diagonaliztion of a matrix, Reduction of Quadratic forms to Canonical form by Linear and Orthogonal transformations</h2>
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Unit I: First Order Ordinary differential Equations &nbsp;Exact differential equations, Equations reducible to exact form. Linear differential equations, Equations reducible to linear form, Bernoulli&rsquo;s equation.
Unit II: Applications of Differential Equations &nbsp;Applications of Differential Equations to Orthogonal Trajectories, Newton&rsquo;s Law of Cooling, Kirchhoff&rsquo;s Law of Electrical Circuits, Rectilinear Motion, Simple Harmonic Motion, One dimensional Conduction of Heat.
Unit III: Integral Calculus Reduction Formulae, Beta and Gamma functions, Differentiation Under Integral Sign and Error functions.
Unit IV: Curve Tracing Tracing of Curves &ndash; Cartesian, Polar and Parametric curves, Rectification of curves.
Unit V: Solid Geometry &nbsp;Cartesian, Spherical polar and Cylindrical coordinate systems, Sphere, Cone and Cylinder.
Unit VI: Multiple Integrals and their Applications (09 Hrs.) Double and Triple integrations, Change of order of integration, Applications to find Area, Volume, Mass, Centre of Gravity and Moment of Inertia

Unit I Resolution and Composition of Forces Principle of statics, Force system, Resolution and composition of forces, Resultant of concurrent forces. Moment of a force, Varignon&rsquo;s theorem, resultant of parallel force system, Couple, Equivalent force couple system, Resultant of parallel general force system
Unit II Distributed Forces and Friction &nbsp;Moment of area, Centroid of plane lamina and wire bends, Moment of Inertia. Friction- Laws of friction, application of friction on inclined planes Wedges and ladders friction Application to flat belt
Unit III Equilibrium &nbsp;Free body diagram Equilibrium of concurrent, parallel forces in a plane Equilibrium of general forces in a plane Equilibrium of three forces in a plane, Types of beams, simple and compound beams, Type of supports and reaction, Forces in space, Resultant of concurrent and parallel forces in a space, Equilibrium of concurrent and parallel forces in a space.
Unit IV Analysis of Structures &nbsp;Two force member, Analysis of plane trusses by Method of joints Analysis of plane trusses by method of section, Analysis of plane frames, Cables subjected to point load multi force member.
Unit V Kinematics of Particle &nbsp;Kinematics of linear motion- Basic concepts Equation of motion for constant acceleration Motion under gravity, Variable acceleration motion curves. Kinematics of curvilinear motion- Basic Concepts Equation of motion in Cartesian coordinates Equation of motion in path coordinates Equation of motion in polar coordinates Motion of projectile.
Unit VI Kinetics of Particle &nbsp;Kinetics- Newton&rsquo;s Second Law of motion Application of Newton&rsquo;s Second Law. Work, power, energy, conservative and non-conservative forces Conservation of energy for motion of particle, Impulse, Momentum, Direct central impact. Coefficient of restitution, Impulse Momentum principle of particle.

GATE CIVIL/MECHANICAL

Validity : 1 Year

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₹8000
30000
74% off

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GATE CIVIL/MECHANICAL

Validity : 1 Year

Description

₹8000 3000074% off

Quick Links

Download App

₹8000
30000
74% off