Section 1: Engineering Mathematics
Systems of linear equations;
Eigen values and Eigen vectors.
Functions of single variable;
Limit, continuity and differentiability;
Mean value theorems,
local maxima and minima,
Taylor and Maclaurin series;
Evaluation of definite and indefinite integrals,
application of definite integral to obtain area and volume;
Divergence and Curl,
Line, Surface and Volume integrals,
Stokes, Gauss and Green’s theorems.
Ordinary Differential Equation (ODE):
First order (linear and non-linear) equations;
higher order linear equations with constant coefficients;
Laplace transform and its application in solving linear ODEs;
initial and boundary value problems.
Partial Differential Equation (PDE):
separation of variables;
solutions of one-dimensional diffusion equation;
first and second order one-dimensional wave equation and two-dimensional Laplace equation.
Probability and Statistics:
Definitions of probability and sampling theorems;
Discrete Random variables:
Poisson and Binomial distributions;
Continuous random variables:
normal and exponential distributions;
Descriptive statistics - Mean, median, mode and standard deviation;
Accuracy and precision,
Numerical solutions of linear and non-linear algebraic equations;
Least square approximation,
Newton’s and Lagrange’s polynomials,
Integration by trapezoidal and Simpson’s rule,
single and multi-step methods for first order differential equations.
Section 2: Structural Engineering
System of forces,
Internal forces in structures;
Friction and its applications;
Kinematics of point mass and rigid body;
Centre of mass;
Euler’s equations of motion;
Principles of virtual work.
Bending moment and shear force in statically determinate beams;
Simple stress and strain relationships;
Theories of failures;
Simple bending theory,
flexural and shear stresses,
shear centre; Uniform torsion,
buckling of column,
combined and direct bending stresses.
Statically determinate and indeterminate structures by force/ energy methods;
Method of superposition;
Analysis of trusses, arches, beams, cables and frames;
Slope deflection and moment distribution methods;
Stiffness and flexibility methods of structural analysis.
Construction Materials and Management:
Structural steel - composition, material properties and behaviour ;
Concrete - constituents, mix design, short-term and long-term properties;
Bricks and mortar; Timber; Bitumen.
Types of construction projects;
Tendering and construction contracts;
Rate analysis and standard specifications;
Project planning and network analysis - PERT and CPM.
Limit state and Ultimate load design concepts;
Design of beams, slabs, columns;
Bond and development length;
Analysis of beam sections at transfer and service loads.
Working stress and Limit state design concepts;
Design of tension and compression members,
beams and beam- columns, column bases;
Connections - simple and eccentric,
plate girders and trusses;
Plastic analysis of beams and frames.
Section 3: Geotechnical Engineering
Origin of soils,
soil structure and fabric;
Three-phase system and phase relationships,
Unified and Indian standard soil classification system;
Permeability - one dimensional flow,
Seepage through soils - two-dimensional flow,
uplift pressure, piping;
Principle of effective stress,
seepage force and quicksand condition;
Compaction in laboratory and field conditions;
time rate of consolidation;
Mohr’s circle, stress paths,
effective and total shear strength parameters,
characteristics of clays and sand.
Sub-surface investigations - scope,
drilling bore holes, sampling, plate load test,
standard penetration and cone penetration tests;
Earth pressure theories - Rankine and Coulomb;
Stability of slopes - finite and infinite slopes,
method of slices and Bishop’s method;
Stress distribution in soils - Boussinesq’s and Westergaard’s theories,
Shallow foundations - Terzaghi’s and Meyerhoff’s bearing capacity theories,
effect of water table;
Combined footing and raft foundation;
Settlement analysis in sands and clays;
Deep foundations - types of piles,
dynamic and static formulae,
load capacity of piles in sands and clays,
pile load test,
negative skin friction.
Section 4: Water Resources Engineering
Properties of fluids,
Continuity, momentum, energy and corresponding equations;
applications of momentum and energy equations;
Laminar and turbulent flow;
Flow in pipes, pipe networks;
Concept of boundary layer and its growth.
Forces on immersed bodies;
Flow measurement in channels and pipes;