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Teachers Recruitment Board
TRB Civil Syllabus
UNIT 1: ENGINEERING MATHEMATICS
Linear Algebra — matrix algebra, linear equations, – eigen values and eigen vectors.
Calculus- Functions of single variable, limit, continuity and differentiability – mean value
theorems, evaluation of definite and improper integrals – partial derivatives, total
derivative – maxima and minima – gradient, divergence and curl – vector identities –
directional derivatives – line, surface and volume integrals – stokes, gauss and green’s
Differential equations — first order equations (linear, nonlinear) — higher order linear
differential equations with constant coefficients – Cauchy’s and Euler’s equations —
initial and boundary value problems — Laplase transformations and equations —
solutions to one dimensional heat and wave equations.
Complex variables — analytic functions — Cauchy’s integral theorem — Taylor and Laurent
series — Fourier series — general, odd and even functions.
Probability and Statistics – probability and sampling theorems- conditional probability —
mean — median, mode and standard deviation — random variables — Poisson, Normal
and Binomial distributions.
Numerical Methods — numerical solutions of linear and non-linear algebraic equations —
integration by trapezoidal and simpson’s rule, single and multistep methods for
UNIT 2: MECHANICS
Simple stress and strain relationships in one, two and three dimensions —
principal stresses, stress transformation — mohr’s circle — properties of surfaces —
friction — principle of conservation of energy — impulse and momentum — relative
motions – bending moment and shear force in statically determinate beams—
simple bending theory — flexural and shear stresses — unsymmetrical bending —
shear center — pressure vessels (thin and thick walled) — uniform torsion—
springs — buckling of columns —combined and direct bending stresses —theories of
failure — shear stress, strain energy and distortion energy theories — residual
UNIT 3: STRUCTURAL ANALYSIS
Analysis of statically determinate and indeterminate trusses — arches — cables and
frames — deflections of statically determinate structures (beams, frames and trusses) —
analysis of statically indeterminate structures (slope deflection, moment distribution
methods) — matrix methods of structural analysis — influence lines for determinate and
UNIT 4: CONCRETE STRUCTURES
Concrete technology — properties of concrete — mix design — working stress and limit
state design concepts — design of all structural components (slab, beam, column,
foundation and stair case) — retaining walls — water tanks — basic elements of
prestressed concrete — methods – analysis of beams at transfer and service loads —
seismic load analysis — theory of vibration — seismology — response of structures —
design methodology – all related IS codes.
UNIT 5: STEEL STRUCTURES
Connections – analysis and design of tension, compression members, beams and beam
columns — trusses – column bases — plate girders — plastic analysis — wind load
analysis-all related IS codes.
UNIT 6: SOIL MECHANICS
Soil classification — engineering properties — three phase system — relationship and
interrelationship — permeability — seepage — effective stress principle — consolidation —
compaction — shear strength — CBR — Safe bearing capacity determination.
UNIT 7: FOUNDATION ENGINEERING
Sub surface investigation — sampling — standard penetration test — plate load test — earth
pressure — effect of water table — layered soil — stability of slopes — foundation types and
design requirements— stress distribution and settlement analysis — shallow and deep
UNIT 8: FLUID MECHANICS AND MACHINES AND HYDROLOGY
Properties of fluid — principle of conservation of mass — momentum — energy and
corresponding equations — potential flow — Bernoulli’s equation it and application
— laminar and turbulent flow — flow in pipes — network — concept of boundary
layer — uniform and non uniform flow — specific energy concept — hydraulic jump
— forces on immersed bodies — flow measurements in open. channels and pipes
dimensional analysis and hydraulic modeling — impact -kinematics of flow — velocity
triangles — pumps and turbines.
Hydrologic cycle — rainfall — evaporation — infiltration — stage discharge relationships
— unit hydrographs — flood estimation — reservoir capacity — reservoir and channel
routing well hydraulics.
Duty — delta — estimation of evapo—transpiration — crop water requirements — design
of lined and unlined canals — waterways — head works — gravity dams and spill ways
— design of permeable foundation — types of irrigation system — irrigation methods —
water logging and drainage.
UNIT 9: WATER SUPPLY AND WASTE WATER DISPOSAL
Quality standards — basic unit processes and operations – water treatment — drinking
water standards — water requirements — surface water treatment — distribution —
sewage and its treatment — quantity and characteristics of waste water — primary,
secondary and tertiary treatment— effluent discharge standards — domestic waste water
treatment — quantity and characteristics — treatment unit operations and unit
processes — sludge disposal. — types of pollutants — their sources and impacts —
standards and limits.
UNIT 10: HIGHWAY ENGINEERING
IRC standards — geometric design of highways — materials — construction and
maintenance — testing and specifications of materials — design of flexible and rigid
pavements — traffic characteristics — theory of traffic flow — intersection design — traffic
signs and signal design — highway capacity — importance of surveying — principles and
classification — mapping — coordinate system — map projections — measurements of
distance and directions — leveling — theodolite traversing —errors and adjustments —
TRB Mechanical Syllabus
UNIT 1: ENGINEERING MATHEMATICS
Linear Algebra: Matrix algebra, Systems of linear equations, Eigen values and
Calculus: Functions of single variable, Limit, continuity and differentiability, Mean
value theorems, Evaluation of definite and improper integrals, Partial derivatives,
Total derivative, Maxima and minima, Gradient, Divergence and Curl, Vector
identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss
and Green’s theorems.
Differential equations: First order equations (linear and nonlinear), Higher order
linear differential equations with constant coefficients, Cauchy’s and Euler’s
equations, Initial and boundary value problems, Laplace transforms, Solutions of
one dimensional heat and wave equations and Laplace equation.
Probability and Statistics: Definitions of probability and sampling
theorems, Conditional probability, Mean, median, mode and standard deviation,
Random variables, Poisson, Normal and Binomial distributions.
Numerical Methods: Numerical solutions of linear and non-linear algebraic
equations Integration by trapezoidal and Simpson’s rule, single and multi-step
methods for differential equations.
UNIT 2: APPLIED MECHANICS AND STRENGTH OF MATERIALS
Engineering Mechanics: Free body diagrams and equilibrium; trusses and
frames; virtual work; kinematics and dynamics of particles and of rigid bodies in
plane motion, including impulse and momentum (linear and angular) and energy
Strength of Materials: Stress and strain, stress-strain relationship and
elastic constants, Mohr’s circle for plane stress and plane strain, thin cylinders; shear
force and bending moment diagrams; bending and shear stresses; deflection of beams;
torsion of circular shafts; Euler’s theory of columns; strain energy methods; thermal
UNIT 3: THEORY OF MACHINES AND DESIGN
Theory of Machines: Displacement, velocity and acceleration analysis of
plane mechanisms; dynamic analysis of slider-crank mechanism; gear trains;
Vibrations: Free and forced vibration of single degree of freedom systems; effect of
damping; vibration isolation; resonance, critical speeds of shafts.
Design of machine elements: Failure theories; principles of design of bolted,
riveted and welded joints, shafts, spur gears, rolling and sliding contact bearings,
brakes and clutches.
UNIT 4: FLUID MECHANICS AND HYDRAULIC MACHINERY
Fluid Mechanics: Fluid properties; fluid statics, manometry, buoyancy; kinematics
and dynamics of flow; Bernoulli’s equation; viscous flow of incompressible fluids;
boundary layer; elementary turbulent flow; flow through pipes, head losses.
Hydraulic machines, Pelton-wheel, Francis and Kaplan turbines, velocity diagrams.
UNIT 5: HEAT TRANSFER
Heat Transfer: Modes of heat transfer; one dimensional heat conduction,
resistance concept, electrical analogy, unsteady heat conduction, fins; dimensionless
parameters in free and forced convective heat transfer, various correlations for heat
transfer in flow over flat plates and through pipes; thermal boundary layer; effect of
turbulence; radiative heat transfer, black and grey surfaces, shape factors, network
analysis; heat exchanger performance, LMTD and NTU methods.
UNIT 6: THERMODYNAMICS
Thermodynamics: Zeroth, First and Second laws of thermodynamics;
thermodynamic system and processes; Carnot cycle. irreversibility and availability;
behaviour of ideal and real gases, properties of pure substances, calculation of
work and heat in ideal processes; analysis of thermodynamic cycles related to
Power Engineering: Steam Tables, Rankine, Brayton cycles with regeneration
and reheat. I.C. Engines: air-standard Otto, Diesel cycles. Refrigeration and airconditioning:
Vapour refrigeration cycle, heat pumps, gas refrigeration, Reverse
Brayton cycle; moist air: psychrometric chart, basic psychrometric processes.
UNIT 7: MANUFACTURING ENGINEERING
Engineering Materials: Structure and properties of engineering materials, heat
treatment, stress-strain diagrams for engineering materials.
Metal Casting: Design of patterns, moulds and cores; solidification and cooling;
riser and gating design, design considerations.
Forming: Plastic deformation and yield criteria; fundamentals of hot and cold
working processes; load estimation for bulk (forging, rolling, extrusion,
drawing) and sheet (shearing, deep drawing, bending) metal forming
processes; principles of powder metallurgy.
Joining: Physics of welding, brazing and soldering; adhesive bonding;
design considerations in welding.
UNIT 8: MACHINING AND MACHINE TOOL OPERATIONS
Machining and Machine Tool Operations: Mechanics of machining, single and
multi-point cutting tools, tool geometry and materials, tool life and wear;
economics of machining; principles of non-traditional machining processes;
principles of work holding, principles of design of jigs and fixtures
Metrology and Inspection: Limits, fits and tolerances; linear and angular
measurements; comparators; gauge design; interferometry; form and finish
measurement; alignment and testing methods; tolerance analysis in
manufacturing and assembly.
Computer Integrated Manufacturing: Basic concepts of CAD/CAM and their
UNIT 9: PRODUCTION PLANNING AND CONTROL
Production Planning and Control: Forecasting models, aggregate production
planning, scheduling, materials requirement planning.
Inventory Control: Deterministic and probabilistic models; safety stock inventory
UNIT 10: OPERATIONS RESEARCH
Operations Research: Linear programming, simplex and duplex method,
transportation, assignment, network flow models, simple queuing models, PERT
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