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## TRB Civil Syllabus

**CIVIL ENGINEERING**

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

theorems.

**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

differential equations.

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**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

stresses.

**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

indeterminate structures.

**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

foundations.

**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 —

curves.

### TRB Mechanical Syllabus

**MECHANICAL ENGINEERING**

**UNIT 1: ENGINEERING MATHEMATICS**

Linear Algebra: Matrix algebra, Systems of 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 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

formulations; impact.

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

stresses.

**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;

flywheels.

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

energy conversion.

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

integration tools.

**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

control systems.

**UNIT 10: OPERATIONS RESEARCH**

Operations Research: Linear programming, simplex and duplex method,

transportation, assignment, network flow models, simple queuing models, PERT

and CPM.

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