# GATE Civil Engineering Syllabus

## Subject Code: CE

### Course Structure

Sections/Units | Topics |
---|---|

Section A |
Engineering Mathematics |

Unit 1 | Linear Algebra |

Unit 2 | Calculus |

Unit 3 | Ordinary Differential Equation (ODE) |

Unit 4 | Partial Differential Equation (PDE) |

Unit 5 | Probability and Statistics |

Unit 6 | Numerical Methods |

Section B |
Structural Engineering |

Unit 1 | Engineering Mechanics |

Unit 2 | Solid Mechanics |

Unit 3 | Structural Analysis |

Unit 4 | Construction Materials and Management |

Unit 5 | Concrete Structures |

Unit 6 | Steel Structures |

Section C |
Geotechnical Engineering |

Unit 1 | Soil Mechanics |

Unit 2 | Foundation Engineering |

Section D |
Water Resources Engineering |

Unit 1 | Fluid Mechanics |

Unit 2 | Hydraulics |

Unit 3 | Hydrology |

Unit 4 | Irrigation |

Section E |
Environmental Engineering |

Unit 1 | Water and Waste Water |

Unit 2 | Air Pollution |

Unit 3 | Municipal Solid Wastes |

Unit 4 | Noise Pollution |

Section F |
Transportation Engineering |

Unit 1 | Transportation Infrastructure |

Unit 2 | Highway Pavements |

Unit 3 | Traffic Engineering |

Section G |
Geomatics Engineering |

### Course Syllabus

**Section A: Engineering Mathematics**

**Unit 1: Linear Algebra**

- Matrix algebra
- Systems of linear equations
- Eigen values and Eigen vectors

**Unit 2: Calculus**

- 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
- Partial derivatives
- Total derivative
- Gradient
- Divergence and Curl
- Vector identities
- Directional derivatives
- Line
- Surface and Volume integrals
- Stokes
- Gauss and Green’s theorems

**Unit 3: Ordinary Differential Equation (ODE)**

- First order (linear and non-linear) equations
- higher order linear equations with constant coefficients
- Euler-Cauchy equations
- Laplace transform and its application in solving linear ODEs
- Initial and boundary value problems

**Unit 4: Partial Differential Equation (PDE)**

Fourier series

separation of variables

solutions of one dimensional diffusion equation

First and second order one-dimensional wave equation and two-dimensional Laplace equation.

**Unit 5: Probability and Statistics**

- Definitions of probability and sampling theorems
- Conditional probability
- Discrete Random variables
- Poisson and Binomial distributions
- Continuous random variables
- Normal and exponential distributions
- Descriptive statistics - Mean, median, mode and standard deviation
- Hypothesis testing

**Unit 6: Numerical Methods**

- Accuracy and precision; error analysis
- Numerical solutions of linear and non-linear algebraic equations
- Least square approximation
- Newton’s and Lagrange polynomials
- numerical differentiation
- Integration by trapezoidal and Simpson’s rule
- Single and multi-step methods for first order differential equations

**Section B: Structural Engineering**

**Unit 1: Engineering Mechanics**

- System of forces, free-body diagrams, equilibrium equations
- Internal forces in structures
- Friction and its applications
- Kinematics of point mass and rigid body
- Centre of mass
- Euler’s equations of motion
- Impulse-momentum
- Energy methods
- Principles of virtual work

**Unit 2: Solid Mechanics**

- 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

**Unit 3: Structural Analysis**

Statically determinate and indeterminate structures by force/ energy methods

Method of superposition

Analysis of trusses, arches, beams, cables and frames

Displacement methods −

Slope deflection and moment distribution methods

Influence lines

Stiffness and flexibility methods of structural analysis

**Unit 4: Construction Materials and Management**

Construction Materials −

Structural steel – composition

Material properties and behavior

Concrete - constituents −

Mix design

Short-term and long-term properties

Bricks and mortar

Timber

Bitumen

Construction Management −

Types of construction projects

Tendering and construction contracts

Rate analysis and standard specifications

Cost estimation

Project planning and network analysis - PERT and CPM

**Unit 5: Concrete Structures**

- Working stress, Limit state and Ultimate load design concepts
- Design of beams, slabs, columns
- Bond and development length
- Prestressed concrete
- Analysis of beam sections at transfer and service loads

**Unit 6: Steel Structures**

Working stress and Limit state design concepts

Design of tension and compression members, beams and beam- columns, column bases

Connections – simple and eccentric, beam-column connections, plate girders and trusses

Plastic analysis of beams and frames

**Section C: Geotechnical Engineering**

**Unit 1: Soil Mechanics**

Origin of soils, soil structure and fabric

Three-phase system and phase relationships, index properties

Unified and Indian standard soil classification system

Permeability - one dimensional flow, Darcy’s law

Seepage through soils - two-dimensional flow, flow nets, uplift pressure, piping

Principle of effective stress, capillarity, seepage force and quicksand condition

Compaction in laboratory and field conditions

One dimensional consolidation, time rate of consolidation

Mohr’s circle, stress paths, effective and total shear strength parameters, characteristics of clays and sand

**Unit 2: Foundation Engineering**

- Sub-surface investigations −
- Scope
- Drilling bore holes
- Sampling
- Plate load test
- Standard penetration
- Cone penetration tests

- Earth pressure theories - Rankine and Coulomb
- Stability of slopes −
- Finite and infinite slopes
- Method of slices
- Bishop’s method

- Stress distribution in soils −
- Boussinesq’s and Westergaard’s theories
- Pressure bulbs

- Shallow foundations −
- Terzaghi’s and Meyerhoff’s bearing capacity theories
- Effect of water table

- Combined footing and raft foundation
- Contact pressure
- 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 D: Water Resources Engineering**

**Unit 1: Fluid Mechanics**

- Properties of fluids, fluid statics
- Continuity, momentum, energy and corresponding equations
- Potential flow, applications of momentum and energy equations
- Laminar and turbulent flow
- Flow in pipes, pipe networks
- Concept of boundary layer and its growth

**Unit 2: Hydraulics**

- Forces on immersed bodies
- Flow measurement in channels and pipes
- Dimensional analysis and hydraulic similitude
- Kinematics of flow, velocity triangles
- Basics of hydraulic machines, specific speed of pumps and turbines
- Channel Hydraulics −
- Energy-depth relationships
- Specific energy
- Critical flow
- Slope profile
- Hydraulic jump
- Uniform flow and gradually varied flow

**Unit 3: Hydrology**

- Hydrologic cycle
- Precipitation
- Evaporation
- Evapo-transpiration
- Watershed
- Infiltration
- Unit hydrographs
- Hydrograph analysis
- Flood estimation and routing
- Reservoir capacity
- Reservoir and channel routing
- Surface run-off models
- Ground water hydrology - steady state well hydraulics and aquifers
- Application of darcy’s law

**Unit 4: Irrigation**

- Duty, delta, estimation of evapo-transpiration
- Crop water requirements
- Design of lined and unlined canals, head works, gravity dams and spillways
- Design of weirs on permeable foundation
- Types of irrigation systems, irrigation methods
- Water logging and drainage
- Canal regulatory works, cross-drainage structures, outlets and escapes

**Section E: Environmental Engineering**

**Unit 1: Water and Waste Water**

Quality standards, basic unit processes and operations for water treatment

Drinking water standards −

Water requirements

Basic unit operations and unit processes for surface water treatment

Distribution of water

Sewage and sewerage treatment, quantity and characteristics of wastewater

Primary, secondary and tertiary treatment of wastewater, effluent discharge standards

Domestic wastewater treatment −

Quantity of characteristics of domestic wastewater

Primary and secondary treatment

Unit operations and unit processes of domestic wastewater −

Sludge disposal

**Unit 2: Air Pollution**

Types of pollutants, their sources and impacts, air pollution meteorology, air pollution control, air quality standards and limits

**Unit 3: Municipal Solid Wastes**

Characteristics

Generation

Collection and transportation of solid wastes

Engineered systems for solid waste management (reuse/ recycle, energy recovery, treatment and disposal)

**Unit 4: Noise Pollution**

- Impacts of noise
- Permissible limits of noise pollution
- Measurement of noise
- Control of noise pollution

**Section F: Transportation Engineering**

**Unit 1: Transportation Infrastructure**

- Highway alignment and engineering surveys
- Geometric design of highways −
- Cross-sectional elements
- Sight distances
- Horizontal and vertical alignments

- Geometric design of railway track
- Airport runway length, taxiway and exit taxiway design

**Unit 2: Highway Pavements**

- Highway materials - desirable properties and quality control tests
- Design of bituminous paving mixes
- Design factors for flexible and rigid pavements
- Design of flexible pavement using IRC: 37-2012
- Design of rigid pavements using IRC: 58-2011
- Distresses in concrete pavements

**Unit 3: Traffic Engineering**

Traffic studies on flow, speed, travel time - delay and O-D study, PCU, peak hour factor, parking study, accident study and analysis, statistical analysis of traffic data

Microscopic and macroscopic parameters of traffic flow, fundamental relationships

Control devices, signal design by Webster’s method

Types of intersections and channelization

Highway capacity and level of service of rural highways and urban roads

**Section G: Geomatics Engineering**

Principles of surveying

Errors and their adjustment

Maps - scale, coordinate system

Distance and angle measurement - Levelling and trigonometric levelling

Traversing and triangulation survey

Total station

Horizontal and vertical curves

Photogrammetry:

Scale, flying height

Remote sensing - basics, platform and sensors, visual image interpretation

Basics of Geographical information system (GIS) and Geographical Positioning system (GPS)

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