GATE Syllabus CE 2025 | Summaries Civil Engineering

Civil Engineering

Section 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, local maxima and minima; Taylor 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.

Ordinary Differential Equation (ODE): First order (linear and non-linear) equations; higher order

linear equations with constant coefficients; Euler-Cauchy equations; initial and boundary value

problems.

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.

Probability and Statistics: Sampling theorems; Conditional probability; Descriptive statistics –

Mean, median, mode and standard deviation; Random Variables – Discrete and Continuous,

Poisson and Normal Distribution; Linear regression.

Numerical Methods: Error analysis. Numerical solutions of linear and non-linear algebraic

equations; 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 2: Structural Engineering

Engineering Mechanics: System of forces, free-body diagrams, equilibrium equations; Internal

forces in structures; Frictions and its applications; Centre of mass; Free Vibrations of undamped

SDOF system.

Solid Mechanics: Bending moment and shear force in statically determinate beams; Simple stress

and strain relationships; Simple bending theory, flexural and shear stresses, shear centre; Uniform

torsion, Transformation of stress; buckling of column, combined and direct bending stresses.

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.

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CE Civil Engineering

Section 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, local maxima and minima; Taylor 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. Ordinary Differential Equation (ODE): First order (linear and non-linear) equations; higher order linear equations with constant coefficients; Euler-Cauchy equations; initial and boundary value problems. 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. Probability and Statistics: Sampling theorems; Conditional probability; Descriptive statistics – Mean, median, mode and standard deviation; Random Variables – Discrete and Continuous, Poisson and Normal Distribution; Linear regression. Numerical Methods: Error analysis. Numerical solutions of linear and non-linear algebraic equations; 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 2: Structural Engineering Engineering Mechanics: System of forces, free-body diagrams, equilibrium equations; Internal forces in structures; Frictions and its applications; Centre of mass; Free Vibrations of undamped SDOF system. Solid Mechanics: Bending moment and shear force in statically determinate beams; Simple stress and strain relationships; Simple bending theory, flexural and shear stresses, shear centre; Uniform torsion, Transformation of stress; buckling of column, combined and direct bending stresses. 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.

Construction Materials and Management: Construction Materials: Structural Steel – Composition, material properties and behaviour; Concrete - Constituents, mix design, short-term and long-term properties. Construction Management: Types of construction projects; Project planning and network analysis - PERT and CPM; Cost estimation. Concrete Structures: Working stress and Limit state design concepts; Design of beams, slabs, columns; Bond and development length; Prestressed concrete beams. 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; Concept of plastic analysis - beams and frames. Section 3: Geotechnical Engineering Soil Mechanics: Three-phase system and phase relationships, index properties; Unified and Indian standard soil classification system; Permeability - one dimensional flow, Seepage through soils – two - dimensional flow, flow nets, uplift pressure, piping, capillarity, seepage force; Principle of effective stress and quicksand condition; Compaction of soils; One- dimensional consolidation, time rate of consolidation; Shear Strength, Mohr’s circle, effective and total shear strength parameters, Stress-Strain characteristics of clays and sand; Stress paths. Foundation Engineering: Sub-surface investigations - 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, Bishop’s method; Stress distribution in soils – Boussinesq’s theory; 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 – dynamic and static formulae, Axial load capacity of piles in sands and clays, pile load test, pile under lateral loading, pile group efficiency, negative skin friction. Section 4: Water Resources Engineering Fluid Mechanics: Properties of fluids, fluid statics; Continuity, momentum and energy equations and their applications; Potential flow, Laminar and turbulent flow; Flow in pipes, pipe networks; Concept of boundary layer and its growth; Concept of lift and drag. Hydraulics: Forces on immersed bodies; Flow measurement in channels and pipes; Dimensional analysis and hydraulic similitude; Channel Hydraulics - Energy-depth relationships, specific energy, critical flow, hydraulic jump, uniform flow, gradually varied flow and water surface profiles. Hydrology: Hydrologic cycle, precipitation, evaporation, evapo-transpiration, watershed, infiltration, unit hydrographs, hydrograph analysis, reservoir capacity, flood estimation and

Photogrammetry and Remote Sensing - Scale, flying height; Basics of remote sensing and GIS.

GATE Syllabus CE 2025, Summaries of Civil Engineering

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CE Civil Engineering