BT-204 Basic Civil Engineering & Engineering Mechanics

BCE Unit 5: Centre of Gravity & Moment of Inertia

Complete RGPV exam-oriented page covering centroid, centre of gravity, moment of inertia, radius of gyration, product of inertia, support reactions, shear force, bending moment, SFD, BMD, cantilever beam and simply supported beam.

Read Notes Important Questions PYQ Analysis

Unit 5 Syllabus

Centre of Gravity & Moment of Inertia important topics

Centroid & C.G.

  • Centroid
  • Centre of gravity
  • Difference between centroid and C.G.
  • Centroid of composite sections

Moment of Inertia

  • Area moment of inertia
  • Mass moment of inertia
  • Moment of inertia of rectangle
  • Moment of inertia of circle
  • Radius of gyration

Beam Analysis

  • Support reactions
  • Shear force
  • Bending moment
  • SFD and BMD
  • Cantilever beam
  • Simply supported beam

Loads

  • Concentrated load
  • Distributed load
  • Couple
  • Point load problems
  • Beam numerical problems

Short Exam Notes

Easy revision notes for RGPV exam

Centroid

Centroid is the geometrical center of a plane figure. It depends only on the shape of the body and is independent of material density.

Centre of Gravity

Centre of gravity is the point through which the total weight of a body acts. It is used in stability analysis, vehicle design and building structures.

Moment of Inertia

Moment of inertia is the property of a body that resists rotational motion. Area moment of inertia is used in bending analysis of beams.

Radius of Gyration

Radius of gyration is the distance from an axis at which the whole area or mass can be assumed to be concentrated.

Product of Inertia

Product of inertia measures distribution of area with respect to two perpendicular axes. It is useful for unsymmetrical sections and structural analysis.

Support Reactions

Support reactions are forces developed at supports of beams and structures. They are calculated using equilibrium equations.

Shear Force

Shear force is the algebraic sum of vertical forces acting on either side of a section. SFD shows variation of shear force along beam length.

Bending Moment

Bending moment is the turning effect produced by external forces on a beam section. BMD shows variation of bending moment along the beam.

Cantilever Beam

Cantilever beam is fixed at one end and free at the other end. Examples include balconies, bridges and aircraft wings.

Simply Supported Beam

Simply supported beam is supported at both ends. It is commonly used in building structures and bridges.

Quick Revision Formulas

Most important formulas

Centroid X-coordinate: x̄ = ΣAx / ΣA
Centroid Y-coordinate: ȳ = ΣAy / ΣA
Area Moment of Inertia: I = ΣAr²
Rectangle M.I. about centroidal axis: I = bd³ / 12
Circle M.I. about centroidal axis: I = πd⁴ / 64
Radius of Gyration: k = √(I/A)
Equilibrium Conditions: ∑Fx = 0, ∑Fy = 0, ∑M = 0

Most Important Questions

High chance RGPV exam questions

14 Marks Questions

  • Explain centroid and centre of gravity with applications.
  • Explain area moment of inertia and mass moment of inertia.
  • Derive moment of inertia for rectangle and circle about centroidal axis.
  • Explain radius of gyration with applications.
  • Explain product of inertia and principal axes.
  • Explain support reactions with equilibrium equations.
  • Explain shear force and bending moment with suitable examples.
  • Draw SFD and BMD for cantilever beam with concentrated load.
  • Draw SFD and BMD for simply supported beam with distributed load.
  • Explain concentrated load, distributed load and couple.
  • Differentiate cantilever beam and simply supported beam.
  • Solve support reaction numerical problems for beams.

7 Marks Questions

  • Define centroid and centre of gravity.
  • Explain radius of gyration.
  • Explain product of inertia.
  • Explain principal axes.
  • Define shear force and bending moment.
  • Explain cantilever beam.
  • Explain simply supported beam.
  • Explain support reactions.
  • Explain distributed load.
  • Explain couple and its applications.

Important Numericals

  • Centroid calculation problems
  • Moment of inertia numerical problems
  • Radius of gyration calculations
  • Support reaction problems
  • Shear force and bending moment numerical problems

PYQ Analysis Table

Repeated questions from RGPV previous year papers

Topic Repeated Questions Frequency Priority
SFD & BMD Cantilever beam, simply supported beam, point load, UDL and numerical problems Very High ★★★★★
Support Reactions Beam reaction problems and equilibrium equations Very High ★★★★★
Moment of Inertia Derivation for rectangle and circle, numerical problems Very High ★★★★★
Centroid & C.G. Definitions, differences and centroid of composite sections High ★★★★
Beam Numerical Problems SFD, BMD, support reactions and loading diagrams High ★★★★
Radius of Gyration Formula, applications and numerical problems Medium ★★★
Cantilever & Simply Supported Beam Differences, behavior and loading diagrams Medium ★★★
Product of Inertia Product of inertia and principal axes Medium ★★★

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FAQs

Common student doubts

Which topic is most important in BCE Unit 5?

SFD & BMD, support reactions, moment of inertia, centroid and centre of gravity are the most important topics.

Which numericals should I practice?

Support reactions, moment of inertia, centroid, SFD, BMD and radius of gyration numericals are important.

Which diagrams are important?

SFD, BMD, cantilever beam, simply supported beam, loading diagrams and centroid diagrams are important.

Related Units

Unit 1 Unit 2 Unit 3 Unit 4