CIVIL AE JE PAGE 01

Civil Engineering Quick Revision Notes

Target PSC JE / AE & Competitive Exams (Set-01)

1. Highway Engineering: Transition Curve

  • IRC Preferred Shape: The Spiral (Euler's Spiral / Clothoid) curve is preferred by IRC for horizontal alignment of highways.
  • Length of Transition Curve (Ls):
    Ls = 0.0215 V3 CR
    Where V = Speed in km/h, R = Radius in meters, C = Rate of change of centrifugal acceleration in m/s3.
  • Formula for C: C = 80 75 + V   (Range: 0.5 ≤ C ≤ 0.8)
    • For speed V > 100 km/h: C ≈ 0.46
    • For speed V < 30 km/h: C ≈ 0.76
  • Shift of Transition Curve (S): S = Ls2 24R
  • Empirical Formula (Plain / Rolling Terrain): Ls = 2.7 V2 R

2. Structural Design: Span to Effective Depth Ratio (IS 456:2000)

Basic values of Span to Effective Depth Ratio for beams up to 10 m span to satisfy deflection limits:

Type of Beam Basic Span / Effective Depth Ratio
Cantilever Beam 7
Simply Supported Beam 20
Continuous Beam 26
  • For Spans > 10 m: Except for cantilevers, multiply basic values by 10 Span in meters .
  • Modification Factors: Depend on Tension Reinforcement (Kt), Compression Reinforcement (Kc), and Flanged Sections (Kf).

3. Geotechnical Engineering: Unconsolidated Undrained (UU) Test

  • Test Type: Quickest form of Triaxial Shear Test.
  • Drainage Conditions: Drainage is not permitted during either consolidation or shearing stages.
  • Testing Time: Very fast; completed in 5 to 10 minutes.
  • Suitability: Suitable for cohesive soils (clay); NOT suitable for sandy soils.
  • Shear Strength Parameters: For saturated clay, φu = 0°, and Shear Strength s = cu = σ1 - σ3 2 .
  • Practical Application: Used for evaluating immediate stability of newly built embankments and foundations.

4. Engineering Mechanics: Polar Moment of Inertia

Polar Moment of Inertia (J or Ip) for a circular section:

J = Ixx + Iyy = π D4 64 + π D4 64 = π D4 32
  • Polar Section Modulus (Zp): Zp = J R = π D3 16
  • Hollow Circular Shaft: J = π (D4 - d4) 32
  • Torsion Equation: T J = τ r = G θ L

5. Dynamics: Motion & Range of Projectile

  • Horizontal Range Formula:
    R = u2 sin 2θ g
  • Maximum Range (Rmax): Achieved when θ = 45°, giving Rmax = u2 g
  • Maximum Height (Hmax): H = u2 sin2θ 2g
  • Time of Flight (T): T = 2u sin θ g
  • Trajectory Path: y = x tan θ - g x2 2u2 cos2θ

6. Structural Analysis: Support Reactions

  • Hinge / Pin Support:
    • Provides 2 reaction forces: Horizontal (PH) and Vertical (PV).
    • Moment Resistance: Moment resistance is zero (M = 0). It is free to rotate.
  • Roller Support: Provides only 1 vertical reaction (PV). (PH = 0, M = 0).
  • Fixed Support: Provides 3 reaction components (PH, PV, and Moment M). Restrains both translation and rotation.

7. Soil Mechanics: Plasticity & Consistency Limits

  • Plasticity: The ability of a soil to undergo deformation without cracking or crumbling.
  • Plastic Limit (wp): The minimum water content at which soil can be rolled into a thread of 3 mm diameter without crumbling.
  • Plasticity Index (Ip): Ip = wL - wP
  • High Plasticity Soil: Clay.
Plasticity Index (Ip) Soil Consistency / Classification
0 Non-Plastic (e.g., Sand)
< 7 Low Plastic (e.g., Silt)
7 - 17 Medium Plastic
> 17 Highly Plastic (e.g., Clay)

A-Line Equation (Plasticity Chart): Ip = 0.73 (wL - 20)

8. Highway Materials: Viscosity Test of Bitumen

  • Purpose: Determines the resistance to flow of a bituminous material.
  • Test Temperatures: Absolute Viscosity measured at 60°C; Kinematic Viscosity measured at 135°C.
  • Apparatus: Vacuum Capillary Viscometer / Tar Viscometer.
  • Bitumen Grading: Graded based on Viscosity Grades (VG-10, VG-20, VG-30, VG-40).
  • Other Important Tests:
    • Penetration Test (Hardness at 25°C)
    • Ductility Test (Briquette apparatus at 27°C, rate 5 cm/min)
    • Softening Point Test (Ring and Ball Apparatus)

9. Environmental Engineering: Rapid Sand Filter (RSF)

Design specifications and operational parameters for Rapid Sand Filters:

Parameter / Property Design Value / Specification
Depth of Tank 2.5 m to 3.5 m
Area of Single Unit 10 m2 to 80 m2
Rate of Filtration 3000 to 6000 Liters/m2/hour
Rate of Backwashing 15 to 90 cm/min
Cleaning Period & Method Every 24 to 72 hours (2 to 3 days) using backwashing.
Turbidity Removal Efficiency Up to 99%
Bacterial Removal Efficiency 80% to 90%
Effective Size of Sand (D10) 0.45 mm to 0.70 mm
Uniformity Coefficient (Cu) Cu = D60 D10 = 1.2 to 1.7
Sand Layer Depth 60 cm to 75 cm
Water Depth Above Sand Layer 1 m to 2 m
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