Columns and Foundation Engineering

Jul 20, 2024

Columns and Foundation Engineering

Loaded Columns

  • Columns equipped with reinforcements.
  • Subjected to axial load (P_O).
  • Resisted by column strength (concrete strength P_C and steel strength P_S).
  • Equilibrium: Summation of vertical forces should be zero.
    • P_O (downward) = P_C + P_S (upwards).
    • Forces expressed as stress times area.

Stress Calculation

  • Concrete stress: 0.85 F'c.
  • Steel stress: F_y.
  • Types of Columns:
    • Tied Column (P_n is 0.8 P_O).
    • Spiral Column (P_n is 0.85 P_O).

Reduction Factors

  • Tied Column: 0.65 (2010, 2015 NSCP codes).
  • Spiral Column: 0.75.
  • Reinforcement ratios: 1% - 8% (0.01 - 0.08).

Column Reinforcements

Maximum Spacing

  • Ties: minimum of 6D main bars, 48D ties, or least side dimension.
  • Spirals: Formula dependent, checked against 25mm to 75mm limits.

Column Dimension Calculation

  • Expression: P_u = reduction factor * nominal load.
    • Tied Column Factor: 0.8.
    • Spiral Column Factor: 0.85.
  • Focus on gross area (A_g) and steel area (A_s).

Problem Solving Example

Given

  • Axial dead load of 560 kN and live load of 750 kN.
  • Column dimension B=360mm.
  • Reinforcement ratio of 2%.

Solution Steps

  1. Factored Load Calculation
    • P_u = 1.2(DL) + 1.6(LL).
    • Substitute values to get P_u = 1872 kN.
  2. Column Dimension Calculation
    • Use the column formula and solve for B.
    • Found B = 360mm.
  3. Reinforcement Calculation
    • Use area of steel formula A_s = (0.02)(A_g).
    • Calculate number of 20mm diameter bars (N_bars).
    • Found number of bars = 9 bars (rounded up).

Situation Analysis - Various Stresses

Two-way Shear Vs One-way Shear

  • One-way shear: Also called wide beam shear.
    • Calculated using effective depth from face of the column.
  • Two-way shear: Punching shear or diagonal tension shear.
    • Calculated based on perimeter of critical section times effective depth.

Reduction Factors Revisited

  • Application varies based on NSCP codes.
  • Reinforcement ratios and geometry considered for both tied and spiral columns.
  • Check against limiting values to ensure safe design.

Columns with Loads and Moments

Example Structure Analysis

  • Axial load, moments provided at top and bottom.
  • Use of nominal shear capacity calculations.
  • Load distribution from columns to footing discussed.

Foundation Design Principles

  • Effective soil bearing pressures calculated based on depth and load distribution.
  • Use of soil and concrete pressure calculations for safe design.
  • Design adjusted for actual field conditions, including allowable shear stress checks.

Example Problem

  1. Calculate effective bearing soil pressure based on given loads and soil properties.
  2. Distance determination from force application points for the resultant load.
  3. Minimum dimension calculation for footing based on load factors and safety criteria.

Pile Foundations

  • Calculation for pile loads considering row configurations.
  • Centroid considerations for pile placement and load transfer.
  • Use of vernier's equation for centroid location calculation.
  • Load distribution factors for rows and centroids considered.

Combined Footings

  • Design of footings to support multiple columns with combined loads.
  • Effective bearing pressures and resultant load distance from column faces used for calculations.

Final Notes

  • Detailed calculations for design of various components to ensure structural integrity.
  • Emphasis on equilibrium, effective areas, and correct factor application as per NSCP codes.
  • Beware of small errors in intermediate steps and always verify input values.