Reinforced Concrete Design Lecture Notes

Jun 29, 2024

Lecture on Reinforced Concrete Design

Introduction

  • Lecturer: Dr. Sherry Fisherman
  • Topic: Design of Reinforced Concrete Beams
  • Part One Overview: Introduction to beam design, requirements, and checks.

Types of Beams

Simply Supported Beams

  • Characteristics: One span, simply supported, or fixed ends.
  • Analysis: Easier structural analysis, bending moment design.
  • Reinforcement Position: Tension at the bottom, main reinforcement placement.

Continuous Beams

  • Characteristics: Multiple spans, indeterminate structures.
  • Analysis: More complex, often uses factors from codes or computer programs for bending moments and load calculations.
  • Reinforcement Position: Top and bottom reinforcement depending on span and support.

Cantilever Beams

  • Characteristics: Free end, tension at the top, main reinforcement at the top.
  • Analysis: Similar to simply supported beams, bending moments

Beam Classification by Span-to-Depth Ratio

Shallow Beams

  • Ratio: Span/depth ratio > 2.5.
  • Design Focus: Bending moments.

Deep Beams

  • Ratio: Span/depth ratio ≤ 0.5.
  • Design Focus: Shear forces.

Drop Beams

  • Characteristics: Beam supports the slab from below.
  • Common Use: Most constructions.

Inverted Beams

  • Characteristics: Slab beneath the beam, often used to maintain smooth rooflines.
  • Application: Roof plans.

Hidden Beams

  • Characteristics: Beam same thickness or slightly thicker than the slab.
  • Usage: Beams not visible post-construction, might require more reinforcement.

Rectangular vs. Flanged Sections

Rectangular Section

  • Design: When flange is in tension (underneath the neutral axis).
  • Application: Beam mostly under tension at top surface.

Flanged Section

  • Design: When flange is in compression (above the neutral axis).
  • Application: Simply supported beams with compression at the top surface.

Process of Load Transfer from Slab to Beam

One-Way Slabs

  • Load Transfer: Short direction transfers load to long beams.
  • Calculation: Partition load in short direction and distribute it to the long beams.

Two-Way Slabs

  • Load Transfer: Load distributed to both long and short beams.
  • Calculation: Uses a combination of triangular and trapezoidal area allocations.

Design Methods for Continuous Beams

  • British Standard Table 3.5: For uniform loads over three or more spans with specific conditions.
  • Limitations: Uniformly distributed loads, live load ≤ dead load, span length variations ≤ 15%.

Table 3.5 Usage

  • Bending Moments and Shear Forces: Method to calculate ultimate load moments and forces.

Initial Beam Proportioning (BS 8110 Table 3.9)

  • Estimation of Effective Depth (d):
    • Simply supported: Span/16
    • Continuous: Span/20
  • Cover Requirements for Durability and Fire Resistance: Table 3.3 for durability, Table 3.4 for fire resistance.
  • Total Height Calculation (h): h = d + cover + 1 + (Φ_bar / 2) + Φ_link.
  • Width (b) Calculation: Usually falls between h/3 and h/2, rounded to the nearest 25 mm.

Calculating Loads on Beams

Dead Load

  • Self-weight of Beam: Volume factor (H - H_f) * B * γ * L
  • Load from Slab: Area supported * load per unit area.
  • Load from Walls: Similar formula as self-weight but uses wall density.
  • Total Dead Load: Sum of self-weight, slab load, and wall load.

Live Load

  • Contribution from Slab: Live load * area supported.

Ultimate Load Calculation

  • Formula: 1.4 * dead load + 1.6 * live load.
  • Uniform Load: Divide ultimate load by span.

Design Steps for Structural Analysis

  • Use of Table 3.5 for Moments and Shear Forces.
  • Reinforcement Calculation: Z = M_ult / (f_cu * b * d^2).
    • Tables for Reinforcement Areas: Guide for selecting bar numbers and diameters.

Checks and Final Proportioning

  • Deflection Checks: Use maximum positive moment, equation for f_s (stress in steel) and appropriate factors.
  • Shear Design and Placement: Tables 3.7 and 3.8 for concrete contributions and shear reinforcement design.
  • Cracking and Spacing Checks: Table 3.25 for minimum reinforcement percentages.

Detailing and Curtailment

  • Curtailment: Cover cutting and extending bar details.
  • Minimum Hanger Reinforcement: 20% of bottom reinforcement.

Additional Notes

  • Transverse Reinforcement: Above the beams, 0.15% of flange area.
  • Side Bars Requirements: For beam height > 750 mm, spacing ≤ 250 mm.

Upcoming Parts (Part 2 and 3)

  • Part 2: Design example of simply supported beam.
  • Part 3: Design of continuous beam, full design example including shear checks and other aspects.