Structural Analysis: Beam Design

Beam Design

Types of Beams

• Simple Beam: A beam that is supported at both ends and is free to rotate at the supports.
• Fixed Beam: A beam that is fixed at both ends and cannot rotate at the supports.
• Cantilever Beam: A beam that is fixed at one end and is free to rotate at the other end.
• Overhanging Beam: A beam that extends beyond its supports.

Beam Design Considerations

• Load: The force applied to the beam, including:
  • Point loads: Concentrated loads applied at a specific point.
  • Uniform loads: Loads distributed evenly along the length of the beam.
  • Moment loads: Loads that cause a rotation or twisting force.
• Material properties: The strength and stiffness of the beam material, including:
  • Modulus of elasticity (E): The measure of a material's stiffness.
  • Yield strength (σy): The maximum stress a material can withstand before deforming plastically.
• Section properties: The geometric properties of the beam cross-section, including:
  • Area (A): The total area of the cross-section.
  • Moment of inertia (I): A measure of the beam's resistance to bending.
  • Section modulus (S): A measure of the beam's resistance to bending and deflection.

Beam Design Equations

• Bending stress (σ): σ = Mc/I
• Deflection (δ): δ = WI/2EI
• Shear stress (τ): τ = VQ/It
• Beam design formula: σ ≤ σy and δ ≤ L/360

Beam Design Steps

1. Determine the load: Calculate the load applied to the beam.
2. Select the material: Choose a material based on its strength, stiffness, and cost.
3. Determine the section properties: Calculate the area, moment of inertia, and section modulus of the beam cross-section.
4. Check for bending stress: Ensure that the bending stress is within the material's yield strength.
5. Check for deflection: Ensure that the deflection is within the allowable limit.
6. Check for shear stress: Ensure that the shear stress is within the material's yield strength.
7. Optimize the design: Iterate the design process to minimize material usage and cost.

Beam Design

Types of Beams

• A simple beam is supported at both ends and is free to rotate at the supports.
• A fixed beam is fixed at both ends and cannot rotate at the supports.
• A cantilever beam is fixed at one end and is free to rotate at the other end.
• An overhanging beam extends beyond its supports.

Beam Design Considerations

• Load is the force applied to the beam and includes point loads, uniform loads, and moment loads.
• Point loads are concentrated loads applied at a specific point.
• Uniform loads are loads distributed evenly along the length of the beam.
• Moment loads are loads that cause a rotation or twisting force.
• Material properties affect beam design, including modulus of elasticity (E) and yield strength (σy).
• Modulus of elasticity (E) measures a material's stiffness.
• Yield strength (σy) is the maximum stress a material can withstand before deforming plastically.
• Section properties include area (A), moment of inertia (I), and section modulus (S).
• Area (A) is the total area of the cross-section.
• Moment of inertia (I) measures a beam's resistance to bending.
• Section modulus (S) measures a beam's resistance to bending and deflection.

Beam Design Equations

• Bending stress (σ) is calculated by σ = Mc/I.
• Deflection (δ) is calculated by δ = WI/2EI.
• Shear stress (τ) is calculated by τ = VQ/It.
• The beam design formula is σ ≤ σy and δ ≤ L/360.

Beam Design Steps

• Determine the load applied to the beam.
• Select a material based on its strength, stiffness, and cost.
• Determine the section properties of the beam cross-section.
• Check that the bending stress is within the material's yield strength.
• Check that the deflection is within the allowable limit.
• Check that the shear stress is within the material's yield strength.
• Optimize the design to minimize material usage and cost.

Foundation Analysis

• Evaluates the capacity of a foundation to support the weight of a structure
• Involves analyzing soil-structure interaction, determining safe bearing capacity of soil, and designing foundation to resist various loads

Types of Foundations

• Shallow Foundations:
  • Spread footings (isolated, combined, and strap)
  • Mat foundations
  • Slab-on-grade foundations
• Deep Foundations:
  • Piles (driven, drilled, and helical)
  • Drilled shafts (caissons)
  • Piers

Soil Investigation

• Site Exploration:
  • Boring and sampling
  • In-situ testing (e.g., cone penetration test, standard penetration test)
  • Laboratory testing (e.g., triaxial test, unconfined compression test)
• Soil Properties:
  • Strength parameters (e.g., friction angle, cohesion)
  • Deformation parameters (e.g., elastic modulus, Poisson's ratio)

Foundation Capacity Analysis

• Ultimate Capacity:
  • Bearing capacity (gross and net)
  • Resistance to sliding and overturning
• Serviceability:
  • Settlement and deformation analysis
  • Pore water pressure and drainage considerations

Design Considerations

• Load Combinations:
  • Dead and live loads
  • Wind and seismic loads
  • Soil and water pressures
• Foundation Design:
  • Selection of foundation type and size
  • Material selection and detailing
  • Construction and installation considerations