Análisis y diseño de vigas de concreto

Beam Analysis

• Types of beam analysis:
  • Elastic analysis: assumes linear stress-strain relationship
  • Inelastic analysis: considers nonlinear behavior of concrete and reinforcement
  • Ultimate strength analysis: focuses on beam's capacity to resist collapse
• Steps in beam analysis:
  1. Determine beam geometry and loading
  2. Calculate internal forces and moments
  3. Check beam's resistance to flexure, shear, and torsion
  4. Verify beam's serviceability (deflection, cracking)

Beam Deflection

• Importance of deflection control:
  • Affects beam's appearance and functionality
  • Influences structural integrity and safety
• Deflection calculation methods:
  • Elastic beam theory (e.g., Bernoulli-Euler equation)
  • Finite element method (FEM)
  • Empirical formulas (e.g., ACI 318-19)
• Deflection limits:
  • Typically L/360 to L/480 for normal beams (L = beam span)
  • May be more restrictive for special cases (e.g., cantilever beams)

Bending Moment Calculation

• Bending moment (M) calculation:
  • M = Σ(F * x) for point loads
  • M = ∫(w * x) dx for distributed loads
  • Consider moment distribution due to supports and restraints
• Types of bending moments:
  • Positive moment (sagging): compression in top fibers, tension in bottom fibers
  • Negative moment (hogging): compression in bottom fibers, tension in top fibers

Shear Reinforcement

• Shear reinforcement types:
  • Stirrups (vertical or inclined)
  • Bent-up bars
  • Shear heads
• Shear reinforcement design:
  • Calculate shear force (V) and shear stress (τ)
  • Determine required shear reinforcement area (Av)
  • Check anchorage and spacing requirements

Concrete Material Properties

• Key properties:
  • Compressive strength (f'c)
  • Tensile strength (fct)
  • Modulus of elasticity (Ec)
  • Poisson's ratio (ν)
• Importance of concrete properties:
  • Affect beam's strength, stiffness, and durability
  • Influence design decisions (e.g., reinforcement ratio, section size)