Transversely Loaded Beams

• Beams of rectangular cross-section with the length much greater than either of their transverse dimensions
  
• Types of supports
  • Clamped (also called fixed or built-in)
    Does not permit the horizontal and vertical movement at the support nor a non-zero slope at the support
    
    
  • Free
    No constraint on the displacement or the slope
    Beam with a free end is called a cantilever beam
    
    
  • Hinged (also called pinned or simple support)
    Fixes both the vertical and horizontal position of the beam end, but does not restrict its slope
    
    
  • Sliding
    fixes the vertical position of the beam, but does not restrict its horizontal position and slope

• Types of external transverse loads

  • Point load
    Can be applied at any position along the beam length
    We will suppose that F is the total force acting at a position x along the length of a beam, uniformly distributed across its width
    Sometimes, if the force per unit width, F' is specified, the total force F = F' w
    
    
  • Distributed load
    Can be applied to a portion of the beam length
    Symbol q is used for the force per unit length of beam, uniformly distributed across its width
    If a portion of a beam is loaded by a uniform pressure P, the equivalent beam load can be expressed as q = Pw