The Influence of Shear and Bending on the Form and Detailing of Beams

• Beams can account for bending by using more material or stronger material (or both) along the beam edges.
  

  

• Beams can account for bending by arranging the material to achieve greater depth.
  

  

  

  

• Beams can account for variation in moment by varying depth along the span.
  

  

• Standard section selection, an approach:

  • Strength:

    • Bending stress: Section Modulus S

      • S_req= M_max / F_b

    • Shear stress: Cross Section Area: A

      • A_req= (3/2) V_max / F_v (for rectangular sections)

  • Stiffness:

    • Deflections at service loads: Moment of Inertia: I

    • Deflection criteria are typically specified as a fraction of the span.

    • A common criteria is:

      • Maximum deflection <= L / 240

    • This can be combined with deflection formulas for various span and loadings to check whether a chosen section is adequate, or to determine the moment of inertia required.

Note: There are many other possible criteria to check, such as floor vibrations, stresses at end connections, and so on. We will used a simplified procedure that is adequate for many cases and illustrates how member design criteria fit into the design process.