Beam Bending


This simple kinematics model was made from a 10 x 10 x 40 cm block of “furniture foam”. A black marker was used to draw a line along the longitudinal centerline of one side, and transverse lines were added at regular intervals, as shown below (Fig. 1).

Figure 1 – The Undeformed Model Beam

Even though the foam material is highly non-linear and behaves quite differently in tension and compression, planes that are normal to the neutral axis remain straight and normal as it deforms (Figs 2 and 3).

Figure 2 – Bending of the Model Beam

Figure 3 – The Model Deformed into a Serpentine Shape

Learning Objectives

The model helps students to:

  1. See how the centerline of a beam curves as the beam is bent
  2. Recognize that the length of the centerline does not change
  3. Visualize how normals to the centerline remain straight during bending
  4. Envision that normals to the centerline remain at 90° to it
  5. Understand the geometric constructions from which beam kinematics is derived
  6. Better understand the derivation of standard beam bending equations, such as ε=-z/ρ, where ε is the axial strain, z is the distance of the point of interest above the neutral axis and ρ is the radius of curvature of the beam, considered positive when its center is above the beam.