Lab 6 – Shear Center
Mechanics of Deformable Solids
Spring 2011
Shear Center
Pure bending can be defined as bending without torsion. For objects under pure bending,
the Flexural Formula can be used to predict the bending stress in the beam as we did in
Lab 5. Let’s consider two cantilever beams as depicted in Figure 1. Beam A has a
symmetric cross-section, while beam B possesses a non-symmetric cross-section with
respect to the loading axis (direction of load P). To achieve a state a pure bending in
Beam A, the load is placed through the centroid of the beam’s cross-sectional area. The
beam will deflect straight down as predicted. Since the load has created a state of pure
bending, the Flexural Formula combined with Hooke’s Law can be used to predict stress
and strain in the bar.
Figure 1. A load P is applied to the centroid of a square cantilever beam and c-channel cantilever
beam
If the same load P is applied at a location right of the vertical section of Beam B, the
beam will bend and twist creating a state of combined loading. This type of loading is
shown in Figure 2. The reason behind this is the object’s cross-sectional area is not
symmetric with respect to the axis of loading. Since the beam is under bending and
torsion, the Flexural Formula cannot be directly used to predict stress in the beam. So the
question becomes, “Where can we place a load on Beam B to create a state of pure
bending?” The answer is at the beam’s
shear center
.

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*