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Lab6-Shear_Center - Lab 6 Shear Center Mechanics of...

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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 .
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