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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Figure 2. A state of combined loading (bending and twisting) occurs when the load is applied at a location other then the c-channel’s shear center The shear center of an object is an imaginary point in space. If a load is applied at a beam’s shear center, the beam will endure a state of pure bending. As previously noted, under conditions of pure bending, both Hooke’s Law and the Flexural Formula can then be used. The purpose of this lab is to apply a load at the presumed shear center of a c- channel beam, then experimentally and theoretically verify the authenticity of the tested location. Deriving the Location of a C-Channel’s Shear Center The following section will be presented in a different format from what you have seen in previous experiments. This section will be divided into steps for how to determine the shear center of a c-channel. These steps can be used to derive the shear center for other objects as will be done in your Report Requirements. These steps do not have to be followed in the same order for which they are presented but it is highly recommended. The reason that the order was chosen was to create a checklist for your analysis. There are 5 steps included in this section. Some objects require only step 1 while others may require all 5 depending on the complexity of the object. Read carefully, think critically, and be patient!
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Lab6-Shear_Center - Lab 6 Shear Center Mechanics of...

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