Mohrs Circle and Strain Gauge Rosette

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Mohr's circle is a graphical method to determine the effect of a coordinate rotation on a tensor quantity. In the engineering sciences it is applied to analyse the effect of a coordinate rotation on stress, strain, second moment of area and moment of inertia.

Introduction


An aluminium alloy beam, clamped at one end within a rig containing a cam whose full-range rotation leads to a repeatable tip deflection of = 0.5" = 12.7 mm, as shown in Figure1. The beam has dimensions as follows: breadth b = 25.4 mm, depth d = 6.35 mm and length (to the cam) L = 254 mm. Three strain gauges are mounted on the upper surface at 94 mm from the clamped end; these gauges are mounted at 15, 45, and 75 with respect to the longitudinal, x-axis, of the beam, as shown in Figure 2. Each of these gauges can be selected using a switchboard, to be one arm of a Wheatstone bridge arrangement [1 research and give reference ], with a dummy strain gauge providing temperature compensation. The Wheatstone bridge is a divided bridge circuit used to measure electrical resistance; these minute changes in resistance correspond to strain in a strain gage in what is known as a bonded resistance strain gage [2]
From a), determine the principal strains I and II, as well as the direction of maximum shear strain. Also, determine the value of Poisson's ratio, , for the material. In this experiment I should theoretically be equal and in the direction of x. Inevitably there will be experimental errors so your result may be different. ...
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