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Lab1-Introduction_to_Strain

# Lab1-Introduction_to_Strain - Lab 1 Introduction to Strain...

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Lab 1- Introduction to Strain Measurement Mechanics of Deformable Solids Spring 2011 Introduction An object will change shape and size when a force is applied to its body. Any temporary or permanent change to a body’s geometry is commonly referred to as deformation. To an observer, the deformation of an object may be either very noticeable or practically undetectable. The degree of deformation will depend on the location and magnitude of the applied force, boundary conditions, object geometry, and material properties. In a general sense, the shape change of an object will not be uniform throughout its volume and thus quantifying an overall deformation is cumbersome. Instead, an assumption is made that stretching about a finite point, line, or small plane in an object is uniform. By focusing efforts on localized deformation, temporary or permanent stretching can be easily quantified by a term known as strain. Strain and Strain Measurement To describe the deformation of an object by changes in length, imagine an elastic rope pulled between two people in opposite directions. If both people pull the rope with an equal force, the length of the rope will stretch and thus change in length. If the change in length is compared to the original length of the rope, we arrive at the engineering concept of strain. Strain ( ε ) can be mathematically shown as the change in length of an object divided by its original length Δ l ( ) l o ( ) . After inspection, strain is known to be a dimensionless parameter, often shown as [m/m], [mm/mm], or [ μ m/m]. ε = Δ l l o = l i l o l o (1) The theoretical knowledge of strain is important while designing objects and structures to withstand deformation under a known load. With too much strain the object may permanently deform or fail. A variety of techniques have been developed to predict and experimentally verify strain within an object. For most measurement applications the change in length is very small and mechanical measurement is difficult. In order to measure these small deformations, principles of electricity are used to measure strain. A common tool used to measure strain is a foil Resistance Strain Gage (RSG). A RSG is a long strand of wire folded back on itself repeatedly as shown in Figure 1. The gage is glued to the surface of a specimen at a location where a strain measurement is desired. Before the specimen is loaded, an electric current will flow through the wire. Since the voltage (V) applied to the gage nodes and electrical current (i) are known, the resistance of the folded wire (R) can be found using Ohm’s Law (V=iR). Since the RSG is glued to the surface, the gage will endure the same magnitude of deformation as the surface of the specimen. When the RSG deforms, the resistance of the folded wire will change and is 1

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