Chapter 23: Transformations of Stress and Strain

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23.10:

Measurements of Strain

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Mechanical Engineering

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Measurements of Strain

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23.9: Three-Dimensional Analysis of Strain

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Strain measures the deformation or displacement in a material. Normal strain is calculated by comparing lengths before and after a load is applied. A more accurate method for measuring normal strains involves using electrical strain gauges consisting of a thin wire cemented to two pieces of paper. When the material elongates, the wire's length increases, and its diameter decreases, causing an increase in electrical resistance. Measuring this change in current determines accurate strain. Strain components at a given point can be determined by measuring the normal strain across the axes drawn through that point. A third measurement along the bisector of the angle formed by the axes determines the shearing strain. Strain measurements are made along three lines drawn through a point, forming respective angles with the horizontal axis. The corresponding strain measurements are substituted into the normal strain equation to form three strain measurement equations. The arrangement of strain gauges used to measure strains is called a strain rosette, typically in 45° or 60° configurations.

23.10:

Measurements of Strain

Strain quantifies the deformation of a material under force, typically measured as normal strain, which represents the change in length when compared with the original length. Electrical strain gauges are used for enhanced accuracy. These devices consist of a conductive wire mounted on a paper backing that adheres to the material's surface. These gauges operate on the piezoresistive effect, where the wire's electrical resistance changes in response to mechanical deformation. The strain gauge adjusts as the material elongates or compresses, altering the wire's resistance proportionally to the strain experienced.

To comprehensively understand strain at a specific material point, consider the normal and shearing strains, which account for shape changes at constant volume. This analysis requires multiple strain gauges arranged at various orientations. Strain measurements are typically conducted along lines set at defined angles to a horizontal axis, with these readings used to compute the overall strain components.

A strain gauge rosette, which positions several gauges in configurations such as 0°, 45°, and 90°, or 0°, 60°, and 120°, enables simultaneous multi-directional strain measurements. Such an arrangement is pivotal for detailed strain analysis at a point and is extensively employed in structural analysis, materials testing, and part validation. These methodologies are vital for engineers to evaluate material behavior, enhancing engineered structures' design and safety.