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Maximum Shear Stress (τmax)
Maximum shear stress refers to the concentrated amount of force an object or material receives in a small area while in shear. Maximum shear stress can be applied in real world applications scenarios such as beams, shafts, bars, and various other material conditions where a calculation is needed to determine if said material is appropriate. Maximum shear stress utilizes Mohrs Circle and the principal stresses that follow to calculate through a mathematical approach. Maximum shear stress is a mathematical function whose applications apply to real world use through formulas and variables that come either pre-determined or need to be solved. Maximum shear stress can be related back to helping understand the Maximum shear stress theory. Maximum shear stress is a crucial part in designing members. Typically the maximum shear stress is located at the centroid of an object but can vary depending on geometry, material,position, and other factors. Maximum shear stress may also be referred to as maximum in plane shear stress. As stated maximum shear stress is the maximum shear stress in a given plane. If out of plane stress is needed refer to 3D stress analysis. Maximum shear stress calculations will result in two values given (σx,σy.) These variables are represented as follows in the section maximum shear stress variables. The third value listed relates to shear stress. This value is needed for the calculation of maximum shear stress.

Maximum Shear Stress Variables
σx: Normal stress in the X direction

σy: Normal stress in the Y direction

τxy: Shear stress perpendicular to X/Y axis

Related terminology

 * Shear Stress (τxy)
 * Normal Stress (σx), (σy)
 * Maximum shear stress theory
 * Mohrs Circle
 * Maximum shear stress angle
 * Principal Stress
 * Stress angle
 * Von mizes stress
 * Average principal stress (σavg)
 * Maximum/Minimum Principle Stress (σmax)

http://www.ecourses.ou.edu/cgi-bin/ebook.cgi?topic=me&chap_sec=07.2&page=theory

https://www.amesweb.info/StressStrainTransformations/PlaneStressPrincipalStressCal/PrincipalStressCalculator.aspx

https://study.com/academy/lesson/maximum-shear-stress-theory-formula.html

https://www.sharcnet.ca/Software/Ansys/17.0/en-us/help/wb_sim/ds_Maximum_Stress.html

https://engineering.stackexchange.com/questions/10938/maximum-shear-stress-in-beams

https://www.amesweb.info/Torsion/Torsion-Circular-Shaft-Problem.aspx