Max shear stress theory

Maximum Shear Stress A decrease of the maximum shear stress without varying the fracture energy entails for an increase of the LSTZ, which produces a downward shift of the end of the linear portion of the load response. From: Advanced Composites in Bridge Construction and Repair, 2014 Related terms: • Warping • Shear Centre Although Hertz’s analysis described surface stresses, abundant evidence indicates that fatigue-related failures of rolling element bearings usually originate from below the surface in the vicinity of the location of the maximum shear stress. Jones considered the stresses arising from a concentrated force applied normal to a surface and calculated that the maximum shear stress produced was [15] (3.87) z o = b t + 1 2 t − 1 Example 3.3 Using the values of a i, b i, and σ icalculated in Example 3.2 for the 7212 angular contact bearing, we can evaluate the maximum shear stress and depth of the maximum shear stress on the inner raceways of the bearing. Two of the three roots of Eq. (3.86) are <1/2 and produce complex values of z ofrom Eq. (3.87). The value and depth of the maximum shear stress estimated from Eqs. (3.85) and (3.87) using the root t=1.00632,are 688MPa and 0.177mm, respectively. In Example 3.3, the maximum shear stress was found to occur at a depth of about z~0.495 b, which is typical for point contact bearings. The maximum shear stress depth is about z~0.786 b for line contact bearings. During the transit of a loaded rolling element over a rac...

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Benjamin Sheldon Benjamin Sheldon has taught elementary, middle school and high school students in general science, physics, physical science and gifted enrichment for over 16 years. He has a bachelors degree in physics teaching with a minor in mathematics from Brigham Young University and a masters degree in special education with an emphasis in gifted education from The University of Missouri in Columbia. • Instructor What is Maximum Shear Stress? Maximum shear stress is the greatest extent a shear force can be concentrated in a small area. Shear force occurs throughout any structural member when an outside force is acting in the opposite unaligned direction from internal forces. These forces will be of different magnitudes at various cross-sections of the structural member, and they will not be evenly distributed along with the entire member. These forces create shear stress on the structural material. According to max shear stress theory, there is a maximum amount of shear stress that the material can handle concentrated in small areas of the member. A structural member must resist too much shear stress. A structural engineer must locate the position and calculate the amount of maximum shear stress to make an adequate design. All load combinations that exist must be taken into account so that shear stress can be adequately evaluated. Shear forces and shear stress are not the only engineering factors that must be evaluated, but only one of many. The maximum bending mome...

DUCTILE MATERIAL One theory that is used for the prediction of failure in a ductile material is the maximum shear stress theory (MSS). The basis of this theory is that failure will occur when the maximum shear stress exceeds the maximum shear stress that exists for yielding in a uni-axial test. Consequences: • The failure boundary corresponds to|τ| max,abs = σ Y/2. • In the principal stress plane (σ P1 vs. σ P2 plane), this failure boundary is the hexagonal region shown to the right. The hexagonal-shaped boundary above is the locus of points in the principal stress plane that corresponds to constant values of |τ| max,abs . How does this locus of points link back to the Mohr’s circle plane? The animation below shows how the Mohr’s circle changes as we move around on this hexagonal-shaped boundary between safe and failure. Observations • In quadrant 3 of the principal stress plane, Mohr's circle is in the left-half plane with the failure boundary prescribed by σ P2 = -σ Y . • In quadrant 1 of the principal stress plane, Mohr's circle is in the right-half plane with the failure boundary prescribed by σ P1 =σ Y . • In quadrant 4 of the principal stress plane, Mohr's circle has a constant radius R = σ Y /2 . • At the beginning and end points of the above animation, the failure boundary is located at σ P2 =σ P1 . As discussed earlier in the course, this corresponds to a state of "hydrostatic" stress. This corresponds to a Mohr's circle with a zero radius. Such a state of stress ...