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Figure 7.1 Plane stress state in a continuum. In continuum mechanics, a material is said to be under plane stress if the stress vector is zero across a particular plane. When that situation occurs over an entire element of a structure, as is often the case for thin plates, the stress analysis is considerably simplified, as the stress state can be represented by a tensor of dimension 2 ...
This way, the shear stress acting on plane B is negative and the shear stress acting on plane A is positive. The diameter of the circle is the line joining point A and B. The centre of the circle is the intersection of this line with the -axis. Knowing both the location of the centre and length of the diameter, we are able to plot the Mohr ...
It gives the contact stress as a function of the normal contact force, the radii of curvature of both bodies and the modulus of elasticity of both bodies. Hertzian contact stress forms the foundation for the equations for load bearing capabilities and fatigue life in bearings, gears, and any other bodies where two surfaces are in contact.
Plates are defined as plane structural elements with a small thickness compared to the planar dimensions. [1] The typical thickness to width ratio of a plate structure is less than 0.1. [ citation needed ] A plate theory takes advantage of this disparity in length scale to reduce the full three-dimensional solid mechanics problem to a two ...
In effect we are concerned with a rigid-plastic material under condition of plane strain. [1] it turns out that the simplest way of solving stress equations is to express them in terms of a coordinate system that is along potential slip (or failure) surfaces. It is for this reason that this type of analysis is termed slip line analysis or the ...
For the plane stress case, the orientation of the plane may be specified by an angle in the plane, and the stresses and strains acting on this plane may be computed via Mohr's circle. For the general 3D case, the orientation may be specified via a unit normal vector of the plane, and the associated stresses strains may be computed via a tensor ...
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The critical value of stress intensity factor in mode I loading measured under plane strain conditions is known as the plane strain fracture toughness, denoted . [1] When a test fails to meet the thickness and other test requirements that are in place to ensure plane strain conditions, the fracture toughness value produced is given the ...