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The maximum stress criterion assumes that a material fails when the maximum principal stress in a material element exceeds the uniaxial tensile strength of the material. Alternatively, the material will fail if the minimum principal stress σ 3 {\displaystyle \sigma _{3}} is less than the uniaxial compressive strength of the material.
and the normal stresses acting on the same planes where the minimum and maximum shear stresses act are equal to . We can choose to either use the double angle approach (Figure 8) or the Pole approach (Figure 9) to find the orientation of the principal normal stresses and principal shear stresses.
Rankine's theory (maximum-normal stress theory), developed in 1857 by William John Macquorn Rankine, [1] is a stress field solution that predicts active and passive earth pressure. It assumes that the soil is cohesionless, the wall is frictionless, the soil-wall interface is vertical, the failure surface on which the soil moves is planar , and ...
Mohr–Coulomb theory is a mathematical model (see yield surface) describing the response of brittle materials such as concrete, or rubble piles, to shear stress as well as normal stress. Most of the classical engineering materials follow this rule in at least a portion of their shear failure envelope.
The strength of materials is determined using various methods of calculating the stresses and strains in structural members, such as beams, columns, and shafts. The methods employed to predict the response of a structure under loading and its susceptibility to various failure modes takes into account the properties of the materials such as its yield strength, ultimate strength, Young's modulus ...
The Hoek–Brown criterion has the form [2] = + + where is the effective maximum principal stress, is the effective minimum principal stress, and , are materials constants. In terms of the mean normal stress and maximum shear stress ()
Modern procedures for critical plane analysis trace back to research published in 1973 in which M. W. Brown and K. J. Miller observed that fatigue life under multiaxial conditions is governed by the experience of the plane receiving the most damage, and that both tension and shear loads on the critical plane must be considered.
Within the branch of materials science known as material failure theory, the Goodman relation (also called a Goodman diagram, a Goodman-Haigh diagram, a Haigh diagram or a Haigh-Soderberg diagram) is an equation used to quantify the interaction of mean and alternating stresses on the fatigue life of a material. [1]