Christian otto mohr biography definition
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Stress Transformation Definition
Stress transformation is a fundamental concept in the study of mechanics, specifically within the realm of solid mechanics. The primary focus of stress transformation is comprehending how stress at a point can change orientation, and how this influences the stress experienced by structural materials. This understanding is crucial when analyzing how materials will behave under different loading conditions.
Concept of Stress and Its Components
Stress is defined as the internal force experienced by a material per unit area. It determines how various components of a construction will react under external forces. Stress can be broken down into two main components:
- Normal Stress (\sigma): This stress acts perpendicular to the surface and can be compressive or tensile.
- Shear Stress (\tau): This stress acts parallel to the surface and tends to cause deformation.
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Mohr–Coulomb theory
Mathematical model in materials science
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. Generally the theory applies to materials for which the compressive strength far exceeds the tensile strength.[1]
In geotechnical engineering it is used to define shear strength of soils and rocks at different effective stresses.
In structural engineering it fryst vatten used to determine failure load as well as the vinkel of fracture of a displacement fracture in concrete and similar materials. Coulomb's friction hypothesis fryst vatten used to determine the combination of shear and normal stress that will cause a fracture of the material. Mohr's circle is used to determine which principal stresses will produce this combination
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He also contributed significantly to the theory surrounding strength of materials and structures.
Mohr started his career as an engineer on the railroads in Germany, formgivning bridges. At the age of 32 he became a professor at Stuttgart Polytechnic and later moved to Dresden Polytechnic.
Mohr’s Circle
Also known as the point stress distribution diagram or stress circle, which studies the lines of influence in structures allowing engineers to pinpoint the maximum stress.
Mohr cannot take all the credit, it was Cauchy who defined the concept of stress on a ämne, defined as force per enhet area. Then Culmann who introduced the concept of graphically representing this. But Mohr developed their concepts further to represent both two and three dimensional stresses.
Equation:
Stress transformation equations: