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influx
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Can someone explain why the angle inside the triangle inside Mohr's circle is θP2 rather than θP1 ? I understand everything else but just this small point is frustrating me.
Thanks
Thanks
θP2 is the angle that corresponds to σ2 and θP1 is the angle that corresponds to σ1 but what I am confused about is why the angle inside the triangle is θP2 rather than θP1? How did they know which one it is?paisiello2 said:
Mohr's circle is a graphical method used in mechanics to determine the stress and strain components acting on a material at a specific point. It is often used in structural and civil engineering to analyze the stability and strength of structures. The circle itself represents the stress state of a point, and its construction involves plotting stress components on a coordinate system and using them to determine the center and radius of the circle.
The angle inside Mohr's circle can be calculated using the formula: θ = (1/2)arctan(2τxy/(σx-σy)), where τxy is the shear stress, σx is the major principal stress, and σy is the minor principal stress. This angle represents the orientation of the plane on which the maximum shear stress acts.
The angle inside Mohr's circle provides important information about the stress state of a material. It can be used to determine the orientation of the principal stresses, the direction of the maximum shear stress, and the magnitude of the principal stresses. It is also used to calculate other important parameters such as the Mohr-Coulomb failure criterion and the principal stresses at failure.
The angle inside Mohr's circle changes with different stress states because it is directly influenced by the values of the principal stresses and the shear stress. As the stress state changes, the values of these parameters will also change, resulting in a different angle inside the circle. For example, a tensile stress state will have a different angle than a compressive stress state.
Yes, Mohr's circle can be used for all types of materials as long as they exhibit linear elastic behavior. This means that the material must obey Hooke's law, which states that stress is directly proportional to strain. However, it is important to note that Mohr's circle is not suitable for materials that exhibit plastic or nonlinear behavior, as it is only valid for linearly elastic materials.