Explore chapters and articles related to this topic
Theory of Stress
Published in Prasun Kumar Nayak, Mijanur Rahaman Seikh, Continuum Mechanics, 2022
Prasun Kumar Nayak, Mijanur Rahaman Seikh
After performing a stress analysis on a material body assumed as a continuum, the components of the Cauchy stress tensor at a particular material point are known with respect to a co-ordinate system. The Mohr circle is then used to determine graphically the stress components acting on a rotated coordinate system, i.e., acting on a differently oriented plane passing through that point. This construction involves three circles, and it is a generalization of Mohr’s circle for plane stress.
Soil Mechanics
Published in P.K. Jayasree, K Balan, V Rani, Practical Civil Engineering, 2021
P.K. Jayasree, K Balan, V Rani
Failure of the material occurs when the Mohr’s circle of stresses touches the Mohr’s envelope. The Mohr’s circle represents all possible combinations of shear and normal stresses at the stressed point. At the point of contact (D) of the failure envelope and the Mohr’s circle, the critical combination of shear and normal stresses is reached and the failure occurs. The plane indicated by the line PD is therefore the failure plane. Any Mohr’s circle which does not cross the failure envelope and lies below the envelope represents a stable condition.
Modelling of stress and strain relationship of dense gravel under large cyclic loading
Published in F. Tatsuoka, S. Shibuya, R. Kuwano, Advanced Laboratory Stress-Strain Testing of Geomaterials, 2018
The quasi-elastic shear modulus Go is representing the maximum shear modulus for the current stress state. In the case of triaxial tests or plane strain tests the major principal stresses are vertical stress σv and horizontal stress σh. Depending on compression or extension under triaxial or plane strain condition, the σv and σh values or σh and σv values will be assigned to major and minor principal stresses, respectively. Under this circumference, from Mohr’s circle at any instant the plane where the maximum shear stress occurs would be 45° inclined to the vertical or horizontal direction. Then; () Go=G45=dτ45dγe=12·dσv−dσhdεve−dεhe
A new paradigm to explain the development of instability rutting in asphalt pavements
Published in Road Materials and Pavement Design, 2020
Reebie Simms, David Hernando, Reynaldo Roque
Mohr circle is commonly used to study the complete in-plane stress state of a material at a single point. However, when multiple locations and their corresponding stress states are to be investigated, Mohr circle becomes impractical. A convenient alternative to simultaneously analyse the stress state of multiple locations is the use of a p-q space diagram, where each point represents the top of the corresponding Mohr circle. The coordinates p and q are the average confinement and maximum shear stress at a point, respectively: where σ1 and σ3 represent the major and minor principal in-plane stresses, respectively.
Examining the effects of liquid–powder binder concentration on the cohesion and friction of a granular bed
Published in Particulate Science and Technology, 2021
Hao Zhou, Muhammad Waryal Dahri, Mingxi Zhou, Zhenya Lai
Next, Mohr’s circle was drawn to obtain the major σ1 and minor σ3 principal stresses by intersecting the σ-axis. The radius of the Mohr’s circle was appraised and found to be equal to the maximum shear stress (τmax) by using Equation (5).