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Chapter 23

Transformations of Stress and Strain

Transformation of Plane Stress
Transformation of Plane Stress
Consider a point on a cube experiencing plane stress, defined by its stress components. If the element rotates by an angle, its stress components change. ...
Principal Stresses
Principal Stresses
The normal and shearing stress equations of the transformed plane, when graphed, form a circle that demonstrates their relationship for any given angular ...
Principal Stresses: Problem Solving
Principal Stresses: Problem Solving
Two planes that are at right angles carry shearing stress along with tensile and compressive stresses. With known stress values, determine the principal ...
Mohr's Circle for Plane Stress
Mohr's Circle for Plane Stress
Mohr's circle is a visual representation of stress transformation on an element. The stress components in this element are plotted on a graph to ...
General State of Stress
General State of Stress
The general state of stress refers to the various forces and pressures an object experiences. Consider a tetrahedron with one face perpendicular to a line ...
Yield Criteria for Ductile Materials under Plane Stress
Yield Criteria for Ductile Materials under Plane Stress
Structural elements and machine parts made from ductile materials are designed to resist yielding under an expected load. The yield point is identified ...
Transformation of Plane Strain
Transformation of Plane Strain
Consider a long bar subjected to uniformly distributed loads on its sides. In such bars, the transformation of plane strain under a rotation of coordinate ...
Mohr's Circle for Plane Strain
Mohr's Circle for Plane Strain
Mohr's circle analyzes plane strain by plotting points with the abscissa equal to the normal strain and the ordinate equal to half the shearing ...
Three-Dimensional Analysis of Strain
Three-Dimensional Analysis of Strain
Three-dimensional strain analysis uses principal stress axes to evaluate deformation in elastic, homogeneous materials. A small cubic element, when ...
Measurements of Strain
Measurements of Strain
Strain measures the deformation or displacement in a material. Normal strain is calculated by comparing lengths before and after a load is applied. A more ...
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