Stress on Inclined Section PQ due to Uniaxial Stress
Consider a rectangular beam and we have to calculate the stress on an inclined section as shown in the figure.
Induced stress is divided into two components which are given as-
Normal stress
Normal Stress on an inclined section.
Tangential stress
Shear Stress on an inclined section.
Stress on Inclined Section PQ due to Shear Stress
Induced stress is divided into two components which are given as -
Normal stress
Normal Stress on an inclined section.
Tangential Stress
Shear Stress on an inclined section.
Stress on Inclined Section PQ due to combination of Axial Stress and Shear Stress
Induced stress is divided into two components which are given as -
Normal stress
Normal Stress on an inclined section.
Tangential stress
Shear Stress on an inclined section.
Principal Stresses and Principal Planes
The plane carrying the maximum normal stress is called the major principal plane and normal stress is called major principal stress.
The plane carrying the minimum normal stress is known as minor principal plane and normal stress is called minor principal stress.
Major principal stress
Minor principal stress
Major & Minor principal plane angle
Note: Across maximum normal stresses acting in plane shear stresses are zero.Computation of Principal Stress from Principal Strain
The three stresses normal to shear principal planes are called principal stress, while a plane at which shear strain is zero is called principal strain.
For two-dimensional stress system, σ3 = 0
Maximum Shear Stress
The maximum shear stress is equal of one half the difference between the largest and smallest principal stresses and acts on the plane that bisects the angle between the directions of the largest and smallest principal stress, i.e. the plane of the maximum shear stress is oriented 45° from the principal stress planes.
Principal Strain
For two-dimensional strain system,
Where, εx = Strain in x-direction εy = Strain in y-direction
γxy = Shearing strain
Maximum Shear Strain
The maximum shear strain also contains normal strain which is given as
Strain Measuring Method - 45° Strain Rosette or Rectangular Strain Rosette
Rectangular strains Rosette is inclined 45° to each other
Principal strains can be calculated from above equations.
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