CE Calculators > Stress Transformation > Maximum In-plane Shear Stress and its orientation

Maximum In-plane Shear Stress Calculator

Maximum In-plane Shear Stresses This calculator is for finding maximum and minimum in-plane shear stress(τmax and τmin) and the angles of orientation (θmax and θmin) of the planes. It also calculates the average normal stress σs acting on the planes of maximum shear stress.
Sign Convention: Positive face of a plane is that on which the outward normal acts in the positive coordinate direction, otherwise it is negative face. Normal Tensile stresses are taken as positive and normal compressive stresses are negative. Shear stress on a plane is taken as positive if it acts in the positive coordinate direction on a positive face, or in a negative coordinate direction on a negative face. Otherwise it is taken as negative. Angle of orientation (θ) is -ve for clock-wise and +ve for anti-clockwise rotation with reference to the positive x-axis

Please note than the maximum and minimum shear stresses are equal in magnitude but opposite in sign. Planes of maximum and minimum shear stress are at 90 degrees to each other.

By default this calculator is using the units of stress as MPa, but other units N/mm2, kN/m2, ksi, psi etc. can also be used without affecting the results.

This calculator can also be used for finding maximum and minimum strain because the equations are same in that case also just by ignoring the units as strains are dimensionless.

Please refer to the figure and enter the required values in the form given below and then click "Calculate"

INPUT VALUES
Normal Stress σx (MPa):
Normal Stress σy (MPa):
Shear Stress τxy (MPa):

all the values are entered

OUTPUT RESULTS
Maximum Shear Stress τmax (MPa):
Angle θmax (degree):
Minimum Shear Stress τmin (MPa):
Angle θmin (degree):
Average Normal Stress σs (MPa):

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