Eigenvalue for maximum shear stress


I found materials using eigenvalue and eigenvector to find the principal stress. but I wonder how can I get the maximum shear stress using Eigenvalue? Thank you!

Soil Mechanics / Geotechnical Rock Mechanics Geophysics Analysis Design Education Research Shallow Foundations Deep Foundations Geotechnical Earthquake Engineering & Soil Dynamics Geotechnical Investigations & In-Situ Testing Ground Improvement Tunneling & Underground Construction

2 Answers

Votes: 0

Mohmad Mohsin Thakur

Eigen Values give us principal stresses. Maximum shear stress would be equal to 1/2 (Major Principal Stress - Minor Principal Stress).


Votes: 0

Mikhail Kholmyansky

From Mohr' circle

tau_max = SQRT( tau^2 + ((sigma_x-sigma_y)/2)^2 ) = SQRT( 32^2 + ((86-28)/2)^2 ) = 43.2