A Review of Shear Stress Sign Convention in Interpreting Mohr's Circle Using the Pole of Planes Method

Abstract

The pole of planes method is a popular technique for interpreting Mohr’s circle to determine the stresses (normal and shear) on planes of differing rotations in 2-D space. A survey of undergraduate textbooks on soil mechanics shows differing viewpoints on the sign convention for interpreting the shear stresses. This paper makes a rigorous evaluation of the consequences of using a clockwise (CW) or counterclockwise (CCW) positive sign convention for the proper interpretation of Mohr’s circle of stresses using the pole of planes method. In either sign convention case, the shear stress axis is considered positive upwards while the normal stress axis is considered positive to the right. It was found that if the shear stresses acting on an element are considered CW positive, the resulting stresses found on a rotated plane do not satisfy static equilibrium. However, the stresses determined using a CCW positive sign convention do satisfy static equilibrium. Hence, when interpreting Mohr’s circle with the Pole method, the use of compression positive normal stresses must also use a CCW (right-hand rule) sign convention for shear stresses.