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Mohr’s Circle Mohr’s Circle The graphical method solution of complex stress problems using Mohr's circle is a very powerful technique, since all the information relating to any plane within the stressed elements are contained in the single construction It provides the convenient and quick solution which is less prone to arithmetical errors and is highly recommended. Mohr’s Circle What is Stress The force of resistance offered by a body against the deformation is called the stress. The external force acting on the body is called the load. The load is applied on the body while the stress is induced in the material of the body Mohr’s Circle Type of stress • Normal stress • Shear stress • Bending stress Mohr’s Circle Principal Stress Any structural member is subjected to different types of stresses such as normal or shear stresses simultaneously. Hence it is necessary to find out the region where the effect of these stresses will be critical from the design point of view When such stresses act at a point in a stressed material, there always exist three principal planes, and the normal stresses acting on them are called principal stresses One of these principal stresses is the greatest normal stress and one of them is the least normal stress Mohr’s Circle Principal Stress Mohr’s Circle Mohr’s Circle Mohr’s circle is a graphical construction making it possible to determine the stresses in a cross section if the principal stresses are known Click to view Image Mohr’s Circle Mohr circle for like forces Click to view Image Mohr’s Circle Mohr circle for unlike forces Click to view Image Mohr’s Circle Unequal Like Principal Stress • Let P1 and P2 be two unequal like principal stresses. Let it be required to find the resultant stress on a plane inclined at an angle θ with the major principal plane. • An axis OX set off OA = P1 and OB =P2 Click to view Image Mohr’s Circle Principal Stress and Stress transformation using Mohr’s Circle Consider a rectangular block ABCD whose thickness perpendicular to the plane of the paper is unity. Here the block be subjected to principal stresses p1 and p2. Consider any oblique sectional plane BE at an angle θ with the principal plane BA Mohr’s Circle Principal Stress and Stress transformation using Mohr’s Circle Click to view Image