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The graphical method of Mohr's circle represents shear stress (╧Д) on ______
X - axis
Y - axis
Z - axis
None of the above
Y - axis
In Mohr's circle representation of stress, normal stresses (\sigma$$) are plotted along the horizontal axis (X-axis), while shear stresses (╧Д) are plotted along the vertical axis (Y-axis). This graphical construction allows determination of normal and shear stress components on any plane at a given point in a stressed body.
IS 456:2000 / Standard Strength of Materials Specifications
In Mohr's circle representation of stress, normal stresses (\sigma$$) are plotted along the horizontal axis (X-axis), while shear stresses (╧Д) are plotted along the vertical axis (Y-axis). This graphical construction allows determination of normal and shear stress components on any plane at a given point in a stressed body.
╧Г╬╕тАЛ=2╧ГxтАЛ+╧ГyтАЛтАЛ+2╧ГxтАЛтИТ╧ГyтАЛтАЛcos2╬╕+╧ДxyтАЛsin2╬╕ тАФ Normal stress on an inclined plane
╧Д╬╕тАЛ=тИТ2╧ГxтАЛтИТ╧ГyтАЛтАЛsin2╬╕+╧ДxyтАЛcos2╬╕ тАФ Shear stress on an inclined plane
R=(2╧ГxтАЛтИТ╧ГyтАЛтАЛ)2+╧Дxy2тАЛтАЛ тАФ Radius of Mohr's circle (Maximum Shear Stress ╧ДmaxтАЛ)
Mohr's circle transforms the two-dimensional stress transformation equations into the geometric equation of a circle. Points on the circumference correspond to normal and shear stress components on planes rotated by an angle ╬╕ relative to the principal planes. The coordinates of any point on the circle are (╧Г,╧Д).
Normal stress (╧Г) is represented on the horizontal axis (X-axis).
Shear stress (╧Д) is represented on the vertical axis (Y-axis).
The center of Mohr's circle lies on the X-axis at (╧ГavgтАЛ,0)=(2╧ГxтАЛ+╧ГyтАЛтАЛ,0).
The radius of the circle is equal to the maximum shear stress ╧ДmaxтАЛ.
Provides a simple visual tool to analyze complex two-dimensional stress states without solving transformation equations analytically.
Easily identifies principal stresses and maximum shear stresses along with their directions.
Less precise compared to analytical methods due to graphical plotting limitations.
Primarily designed for 2D plane stress/plane strain problems and becomes complex when extended to 3D stress states.
Determination of principal stresses and principal planes in structural components.
Soil mechanics and geotechnical engineering to represent failure envelopes (Mohr-Coulomb theory).
Tensile normal stresses are usually plotted as positive on the right side of the origin along the X-axis.
Option A is incorrect because the X-axis represents Normal Stress (╧Г).
Option C is incorrect because Mohr's circle in 2D is plotted on a 2D Cartesian coordinate plane (X-Y).
B is correct тАФ Shear stress (╧Д) is represented on the vertical axis (Y-axis) in Mohr's circle.
Remember the axis convention: 'N' in Normal aligns with X-axis (Horizontal), while Shear (╧Д)goes vertically along the Y-axis. The radius of Mohr's circle directly gives the maximum shear stress (╧Д_{max}).