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In Mohr's circle method, compressive direct stress is represented on ____
Positive x-axis
Positive y-axis
Negative x-axis
Negative y-axis
Negative x-axis
In Mohr's circle, compressive direct stress is plotted on the negative x-axis by engineering convention. Tensile stress is plotted on the positive x-axis, establishing the standard sign convention for stress representation.
In Mohr's circle, compressive direct stress is plotted on the negative x-axis by engineering convention. Tensile stress is plotted on the positive x-axis, establishing the standard sign convention for stress representation.
Center of circle = (sigmaxโ + sigmayโ) / 2 โ average normal stress
Radius of circle = sqrt[((sigmaxโ - sigmayโ) / 2)^2 + tauxyโยฒ] โ represents stress variation
sigma1โ, sigma2โ = Center ยฑ Radius โ principal stresses
Mohr's circle is a graphical method for analyzing 2D stress states. The horizontal axis represents normal stress (sigma), with tensile stress (positive) on the right and compressive stress (negative) on the left. The vertical axis represents shear stress (tau). This sign convention allows engineers to visualize all possible stress combinations on a circular diagram, with the circle's center, radius, and points indicating principal stresses and their magnitudes.
Compressive stress is negative and plotted leftward on the x-axis (negative x-axis)
Tensile stress is positive and plotted rightward on the x-axis (positive x-axis)
Shear stress is plotted on the vertical y-axis (positive upward, negative downward)
The horizontal x-axis is also called the 'normal stress axis' or 'sigma axis'
This sign convention follows standard mechanics of materials and is universal in structural analysis
Provides quick visual identification of principal stresses and maximum shear stress
Eliminates need for complex calculations in stress transformation
Graphically shows all possible stress states for a given loading condition
Limited to 2D stress analysis (cannot directly represent 3D stress tensors)
Requires accurate plotting for precise results; computational methods are preferred for critical designs
Manual construction is time-consuming in modern engineering practice
Analyzing stress states in beams, columns, and plate structures
Finding principal stresses and maximum shear stresses in 2D loading conditions
Determining failure criteria and safety margins in structural design
Quality control and design verification in civil and mechanical engineering
| Feature | Positive x-axis | Negative x-axis |
|---|---|---|
Stress Type | Tensile Stress | Compressive Stress |
Direction on Mohr's Circle | Right side of circle | Left side of circle |
Sign Convention | Positive (+) | Negative (-) |
| Parameter | Detail |
|---|---|
| Also Known As | Stress circle, Mohr's stress circle, graphical method for stress transformation |
| Developed By | Christian Otto Mohr (German engineer) in 1882 |
| Axis Convention | Horizontal X-axis = Normal stress (sigma); Vertical Y-axis = Shear stress (tau). Compressive stress is negative, tensile is positive. |
| Principal Stresses | Located at the rightmost (maximum, sigma1โ) and leftmost (minimum, sigma3โ or sigma2โ) points where the circle intersects the x-axis |
| Maximum Shear Stress | Equals the radius of the Mohr's circle; taumaxโ = (sigma1โ - sigma3โ) / 2 |
| Wrong Options Explained | A (Positive x-axis) = Represents tensile stress, not compressive; B (Positive y-axis) = Represents positive shear stress, not normal stress; D (Negative y-axis) = Represents negative shear stress, not compressive normal stress |
C is correct โ Compressive direct stress is represented on the negative x-axis in Mohr's circle following the standard engineering sign convention where compression is negative and tension is positive.
Mohr's circle is closely related to topics on principal stresses, Lame's equations, and failure theories (Von Mises, Tresca). Understanding the sign convention here is essential for subsequent topics in structural mechanics and soil mechanics (earth pressure theories).