In Mohr’s circle for plane stress (σ on horizontal axis, τ on vertical axis), the horizontal coordinate of the circle’s centre measured from the Y-axis equals which quantity?

Introduction / Context:Mohr’s circle provides a geometric method to transform stresses on inclined planes. Identifying the centre and radius allows quick determination of principal and shear values.

Given Data / Assumptions:

• Plane stress components σx, σy, and τxy are known.
• Mohr’s circle is plotted with σ on the horizontal axis and τ on the vertical axis.
• Centre and radius definitions follow standard conventions.

Concept / Approach:The centre C of Mohr’s circle lies midway between the points representing stresses on two orthogonal faces. Therefore, its σ-coordinate is the average of σx and σy, while its τ-coordinate is zero.

Step-by-Step Solution:

Verification / Alternative check:Analytical stress transformation confirms that principal stresses are at σ = (σx + σy)/2 ± R with τ = 0, reinforcing the centre location.

Why Other Options Are Wrong:Sum or difference alone is not the centre coordinate.Maximum shear is the radius, not the centre abscissa.Zero applies only to special cases (σx = −σy and τxy = 0 does not generally make the centre zero).

Common Pitfalls:Confusing the centre coordinate with the radius; mixing sign conventions for τ that mirror the circle about the σ-axis.

Final Answer:

The average normal stress ((σx + σy) / 2)