Principal normal stress under uniaxial tension A body is subjected only to a direct tensile stress σ (no other stresses). The maximum normal stress in the body equals:

Introduction / Context:
Principal stresses represent extreme normal stresses at a point. For basic stress states, being able to identify principal values without constructing Mohr’s circle is a key skill in mechanics of materials.

Given Data / Assumptions:

• Only one nonzero stress component: σ_x = σ (tension); σ_y = 0; τ_xy = 0.
• Continuum is homogeneous; small deformations.

Concept / Approach:
Principal stresses for a 2D state satisfy τ_n = 0 on principal planes. With σ_x = σ, σ_y = 0, τ_xy = 0, the principal stresses are simply σ_1 = σ and σ_2 = 0. Therefore, the maximum normal stress equals σ.

Step-by-Step Solution:
General principal stress formula: σ_{1,2} = (σ_x + σ_y)/2 ± sqrt[((σ_x − σ_y)/2)^2 + τ_xy^2].Substitute σ_x = σ, σ_y = 0, τ_xy = 0 → σ_{1,2} = σ/2 ± sqrt[(σ/2)^2] = σ and 0.Hence maximum normal stress = σ.

Verification / Alternative check:
Mohr’s circle reduces to a circle with center at σ/2 on the σ-axis and radius σ/2. The rightmost point corresponds to σ.

Why Other Options Are Wrong:
σ/2 confuses center value with principal maximum; 2σ is impossible without other stresses; zero is only the minor principal stress; dependence on Poisson’s ratio is irrelevant to principal stress magnitude here.

Common Pitfalls:
Mixing true and engineering stress; assuming lateral contraction affects principal stress magnitude; forgetting that shear is zero on principal planes.

Final Answer:
the direct tensile stress σ