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Stress in S.I. units: select the correct unit for normal or shear stress.

Difficulty: Easy

Correct Answer: Newton per sq m

Explanation:


Introduction / Context:
Stress is force per unit area and underpins the analysis of bars, beams, columns, shells, and pressure vessels. While many older texts used mass-based units (kgf/cm^2), the S.I. standardizes stress as pascals (Pa = N/m^2), enabling consistent integration with material properties like modulus (also in Pa).


Given Data / Assumptions:

  • Stress = Force / Area.
  • Force in S.I. is the newton (N).
  • Area uses square metres (m^2) in S.I.


Concept / Approach:
By definition, stress sigma or tau has the unit N/m^2 (pascal). Submultiples like MPa (10^6 Pa) and GPa (10^9 Pa) are common in structural design. Using “kg per square cm” is dimensionally inconsistent for stress in S.I. because kilogram is mass, not force; if using legacy gravitational units, “kgf/cm^2” would still not be S.I.


Step-by-Step Solution:

Write sigma = F / A.Insert S.I. units: F → N; A → m^2; therefore sigma unit = N/m^2.Relate to common design numbers: structural steels often have yield strengths ~250–500 MPa (i.e., 250 × 10^6 to 500 × 10^6 Pa).


Verification / Alternative check:

Check dimensional consistency with Hooke’s law: E (Pa) = stress/strain; strain is dimensionless, so stress must be in Pa as well.


Why Other Options Are Wrong:

kg per sq cm / kg per sq mm: mass/area, not force/area.N per sq mm / N per sq cm: although convertible to S.I., the question asks for S.I. unit, which is N/m^2 (Pa) in base form.


Common Pitfalls:

Confusing kgf with kg and mixing legacy units with S.I.Forgetting that MPa and GPa are standard multiples in engineering practice.


Final Answer:

Newton per sq m
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