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7.5: Identify Constraints

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    142401

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    7.5 Step 2 — Identify Constraints and Requirements

    Constraints define the space within which acceptable designs live. If you ignore them, you are not doing engineering.

    Hard and soft constraints in engineering design.
    Type Definition Examples
    Hard constraint Must never be violated SF ≥ 2; power rating not exceeded; bridge must span 50 cm
    Soft constraint A preference — violation may be acceptable with justification Minimize mass; prefer standard component values; stay under cost target

    Hard constraints come first. Every design candidate must satisfy all hard constraints before it is even considered for evaluation.

    For the bracket thread, the constraints yield a design space. Given \(F = 500 \text{ N}\), \(\sigma_\text{allow} = 80 \text{ MPa}\), SF ≥ 2:

    \[ \sigma_\text{work} = \frac{\sigma_\text{allow}}{\text{SF}} = \frac{80 \text{ MPa}}{2} = 40 \text{ MPa} \nonumber \] \[ A_\min = \frac{F}{\sigma_\text{work}} = \frac{500 \text{ N}}{40 \times 10^6 \text{ Pa}} = 1.25 \times 10^{-5} \text{ m}^2 = 12.5 \text{ mm}^2 \nonumber \]

    Any bracket with cross-sectional area below 12.5 mm² violates the hard constraint and is eliminated before any other evaluation.

    ✓ Worked Example 7.1 — Constraint Calculation

    Problem: A rod supports 2000 N. Allowable stress = 120 MPa. Required SF = 3. Find minimum area.

    \[ \sigma_\text{work} = \frac{120 \text{ MPa}}{3} = 40 \text{ MPa} \nonumber \] \[ A_\min = \frac{2000 \text{ N}}{40 \times 10^6 \text{ Pa}} = 5.0 \times 10^{-5} \text{ m}^2 = 50 \text{ mm}^2 \nonumber \]

    Interpretation: Any cross-section below 50 mm² is automatically eliminated. A 5 mm × 10 mm section (50 mm²) exactly meets the minimum; a 6 mm × 10 mm section (60 mm²) provides additional margin.

    Practice 7.2 — Write a Constraint Statement

    A resistor is rated at 0.25 W. Write a constraint statement using \(P = V^2/R\) that specifies the minimum resistance for a 9 V source.


    This page titled 7.5: Identify Constraints was last modified on Thu, 24 Sep 2026 17:35:38 GMT and is shared under a CC BY-NC license and was authored, remixed, and/or curated by .

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