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    "Ix = b h³/12 and Iy = h b³/12",
    "Sx = b h²/6 and Sy = h b²/6",
    "Not a composite section, a circle, bending stress, or a plastic modulus"
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    "missing b or h → MISSING_REQUIRED_INPUT",
    "b ≤ 0 or h ≤ 0 → VALUE_MUST_BE_POSITIVE"
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      "title": "Hibbeler, Engineering Mechanics: Statics",
      "section": "Moments of inertia — rectangular area",
      "supports": "The centroidal moments of a rectangle are b h³/12 and h b³/12.",
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        "Iy": 4,
        "Sx": 12,
        "Sy": 4,
        "kx": 1.7320508075688772,
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        "area": 12,
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        "Iy": 4,
        "kx": 1.7320508075688772,
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      },
      "tol": 1e-12
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        "b": 1,
        "h": 1
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      "expect": {
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        "Ix": 0.08333333333333333,
        "Iy": 0.08333333333333333,
        "Sx": 0.16666666666666666,
        "Sy": 0.16666666666666666
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        "b": 1,
        "h": 1,
        "area": 1,
        "Ix": 0.08333333333333333,
        "Iy": 0.08333333333333333,
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        "ky": 0.28867513459481287,
        "Sx": 0.16666666666666666,
        "Sy": 0.16666666666666666,
        "solver": "area moment + section modulus",
        "convention": "b is the width parallel to x. h is the height parallel to y. Centroidal Ix = b h³/12 and Iy = h b³/12. Sx = b h²/6 and Sy = h b²/6. A composite section is the area-moment page. A circle is its own page."
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        "area": 12
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