6e. Shape  (SSES Ch. 6.5)
Section Modulus Shape Factor
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Section Modulus

The section about the z-axis is:

where Iz is the moment of inertia about the z-axis, and cz = ymax is the distance from the neutral axis to the material furthest from the z-axis. Two geometric properties of the cross-section are conveniently combined into one property.

The maximum bending stress due to a moment about the z-axis can the be written:

Likewise, for bending about the y-axis: Zy = Iy/cy.

Shape Factor

The shape factor concept was developed by Prof. M.F. Ashby of Cambridge University (see his work Materials Selection in Mechanical Design).

The shape factor for elastic bending (fBe) - i.e., for bending stiffness - is defined as:

Since I is the geometric property that governs beam stiffness, and A is proportional to the weight of the beam, the shape factor is a measure of the effectiveness (stiffness per weight) of a beam. The greater the value of f, the lighter the beam for a certain given value of I.

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Updated: 05/25/09 DJD