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