A thin-walled open Z-section has identical horizontal flanges of width $b$ and a vertical web of height $h$. The shear center of any thin-walled open cross-section having point symmetry (such as an equal-flange Z-section) is located at:

(A) The geometric centroid of the cross-section (midpoint of the vertical web)

(B) The junction between the upper flange and the web

(C) A distance $e = b/2$ outside the web

(D) Infinity along the horizontal principal axis

Answer Key:

Verified in official key

### 1. Strategy & Theoretical Principles By the symmetry theorems of structural mechanics: 1. If a cross-section has an axis of symmetry, the shear center must lie on that axis of symmetry. 2. If a cross-section has two orthogonal axes of symmetry (such as an I-section or rectangular tube), the shear center lies at their intersection, which is the centroid. 3. If a cross-section possesses **point symmetry** (inversion symmetry through the centroid, where for every point $(x, y)$ there is an identical material point at $(-x, -y)$), the shear center must coincide identically with the centroid. ### 2. Analytical Application to Z-Section An equal-flange Z-section has point symmetry about the midpoint of its vertical web. Therefore, its shear center coincides exactly with its centroid at the center of the web. ### 3. Distractor Forensics - Candidates frequently confuse open channel sections (where the shear center lies outside the web) with Z-sections (where point symmetry pins the shear center directly to the centroid). ### 4. Exam Trap & Standard Reference - **Trap Alert:** Remember the golden rule: Point symmetry $\implies$ Shear Center coincides with Centroid. - **Standard Reference:** Megson, T.H.G., *Aircraft Structures for Engineering Students*, Chapter 17.

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