Shear centre locations – identify the single incorrect statement Consider the following statements about the shear centre (elastic center) of open thin-walled sections. Which one is incorrect?
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AThe shear centre is the point through which the resultant shear must pass to produce no twisting of the section
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BFor standard rolled channel sections, the shear centre lies on the horizontal line through the centroid but outside the web, on the open side
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CFor equal-leg angle sections, the shear centre lies outside the section along the bisector of the legs (away from the centroid)
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DFor T-sections, the shear centre always coincides exactly with the centroid of the section
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ENone of these
Answer
Correct Answer: For T-sections, the shear centre always coincides exactly with the centroid of the section
Explanation
Introduction / Context:The shear centre (elastic centre) is crucial when transverse shear is applied. Loading away from this point induces twist in open sections. Designers must know where it lies for channels, angles, tees, and I-sections.
Given Data / Assumptions:
- Open, thin-walled prismatic sections.
- Shear flow derived from elementary bending theory.
- No warping restraint and Saint-Venant torsion assumptions.
Concept / Approach:By definition, the shear centre is where the resultant shear force must act to cause bending without twist. For doubly-symmetric sections (e.g., I or rectangular), it coincides with the centroid. For singly-symmetric sections (channel, tee), it lies on the axis of symmetry but generally not at the centroid. For unequal or angle sections (no symmetry axes coinciding with shear), it lies outside the material, often along the angle bisector.
Step-by-Step Solution:(a) Matches the definition → correct.(b) Channels: shear centre outside web on symmetry line → correct.(c) Equal angles: shear centre outside along leg bisector → correct.(d) T-sections: only one symmetry axis; shear centre lies on that axis but not necessarily at the centroid → statement is incorrect.
Verification / Alternative check:Handbooks list e-values for channels and tees showing offsets from centroid; for tees, the shear-centre offset depends on flange/web proportions.
Why Other Options Are Wrong:
- (a)–(c) are standard results for open sections.
- (e) cannot be chosen because one specific incorrect statement exists, namely (d).
Common Pitfalls:Assuming “centroid = shear centre”; this is true only for doubly symmetric sections or closed thin-walled sections with uniform thickness.
Final Answer:For T-sections, the shear centre always coincides exactly with the centroid of the section