How Is the Centroid of a Composite Area Calculated Incorrectly Here?

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SUMMARY

The discussion centers on the incorrect calculation of the centroid of a composite area in a structural engineering context. The user attempted to compute the centroid using the formula for weighted averages, but arrived at an incorrect result of 215.8 instead of the expected 112. The error stems from miscalculating the Y-bar positions, specifically by not accurately accounting for the vertical distance from the top of the structure to the centroid of each area component.

PREREQUISITES
  • Understanding of composite area calculations in structural engineering
  • Familiarity with centroid and center of mass concepts
  • Knowledge of weighted averages in geometry
  • Proficiency in using structural analysis tools
NEXT STEPS
  • Review the principles of calculating centroids for composite shapes
  • Study the method for determining Y-bar positions in structural components
  • Learn about common mistakes in centroid calculations and how to avoid them
  • Explore software tools for structural analysis that can automate centroid calculations
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Students in structural engineering, civil engineers, and professionals involved in the design and analysis of composite structures.

werson tan
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Homework Statement


As in the photos

Homework Equations

The Attempt at a Solution


my working is
(6.43x10^-3)(310+10) + (11x10^-3)(155) / (6.43x10^-3 +11x10^-3 ) = 215.8 , but the ans is 112 , what's wrong with my working ?
 

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All of the Y-bars are measured from the top of the structure. So the position of the vertical I is 10.2+155
 

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