Find Shear Centre of Cross Sections

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SUMMARY

The discussion focuses on locating the shear center of specific cross sections using the shear formula τ=VQ/IT. Participants detail the process of calculating the moment and shear flow for various geometries, emphasizing the importance of determining the moment of inertia (I) through the equation I=2(I1) + 2(I2) + 2(I3) + I4. The challenge arises in applying these principles to circular cross sections, where an elemental length of the circumference is analyzed. Clear steps are provided for both sections, though additional guidance is sought for the circular geometry.

PREREQUISITES
  • Understanding of shear flow and shear center concepts
  • Familiarity with the shear formula τ=VQ/IT
  • Knowledge of moment of inertia calculations for composite shapes
  • Basic principles of geometry related to circular sections
NEXT STEPS
  • Study the derivation and application of the shear formula τ=VQ/IT
  • Learn how to calculate the moment of inertia for various cross-sectional shapes
  • Explore methods for determining the shear center in complex geometries
  • Investigate the analysis of circular cross sections using elemental calculus
USEFUL FOR

Mechanical engineers, structural engineers, and students studying mechanics of materials who are involved in analyzing shear forces and moments in cross-sectional geometries.

womanengineer
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Please Help.
Trying my best


Homework Statement



Locate the Shear Center of the Cross Sections Below:

1. http://tinypic.com/r/98xfd3/5
2. http://tinypic.com/r/15s4hfk/5

Homework Equations



τ=VQ/IT


The Attempt at a Solution



1.
Moment = O
Solve for Ve


τ=VQ/IT
Solve for τ

For each section
V=∫τtdy

Find I
I=2(I1) + 2(I2) + 2(I3) I4
solve for I
solve for e


Do not know how to start 2.
 
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For the circular part, consider a radius angle theta with the horizontal. Then consider an elemental length of the circumference delta s subtending an angle delta theta at the centre.
 

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