What is the Moment of Inertia of a T-Shaped Object?

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SUMMARY

The discussion focuses on calculating the moment of inertia for a T-shaped object using both the parallel axis theorem and a direct equation found on efunda.com. The user provided specific dimensions: b1=100mm, h1=12mm, b2=12mm, h2=75mm, and q=12.643mm. The calculations yielded two different results: 1.4094e-006 m4 using the parallel axis theorem and 7.6247e-006 m4 using the direct equation. The user seeks clarification on the discrepancy between these two methods.

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  • Understanding of moment of inertia calculations
  • Familiarity with the parallel axis theorem
  • Basic knowledge of geometry related to T-shaped objects
  • Experience with dimensional analysis in engineering contexts
NEXT STEPS
  • Review the derivation of the parallel axis theorem in structural engineering
  • Study the specific equation for moment of inertia of T-shaped beams on efunda.com
  • Explore common errors in moment of inertia calculations
  • Learn about software tools for structural analysis, such as AutoCAD or SolidWorks
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Mechanical engineers, civil engineers, and students studying structural analysis who need to calculate the moment of inertia for complex shapes like T-beams.

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h have a T shaped object (2-d) for which i need to find the moment of enertia,
i used a parallel axis theorem, then to check myself i found i site which had a direct equation for it
http://www.efunda.com/designstandards/beams/SquareTbeam.cfm

what i did

b1=100mm
h1=12mm
b2=12mm
h2=75mm
q=12.643mm(the distance from the joint of the 2 shapes to the centroid of the T)

>> ((b1*h1^3)/12)+((b1*h1)*(q+h1/2)^2)+((b2*h2^3)/12)+((b2*h2)*(h2/2-q)^2)

1.4094e-006 m4

using their equation

t=12mm
y=75-12.643=62.357mm
b=100mm
s=12mm
d=87mm

>> (t*y^3+b*(d-y)^3-(b-t)*(d-y-s)^3)/3

7.6247e-006m4


where have i gone wrong here?
 
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sorry posted this in the wrong category
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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