Finding second moment of area using Euler's theory?

In summary, the speaker is a HND student in Aeronautical Engineering who needs help with finding the second moment of area using Euler's theory. They provide the equation for Euler's theory and their own calculation for I. They also mention the values for P, L, and E, and their struggle with converting I into cm4. They receive advice to solve the equation for m^4 and then convert it into cm^4 by multiplying by 10^4, and to double check the formula for I in their textbook or lecture notes.
  • #1
dave.hills
1
0
Hi, I have just started a HND in Aeronautical Engineering and its been awhile since I have done any maths, need help with finding the second moment of area using Euler's theory!

I have Euler's equation : Force (P)= (pi squared (pi2)) * (modulus of elasticity (E)) * (second moment of area (I)) / (effective length squared (L2))

I then got I = P*L2/pi2*E (is that correct?)

P = 170KN - factor safety of 3 needed - 510KN
L = 8m
E = 200 GPa

I am struggling with the units, I need I in cm4 and can't work it out!

Thanks
 
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  • #2
solve it for m^4 by taking P=170*1000N; L=8m, E=200*10^9Pa. You will get ur answer in m^4. Convert it into cm^4 by dividing it by 100^4. Also check the question carefully to make sure ure using the correct formula for I as it is different for different euler conditions which u'll find in ur textbook or lecture notes.
 
  • #3
wsaleem said:
solve it for m^4 by taking P=170*1000N; L=8m, E=200*10^9Pa. You will get ur answer in m^4. Convert it into cm^4 by dividing it by 100^4. Also check the question carefully to make sure ure using the correct formula for I as it is different for different euler conditions which u'll find in ur textbook or lecture notes.

sorry my bad make the conversion by multiplying by 10^4 instead of dividing
 

FAQ: Finding second moment of area using Euler's theory?

What is the second moment of area?

The second moment of area, also known as the moment of inertia, is a measure of an object's resistance to bending. It is calculated by integrating the product of a shape's cross-sectional area and the square of its distance from a reference axis.

How is the second moment of area calculated using Euler's theory?

Euler's theory, also known as the parallel axis theorem, states that the second moment of area for a shape can be found by adding the second moment of area for a parallel axis passing through the centroid of the shape and the product of the shape's cross-sectional area and the square of the distance between the two axes.

What are the practical applications of finding the second moment of area?

Calculating the second moment of area is important in many engineering and scientific fields, such as structural analysis, material strength, and fluid mechanics. It is used to determine the bending stress and deflection of beams, as well as the torsional stress and strain in shafts.

What factors affect the second moment of area?

The second moment of area is influenced by the shape and size of an object's cross section, as well as the location and orientation of the reference axis. In general, a larger cross-sectional area and a greater distance from the reference axis will result in a higher second moment of area.

Are there any limitations to using Euler's theory for calculating the second moment of area?

While Euler's theory is a useful and commonly used method for finding the second moment of area, it is not always accurate for complex or irregular shapes. In these cases, more advanced mathematical methods such as integration or finite element analysis may be necessary.

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