Question about max stress on circular cross section with two moments

In summary, two perpendicular bending moments will cause the highest stress to be located at the intersection of y and z-axis.
  • #1
grotiare
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Homework Statement
This is more of a conceptual understanding. HW problems given do not deal with this specific scenario
Relevant Equations
σmax = (M*c)/I
I couldn't fit in the title, but this is with a hollow circular cross section

So currently I am trying to figure what occurs when two, perpendicular bending moments are applied to a hollow circular cross section (one about the z axis, and the other about y). I know that if I was dealing with a square cross-section, the stress caused by bending moment will be greatest at the corners and you simply add the max bending stress caused by each moment. But, for a circular cross section, I am unsure of the location of when the stresses are greatest. I attached a photo of what I am visualizing, thanks.
 

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  • #2
For a linear-elastic, prismatic body with symmetric cross-section, the normal stress varies linearly with the distance from the neutral axis and the flexure formula is simply sigma=M*y/I... Just as in the case of a rectangular cross-section, the two resulting sets of normal stresses (from the applied moments) can simply be added together - or subtracted if, for instance, one produces compression and the other tension...

1627408880203.png


Assuming Mz=My and Iz=Iy, the highest stress would occur where y+z is a maximum... Without thinking too much about it, I would expect this to occur at 45 degrees.
 
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  • #3
Certain amount of those two moments will cancel each other and you will have one single equivalent moment acting on your circular section.
 
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  • #4
It is best to find the resultant moment and use the radius of the circle as the c value. The angle of the resultant moment can also be calculated using vector analysis.
 
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  • #5
Thanks guys for all the tips! I figured it out shortly after, but yes like what everyone above said I had to find the resultant moment of both, which can simply be found be treating the two moments as vectors and utilizing magnitude formula sqrt(x^2 +y^2) to get the magnitude, and then plugging that resultant magnitude into the stress from bending moment formula.
 
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What is the formula for calculating the maximum stress on a circular cross section with two moments?

The formula for calculating the maximum stress on a circular cross section with two moments is σmax = (M1 + M2)/I, where σmax is the maximum stress, M1 and M2 are the applied moments, and I is the moment of inertia of the cross section.

What is the significance of calculating the maximum stress on a circular cross section with two moments?

Calculating the maximum stress on a circular cross section with two moments is important in determining the structural integrity and stability of a circular component under loading conditions. It helps in identifying potential failure points and designing for optimal strength and safety.

How do I determine the moment of inertia of a circular cross section?

The moment of inertia of a circular cross section can be calculated using the formula I = πr^4/4, where r is the radius of the circular cross section. Alternatively, it can also be found in standard tables or by using computer-aided design (CAD) software.

What factors can affect the maximum stress on a circular cross section with two moments?

The maximum stress on a circular cross section with two moments can be affected by various factors such as the magnitude and direction of the applied moments, the material properties of the cross section, and the geometry of the cross section. Other factors like temperature, loading rate, and environmental conditions may also play a role.

Are there any limitations to the formula for calculating the maximum stress on a circular cross section with two moments?

Yes, the formula for calculating the maximum stress on a circular cross section with two moments assumes that the material is homogeneous, isotropic, and follows Hooke's law. It also assumes that the cross section is perfectly circular and the applied moments are acting in the same plane. Real-world structures may have more complex loading conditions and material properties, which may require more advanced analysis methods.

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