Need Verification: Combined Loads Finding Stress

[tangodirt]

Homework Statement

I think I've solved this properly, but if you guys wouldn't mind verifying my work and pointing out any errors (if there are any), it would be much appreciated.

http://img391.imageshack.us/img391/6520/problemvm0.jpg

I've already calculated the equivalent force-couple system at the plane of the elemental stress block, which is shown above. That's completely right, I know of it :). Now, I need to solve for the components of normal and shearing stress associated with that elemental stress block.

Homework Equations

$$\sigma$$_Axial = P / A
$$\sigma$$_Bending = Mc / I
$$\tau$$_Shear = VQ / IT
$$\tau$$_Torque = Tc / J

We already are given:
A = 12.57 in^2
J = 25.13 in^4
I = 12.57 in^2
Q = 5.33 in^3
D = 4 in

The Attempt at a Solution

Using the equations above, I've calculated:

$$\sigma$$_Axial = 477.46 psi
$$\sigma$$_Bending = 12,414.09 psi
$$\tau$$_Shear = 106.10 psi
$$\tau$$_Torque = 5729.58 psi

Did this all with excel :).

Do those answers sound right? The next step which I am having difficulty with is calculating the $$\sigma$$_X, $$\sigma$$_Y, and $$\tau$$_XY. I understand that I'm just using super position for this, but I'm not sure whether to add or subtract the two.

Thanks!

 

[KataKoniK]

Hello,

First of all, great job on calculating the equivalent force-couple system at the plane of the elemental stress block! Your calculations for the normal and shearing stress components also seem to be correct.

To calculate the components of normal and shearing stress at the elemental stress block, you can use the following equations:

\sigmaX = \sigmaAxial + \sigmaBending
\sigmaY = \sigmaAxial - \sigmaBending
\tauXY = \tauShear + \tauTorque

In this case, since the bending stress is causing compression, you would add the bending stress to the axial stress to get the \sigmaX component. Similarly, you would subtract the bending stress from the axial stress to get the \sigmaY component. As for the shearing stress, you would add the shear stress and the torque stress together to get the \tauXY component.

I hope this helps and let me know if you have any further questions. Keep up the good work!

 

[Mene]

I would first like to commend you for showing your work and seeking verification on your solution. It is always important to double check calculations and make sure that all assumptions and equations are correct.

In terms of your solution, the values you have calculated seem reasonable and are in the correct units. However, without knowing the specific problem and its context, I cannot confirm if they are completely accurate.

To calculate the components of normal and shearing stress, you are correct in using the principle of superposition. This means that you would add the normal and shearing stresses from the axial and bending loads.

However, it is important to note that the axial and bending stresses are acting in different directions (tension and compression), so they would have opposite signs. This means that when adding the two stresses, you would need to take into account their direction and make sure they are acting in the same direction.

Overall, your approach and calculations seem correct, but I would suggest double checking your answers and making sure to include the direction of the stresses in your solution.

 

[piercas]

Hello,

Thank you for sharing your work and asking for verification. Your calculations for the normal and shearing stress components seem correct based on the given equations and values. However, it would be helpful to see your work and the specific steps you took to arrive at these values in order to provide more detailed feedback.

As for calculating the \sigmaX, \sigmaY, and \tauXY, you are correct that you will need to use superposition. The key here is to remember that the normal stresses are additive while the shearing stresses are subtractive. This means that \sigmaX and \sigmaY will be the sum of the axial and bending stresses, while \tauXY will be the difference between the shearing stresses caused by the axial and bending loads.

I hope this helps and please let me know if you have any additional questions or concerns. Keep up the good work!