Calculating stress given torque

In summary, the person is trying to determine the stress on member AB, given a load of 250lbs at point C. They mention there is a torque of 250ft-lbs at point B, but they are unsure how to translate that into stress on member AB. Their ultimate goal is to size member AB so that the stress stays below the yield strength, but they are not sure how to calculate the stress. They ask for help and later provide their own solution, which involves finding the bending stress on AB as it is a cantilever.
  • #1
InterestedGuy
4
0
I'm trying to figure out the stress on member AB in the attached diagram, given a load of 250lbs at point C.

Obviously there is a torque of 250ft-lbs at point B, but I'm not sure how to translate that into stress on member AB? My end goal is to size member AB so that the stress is stays below the yield strength, but I'm not sure how the calculate the stress.

Can anyone help?

Thanks,

Edit:

I've been thinking about this and I think the answer is pretty simple. Let me know if this is correct.

I essentially have a force vector AC. 250lbs represents the x component of this force. Thus the y component is 83.3 lbs at point B. From there I can figure out the bending stress on AB as it is essentially a cantilever.

Does that make sense?
 

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  • #3
haruspex said:
I see no diagram.

Not sure what happened there, I've added the diagram to my post.
 
  • #4
The statically equivalent loads on member AB would be an axial force of 250 lbs at B directed from B to A and a couple of 250 ft-lbs clockwise located at B. I don't think you can suppose an equivalent force vector acting thru AC.
 
  • #5


Hello,

Your thinking is on the right track. To calculate the stress on member AB, you will need to use the formula for bending stress, which is stress = (M * c) / I, where M is the bending moment, c is the distance from the neutral axis (in this case, the distance from point B to point A), and I is the moment of inertia of the cross-sectional area of the member.

In this case, the bending moment (M) is equal to the torque (T) at point B multiplied by the distance from B to A, which is the length of member AB. So M = T * length of AB.

To calculate the moment of inertia (I), you will need to know the cross-sectional area of member AB and its moment of inertia about its centroid. Once you have that information, you can use the formula for moment of inertia (I = (bh^3)/12) to calculate I.

Once you have all the necessary values, you can plug them into the formula for bending stress to calculate the stress on member AB. Make sure to also check the yield strength of the material you are using for member AB to ensure that it can withstand the calculated stress.

I hope this helps. Let me know if you have any further questions. Best of luck with your calculations!
 

1. What is torque and how is it related to stress?

Torque is a measure of the rotational force applied to an object. It is related to stress because when a torque is applied to an object, it causes the object to experience internal forces that can lead to deformation and stress.

2. How do you calculate stress given torque?

To calculate stress given torque, you need to know the distance from the axis of rotation to the point where the torque is applied, as well as the moment of inertia of the object. The stress can then be calculated using the formula stress = torque * distance / moment of inertia.

3. What units are used for torque and stress?

Torque is typically measured in units of newton-meters (Nm) or foot-pounds (ft-lb), while stress is typically measured in units of pascals (Pa) or pounds per square inch (psi).

4. How does the angle of the applied torque affect stress?

The angle of the applied torque can affect the magnitude and direction of the resulting stress. For example, if the torque is applied perpendicular to the axis of rotation, it will cause a direct tensile or compressive stress. If the torque is applied at an angle, it will cause a combination of tensile, compressive, and shear stresses.

5. What are some real-world applications of calculating stress given torque?

Calculating stress given torque is important in many engineering and physics applications, such as designing and analyzing structures that experience rotational forces, such as bridges and cranes. It is also used in the development of machinery and equipment that require precise torque specifications, such as engines and turbines.

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