Showing resultant stresses on a volume element

In summary, the conversation is about a person asking for help on a combined loadings question involving a 60 mm diameter rod. They are able to do the calculations for normal and shear stresses, but are unsure of how to show the resultant stresses on a volume element. They also mention that a diagram would be helpful in getting feedback. Another person suggests looking up the definition and direction of normal and shear stresses in relation to the coordinate system used in the problem.
  • #1
Mairi
5
0
Me again, (this is what happens when you make a designer do mechanics, and give her a lecturer she doesn't understand :P ).

I'm stuck on a combined loadings question. This is the question:

"The 60 mm diameter rod (fixed at end C on the wall) is subjected to the loads shown.
1) Transform all the loads (forces and moments) to the centre of section A-B, determine the values, and draw them on a graph clearly showing the directions of coordinate axes and all loads
2) Calculate the normal stresses at point A, caused by the normal force, by the bending moments, and by the combined loading respectively
3) Calculate the shear stresses at point A, caused by the shear forces, by the torsional moment, and by the combined loading respectively
4) Show the final resultant stresses at point A on a volume element
"

I can do all the normal/shear stress sections, I've just got no idea how to show the resultant stresses on a volume element!

I've got normal stress at A as being 9.71MPa, shear stresses ([itex]\tau[/itex]zx) at A as 2.15MPa. I'm not sure how to split this up into σx, σy and itex]\tau[/itex]xy, which is how I'm used to seeing elements.

Any help with how I go about this would be greatly appreciated!
 
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  • #2
If you attach a diagram showing the loading of the beam, you may get some feedback.
 
  • #3
Yeah, a diagram always helps. You pretty much answered your own question though. You have NORMAL stresses and SHEAR stresses. Look up the definition of these and the direction they act accroding to the coordinate system you are using in the problem.
 

1. What is the purpose of showing resultant stresses on a volume element?

The purpose of showing resultant stresses on a volume element is to understand the distribution and magnitude of internal stresses within a material. This information is crucial for analyzing the structural integrity and performance of a material under different loading conditions.

2. How are resultant stresses on a volume element calculated?

Resultant stresses on a volume element are calculated using principles of mechanics and mathematical equations, such as the Cauchy stress tensor. They take into account the external forces acting on the material, its geometry, and its material properties.

3. What factors can affect the resultant stresses on a volume element?

The resultant stresses on a volume element can be affected by a variety of factors, including the type and magnitude of external forces, the shape and size of the material, and its internal structure and material properties. Other factors such as temperature, strain rate, and environmental conditions can also play a role.

4. How are resultant stresses on a volume element visualized?

Resultant stresses on a volume element are often visualized using stress contour plots, which display the distribution of stress values across a material. Other methods include stress tensors, which show both the magnitude and direction of stresses, and Mohr's circle, which is used to analyze the stress state at a specific point in a material.

5. What are the applications of showing resultant stresses on a volume element?

Showing resultant stresses on a volume element is essential for understanding the behavior of materials under different loading conditions. This information is used in various fields, such as civil and mechanical engineering, materials science, and manufacturing, to design and optimize structures and materials for specific applications.

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