Showing resultant stresses on a volume element

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SUMMARY

The discussion focuses on calculating resultant stresses on a volume element for a 60 mm diameter rod subjected to combined loadings. The user successfully determined normal stress at point A as 9.71 MPa and shear stress (\tau_{zx}) at A as 2.15 MPa. The challenge lies in expressing these stresses in terms of \sigma_x, \sigma_y, and \tau_{xy}. Participants emphasize the importance of understanding the definitions and directions of normal and shear stresses according to the specified coordinate system.

PREREQUISITES
  • Understanding of normal and shear stress concepts
  • Familiarity with mechanics of materials
  • Knowledge of coordinate systems in stress analysis
  • Ability to interpret and create stress diagrams
NEXT STEPS
  • Review the definitions of normal and shear stresses in mechanics
  • Learn how to transform loads to a specific section in structural analysis
  • Study the Mohr's Circle for stress transformation
  • Explore software tools for stress analysis, such as ANSYS or SolidWorks
USEFUL FOR

Mechanical engineers, civil engineers, and students studying mechanics of materials who are involved in stress analysis and design of structural elements.

Mairi
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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 (\tauzx) 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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If you attach a diagram showing the loading of the beam, you may get some feedback.
 
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.
 

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