Finding stress in non symetric cross section

Click For Summary
SUMMARY

The discussion focuses on calculating maximum shear stress and angle of twist in a shaft with a non-symmetric circular cross-section where the radius changes linearly. The user applies the formula T*r/J for shear stress, noting that the smallest radius experiences the highest stress due to the J value being dependent on r^4. They also explore the implications of reinforcing the shaft by thickening it to 2t and question the applicability of the equation T/(2A*t) for maximum stress calculations in this context.

PREREQUISITES
  • Understanding of shear stress calculations in mechanical engineering
  • Familiarity with torsion formulas, specifically T/(GJ)
  • Knowledge of polar moment of inertia (J) and its dependence on cross-sectional geometry
  • Concept of area moments and their application in stress analysis
NEXT STEPS
  • Research the derivation and application of the polar moment of inertia (J) for non-symmetric cross-sections
  • Study the effects of shaft reinforcement on torsional strength and performance
  • Learn about the relationship between shear stress and bending moments in mechanical components
  • Examine case studies involving thick-walled and thin-walled circular shafts under torsion
USEFUL FOR

Mechanical engineers, structural analysts, and students studying torsion and stress analysis in non-standard cross-sectional geometries.

Dell
Messages
555
Reaction score
0
in a given shaft with a circular cross section, the radius changes linearly
Capture.JPG


find the maximum shear stress

i used T*r/J
and since J is dependent on r^4, i found that the cross section with the smallest radius will feel the largest stress.

find the angle of twist at the end of the shaft

T/(GJ)*dx while J is a function of X and i integrate from 0 to L

if the bottom of the shaft is reinforced, -thickened- to 2t, what is the largest shear stress felt in the shaft??
Captu?re.JPG


up till now i have only solved questions with either circular/ rectangular closed cross sections, or other open cross sections

can i use the equation for maximum stress
T/(2A*t)

where A is the area surrounded by an axis through the center of the side of the shape?? if so how do i do this ? what would that axis look like? would it be 2 half circles with 90 degree joints? meaning the area would be pi/2*(R12+R22) where R1 and R2 are the average radii of the 2 half circles??

using this logic i would find the maximum stress in the thin walled circle

is this correct? can i do this?

this is where i am stumped,
 
Physics news on Phys.org
also what are the advantages of thickening parts of the shaft, i think if it was subjected to bending this might improve its performance as far as max moment that can be applied, but in torsion what would this do? there any other advantagees?
 

Similar threads

  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 2 ·
Replies
2
Views
4K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 2 ·
Replies
2
Views
8K
  • · Replies 9 ·
Replies
9
Views
3K
  • · Replies 4 ·
Replies
4
Views
2K