Calculate the angle of the neutral axis from the x-axis

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Discussion Overview

The discussion revolves around calculating the angle of the neutral axis from the x-axis for a beam subjected to a positive couple of 6 kNm. Participants explore the implications of the given loading conditions, the calculations of moments of inertia, and the resulting angle.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant calculates the moments of inertia (Ixx, Iyy, Ixy) and seeks clarification on whether Mx equals 6 kNm.
  • Another participant confirms that Mx does equal 6 kNm and provides guidance on unit notation.
  • There is a discussion about the sign of Ixy, with one participant suggesting it might be positive, while another mentions a discrepancy with SolidWorks outputs.
  • Participants share their calculated values for Ixy and the angle, with one stating a positive angle of 38.66 degrees.
  • Questions arise regarding the coordinates used in stress calculations, with participants discussing their methods for determining these values.
  • Disagreement occurs regarding the final stress value, with one participant consistently obtaining a different result than another.
  • Participants express confusion over coursework questions and seek clarification from peers.

Areas of Agreement / Disagreement

There is no consensus on the sign of Ixy or the final stress values, as participants report differing results. The discussion remains unresolved regarding the correct values and methods used in calculations.

Contextual Notes

Participants mention potential issues with software outputs and the importance of correctly defining axes, which may affect calculations. There are also noted discrepancies in unit notation and the interpretation of the problem statement.

Who May Find This Useful

This discussion may be useful for students working on beam mechanics, particularly in understanding the calculations related to moments of inertia and neutral axes in structural analysis.

vtaela
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Homework Statement


Calculate the angle of the neutral axis from the x-axis when the beam is loaded with a positive couple of 6kNm acting around the X-axis



Homework Equations


i have calculated:
Ixx: 2854758.6 mm^4
Iyy: 1429034.6 mm^4
Ixy: -1143476 mm^4


The Attempt at a Solution



i know that to calculate the angle:

tanθ= - (IxxMy -IxyMx)/(IyyMx-IxyMy)

since i am confused with the statement "positive couple of 6kNm acting around the X-axis"

does that mean that Mx= 6KNm?

thank you
 
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Ya got any pictures of this problem?
 
ImageUploadedByPhysics Forums1363452818.241318.jpg


This is the the question
 
Mx is a couple which is acting as a bending moment on the cross section.
 
vtaela said:
Does that mean Mx = 6KNm?
That is correct.

(1) By the way, always leave a space between a numeric value and its following unit symbol. E.g., 6 kN, not 6kN. See the international standard for writing units[/color] (ISO 31-0[/color]).

(2) The unit symbol for kiloNewton is spelled kN, not KN. Capital K means kelvin.

(3) Two unit symbols multiplied together cannot be written together, and must be separated by, e.g., an asterisk or a space. E.g., kN*m or kN m, not kNm.
 
Last edited:
Thank u! I will have it in mind! In addition my ixy when i calculate it is positive and when i got the answer from solidworks i get a negative value! Which one is the correct?
 
vtaela: Although I have not tried it, it looks like Ixy perhaps should be positive. I do not know what SolidWorks is doing. Ensure your positive axes are pointing in the correct direction in SolidWorks.
 
Thank you very much
 
vtaela said:

Homework Equations


i have calculated:
Ixx: 2854758.6 mm^4
Iyy: 1429034.6 mm^4
Ixy: -1143476 mm^4

I got this except the Ixy was plus 1143476. Is this what you got when you did it again?
 
  • #10
Yes i calculates a positive ixy and a positive 38.66 degree
 
  • #11
When calculating the maximum stress did you use the unsymmetric bending equation? If you did what did you use as your x and y co-ordinates to input in that equation?
 
  • #12
X = -13.78 and y+= 38.11 getting a maximum stress of 136.7119
 
  • #13
How did you get them? Did you draw it out or is there a way to calculate them?
 
  • #14
Actually think i understand it.

X = Xc - bredth of rectangle 1
Y = height of rectangle 1 - Yc

That how you got them?
 
  • #15
Yes that's right
 
  • #16
Are you sure about your final stress value? I get 151.9855 N/mm^2 every time.

I've tried using hand calculations as well as using excel to double check the values and get that everytime.
 
  • #17
Take a picture of what you have done to compare the solution! I will reply tmr since i am not home now
 
  • #18
Heres my solution.
 

Attachments

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  • #19
Same procedure except i used a positive Mx
 
  • #20
Any idea how to do question 1 of the coursework?:p
 
  • #21
Can you stick a pic of your solution up please. I completely missed the positive couple part in the question so can see where the positive mx comes from but now i now get -117.879 - 34.1061 = -151.99! Absolute nightmare haha.

Haha no idea, think everyone is stumped with that one.
 
  • #22
ImageUploadedByPhysics Forums1364731019.105529.jpg
 
  • #23
Cheers, i think you have your x and the y mixed up at the end. You have -3.09x + 2.475y when it should be -3.09y + 2.475x according to the equation?
 
  • #24
Yes you are right thank you for that
 
  • #25
No problem
 

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