Beam Bending and Moments of Inertia

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Discussion Overview

The discussion revolves around a homework problem related to beam bending and the calculation of moments of inertia when bending about different axes (y-axis and z-axis). Participants explore the implications of bending about these axes and the associated calculations, including the use of the parallel axis theorem.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant expresses confusion about the differences in bending a beam about the y-axis versus the z-axis and seeks clarification on visualizing these differences.
  • Another participant suggests that the issue involves the second moment of area being different for the two axes and mentions the need to calculate properties to determine maximum allowable moments.
  • A participant confirms that the problem specifically asks for calculations about the z-axis and provides a link to an image for further context.
  • It is noted that the calculation for the y-axis requires the parallel axis theorem because the axis does not pass through the centroid of the rectangles, while the z-axis calculation can be done simply as it passes through the centroid.
  • One participant expresses gratitude for the assistance received in the discussion.

Areas of Agreement / Disagreement

Participants generally agree on the need to calculate moments of inertia differently for the two axes, but there is no consensus on the visual understanding of the bending differences or the specific calculations involved.

Contextual Notes

There are limitations regarding the visibility of attachments, which may affect the clarity of the discussion. The use of the parallel axis theorem is mentioned but not fully resolved in terms of its application to the problem.

Who May Find This Useful

This discussion may be useful for students studying beam mechanics, particularly those dealing with moments of inertia and bending in structural engineering contexts.

ACE_99
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Homework Statement


This is a two part question. In the first part you are asked to determine the mam moment that can be applied to the beam if it is bent about the z axis. They then ask you to redo the question bending about the y axis. This is probably a really simple question but what is the difference in bending about different axis? I understand what I need to do in order to solve the question I'm just having trouble visually picturing and understanding what the difference is when you bend it about the y-axis and when you bend it about the z axis. I've posted the solutions that were provided to me by my prof. In this question I'm unsure why it is they use the parallel axis theorem to calculate the moments of inertia of pieces 1 and 3.

Sorry if this is posted in the wrong place.
 

Attachments

  • beambending.jpg
    beambending.jpg
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First, since it usually takes a certain time before attachments are approved for display to the public, we are not yet able to see your illustration. Your description alone permits me to make a guess, but not understand your problem.

It sounds to me that it is a problem of a beam section where the second moment of area is different between the y and z axes. You may be required to calculate the properties and given the maximum stress, calculate the maximum moment allowable at this section.

You are likely to get faster responses if you post your attachments (.jpg) at a photo server and post us the link. Sometimes it takes a couple of days to get the attachment approved.
 
Actually mathmate that's exactly what the problem is asking. In the question just before this one they asked us to calculate it about the z axis. Heres a link to the image.

th_beambending.jpg
 
The example does the more difficult part, where the y-axis does not pass through the centroid of each of the component rectangles, thus the calculation of second moment of area (loosely called moment of inertia by most civil engineers) for the section requires the use of the parallel axis theorem.

In the case of the z-axis, the axis passes through the centroid of the three rectangles, therefore the second moment of area is simply the sum of the three components calculated through the centroid using the formula
Izz=bd3/12
After that, the simple application of the formula
\sigma = My/I
should be no mystery to you.
 
Great thanks a lot for the help.
 

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