Understanding Bending Moment Diagrams for Multiple Planes

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Discussion Overview

The discussion revolves around the necessity of creating two bending moment diagrams for a problem involving forces applied at oblique angles, specifically in the xy and xz planes. Participants explore the determination of reaction forces at supports B and C and the implications of decomposing forces into their components for analysis.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants question why two bending moment diagrams are needed, suggesting that the oblique application of force F necessitates decomposition into horizontal and vertical components for clarity.
  • Others propose that the same static equilibrium equations apply for determining reaction forces at supports B and C, emphasizing the importance of resolving forces into components.
  • It is noted that breaking forces into perpendicular components can simplify the calculation of moments and reactions at supports.
  • One participant raises a question about the moment arm of the F_r component, asking if it generates a moment about both the xy and yz planes, indicating a potential area of confusion.
  • Another participant points out that both moment arms from the bearing at C are equal, specifically 100 mm, but expresses uncertainty about the overall purpose of the analysis.

Areas of Agreement / Disagreement

Participants generally agree on the utility of decomposing forces into components for analysis, but there remains uncertainty regarding the necessity of two bending moment diagrams and the implications of the moment arms involved.

Contextual Notes

Some assumptions about the application of static equilibrium equations and the specific geometry of the problem may not be fully articulated, leading to potential gaps in understanding the analysis.

pinkcashmere
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can someone explain why this problem would involve two bending moment diagrams, one for the xy plane and another for the xz plane? Also, how are the reaction forces at B and C determined each time?
 

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pinkcashmere said:
can someone explain why this problem would involve two bending moment diagrams, one for the xy plane and another for the xz plane?
I think since the drive force F is applied at an oblique angle, the author thought it would be clearer to the student to decompose this force into its horizontal and vertical components, and work out the reactions and bending moments created by each component separately.

Also, how are the reaction forces at B and C determined each time?
The same equations of static equilibrium apply in each case. The author has resolved F into its components on the overhung end of the shaft. There are two bearings where reactions develop. Write the standard sum of the forces and sum of the moment equations for each case and solve for the unknown reactions.
 
It is often convenient to break up the forces which cause the moments into its perpendicular components so that the moments about each axis and the axis reactions at the supports can be calculated separately. The reactions are determined from the equilibrium equations. The force reactions in each direction are particularly useful for the bearing bolted connection design.
 
SteamKing said:
I think since the drive force F is applied at an oblique angle, the author thought it would be clearer to the student to decompose this force into its horizontal and vertical components, and work out the reactions and bending moments created by each component separately.

So the F_r component for example, it generates a moment about the xy plane because it has a moment arm to the xy plane? But doesn't it also have a moment arm to the yz plane?
 
pinkcashmere said:
So the F_r component for example, it generates a moment about the xy plane because it has a moment arm to the xy plane? But doesn't it also have a moment arm to the yz plane?
Both moment arms are the same distance from the bearing at C, namely 100 mm.

It's not clear from the attachment what the purpose of this analysis is.
 

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