Shear Stress Distribution Along a Beam

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Discussion Overview

The discussion focuses on the distribution of shear stress along a beam, particularly in the context of horizontal beams subjected to distributed loads. Participants explore the relationship between shear force and shear stress, as well as the variation of shear stress along the length of the beam.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • One participant asserts that shear stress in horizontal beams has a parabolic distribution, with maximum shear stress occurring at the neutral axis.
  • Another participant questions whether the magnitude of shear stress varies along the horizontal length of the beam, seeking clarification on this aspect.
  • A participant mentions that shear force is positive at the left support, negative at the right support, and zero at the center of the beam, indicating a need to connect shear force to shear stress.
  • It is noted that while shear stress varies vertically, the horizontal variation along the beam axis is less understood by some participants.
  • One participant suggests that shear stress can be calculated using either the average shear stress formula or the full formula, indicating that the shear force diagram is essential for these calculations.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the relationship between shear force and shear stress, with some uncertainty about how shear stress varies along the beam's length. No consensus is reached on the specifics of this variation.

Contextual Notes

Some participants highlight the need for a clearer connection between shear force diagrams and shear stress calculations, indicating potential limitations in understanding the underlying principles.

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I know that shear stress in horizontal beams has a parabolic distribution, so that the max shear stress occurs at the neutral axis. I also understand that for a beam subject to a distributed load with supports at its ends, the magnitude of the shear force is highest at the left and right ends of the beam. However, does the magnitude of the shear stress also vary along the horizontal length of the beam? If so, how?
 
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Do you know how to make a shear diagram? A moment diagram? And do you know the relationship between shear and moment diagrams?

What is the sign of the shear stress at the left support? At the right support? And what is the shear stress in the center (halfway between the supports) of the beam?
 
Shear force is positive at the left support, negative at the right support, and zero at the center of the beam. I don't fully understand how to connect the shear force along the length of the beam to its stress. I see how the shear stress varies vertically, but not horizontally along the axis of the beam.
 
Variation along the axis of the beam is shown on the shear force diagram:

shear.PNG


Then if you select some point along the beam axis you can calculate shear stress either using formula for average shear stress: ##\tau=\frac{V}{A}## or full formula: ##\tau=\frac{VQ}{Ib}##. In both cases V is the value obtained from shear force diagram at selected.
 

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