Solid Mechanics Beam Stress Question

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Discussion Overview

The discussion revolves around a solid mechanics problem related to beam stress, specifically focusing on the use of singularity functions to determine deflections and the formulation of moment as a function of position along the beam. The conversation includes aspects of technical reasoning and problem-solving in the context of structural analysis.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant suggests using the singularity function to find deflections by writing the moment as a function of ##x## and integrating twice.
  • Another participant questions the relevance of finding shear stress in this context.
  • A participant notes that a constant moment may be missing from the moment function ##M(x)## and mentions the need to consider vertical reactions and moments at point A for equilibrium.

Areas of Agreement / Disagreement

Participants express differing views on the approach to the problem, particularly regarding the inclusion of shear stress and the formulation of the moment function. The discussion remains unresolved with multiple competing perspectives.

Contextual Notes

There are indications of missing assumptions regarding the moment function and equilibrium conditions, which have not been fully addressed in the discussion.

Leighanne
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Homework Statement
Looking for some help in solving this practice problem, I have tried multiple times and can't seem to get to the correct answers.
Relevant Equations
The solid 30 mm diameter steel [E = 200 GPa] shaft shown in Figure supports two pulleys. For the loading shown, use discontinuity functions to compute:

(a) the deflection of the shaft at pulley B.

(b) the deflection of the shaft at pulley C.

answers: (1.539mm, 6.15mm)
1704649582788.png
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You are supposed to use the singularity function to find the deflections. You need to write the moment as a function of ##x##. Then the deflections come from integrating twice:

$$EI \frac{d^2y}{dx^2} = M(x)$$

Why are you trying to find the shear stress?
 
Uploaded the wrong solution attempt whoops!
heres the correct one.
1704650460080.png
 
Leighanne said:
Uploaded the wrong solution attempt whoops!
heres the correct one.
View attachment 338230
There should be a constant moment that you have not included in ##M(x)##. There may be more, but start there( i.e there is vertical reaction and moment at A under equilibrium).
 

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