Finding Reactions of Cantilever Beam Inserted Into Wall

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Discussion Overview

The discussion revolves around the analysis of a cantilever beam that is inserted into a wall, focusing on determining the reactions at the wall due to a concentrated load at the free end. The context includes aspects of structural analysis and equilibrium conditions.

Discussion Character

  • Homework-related, Technical explanation

Main Points Raised

  • One participant seeks clarification on the location of unknown reactions for a cantilever beam inserted into a wall.
  • Another participant suggests that there will be a vertical reaction force and a moment at the wall, which can be solved using equilibrium equations, advising not to focus on the wall thickness.
  • A further contribution indicates that in practice, the beam reactions consist of two forces, with one located near the inner wall face and another near the outer wall face, noting that the analysis is based on equilibrium and involves assumptions about pressure distribution between the beam and wall.
  • This participant references the combined stress formula, suggesting a more complex analysis is required.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and approaches to the problem, with no consensus on the specifics of the reaction forces or the assumptions required for analysis.

Contextual Notes

There are unresolved aspects regarding the assumptions about pressure distribution and the specific application of equilibrium equations, which may affect the analysis.

kaizokonpaku
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Homework Statement



a cantilever beam 5 m long with a mass of 100 N/m carries a concentrated load of 1000 N at its free end. The end of the beam is inserted into a wall 0.5 m thick. What are the reaction on the beam.


Homework Equations





The Attempt at a Solution



My problem is I cannot imagine the location of the unknown reactions of the beam which is inserted into a wall. Please to identify the location of these reactions so I can start solving.
 
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can anybody explain it to me?
 
There will be a vertical reaction force and a moment (couple) at the wall for which you can solve using the equilibrium equations. Don't get hung up on the wall thickness.
 
In practice, the beam reactions each consist of two forces, one up close to the inner wall face, larger than the one down, which is located near the outer wall face. The analysis is equilibrium based but a bit long to explain here, and involves making an assumption about the distribution of pressure between beam and wall. It's an application of the combined stress formula N/A +- M/Z.
 

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