Finding Reactions of Cantilever Beam Inserted Into Wall

In summary, a cantilever beam with a length of 5 m and a mass of 100 N/m has a concentrated load of 1000 N at its free end. The beam is inserted into a wall that is 0.5 m thick. The question is asking for the reactions on the beam, which can be solved using equilibrium equations. In practice, the reactions consist of two forces, one up and one down, and the analysis involves making an assumption about the distribution of pressure between the beam and wall. This can be solved using the combined stress formula N/A +- M/Z.
  • #1
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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  • #2
can anybody explain it to me?
 
  • #3
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.
 
  • #4
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.
 
  • #5


I understand your confusion about the location of the reactions on the cantilever beam inserted into a wall. In order to determine the reactions, we must first consider the equilibrium of forces acting on the beam. Since the beam is inserted into the wall, there will be two reactions at the point of insertion - a horizontal reaction and a vertical reaction. The vertical reaction will be equal to the sum of the beam's weight (100 N/m) and the concentrated load (1000 N). The horizontal reaction will depend on the angle at which the beam is inserted into the wall and the coefficient of friction between the beam and the wall. Once these reactions are determined, we can use the equations of static equilibrium to solve for the remaining unknowns. I suggest drawing a free body diagram of the beam to help visualize the forces acting on it and to better understand the location of the reactions. I hope this helps and good luck with your homework!
 

1. How do I determine the reactions of a cantilever beam inserted into a wall?

The reactions of a cantilever beam inserted into a wall can be determined by using the equations of static equilibrium. These equations state that the sum of all forces acting on a structure must equal zero and the sum of all moments (or torques) must also equal zero. By setting up and solving these equations, the reactions at the wall can be determined.

2. What factors affect the reactions of a cantilever beam inserted into a wall?

The reactions of a cantilever beam inserted into a wall can be affected by various factors such as the material properties of the beam and wall, the dimensions of the beam, and the applied loads. Additionally, the support conditions at the wall, such as whether it is simply supported or fixed, can also affect the reactions.

3. Can the reactions of a cantilever beam inserted into a wall be negative?

Yes, the reactions at the wall can be negative in certain cases. This occurs when the applied load is greater than the maximum load that the beam can support, causing the beam to deflect downwards and creating a downward force at the wall. In this case, the reactions would be considered negative as they are acting in the opposite direction of the positive forces applied to the beam.

4. How do I calculate the maximum load a cantilever beam inserted into a wall can support?

The maximum load that a cantilever beam inserted into a wall can support can be calculated using the equations for bending moment and shear force. By setting the bending moment and shear force equal to zero and solving for the maximum load, the value can be determined. Additionally, factors such as the material properties and dimensions of the beam also play a role in determining the maximum load.

5. How can I ensure the stability of a cantilever beam inserted into a wall?

To ensure the stability of a cantilever beam inserted into a wall, it is important to consider the structural design and support conditions. The beam must be able to resist the applied loads without exceeding its maximum load capacity. Additionally, proper anchoring and support at the wall can help to prevent buckling or failure of the beam. It is also important to consider potential external factors such as wind or seismic loads that may affect the stability of the beam.

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