# Calculating forces on a rod with bearings leaning against a wall

• g2c
In summary, the force exerted on the floor end of a zero weight rod with zero friction bearings, when a vertical force is applied to the wall end, can be calculated using the formula Fh = Fv / tan(alpha). This is due to the mechanical advantage generated by the geometry of the setup, where the ratio of the horizontal and vertical distances covered by the ends and middle of the rod determines the ratio of the pushing and resulting forces. Additional anchorage may be needed to prevent buckling during normal operation.
g2c
TL;DR Summary
Deriving the force in a given direction from force in in a other
Hello, id appreciate your help for the following case: in a room, a zero weight rod has zero friction bearings at its extremities. One of his ends lies on the floor, the other is against a wall, forming with it an angle alpha. A verical force fv is applied to the 'wall end'. How to calculate the resulting horizontal force fh at the 'floor end'. Thank a lot

g2c said:
TL;DR Summary: Deriving the force in a given direction from force in in a other

Hello, id appreciate your help for the following case: in a room, a zero weight rod has zero friction bearings at its extremities. One of his ends lies on the floor, the other is against a wall, forming with it an angle alpha. A verical force fv is applied to the 'wall end'. How to calculate the resulting horizontal force fh at the 'floor end'. Thank a lot
Sounds a bit like a schoolwork question. Is this for school or self-study, or part of a project you are working on?

Show us a sketch please, and your Free Body Diagram (FBD) for the setup. Thanks.

berkeman said:
Show us a sketch please, and your Free Body Diagram (FBD) for the setup. Thanks.

berkeman
@berkeman - I used intuitively this setup to repair a broken pvc pipe and it did generate a large enough horizontal force but i don't know how to derive the formula. I "guess" though it could be fh=fv*tg(alpha). I dont know what is fdb and how to build it. Do you mean a drawing?

g2c said:
... a zero weight rod has zero friction bearings at its extremities. One of his ends lies on the floor, the other is against a wall, forming with it an angle alpha. ...
That "zero weight rod" really confuses me.
How is it possible to rest a zero weight rod on the floor, or lean on a wall?

g2c said:
Do you mean a drawing?
Yes, a drawing would be a big help. Or a picture, since it sounds like you actually built it.

User the "Attach files" link below the Edit window to upload PDF or JPEG files...

g2c said:
@berkeman - I used intuitively this setup to repair a broken pvc pipe and it did generate a large enough horizontal force but i don't know how to derive the formula. I "guess" though it could be fh=fv*tg(alpha). I dont know what is fdb and how to build it. Do you mean a drawing?
From the opening post, the way it was written, at floor end the force horizontal = 0, same for horizontal force from the wall onto the rod.

But,
From this post, it appears that the floor end is constrained horizontally.
Some information is missing.

berkeman
For Fv, applied downwards at the wall end.
Fh, along the floor, will depend on the rod angle, α.

For a near horizontal rod, α = 0; Fh = ∞
For a diagonal rod, α = 45°; Fh = Fv
For a near vertical rod, α = 90°; Fh = 0

That appears to be a cotangent function. Fh = Fv / tan( α ).
The rod will fail, probably due to buckling, for high axial forces at low α.

g2c said:
... i don't know how to derive the formula. I "guess" though it could be fh=fv*tg(alpha). I dont know what is fdb and how to build it....
Could it be something like what is represented in the attached PDF file?

#### Attachments

• Rod against wall and grade.pdf
33.3 KB · Views: 82
@Lnewqban - exactly! Can you please detail the fondement of this result? Or send a link to literature dealing with such kind of forces problems? Below a picture of the worksite
1- fulcrums
2- long rod
3- short rod
4- clamps for adjusting the short rod length so as to have short + long = a bit longer than current visible length of pipe

#### Attachments

• pipe repair.pdf
2.6 MB · Views: 90
Thanks, It states the formula nut doesn't tell why this is so

g2c said:
Thanks, It states the formula nut doesn't tell why this is so
The reason is a mechanical advantage generated by the geometry.
Work or energy in = Work or energy out

The pushing vertical/horizontal forces ratio is proportional to the ratio of the horizontal/vertical distances covered by the ends/middle of the pipe.

## 1. How do I calculate the forces on a rod with bearings leaning against a wall?

To calculate the forces on a rod with bearings leaning against a wall, you will need to use the principles of statics and apply them to the specific situation. This involves analyzing the forces acting on the rod and bearings, taking into account their magnitudes, directions, and points of application. You will also need to consider the rotational equilibrium of the system.

## 2. What factors affect the forces on a rod with bearings leaning against a wall?

The forces on a rod with bearings leaning against a wall can be affected by several factors, including the weight of the rod, the weight of any objects attached to the rod, the angle at which the bearings are leaning against the wall, and the coefficient of friction between the bearings and the wall.

## 3. How do I determine the angle at which the bearings should lean against the wall?

The angle at which the bearings should lean against the wall can be determined by considering the forces acting on the rod and bearings. The angle should be such that the forces are in equilibrium, meaning that the net force and net torque on the system are both equal to zero. This can be achieved by adjusting the angle until the forces are balanced.

## 4. What is the purpose of calculating the forces on a rod with bearings leaning against a wall?

Calculating the forces on a rod with bearings leaning against a wall is important for understanding the stability and safety of the system. By determining the forces, you can ensure that the rod and bearings are strong enough to support any weight or external forces applied to them. This information can also be used to design and improve similar structures in the future.

## 5. Are there any assumptions that need to be made when calculating the forces on a rod with bearings leaning against a wall?

Yes, there are some assumptions that need to be made when calculating the forces on a rod with bearings leaning against a wall. These include assuming that the rod and bearings are rigid, that there is no external force acting on the system, and that the bearings are in contact with the wall at a single point. These assumptions may not always hold true in real-world situations, so it is important to consider their limitations when interpreting the results of the calculations.

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