# Force transmitted to base

• Dustinsfl
In summary,-A steel cantilever beam with end load is subjected to a moment of inertia and unbalance, and the oscillation cycle of the beam is determined by the natural frequency and the equivalent mass of the beam.

## Homework Statement

How does one determine the amplitude of the force transmitted to the base of a beam?

## The Attempt at a Solution

The ODE modeling displacement is
$$-0.000891(9.60875\sin(183.26t) - 323.778\sin(5.4386t))$$

Dustinsfl said:
How does one determine the amplitude of the force transmitted to the base of a beam?
In what set-up?

haruspex said:
In what set-up?

What do you mean?

Dustinsfl said:
What do you mean?
I mean, describe what's going on. What beam, what forces, ...?

haruspex said:
I mean, describe what's going on. What beam, what forces, ...?

It is a cantilever beam with end load.

Dustinsfl said:
It is a cantilever beam with end load.
OK, and what facts are you given - lengths, masses, moduli..? In the OP you mention ODE and quote an expression involving time, so I guess this is not a statics question. Is there some perturbation applied?

haruspex said:
OK, and what facts are you given - lengths, masses, moduli..? In the OP you mention ODE and quote an expression involving time, so I guess this is not a statics question. Is there some perturbation applied?
A steel cantilever beam is ##120## in long by ##1\times 1## in##^2## which has a motor that weighs ##100## lb##_f## mounted at the end. The motor runs at 183.26 rad/sec. The motor has an unbalance of ##0.1## lb##_m## located at a radius of ##0.1## in from the axis of the shaft. Assume that for the steel ##E = 30\times 10^6## psi, the density is ##0.28## lb##_m##/in##^3##, and that the damping ratio is ##0.01##.

What I did was then:
First, let's convert Young modulus from psi to Pascals, 1 psi is ##6894.76## Pascals. Then ##E = 2.07\times 10^{11}## pascals. The moment of inertia is ##I = \frac{bh^3}{12} = 3.47\times 10^{-8}## m since 1 in is ##0.0254## m. The equivalent spring constant is
$$k_{eq} = \frac{3EI}{\ell^3} = 760.985\text{ N/m}.$$
The relation of mass with density is ##\rho = \frac{m}{V}##. The volume of the cantilever beam is ##V = 1^2(120) = 120## in##^3##. Then ##m = V\rho = \frac{120(0.28)}{2.2} = 15.273## kg. The equivalent mass
$$m_{eq} = 15.273 + \frac{100}{2.2}0.23 = 25.7275\text{ kg}.$$
Then the natural frequency of the beam and the motor system is
$$\omega_n = \sqrt{\frac{k_{eq}}{m_{eq}}} = 5.4386\text{ rad/sec}.$$
Then I used a Laplace transform to determine ##y(t)##

OK, well there's a lot there I could not have guessed at.
Plugging all these numbers in straight away makes it unnecessarily hard to follow.
Dustinsfl said:
##I = \frac{bh^3}{12} ##
what is b?
Dustinsfl said:
##m_{eq} = 15.273 + \frac{100}{2.2}0.23 = 25.7275\text{ kg}.##
Where does the 0.23 come from?
Dustinsfl said:
Then I used a Laplace transform to determine y(t)
And that is the time-dependent expression in the OP, right?
I assume you want the max stress at the beam support. In terms of the oscillation cycle, when will that occur?

haruspex said:
OK, well there's a lot there I could not have guessed at.
Plugging all these numbers in straight away makes it unnecessarily hard to follow.

what is b?

Where does the 0.23 come from?And that is the time-dependent expression in the OP, right?
I assume you want the max stress at the beam support. In terms of the oscillation cycle, when will that occur?

b = 1in or 0.0254 m 0.23 is by definition of equivalent mass of a cantilever beam.

I don't know. I am trying to determine the force transmitter to the base.

## 1. What is force transmitted to base?

Force transmitted to base is a term used in physics to describe the force that is applied to the base or foundation of an object. It is the force that is exerted on the ground or surface that the object is resting on.

## 2. How is force transmitted to base calculated?

Force transmitted to base is calculated by multiplying the mass of the object by the acceleration due to gravity (9.8 m/s²). This calculation gives the force of gravity, which is then balanced by the normal force exerted by the surface the object is resting on.

## 3. What factors affect force transmitted to base?

There are several factors that can affect force transmitted to base, including the mass of the object, the acceleration due to gravity, and the type of surface the object is resting on. Other factors such as friction, air resistance, and external forces can also play a role.

## 4. How does force transmitted to base impact stability?

Force transmitted to base is directly related to an object's stability. If the force transmitted to base is greater than the object's weight, it will cause the object to tip or fall. On the other hand, if the force transmitted to base is equal to or less than the object's weight, it will remain stable.

## 5. Can force transmitted to base be reduced?

Yes, force transmitted to base can be reduced by increasing the size of the base of an object. This will distribute the force over a larger area, decreasing the pressure on the surface and reducing the force transmitted to base. Additionally, adding stabilizing elements such as counterweights or support structures can also help reduce force transmitted to base.