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Let me state I was once an Engineering student but am now a professional software engineer working on a side project that involves something similar to the question below.

I have a box hanging from a beam and the box weighs 200 pounds. The beam is parallel to the ground and it can safely support the weight of the box.

My question is does the ability of the beam to safely support the weight of the box change as the box moves from one end of the beam to the other. Does the speed at which the box moves affect the ability of the beam to support the weight? (for example, 1 mph vs. 300 mph).

Basically if the beam supports the weight of the box when it's not moving, is it safe to assume it will continue to support the weight when it's zooming from one end of the beam to the other?

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At low speed and acceleration it's probably ok. At high speed, please consider the following:

I'm going to make a couple assumptions and will speak to concepts because we only have a detail about the suspended mass:

  1. The hanging mass is hanging significantly far below the beam
  2. The hanging mass is rigidly connected to beam with 1 degree of freedom. (Not suspended by a cable or something which would make your mass a pendulum(think wrecking ball)

Moving a mass at significant speed is going to have momentum. When you start and stop the momentum you have an acceleration and deceleration.

Momentum = mass * velocity (for reference) Force = mass * acceleration Acceleration = (delta)speed/time Torque or Moment = force*distance

So, if you significantly accelerate or decelerate your mass you have a high force. Multiply that force by the distance it's suspended from from the beam/track and now you have induced a moment load into the beam. This alone may be an issue for your beam. It may not.

Next, depending on the motion of your mass, for example if it moves only between two fixed locations, you might see fatigue at the two locations due to the cyclic or repeated stress at those same locations. If the mass can start and stop in any location along the beam it will have different implications. Also, you would need to calculate the combined load in the worst location(furthest point away from any supports.)

Last thoughts, the design of your "trolley" or skate which lets the mass slide along the beam could better distribute the load applied along the beam making it more capable to sustain the loads applied as described above.

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If the beam is initially supporting your box hanging at its center where it creates the most moment, usually moving the load to the sides of the beam back and forth should be ok.

This is the case with most common beams made up of extruded prismatic matterials such as wood or metal.

However if you need to make sure you have to check your moment and shear diagrams. Shear forcce in a typical point load case decreases from a maximum on one side going to zero under the load to the other maximum on the other side, under what is called influence line shear. The maximum shear is equal to your load when it is applied right over the support.

As far as moving the load fast back and force that is a whole new ballpark.

When you move your load across the length of the beam you are vertically inducing a perturbation to the beam and hence the beam and your weight may start to vibrate vertically and therefore increase momentary live load force fluctuations beyond the static design of the beam.

If the frequency of this back and forth vibration is close to natural frequency of this system then you are dealing with harmonic resonance, which could increase the amplitude of vibration in this beam and lead to catastrophic failure.

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