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I am bit confused in considering the methods to apply for designing.

Consider a machine, which as several parts mounted on the frame (frame is of any sectional shape for exampe: ´I´ section). Let the length and width of the frame is 2m and 0.6m respectively. Here the Distribution of the masses of the different components on the frame are eccentric in nature. And the machine supports at the four cornes which is similar to the support of the chair.

My question is, how do I calculate the deflection, bending moment, shear stress etc of the Frame or whole machine due to the Forces acting on it.

Since the Forces acting here are eccentric and not exactly on the beam, I think it is not possible to solve it by using Beam theory.

enter image description here enter image description here

So, could anyone suggest me how to carry out this problem to solve it analytically. Or any advices on the study of any related topics are appreciated.

Thank you

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  • $\begingroup$ As you can see the Frame, consider I have mounted different machine components at different points on the frame and then it will become eccentric to the Frame axis. $\endgroup$ – Ranjith May 9 '18 at 8:26
  • $\begingroup$ I still don't understand where the loads are applied. Can you expand on your diagram and/or explain what you mean by "eccentric to the frame axis"? Do you mean that the loads aren't applied on the beams' centerlines? $\endgroup$ – Wasabi May 9 '18 at 9:01
  • $\begingroup$ This is the frame which is used for mounting different devices. For eg, consider horizontal casting machine, then a rotating cylinder will be placed in front portion of the frame and pouring assembly will be placed on the rear end of the frame. Hence loads of the cylinder and pouring assembly are not entirely concentrated on one side of the frame since these parts are mounted at the center of the whole frame, both the frame carries equal amount of the weight. In this case, how do I consider the amount of the load acting on each frame and carry out the calculations as mentioned previously $\endgroup$ – Ranjith May 9 '18 at 9:13
  • $\begingroup$ It looks like the beams a re twice as wide as the supports, the loads from above appear to rest outside the centerline & the rollers on the left will apply an outward torque on the beams. I think I understand why the OP is wary, but I wish @Ranjith would show more of their work so we only need to fill in the gaps. $\endgroup$ – mart May 9 '18 at 10:03
  • $\begingroup$ The Dimension of the beam is taken as a orbitarty, just for calculation. It could be the I section and Support will be decided later depends on the reactions required at the support. The main Goal is now to find whether the Frame can withstrand the loads mounted on it. And the centerline of the roller does not coincide the top cylinder as you can see in the fig.2. $\endgroup$ – Ranjith May 9 '18 at 10:18
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This case can be easily considered using standard beam theory, though analytical software will make things much easier by letting you use offsets.

The load from your equipment will be naturally transferred to the frame. This can be understood by imagining the equipment (or its own support structure) as additional transversal beams on the frame, such as below:

enter image description here

This implies that the equipment (or its support structure) suffers bending moment, which may or may not be transferred to your frame (as torsion) depending on how the connection is made (whether the connection can be considered pinned or fixed).

Regardless, the vertical load will be transferred to the frame, which will lead to bending moments on the frame. Depending on the connection, this vertical load might itself generate torsion on the frame, in which case the connection would have to be modelled with offsets to guarantee this effect is modelled correctly.

As mentioned by @mart's comment on the OP, there's also the issue of the supports being off-center. This will undoubtedly lead to torsion on the frame, but this can also be easily modelled with offsets.

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  • $\begingroup$ The force of the large drum on the rollers has a downward and an outward component, the letter results as a torque on the beam. So modelling the drum + rollers as two beams is not correct. (the other structure can be modeled as you describe) $\endgroup$ – mart May 9 '18 at 10:36
  • $\begingroup$ Yes, vertical load of the equipment as you have mentioned will fall on the beam which in turn creates bending moment of the whole frame and it also depends on how the connections are made between equipment and the frame. But, I wanted to know how to determine analytically. Because, I cannot consider it as a beam problem beacuse weight of the equipment is eccentric to frame. Let us consider, weight of the front and back assemblies as 200kg and 150kg resp´ly. And I do not whether it is UDL or UVL or single Point load and also do not know where it is acting which is neccessay while calculating. $\endgroup$ – Ranjith May 9 '18 at 10:40
  • $\begingroup$ The roller is given a drive and hence drum mouted on it roates. Hence the drum has to be mounted on it at certain angles and distance so that there exists a point contact between them @mart. Which can be seen in any horizontal casting machine that are available today. $\endgroup$ – Ranjith May 9 '18 at 10:44
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Lets handle fore the sake of illustration just the horizontal cylinder being supported by four rollers and later we can add the stresses caused by other parts and superpose all of them.

Lets assume the cylinder weighs 400lbs and is touching the bearings at 45 degrees angle, and is not imposing an dynamic loading, or else we need to refer to its manual for dynamic load factors.

The bearings horizontal and vertical reaction is each $$ R_h = 100\sqrt(2) \space = 141lbs \space , \space and \space R_v =100lbs $$

Say the arm of roller bearing is 6inch high and 2 inch in. So we have $$ 6\times 141 = 846 \space lb.in \space - 2\times 100 =646lb.in$$ total clockwise torque to the right beam at each bearing and symmetrical torque at the left beam supports. This causes torsional stress at 2 points on the beam, which we can calculate, given the beam's cross section.

As for the vertical loads which create moment and shear we have for point loads of 100lbs each and again we can calculate the bending moment and shear.

Now we go back to vertical cylinder on the back of diagram. That part can slide back and forth so we have to consider the influence line momentum and shear. But in this case for simplicity we consider the bending moment when the part is at most critical position at mid span and shear when it is at either support.

So now we can apply all the loads at their proper offset from the start of the beam and calculate bending moment and shear and torsion for a two span continuous beam.

I usually use factor of safety of 2.8 for these situations in the absence of a code load factor, but as we said this was just an illustration. Most of the compressors and moving machines have recommended design charts for foundation and support.

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  • $\begingroup$ My question is, suppose while calculating the bending moment, deflection in a simply supported beam with UDL on it, we can achieve it by normal methods. Here, I guess I can not able to consider it as a beam since it is a rectangular frame and also having mass distribution eccentric to the beam´s central Point. How would I approach this case? Or are there any refences or tutorials? @kamran $\endgroup$ – Ranjith May 14 '18 at 9:40
  • $\begingroup$ The cross members of the frame do not participate in supporting vertical loads. They are however considered fix end support for torsion. You have two point loads of torque on each beam with three fix supports. And because of symmetry of the frame you handle only one side. $\endgroup$ – kamran May 14 '18 at 15:07

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