Is my eccentrically loaded column design safe and efficient?

[EspElement]

My problem is proving my structure is sound. Currently i want to know my deflection from my loads applied.

See attachment. My load is 4000 lb. My carriage weight is 1200 lb. My upright column or tube is a 6" x 4" x 1/4" structural steel which i have 2 of these. I have distances to my CoG (Center of Gravity) of the carriage. I'm not sure if this is the variable i need or not for this.

I started with deflection of a cantilevered beam. Deflection = PL^3/3EI. I attempted to use torque ratios to determine my load. Shown I have 25.125" = X and 87.1875" = Y. So i took 25.125/87.1875 ~ 0.288. I then used that value to my calculations for the load on the column. 5200 * .288 ~ 1500 lb.

I of beam3 is ((6^3)(4)-(5.5^3)(3.5))/12 ~ 23.5 * 2 = 47in^4

(1500)(87^3)/(3)(30 mil)(47) ~ 0.234"

The reason I raise this question is 1 it seems unlikely the deflection is that high, I could be wrong and 2 i want to prove that value i have calculated is correct.

I think the correct way to do this is by an eccentrically loaded column formula but i can't seem to gather enough information in my young career to evaluate that.

Notes:
I put a SF into the load from 2000 to 4000. Obviously a 1/4" sounds like a lot and is certainly not acceptable. The actual value would be like 1/8" if this is calculated properly which is still not ideal. I also am not considering the tracks I and other components within the design for this calculation.

If anyone can back me up or guide me in the proper direction that would be great! Thanks in advance.

 

[pongo38]

You say you want the deflection of the column. At which point, exactly? I see there is a triangular brace to a base beam that looks as if it will move, thus contributing to the deflection of the column. You need to say in advance what sort of error or accuracy you will find acceptable, going beyond your 1/8" acceptable, 1/4" acceptable. Then, you want a mathematical model of the column, showing all the points where there is a load or reaction. Given that bending will be the cause of most of the deflection, can you draw the bending moment diagram. Use this for a first order analysis. Because the column has both axial load and bending, it is essentially a non-linear structure where the deflections due to bending can be increased by the presence of axial load. Do you want an estimate of that as well? I don't want to scare you, but this is a practical case rather than a textbook question, and I feel your approach is overly simple.

 

[EspElement]

Thank you for the response pongo38. You have been a lot of help for me on here. We spoke before i was using a formula that involved calculus and dx and integrals and i hadn't studied calc yet. I'm in the middle of calc 1 now and am grasping the concepts a lot better we are working with dx and dy currently and linear approximation.

I attempted to solve this with the load and an approximated reaction against the column and used that to determine my deflection as if it were a cantilevered beam. You are right, the deflection i calculated for would be at the point of my approximated reaction and not the entire length of the beam.

I personally do not have an exact limit on the amount of deflection. I mainly want to ensure the deflection/stress is not going to cause fatigue over time. The loading and unloading of this could happen up to 100000 times a year. The machine will work just fine with bending so more so then the deflection values the fatigue and failure are most important. I myself don't envision failure here but i can't seem to gather values to back that up.

Yes there is some rotational loading from the cams inside the tracks being mounted to the side of the tubing. I right now am trying to find a hard value i can use as worse case scenario. Can this be done or is there a lot more evolved?

None of my co-workers know how to calculate this type of loading as well. We are trying to trim the fat as you could say. The current machine we have uses 8" x 4" x 1/4" tubing and i am trying to justify 6" instead.

 

[nvn]

EspElement: Can you provide length and cross-sectional dimensions, preferably in mm, of your bottom, horizontal tube, and your diagonal brace? It appears your upright tube can be initially approximated as a cantilever beam with an end moment. P = 23 130 N, X = 638.18 mm, L = Y + 57.15 mm = 2271.7 mm, E = 200 000 MPa, I = 19.541e6 mm^4. Therefore, deflection, delta = M*(L^2)/(2*E*I) = (P*X)(L^2)/(2*E*I) = 9.75 mm.

The diagonal brace will decrease this deflection slightly, but the bottom, horizontal tube will increase it. Therefore, we will wait until you post the above dimensions and joint centerpoint dimensions. Also, are you using fillet welds, groove welds, or what? What is the material specification for the tubes, and what is the weld material? You might also want to include the dimensions to the upper and lower carriage pins.

 

[pongo38]

I won't advise you on fatigue, because I don't know enough about it, and I don't carry professional indemnity insurance. It seems to be important in your case. If you have an existing machine, I would measure the deflection with a dial guage, and use the relationships in the next sentence to estimate the CHANGES to deflection and stress. If we call your original 8" and proposed 6" dimensions d, then you need to realize that deflection is inversely proportional to d^4, and stress inversely proportional to d^3.

 

[pongo38]

I should have added that a suddenly applied load gives rise to double the stress from a gradually applied load, and a dynamic load even more than that. If you are trying to do an equivalent static analysis, maybe you should consider a factor of safety greater than 2. Also I would be interested to know what are the consequences of failure, from the point of view of danger to life, property, and the economics of the situation. Is it possible for operatives to abuse the system, for example by overloading it? These considerations perhaps could and should outweigh the small saving from a marginally smaller column. Of relevance to optimising designs, here is the link to a great poem "the wonderful one-hoss shay" that was designed perfectly so that nothing was stronger than it need be. http://www.legallanguage.com/resources/poems/onehossshay/