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structure dimension 6
- Thread starter ash1982
- Start date
ash1982:
Assume a simply support beam loaded on mid-span with a concentrate load:
L = beam length between center of verticals (say 300 mm)
P = applied load (200 kg + assumed/estimated beam weight)
b = frame/member width (40 mm)
h = member depth to be determined
va = allowable shear stress (0.4*fy, fy = yield strength, mpa)
fa = allowable flexural stress (0.6*fy)
From above we derive two relationships:
P <= 2*va*b*h
--> h >= P/(2*b*va) (1)
M = P*L/4
S = section modulus = b*h^2/6
M <= fa*S
--> h >= [6*M/(fa*b)]^0.5 (2)
The larger h from above satisfys strength requirement. Now check performance of service:
D = deflection
E = modulus of elasticity
I = moment of inertia (b*h^3/12)
D (max) = P*L^3/(48*E*I), at center of the beam
Select a bigger size beam if deflection is too large, and repeat the steps. The result would be conservative for a statically loaded beam.
You may wish to check the vertical members:
1. Assume column simply supported on both ends, k=1.
2. Find allowable stress for respective k*L/r
L = column length
r = radius of gyration (of the weak axis)
3. Check compression stress (P/(2*b*h)) against the allowable. Repeat steps 2 & 3 if necessary.
Finally, check the bottom beam use the same approach as for the top beam. However, P = 200 kg + weight of all 4 members. So the bottom member shall be bigger than the top as the result.
Check my formulations for correctness. Good luck.
Assume a simply support beam loaded on mid-span with a concentrate load:
L = beam length between center of verticals (say 300 mm)
P = applied load (200 kg + assumed/estimated beam weight)
b = frame/member width (40 mm)
h = member depth to be determined
va = allowable shear stress (0.4*fy, fy = yield strength, mpa)
fa = allowable flexural stress (0.6*fy)
From above we derive two relationships:
P <= 2*va*b*h
--> h >= P/(2*b*va) (1)
M = P*L/4
S = section modulus = b*h^2/6
M <= fa*S
--> h >= [6*M/(fa*b)]^0.5 (2)
The larger h from above satisfys strength requirement. Now check performance of service:
D = deflection
E = modulus of elasticity
I = moment of inertia (b*h^3/12)
D (max) = P*L^3/(48*E*I), at center of the beam
Select a bigger size beam if deflection is too large, and repeat the steps. The result would be conservative for a statically loaded beam.
You may wish to check the vertical members:
1. Assume column simply supported on both ends, k=1.
2. Find allowable stress for respective k*L/r
L = column length
r = radius of gyration (of the weak axis)
3. Check compression stress (P/(2*b*h)) against the allowable. Repeat steps 2 & 3 if necessary.
Finally, check the bottom beam use the same approach as for the top beam. However, P = 200 kg + weight of all 4 members. So the bottom member shall be bigger than the top as the result.
Check my formulations for correctness. Good luck.
Hi ash1982
I have uploaded a file which gives a formula for the depth of the top member making the assumption that the top member is a simply supported beam in truth of course its far from it but it might get you started.
I got the formula by manipulating the standard bending stress formula ie
[σ]= M*y/(I) I= b*d^3/12
y = d/2
where b= beam width 40mm
M= bending moment
I = second moment of area
You need to check the vertical legs as suggested cntw1953.
Also if your profiling this plate I would put large radius on all the internal edges, square corners as you have them in your model will give rise to large stress concentrations which might cause you problems.
Seriously you need to get some help from someone your working with as we cannot see or know all the issues.
Personally I would do some ballpark calculations and ask the stress guys to model it to finalise the design.
I have uploaded a file which gives a formula for the depth of the top member making the assumption that the top member is a simply supported beam in truth of course its far from it but it might get you started.
I got the formula by manipulating the standard bending stress formula ie
[σ]= M*y/(I) I= b*d^3/12
y = d/2
where b= beam width 40mm
M= bending moment
I = second moment of area
You need to check the vertical legs as suggested cntw1953.
Also if your profiling this plate I would put large radius on all the internal edges, square corners as you have them in your model will give rise to large stress concentrations which might cause you problems.
Seriously you need to get some help from someone your working with as we cannot see or know all the issues.
Personally I would do some ballpark calculations and ask the stress guys to model it to finalise the design.
Things you need to do:
1. You need to come up with a free-body-diagram to solve for the weight distribution (which will include finding the CG). If parts can move, you may have to consider several different orientations. You may also need to think about other possible loads on your parts.
2. Determine exactly what material you will be using and what it's properties and capabilities are - then knock the capabilities down at least by half (you should probably have an even larger factor of safety for something like this - it looks like something that might end up being beat to crud)
3. Once you know the weight distribution and the material specifications, you'll have to look at buckling and yielding in your structure for your worst case load condition. If there's any question about which case is the worst case, you should calculate it for all the cases that look like they might be the worst. Pay special attention to stress concentrations in areas such as holes, fillets, and larges changes in net section. Welds are an area of special concern because the material properties of a weld are often lower than that of the parent material. In addition, welds are often at the same locations as stress concentrations. Check literature for information on analyzing weld joints (Shigley's Mechanical Engineering Design is good for basic analyses)
4. You'll have to determine what an acceptable deflection for your part is and make sure the cross section of your supports. You should calculate the deflection your parts under worst case loading. If there's any question about what is the worst case, calculate all cases in question.
5. If your structure fails to meet your requirements in any of the calculations you performed, change your geometry (or material) and iterate until you have a design that works.
If you don't have experience with the types of analysis that I mentioned above, you may need to go get outside help. It looks like you're dealing with some pretty heavy parts, and that a failure could end up hurting someone. You could always try your own hand at an analysis, then hire a consultant to check your work.
1. You need to come up with a free-body-diagram to solve for the weight distribution (which will include finding the CG). If parts can move, you may have to consider several different orientations. You may also need to think about other possible loads on your parts.
2. Determine exactly what material you will be using and what it's properties and capabilities are - then knock the capabilities down at least by half (you should probably have an even larger factor of safety for something like this - it looks like something that might end up being beat to crud)
3. Once you know the weight distribution and the material specifications, you'll have to look at buckling and yielding in your structure for your worst case load condition. If there's any question about which case is the worst case, you should calculate it for all the cases that look like they might be the worst. Pay special attention to stress concentrations in areas such as holes, fillets, and larges changes in net section. Welds are an area of special concern because the material properties of a weld are often lower than that of the parent material. In addition, welds are often at the same locations as stress concentrations. Check literature for information on analyzing weld joints (Shigley's Mechanical Engineering Design is good for basic analyses)
4. You'll have to determine what an acceptable deflection for your part is and make sure the cross section of your supports. You should calculate the deflection your parts under worst case loading. If there's any question about what is the worst case, calculate all cases in question.
5. If your structure fails to meet your requirements in any of the calculations you performed, change your geometry (or material) and iterate until you have a design that works.
If you don't have experience with the types of analysis that I mentioned above, you may need to go get outside help. It looks like you're dealing with some pretty heavy parts, and that a failure could end up hurting someone. You could always try your own hand at an analysis, then hire a consultant to check your work.
I just looked at this thing again and you mentioned that it's a "manipulator". I assume that this means it's moving in some way. Make sure that you understand both the dynamic and static loads on the part, as they're both important. Understanding the loading can sometimes be a very challenging part of the analysis.
let's start at the beginning ...
can you solve the reactions of a beam ? that's what the green arm looks like to me. if you can, consider the two extremes on position of the arm. this will give you the load into the grey frames (that you're designing). hint, if someelse is designing the green arm, you could ask for their reactions.)
once you've got the load applied, the frame divides into beams and columns; each can be analyzed in turn.
point to ponder ... consider lateral load, what looks to be your x-direction, along the green arm ... the grey supports are not very effective in this direction.
each of your frames will be supporting something like 200 kg (mass, i assume) = 2000N ... not a heck of a lot. what safety factor will you apply ? 2?, 4??
btw ... rant removed ('cause i couldn't be bothered to type it a 2nd time)
can you solve the reactions of a beam ? that's what the green arm looks like to me. if you can, consider the two extremes on position of the arm. this will give you the load into the grey frames (that you're designing). hint, if someelse is designing the green arm, you could ask for their reactions.)
once you've got the load applied, the frame divides into beams and columns; each can be analyzed in turn.
point to ponder ... consider lateral load, what looks to be your x-direction, along the green arm ... the grey supports are not very effective in this direction.
each of your frames will be supporting something like 200 kg (mass, i assume) = 2000N ... not a heck of a lot. what safety factor will you apply ? 2?, 4??
btw ... rant removed ('cause i couldn't be bothered to type it a 2nd time)
ash1982,
I agree with EngineerTex. If you have to ask questions like this, you should not be doing the job. Even if we do provide useful help on your wall thickness, that is not the only thing that might cause a catastrophic failure.
Even if people are not hurt, you could still be producing something that will not work. Your company will be embarrassed. You will be embarrassed. Your customer will be pissed off.
JHG
I agree with EngineerTex. If you have to ask questions like this, you should not be doing the job. Even if we do provide useful help on your wall thickness, that is not the only thing that might cause a catastrophic failure.
Even if people are not hurt, you could still be producing something that will not work. Your company will be embarrassed. You will be embarrassed. Your customer will be pissed off.
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