Optimizing Support Location for Workshop Crane Design

[woodywheel]

Homework Statement

I am trying to design a workshop crane and have found a considerable success so far. It is a maximum 2 ton crane and i have found which I beam to use by the method mentioned below.
Some of the specifications are
boom length(span) = 3 m
mast length(vertical portion) = 4 m
the boom is connected at 3m height remaining 1m to fix a support
I beam of 250x125x6/9 used has a yield point of 350 N/mm2, where 6mm is web thickness and 9 is flange thickness.
the beam will be welded to a round bar(with a pin inside) which in turn will be connected to a flange that again be welded to the mast. the calculation done is by taking into consideration if I beam is fixed at one end. My doubts are below
1.how can I find factor of safety here(dividing experimental by theoretical yield stress?? )
2. i want to fix a support on the boom of the crane which will be connected to vertical portion or mast of the crane which will be joined above the connecting point of boom, but i am not able to decide the exact location to connect the support on the boom. I am resolving forces here and there but i want the optimum position and angle of the support.
3.any good literature on the internet i can find

Homework Equations

Bending Moment= FxL
Second moment of inertia for I beam= (bh^3-(b-tw)xh1^3)/12
and bending Force is F/y=M/I

The Attempt at a Solution

Bending Moment= 5880 Nm
I= 333783168 mm^4
Bending stress= 21.7 N/mm^2
even my bending stress is 21.7 and selected I beam has a yield point of 350 N/mm^2

 

[woodywheel]

anyone??

 

[turbo]

Why not use a movable hoist on overhead rails? Depending on the spacing and strength of your rafters, you can get some really impressive loads in the air, and just stow the hoist off to one end of the building when not in use. No storage issues.

 

[PhanthomJay]

You don't wnat to mix the common USA units (inches, tons) with metric units (mm, Newtons).

The critical elements may very well be the mast, not the I beam, as well as the cable supporting the boom, and the connections. I don't have my tables in front of me. What's the I of the mast and the yield stress? Also, your calc for the I of the I beam might be off by a factor of 10, I can't be sure because of all the zeros of the SI units. Note that if the support cable is attached to the point of the load, the boom has no bending load, provided that the cable is stiff enough. Please clarify units and dimensions. Is the mast height of fixed height 4 m?

 

[nvn]

woodywheel: Your current second moment of area (I) value might be erroneous. Your formula looks correct, but your value might be off by a factor of ~8.6. Try it again, and show your work.

 

[woodywheel]

First of all thanks a lot for replies
@turbo- It is attached with a 2 ton movable hoist only
@phantom jay- since it is attached with movable hoist there will always be bending at some points, I am also including my calculations
@nvn- have a look at my calc

The boom is connected at 3m above the ground and remaining 1m height is left for fixing the supporting beam.
what factors should i consider to calculate load on joints, support and mast ?

1.Beanding Moment
=2000kgx3m
=6000kgm
=5880Nm
M=5880x10^3 Nmm

2. Second Moment of Inertia for I beam

((124)(248)^3 - 2(119/2)(232)^3)/12
I=33783168mm^4

3. Bending stress
f/y=M/I where Y= 125mm
f= (5880x10^3)x(125)/333783168
f=21.7 N/mm2

 

[nvn]

woodywheel: In post 1, you said the web and flange thickness is 6 mm and 9 mm, but now you seem to be using 5 mm and 8 mm. Your value for I is much better now, but then you failed to list it in item 3 of post 6. You currently have several problems in the way you are writing units, and you are violating the international standard. Please learn the correct way to write units.

1. Always leave a space between a numeric value and its following unit symbol. E.g., 125 mm, not 125mm. See the international standard for writing units (ISO 31-0).
2. N/mm^2 is called MPa. Always use the correct, special name for a unit. E.g., 21.7 MPa, not 21.7 N/mm^2.
3. When you multiply two unit symbols together, you must show a multiplication symbol, or at least a space. You cannot omit the multiplication symbol. E.g., you must use 5880 N*m, not 5880 Nm.
4. For long numbers having five or more digits, the international standard says you can write the digits in groups of three, separated by spaces. E.g., 33 783 168 mm^4, instead of 33783168 mm^4.

You are currently getting mixed up on unit symbols and decimal points. Learn and use the above international standard, to avoid mistakes. E.g., 5880 looks like it might be yet another mistake. Also, your y value is incorrect.

 

[woodywheel]

woodywheel: In post 1, you said the web and flange thickness is 6 mm and 9 mm, but now you seem to be using 5 mm and 8 mm. Your value for I is much better now, but then you failed to use it in item 3 of post 6. You currently have several problems in the way you are writing units, and you are violating the international standard. Please learn the correct way to write units.

1. Always leave a space between a numeric value and its following unit symbol. E.g., 125 mm, not 125mm. See the international standard for writing units (ISO 31-0).
2. N/mm^2 is called MPa. Always use the correct, special name for a unit. E.g., 21.7 MPa, not 21.7 N/mm^2.
3. When you multiply two unit symbols together, you must show a multiplication symbol, or at least a space. You cannot omit the multiplication symbol. E.g., you must use 5880 N*m, not 5880 Nm.
4. For long numbers having five or more digits, the international standard says you can write the digits in groups of three, separated by spaces. E.g., 33 783 168 mm^4, instead of 33783168 mm^4.

You are currently getting mixed up on unit symbols and decimal points. Learn and use the above international standard, to avoid mistakes. E.g., 5880 looks like it might be yet another mistake.

I am sorry for the above errors
the value of I used in 3 of post 6 is 33 783 168 only

here are my calculations again
the I beam used is 248*124*5 / 8

1.Bending Moment
= F*D
where F = 2 ton
= 2000 kg
= 2000*0.98 N
= 1960 N
and D= 3000 mm
so,
F*D= 1960*3000
= 5880 * 10^3 N*mm

2. Second Moment of Inertia
I= (b*h^3 - 2((b-tw)/2 *h1^3)/12

where b= 124 mm
h = 248 mm
tw = 5 mm
h1= 232 mm

I= 33 783 168 mm^4

3. finding stress

F/y= M/I
where y= 248/2 = 124 mm
M = 5880 * 10^3 N*mm
and, I= 33 783 168 mm^4

F= 21.5 MPa

 

[nvn]

woodywheel: Gravitational acceleration constant is g = 9.807 m/s^2, not 0.98. Try again.

 

[woodywheel]

woodywheel: Gravitational acceleration constant is g = 9.807 m/s^2, not 0.98. Try again.

oops...I did a silly mistake...got it confused with something else
well now its coming to be 215 MPa
so will the factor of safety be 350/215 = 1.59
and what about the other factors, I have to resolve the moment at different points in order to get most optimum position for the support?

 

[PhanthomJay]

I am not sure what you are doing in saying that the max moment is the load times 3 m. That is the max moment in the mast when the load is at the end of the boom. I think you are trying to find the boom (beam) moments and forces, and the best place to attach the cable to the boom for all movable load positions along that boom, is that correct?? And at any rate, the mast needs to be checked also, it might be fine, but I don't have a feel for SI units.

 

[woodywheel]

I am not sure what you are doing in saying that the max moment is the load times 3 m. That is the max moment in the mast when the load is at the end of the boom. I think you are trying to find the boom (beam) moments and forces, and the best place to attach the cable to the boom for all movable load positions along that boom, is that correct?? And at any rate, the mast needs to be checked also, it might be fine, but I don't have a feel for SI units.

yes I am trying to find out the the best place to attach the cable to the boom and i am aware that this will give the bending moment at the mast, but won't the value which we got for the stress in Mpa give us an idea that this beam can withstand this load by comparing this value by the yield strength of the material used ?

 

[PhanthomJay]

yes I am trying to find out the the best place to attach the cable to the boom and i am aware that this will give the bending moment at the mast, but won't the value which we got for the stress in Mpa give us an idea that this beam can withstand this load by comparing this value by the yield strength of the material used ?

What stress? You have not yet properly calculated the moment or the stress in the I beam. What you have calculated so far is the max moment in the 10 inch pipe mast.

 

[woodywheel]

What stress? You have not yet properly calculated the moment or the stress in the I beam. What you have calculated so far is the max moment in the 10 inch pipe mast.

how will I calculate the same for I beam then ?
and the value of F that is been found is the surface stress of the mast and can i compare it to tensile stress if the material for the mast ?
thnx

 

[PhanthomJay]

Design Optimization is not always an easy task. If you are trying to optimize the I beam design, you might want to consider different locations of the cable to beam attachment and different locations of the load point locations for each of those cable to beam atachment locations, and calculate the max moment in the beam under all cases. A little time consuming. But first you need to draw a free body diagram of the beam under each case, and calculate moments and axial forces. For example, if the cable is attached to the far end of the beam, and the laod is also at that point, the beam has no moment but high axial load. If the load is now moved toward the center of the beam, the moment increases and the axial load decreases.

Now if you move the cable -to -beam attachment to the midpoint of the beam, when the load is at the far end of the beam, you have a high moment at that midpoint...and when the load is moved toward the left, the momenet is lower, etc.

For now, ignore axial load and shears and focus on bending moments and stresses. How about matching cantilever moment with simple support moments for the optimum case?

BTW, is this a homework problem??

 

[nvn]

But won't the value we got for the stress in Mpa give us an idea that this I-beam can withstand this load, by comparing this value by the yield strength of the material used?

Yes, if the boom support cable goes completely slack. If the boom support cable goes completely slack, then you computed the bending stress on the I-beam correctly. (And you computed the factor of safety correctly, except it is ~1.62, not 1.59. Why did you say 350/215 = 1.59? Also, what minimum factor of safety is required for your project?)

Also compute the mast second moment of area (I) and mast bending stress. And as PhanthomJay asked, what is the mast material tensile yield strength? By the way, always use correct capitalization of unit symbols. E.g., MPa, not Mpa. See NIST for the correct spelling of any unit symbol.

PhanthomJay or turbo-1: Should woodywheel compute the I-beam stress for the above case assuming the boom support cable goes completely slack? Or is that too illogical or inapplicable? You know the I-beam would probably be OK if woodywheel does this quick check and the factor of safety already meets the minimum requirement.

 

[PhanthomJay]

.

PhanthomJay or turbo-1: Should woodywheel compute the I-beam stress for the above case assuming the boom support cable goes completely slack? Or is that too illogical or inapplicable? You know the I-beam would probably be OK if woodywheel does this quick check and the factor of safety already meets the minimum requirement.

That would be a conservative way to design the beam, however, if the cable goes slack, the beam is now unstable because of the pinned joint from beam to mast. I believe the OP is looking for the optimum point to locate the cable on the beam to cover all cases of the moveable load position along the beam's length, to minimize the size of the I beam. It appears that that point would be where the cantiliver moment from the load at the far end to that point, is equal to the simple suport moment when the load is at midpoint between the near end and that cable support point on the beam.