Scaling Beam Problem. 2X - 0,5X 5

[X4vier]

Hi,

I need a beam for a crane but I'm out of commercial W shapes.

I tried to reduce the problem in scale by 0,5X to use the commercial W shapes range to predict my beam and later, to scale the W-beam to a Built-Up beam with 2x dimensions.

This beam the large one, must comply L/800 in vertical deflection, I was using L/800 in the small one (the 0,5X beam), considering the span as half the span. But the predicted beam doesn't comply with the deflection.

What am I doing wrong??

 

[centondollar]

Presumably, you know how to design a plated girder, so perform the calculations (MathCAD and similar programs allow for easy parameter updating and thus allow quick iteration of design) and choose the required web and flange sizes.

Presumably, you also have access to FEA software to receive the internal forces. If so, you should be aware that most software allows for custom stiffness properties (elastic modulus, second moments of area, torsion constants, warping constants etc.) to be input into the program, so I do not see how that would be an issue either.

What is the issue?

PS. You cannot "reduce scale" without changing the problem setting. If you have a span and loads, you must design to those - not to some "scaled" span and loads!

 

[CANPRO]

I hate to pile on to X4vier, but with all due respect, if you can't re-create the capacity tables for commercially sized sections by hand with any sort of reasonable accuracy, you have no business using those tables. If you can re-create those tables by hand then designing a custom built-up plate section is not difficult. What have been proposing to do in this thread doesn't make any sense and the amount of effort you spent running down this bizarre road could have been spent learning how to do it properly.

 

[dhengr]

X4vier:
To answer your first question..., “What am I doing wrong??” Everything!!

IF you are a Structural Engineer, you are not showing much knowledge of the subject with the way you are going about this problem. You are barking up the wrong tree here, and absolutely wasting everyone’s time as they try so hard to help and steer you in the right direction. You aren’t hearing/reading and understanding what they are saying. You should really put an end to this thread, and spend your time reading a few good textbooks on Engineering Mechanics, Strength of Materials, Theory of Elasticity, basic Structural Analysis and Design. And, since you are so confused about what you are doing, you really complicate your misunderstanding by the mid-stream problem change from a fairly simple beam problem to a column problem with a bunch of extraneous conditions added to an already complex stability problem. You are really hurting your understanding of the basics of the problem by trying to do something that you call scaling the problem down, that just drastically confuses the issues which you already seem to be having trouble with, issues you are having trouble understanding.

Just get this crazy scaling idea out of your head, eliminate all of the confusion it is causing and approach the problem is a straight forward fashion. The idea of using std. sections is all fine and good, but there is nothing magical about them and sometimes you can’t find one that works for your conditions. Then, you need to either reinforce an available std. section or design a built-up section of your own, which does fit your needs. Std. sections come in many sizes, and with increments within those sizes to allow them to fit/fill most structural needs. These exact sizes are based more on what the mills can do with their std. rolling sets and stands, in the way of manipulating/setting them, to produce thicker, wider flanges and thicker webs, than they are on some magic optimization of each shape. This produces groups of industry std. sizes for the market. In the process, they do pay some attention to thickness and width/thickness rations which make the sections less prone to buckling when fully stressed in normal usage. But, these are still not some magical optimized dimensions and sizes. They certainly can/do act as a guide for reasonable proportions though.

Go back to the beam problem for starters, a cleaner/simpler problem, and approach the problem in a straight forward fashion. You know the real span length, the beam bearing and end conditions, the actual moving load weight, etc. Draw moment and shear diagrams, looking for the max. moments and shears, and the ranges of same, with due consideration for load factors and the like.
1. Now, the normal beam design formulas and procedures from the/any steel manual will apply in designing the beam, with appropriate factors of safety or load factors and resistance factors, etc. You know/select Fy for the material you’ll use, and thus the various allowable stresses. You know the deflection limits you want, so now it is kind of a matter of working backwards to find the moment of inertia and section modulus you need. Stability, buckling, fatigue and connection details and the like come into play too, on down the design page.
2. Now, look at the std. sections tables and see if you can find a section that works for your needs. Many times you will put a cap channel on the top flg. of a std. section to improve its lateral stability, and you might put a cover pl. on the bot. flg. to further improve the moment and deflection cap’y. And now, you have to figure the improved section properties of this reinforced std. section, does it still not work. You might have to design your own built-up section to meet your needs, and here, the std. section table can kinda guide you in proportioning your new section, nothing magical or optimized, just a guide. A thicker flgs. will increase Ixx (the primary moment of inertia) quickly for moment and deflection considerations, and a thicker web, near the reactions will help with high shear stresses. As someone mentioned, this might start being a plate girder problem.
3. Of course, you have to calculate the section props. for your new built-up section, and this is an iterative process if your first selection is too light. You also have to design appropriate welding details for your built-up section, and they do not all have to be full pen. welds. Experience in the design process will help with the correct steps and selecting member sizes, but we all started at the beginning at one point in time. Just get this damn scaling thing out of your head.

You are really a baby wondering in the dark, based on your OP. Get your boss or some local mentor to help you with this because your are just spinning your wheels right now. They should know what you know and what you don’t know so as to keep you and the company out of trouble. It is dangerous pretending to be an engineer when you are so obviously not one yet. So, get with it, and get some local help in your technical training.