Steel to wood

[WBUW]

I've been asked to compare the strengths of a couple different sections, without the use of loads. (consider it to be flexural failure)

I seem to recall a procedure that was used way back when I took mechanics of materials.

I have the sizes of the steel and the wood member. To ballpark it I used the prismatic method, using the section moduluses, but I have a very strong memory of a more specific example in my mind. I have the 4th ed hibbler if anyone else recalls what I am talking about.

Thanks
Will

 

[rday]

The problem with the section moduli is they a purely shape dependant and the same from material to material.

You want to look at transforming sections, which uses the elastic moduli to equate one material to another.
Used in analyzing composite beams.

 

[msquared48]

Right. The area, S and I values drop out for the same section regardless of the material, leaving only the relative E (Elastic Modulus) for Deflection , and G (shear modulus) for shear values. You could also compare the relative Yield stresses for bending.

Mike McCann
McCann Engineering

 

[WBUW]

Thanks guys, just happened to flip to it in the book. Its been a while.

 

[Lion06]

I am not sure I agree completely with the above posts. To compare the STRENGTHS of different materials would not require the use of n=(Es/Ew). That would be used for stiffness (deflection calcs), or transforming one material to another for a composite section check.
When comparing the STRENGTHS of two different members made of two different materials, I would compare the allowable moments (that is the strength after all, right?). I guess you should compare allowable shears to be correct, also.
I would compare S*(fb) for wood - and S*fb for steel.
That will give you a comparison of strengths.
Please let me know if I missed something in the OP.

 

[csd72]

I 100% agree with structuralEIT on this one. It is no more complicated than that.

That is assuming that it has continuous lateral restraint, if not buckling will need to be considered.

csd

 

[msquared48]

csd72 and StructuralEIT:

If I understand the problem correctly, I believe you've both missed the point of the problem here...

I understand that the same shape is being used, just different materials. Consequently, any properties relating to the section used would fall out of the equation since they are equal - A, S, and I in particular, so they are irrelevent in the solution. The only factors that do not fall out, are E, G and the ultimate / allowable bending and shear stresses, which vary with the materials used.

Did I miss something?

Mike McCann
McCann Engineering

 

[Lion06]

msquared-
The OP says, "I've been asked to compare the strengths of a COUPLE different sections". It doesn't say the strength of A section using a couple different materials.
The way csd and myself have interpreted this problem is the only one that seems to make sense. If you are comparing a single section, one made of wood and one made of steel, there really is no comparison. Steel is MUCH stiffer and MUCH stronger. You don't need to go beyond comparing E and fb. Nothing more is needed unless you are comparing a steel plate in strong axis bending, but that doesn't seem to be what the OP is implying as no information regarding that is given.
He also says, "I have the SIZES of the steel and the wood member." To me, sizes means that there is a different size wood member and a different size steel member.

WBUW-
Can you please clarify your question.

 

[WBUW]

I have specific sections in mind. Since there appears to be some interest here lets just go through the calcs.

The root of the problem is that they want to replace a 4x12 we'll call it a DF-L#1 with a 2x10x1/2 HSS (assume A36 for now) steel section. I have not been given any loads to size the member as one normally would.

My first through was to use the transformation method, but I could not remember where it was. Knowing the properties of the HSS I was going to try to calc out its wood equivalent, or visa versa.

As I could not remember how to do this, I thought I would ballpark it using the prismatic method. Section Mod = Mmax / Allowable Stress. => Mmax = Section Mod x Allowable Stress.

Steel => Mmax = 36ksi x 11.1 in^3 = 399.6 k-in

Timber, as timber is not a homogenous material comparison using this method is not really that accurate...looking at the NDS the flexural strength (lets just assume flexural failure) is about 1 ksi.

Wood => Mmax = 1ksi x 78.83in^3 = 78.83 k-in

Comparison of max moments = 399.6 / 78.83 = 5.07

Hense the steel section is roughly 5x flexurally stronger than the wood.

I have not yet ran through the transformation calcs...will post when I do. Got busy yesterday, will be out of the office for a while today too...

 

[WBUW]

Whoops that should be a 2x10x1/4 HSS

 

[Lion06]

Based on your needs, I think what you did is fine. There is no need to do a section transformation using n. It just is not necessary in this situation. I would caution against using the yield stress for an allowable stress for the tube steel. The allowable would be more along the lines of 23.76 ksi. This would get you an allowable moment around 264 k-in. This is still much stronger than the wood member, but that was not hard to figure out and you needn't go further.
Also, I don't know why you are saying that this isn't a good (accurate) comparison. I think this comparison is fine and see no problems with it at all.

 

[WBUW]

Eh, I will run it anyway just to see what the difference is.

How are you coming up with 23.76 for the allowable. I throught about taking some reductions off the yield strengths, but I wasn't sure what the appropriate reduxs were.

I am just assuming 36ksi, for HSS's isn't it more common to see 42 ksi? What is the common strength for them, anyone? I seem to remember pipe steel being stronger...

 

[csd72]

WBUW,

A transformed section of a single material is meaningless as far as strength comparison is concerned.

Transformed section is for composite or built up sections as the stress induced in the materials is relative to the stiffnes of the material. n is meaningless when you are talking about 2 separate sections .

Deflection and shear will not be an issue on this section, but you may want to compare the I and Vmax values just for completeness.

You are definately thinking too complex for this simple problem.

csd

 

[Lion06]

It still looks like csd and I are on the same page.

Yes, 42ksi is more common for tubes, but you did say assume 36ksi.
I came up with 23.76 from fb=0.66fy. Check out the green book for tubes. For fy=42ksi, your fb would be 27.72ksi and produce an allowable moment of 308 k-in - still way higher than the wood, but still lower than 36ksi using the full fy.

 

[WBUW]

Ok, well re-running the numbers at 27.72 the steel is 3.9 times the wood section.

Running the transformation (I'm was to see)

n = Ew/Es = 1.7/29 = 0.059

Bst = nBw = 0.059 * 3.5 = 0.207 inches

This equates to a 0.207 x 11.25 steel plate. Calculating I = bh^3/12 = 24.56 in^4

I'm unsure if a linear comparison is very accurate here, but the Ixx of the steel is 78.83 / 24.56 = 3.2

So, 3.9 to 3.2, unless someone knows quick and dirty better relationship to use than the linear comparison of the Ixx values.

StructuralEIT
Yeah, honestly I haven't looked up the spec yet, so I wasn't sure what the steel strength was.

fb = 0.66fy sounds familiar, I do mostly wood and concrete so not as familiar with steel as I could be. I have the 9th edition of the AISC ASD, do you have a page for the formula and where you are finding the allowable moment so I can toss in a couple markers?

Think that pretty much takes care of it, thanks guys.

 

[Lion06]

page 5-48. You will see there are some other criteria there regarding compact sections, but most tubes fall into this category and the 0.66fy is applicable.

 

[Lion06]

also, the 3.9 value you reference is for STRENGTH. The 3.2 value is for STIFFNESS (this would be used in deflection calcs, not strength calcs).

 

[csd72]

Page 5-45.

 

[WBUW]

Thanks

 

[nutte]

Fy for rectangular HSS is 46 ksi. Round HSS has a yield of 42 ksi. These are both ASTM A500 Gr. B