Combined Sections in AISCM ASD 9th Edition

[pflow]

Part 1 of AISCM ASD 9th Edition tabulates properties for combined sections.

I know the general practice is to weld the beams to form the combined sections.

However, is there a method, procedure, or calculation, to determine bolt size and spacing for joining two beams so they may be considered a combined sections (i.e their moment of inertia may be combined)?

 

[SteelPE]

Your standard mechanics of materials text should cover this. The standard equation is q=VQ/I where q is the shear flow required per unit length that must be transferred from one section of a beam to another so they act together.

 

[TLHS]

Shear flow will govern in primarily shear and bending loaded members. However, there are also requirements if it's a built up column to control local buckling. I'm assuming they're listed in the AISC code. We've got three or four pages of it in CISC S16.

 

[pflow]

Thank you for the replies. Good information.

I found shear flow in my mechanics of material by Beer. Looking forward to doing the math.

 

[SteelPE]

Depending on how complex your shapes are, the math is really quite simple. Recently I needed to stitch weld a beam to a channel, the calculation took only a few minutes to complete.

 

[pflow]

SteelPE, I am finally getting back to this. If I could exploit your expertise again to quickly check my calc below:

Combined Section W12 x 40 on bottom and C15 x 33.9 bolted on top of it (long side of C15 x 39.9 up)

Input

Beam 1: W12 x 40

I1 = 310 in^4
A1 = 11.8 in^2
yc1 = 11.94 in / 2 = 5.97 in

Beam 2: C15 x 33.9

I2 = 315 in^4
A2 = 9.96 in^2
yc2 = yc1 + 15 / 2 = 19.4 in

Shear Load: V = 10.3 kip
Bolts: 5/8” dia. A325 with 30 ksi allowable per AISCM Table I-D

Calculation

The centroid of the combined section is( as measured from the bottom of the W12 x 40):

yc = A1 * yc1 + A2 * yc2 / (A1 + A2) = 12.1 in

Using parallel axis theorem,

Ic1 = I1 + (yc – yc1)^2 * A1 = 310 in^4 + (12.1 – 5.97)^2 * 11.8 in^2 = 759 in^4
Ic2 = I2 + (yc2 – yc)^2 * A2 = 315 in^4 + (19.4 – 12.1)^2 * 9.96 in^2 = 846 in^4

I_comb_sect = Ic1 + Ic2 = 1605 in^4

Q = (yc2 – yc) * A2 = 72.8 in^3

q = V * Q / I_comb_sect = 5.6 kip / ft

Abolt = (PI/4) * dbolt^2 = 0.31 in^2

V_bolt_allow = 30 ksi X 0.31 in^2 = 9204

s_bolt_min = V_bolt_allow / q = 19.7 inch

 

[BAretired]

Provide a cross section.

BA

 

[pflow]

Cross section sketch is attached.

I lnow buckling may be a concern as TLHS mentioned.

 

[BAretired]

Beam 1: W12 x 40

I1 = 310 in^4
A1 = 11.8 in^2
yc1 = 11.94 in / 2 = 5.97 in

Beam 2: C15 x 33.9

I2 = 315 in^4
A2 = 9.96 in^2
yc2 = yc1 d1 + 15 / 2 = 19.4 okay in

Shear Load: V = 10.3 kip
Bolts: 5/8” dia. A325 with 30 ksi allowable per AISCM Table I-D

Calculation

The centroid of the combined section is( as measured from the bottom of the W12 x 40):

yc = A1 * yc1 + A2 * yc2 / (A1 + A2) = 12.1 in

Using parallel axis theorem,

Ic1 = I1 + (yc – yc1)^2 * A1 = 310 in^4 + (12.1 – 5.97)^2 * 11.8 in^2 = 759 in^4
Ic2 = I2 + (yc2 – yc)^2 * A2 = 315 in^4 + (19.4 – 12.1)^2 * 9.96 in^2 = 846 in^4

I_comb_sect = Ic1 + Ic2 = 1605 in^4

Q = (yc2 – yc) * A2 = 72.8 73.1? in^3

q = V * Q / I_comb_sect = 5.6 kip / ft

Abolt = (PI/4) * dbolt^2 = 0.31 in^2

V_bolt_allow = 30 ksi X 0.31 in^2 = 9204

s_bolt_min = V_bolt_allow / q = 19.7 inch

Looks good to me except as noted.


BA

 

[pflow]

Thanks BA, I appreciate it.

 

[BAretired]

To prevent buckling, the top flange of the channel will have to be laterally braced. Because of lack of symmetry, it might not hurt to brace the top flange of the WF as well, although it is completely in tension by calculation.

BA

 

[pflow]

BA, Thanks, yeah I have been using the formulas in AISCM Chapter F for this. Is this the right way to do this?

 

[BAretired]

Don't know. I'm Canadian.

BA

 

[dhengr]

You would do well to actually work on understanding your problem in a fundamental way, rather than being a blind follower of some obtuse code which you don’t really understand either. You would also do well to explain the reasons for what you are trying to do with that combined section and insistence on bolting; because without a really good explanation and reason for what you are trying to do, anyone in their right mind would think/say that was the worst combined section they had ever seen. Give us a clue as to what the heck you are trying to do; loading, span length, supports, means of bracing, type of structure which dictates those two sections, etc. etc. Just running a few calcs. which don’t have any major math errors, doesn’t make for good design. BA is a very good teach and mentor, but maybe a little too kind and easy going, on you. The calc. is correct, I have very little doubt about that if he says so, but there are still a dozen details that go unanswered, since you didn’t ask, didn’t even know to ask. How do you intend to brace that combined member? How efficient is that combined member when that little top flange of 15C will be buckling or at Fy, when the rest of the section is working at 15% of Fy? Is there a better way to detail this? Many times two rolled shapes are not the best answer.

 

[pflow]

dhengr,

Thanks for the feedback.

I was not aware the Manual of Steel Construction, Allowable Stress Design, 9th Edition was an obtuse code.

Anyway, the application is assembling a purchased enclosure provided with C Channels onto a skid frame composed of W flange beams. Bolting is preferred so they may be shipped separate. Loading is from lifting which is about eight point loads. The W flange beams on the bottom are sized for the whole lifting load but I wanted a basis for bolt spacing.