Shear Strength of Wide Flange Steel Beams 2

[J1D]

In codes, text books we can find well established curves between the critical shear stress and the shear slenderness. In industrial field, it is common to have beam flanges coped at ends and connected to perpendicular beams with end plates and bolts. The coped length can be anywhere from say 3” to 12”. Can anybody advise how to calculate the local shear buckling strength (of the coped segment) and the entire shear buckling strength of this kind beams?

Thanks in advance.

 

[Lutfi]

First when I am computing shear stresses on beams I simply use the web area only and totally disregard the portions of the flanges. I think this is conservative.

I have done more sophisticated calculations considering bi-axial bending and torsion. In these cases I reverted to basic strength of materials using the following equation:

Stress = (Sx+Sy/2) + or – [(Sx-Sy)^2 + Tau^2]^0.5

Good luck

 

[jec67]

I agree with Lufti's response. To further the discusssion: Your inquiry about the conditions at the coped section of the beam are addressed in the AISC ASD 9th edition. It is in the section on connections.

Basically, when the beam is coped, one has a situation which involves block shear and tension at the connection. The AISC contains a full explanation on the design for coped section.

 

[BFPartners]

As mentioned above, the flanges of beams are not included in the shear capacity of a section. When calculating the shear capacity, there are several calculations which should be performed to determine the shear capacity of the section. Normally, clip angles or plates are sized to carry the total shear capacity of the member thus no failure is anticiapted in the clip design before excessive deformation occurs in the beam. Most clip designs of beams are by the steel fabricator and are shown on the steel fabrication or shop drawings. The capacity should be sized based on:
1. Gross cross section of the web
2. Net cross section of the web (minus the bolt holes)
3. Capacity of the bolts in shear
4. Capacity of the clips in shear
5. capacity of the perpendicular beam in shear
6. Bolt tearout distances
7. Web Crippling...

The designer has to determine the mode of failure before the faiure load can be stated.

As for crippling of the web within a bolt group, this is unlikely since the short web length (between the bolt holes) will not follow "typicaly buckling formulas" due to the length :width ratio being too low. This becomes a shear or crushing mode of failure. As for other locations where there are large concentrated loads on beams, buckling of the web may occur due to sufficient length:width ratios thus the reason for bearing stiffeners or traverse stiffeners where the calcualtions dictate or for "good practice".

(Most Steel handbooks have design data for eccentric loads on weld or bolt groups)

 

[J1D]

Thanks for the input. Very helpful!

I used Eq. A-F2-1, A-F2-2 and A-F2-3 of AISC LRFD Specification to calculate the shear strength Vr of wide flange beams and used the procedure described in Part 9, DESIGN OF CONNECTION ELEMENTS, of AISC steel construction manual (LRFD) to calculate Vr of beams with flange coping.

It’s interesting to notice, based on the calculation, that Vr of a WF beam without coping is much higher than that with even one flange coped, although in Vr calculation we consider only the web to resist the shear force. In addition, Vr of a WF beam with both flanges coped is much lower than the beam with only one flange coping.

 

[SlideRuleEra]

J1D - The definition of a beam's "web", as applied to shear calculations, is quite different than what we usually refer to for other purposes. This is best demonstrated as an example - consider an uncoped W12x50 - for shear calculations the crossection of the web is 0.370" x 12.19" (including a little slice passing through what is usually considered to be the flanges).
When the beam is coped, you not only "loose" the flange, but also a portion of the (shear calculation) web. This explains your observation that shear capacity goes down when one side is coped, and goes down even more when both sides are coped.

 

[J1D]

The reason of the significant drop of the shear strength is mainly due to the loss of the web stability. Without the top flange a wide flange section is no longer qualified “compact”, different critical stress calculation criteria then dictate. Also, flange coping means big loss of moment of inertia, which controls the shear strength as well.

Taking the W12x50 beam as an example. With full section, Vr = 124 kips. When the top flange is coped 2” deep by 6” long, Vr = 80 kips. If both flanges have the same coping, Vr = 32 kips!