combined shear and bending fv/Fv + fb/Fb 2

[delagina]

sqrt((fv/Fv)2 + (fb/Fb)2)

i am checkin a calc for steel with this equation.
where can i find this.

i know combined axial and bending but shear and bending.

 

[Lion06]

I've never checked this. The max shear stress is always at a different location than the maximum bending stress. I suppose that at some point along the height of the cross section there will be more substantial shear and bending stress at the same location, but never the maximums.

 

[delagina]

if it's a cantilever?

he also has same combined check for the welding of cantilever beam to plate.

 

[Lion06]

Even on a cantilever - max bending stress is in the flanges, but max shear stress is at the centroid of the section.

 

[ToadJones]

I'm with Lion on this one.

 

[delagina]

thanks lion

how about the welds?

 

[Lion06]

Even for the welds. I typically see the flanges full-pen welded and a shear connection provided in the web. The weld provides the moment capacity of the section and the shear takes the shear. Sure, they're probably sharing a little, but not enough to make me check it.

Even if you full-pen weld the flanges and fillet weld the web, I still would check the web weld for the shear and the flange welds are ok for bending (tension/compression) simply by the beam section being ok.

I suppose there's a case to make for checking the entire I-shaped weld for combined shear and bending with V/A + M/Sw, but I think the web is so stiff compared to the flanges (from a shear standpoint) that the flange welds see very little direct shear stress

 

[JRGse]

Keep in mind that the combined shear and bend is a check required in design with coldform members.

 

[delagina]

per blodgett 3.3-11 it does have combined shear and bending for shear.

 

[Lion06]

I think the weld in the example that you reference in Blodgett is a little different the cantilever beam connection. The angle leg in the Blodgett example can be assumed a rigid body that is capable of delivering a uniform shear to every weld element. I don't know that the same is true of a WF section. From a shear standpoint, the web is much stiffer than the flanges and, while you'll get shear stresses in the flange welds, it will taper off quickly.

 

[Lion06]

I should clarify...... you'll get shear stresses in the flange welds near the web, where it's still reasonably stiff. As you get away from the web, the shear stress in the flanges will taper off quickly.

 

[WillisV]

There are a variety of situations in steel design (primarily connections) where one might want to check the effect of shearing stresses on the available flexural stress. For instance, the procedure for an extended shear plate in the 13th Ed. Manual uses a form of von-Mises criterion to reduce the available flexural strength based on the applied shear (see p10-103 13th ed manual - the Fcr equation). Though, somewhat amusingly, the manual itself notes that this is a bit silly on the bottom of pages 9-3 and 9-4 (I highly recommend reading this section to see why).

This topic generally comes up for gusset plate design by the uniform force method where the welds are designed for combined axial load, shear, and perhaps bending. In this case, in my opinion the easiest way to design the gusset itself is to determine the peak weld stress using typical elastic combination of stresses and then make sure the gusset plate is thick enough to develop the size of weld required using the equations on p9-5 of the 13th ed. manual.

Alternatively, if you really feel the need to check an interaction equation, I would recommend using a plasticity interaction check from Astaneh:

(Mu/PhiMn)+(Pu/PhiPn)^2+(Vu/PhiVn)^4 <= 1

As you can see from this equation, the shear contribution is quite small (to the fourth power).

 

[ToadJones]

If sizing a weld for combined stress, it makes sense to combine all forces/stresses at the point where the combined stress is the highest.

For example, if you are using an all-around weld of a wideflange cantilever to a column flange, at the top flange you MAY have:
max strong axis tensile bending + max weak axis tensile bending shear + any axial tension + any torsion

In this case the highest stress in the top flange would be at the tip of the top flange that is in tension. In a case like this (and I believe Blodgett does this...) one usually uses an average shear stress for the entire wideflange shape. This is, like Lion is saying, conservative.

 

[ToadJones]

revised...

max strong axis tensile bending + max weak axis tensile bending + shear + any axial tension + any torsion

 

[csd72]

Many codes say that the combined shear and bending only needs to be checked at locations where the shear is more than 60% of the shear capacity. Otherwise, agree with Lion06.

 

[RFreund]

WillsV - Where does Astaneh's equation come from?

Thanks

EIT

 

[WillisV]

@RFreund - the short answer is it comes from Astaneh.

...though I assume you are asking for the actual reference =).

So for the long answer see equation 4.2 from his 12/1998 Steel Tips article "Seismic Behavior and Design of Gusset Plates". Steeltips articles can be downloaded (for a nominal price) here:

http://www.steeltips.org/steeltips/index.php

The original equation was actually proposed by Neal in 1977 I believe. Thornton discusses combined stresses in the attached white paper and, if you are going to check interaction, proposes this same equation (the one in my previous post from Astaneh / Neal) on the bottom of page 4 in the attached.

 

[RFreund]

Thanks!

EIT