Block shear equation terms

[nicomachus]

Hello all:
I am trying to teach myself LFRD steel design from an outdated textbook and came across block shear in the chapter about tension members. Sorry if this is a little obvious, but I am new to this. The section about block shear repeats from the AISC manual section J4.3, equation J4-3a: (phi)*Rn = (phi)[0.6*Fy*Agv + Fu*Ant] & equation J4-3b: (phi)*Rn = (phi)[0.6*Fu*Anv + Fy*Agt]. Now, I get that the sum of the strengths of the shear surface and the tension surface will contribute to the total resistance, but what I don't understand is why gross areas are being considered at all. My understanding is that gross areas are the "full" area under consideration and omits holes. So for example, it is used to determine the yielding limit state of a simple bar which occurs in the middle of the bar before it occurs in the area where holes are (obviously you would use the cross section of the bar perpendicular to the load for Ag, it's not the orientation of the gross area that is confusing me). But in the case of block shear, failure will occur along the bolt holes, so why use a gross area that omits them in determining the resistance to block shear? They just kinda declare that this is the equation you should use from the AISC manual and then go on to an example. Any help would be greatly appreciated.

Thanks!

 

[cliff234]

The block of steel at the connection could rip out through the hole (net section) or it could rip out right at the edge of the hole (gross section). When checking the potential weak link though the hole you use Fu. When checking the potential weak link at the edge of the hole you use Fy. If the holes are very small (or spaced far apart) then the gross section through the tear-out block will be the weak link. If the holes are very big (or spaced very close together) then the net section might be the weak link. The gross section that is used when checking block shear is not based on the entire depth of the member. (You do have to check that as well but it’s not part of the block shear check.) It’s based on the block that might rip out at the connection. Look at figure C-J4.1 in the 14th edition AISC Manual. That figure shows the block of steel through the net section. What is not shown is the slightly wider block that extends to the edges of the bolts, which would be the block of steel through the gross section. Note that the tension component of block shear strength equation is only calculated at the net section for both the gross and the net section calculations. (If I remember correctly the equation used to be more complicated, but it was simplified to eliminate having to check the tension component at the gross section because testing showed that the net tension component always controlled over the gross tension component.)