Allowable Shear in Beam Table vs Equ. F4-1 2

[Tim76]

I am looking at the value in the beam tables for A36 channels C15x40. The allowable load where shear starts to control is 225k. When I use F4-1 i only get a allowable of 87.3k. Where am I missing something? I'm using the dimensions "T" and "tw" for the area of the web. Thanks.

 

[DRW75]

Tim76
Although this won't be terribly useful to AISC & Eq F4.1, following the CSA standard, this channel would have a pure shear capacity of 746 kN (168k) at yield of 250 MPa (36 ksi) - this is factored & follows a limit state design philosophy. However if considering web crippling & web yielding effects, these could govern depending on stiffeners & bearing length.

Hope this doesn't confuse, but may make an interesting comparison.

DRW75

 

[Tim76]

I should clear this up so you don't think I was trying to compare the 225k to 87.3k I was comparing 225k/2 to the 87.3k.

 

[Taro]

Recheck your calculations. The allowable shear is:

0.40*Fy*d*tw = 0.4*36ksi*15"*0.52" = 112.3 kips

The table gives an allowable load on the beam of 225 kips. Assuming a uniformly loaded, simply supported single span beam, the shear at each end is 225/2 = 112.5 kips

 

[SlideRuleEra]

Tim76 - Taro is correct. For shear calculations the web is assumed to be the full depth of the member, "d". In effect, you ignore the minimal shear capactity of the flanges that project beyond the plane of the web.

 

[JAE]

That's what I get too -
For a C15x40

d = 15"
tw = 0.52"
Fy = 36 ksi

h/tw = 15/.52 = 28.84
380/sqrt(Fy) = 380 / sqrt(36) = 63.33 therefore F4-1 valid to use.

Fv = 0.4 x 36 = 14.4 ksi

Max shear on C15 = Fv x d x tw = 14.4 x 15 x .52
= 112.32 kips

Beam table max load = 225 kips
225 / 2 = 112.5 kips max. end reaction

 

[DRW75]

I find it interesting that the AISC uses factor of 0.4.

The CISC allows for 0.66 shear factor and a material factor of 0.9.

I assume that it is simply the difference between LRFD & limit states.

DRW75

 

[UcfSE]

Shear yield is derived as 1/sqrt(3)*Fy, approximately 0.577Fy, which AISC rounds to 0.6Fy. With a safety factor of 1.5 the allowable shear stress is 0.6/1.5=0.4*Fy. I'm not sure what the 0.66 is for in other codes. The shear yield stress given in the AISC is derived using energy methods and can be found in mechanics of materials books.