PCI 7th edition handbook issue

[JStructsteel]

For those that have the 7th edition, on page 6-37 they are going thru a angle design. They have the formula for Vu close to the bottom. Tell me what value you get for that, and then on page 6-38 tall me how they got their value for Vu. Im not getting it to match. Thanks

 

[Celt83]

pg. 6-37 and 6-38 are showing the computations for two different limits on the shear.
Limit 1 is Vu based on leg flexure:
Mu = phi*Fy*z
z = b t² /4
Mu = Vu*e

so Vu = phi*fy*b*t²/ 4*e

Limit 2 is Vu based on the anchor failure modes:
they work this out to an equation based on the tension and shear interaction equation and solve via iteration. the Vu they note under given on 6-38 is just a starting guess.

The Vu capacity is then the min[Vu,limit 1 , Vu,limit 2]

I'm making a thing:

http://www.thestructuraltoolbox.com

(It's no Kootware and it will probably break but it's alive!)

 

[JStructsteel]

If thats the case, then the value for Vu at the end of the calc (5805lb) gives a ecc equal to 2.33". how is that correct?

Disregarding everything else, the bending capacity of the leg (vu) is Vu = phi*fy*b*t2/ 4*e correct? Thus 4.556K (Im assuming critical section is above the bolt on the vertical leg).

What am I missing?

 

[Celt83]

If thats the case, then the value for Vu at the end of the calc (5805lb) gives a ecc equal to 2.33". how is that correct?

how are you back calculating e?
plugging their values back into the formula for a I get 3.0046" so correct to two decimal places.

Disregarding everything else, the bending capacity of the leg (vu) is Vu = phi*fy*b*t2/ 4*e correct? Thus 4.556K (Im assuming critical section is above the bolt on the vertical leg).

thats what I get. So limiting capacity for Vu in this case is governed by leg flexure.


I'm making a thing:

http://www.thestructuraltoolbox.com

(It's no Kootware and it will probably break but it's alive!)

 

[JStructsteel]

If ecc is 3.0, then Vu is 4.556K correct, not 5.805K? Based on the sketch, this is the only limit state for angle bending, ecc-3", and thus Vu is 4.556K

 

[Celt83]

yes

you are checking two limit states steel flexure and concrete anchorage
V_{u,steel flexure} = 4.6 k
V_{u,concrete anchorage} = 5.8 k

V_{u, design} = min[V_{u,steel flexure}, V_{u,concrete anchorage}] = 4.6 k

I'm making a thing:

http://www.thestructuraltoolbox.com

(It's no Kootware and it will probably break but it's alive!)

 

[JStructsteel]

Thanks Celt83. Its unfortunate they dont report it that way in the calc so its clear. I just wonder where they got the 5854 value they used?

 

[Celt83]

If you graph the function they derived you could eyeball that value being near the root. More likely they solved it previously and just used a close enough value to illustrate the iterative procedure for a solution.

I'm making a thing:

http://www.thestructuraltoolbox.com

(It's no Kootware and it will probably break but it's alive!)