Statics Brainfart

[jpcp]

I'm sorry to post this here but I seem to be having a brainfart. I've been looking at this problem for too long and I need imput from others.

I'm working on a simple problem:

I'm analyzing a shelf angle, 4"x8" - 8" portion abuts wall, supporting a beam. I'm trying to use two rows of "drill-in" concrete anchors to support the beam.

I'm just trying to determine the pull-out force exerted on each anchor. The problem I'm analyzing has a 12kips at the tip of the 4" end. The first anchor is spaced 3" from the top of the angle, the next anchor is 2.5" below the first anchor.

What is the pull-out on the anchors?? Again, I should have solved this but I've been looking at it too long and now I think I'm over analyzing it.

All comments appreicated (except the mean one's)

 

[LPPE]

4" leg should act like a cantilever, then the 8" leg will pull away at the top, and push at the bottom. If your bolts are in the middle of the 8" leg, then the force should all be shear.

 

[AJUK]

jpcp

pylko is right to state that the bolts will be mainly subject to shear. However, if you feel the need to work out the pull out force you will need to determine the moment about the face of the wall, in this case 12 kips x 4" and divide that by the distance between the bolts, i.e. 2.5". This is a slight overestimation as some of the pull out load will be shared by the lower bolt but it is close enough on such a small scale.

Good luck

 

Okay, it's coming back now That's what I was thinking but I didn't want to underestimate the pull-out.

Your max pull-out would be at the top and then you would have compression at the bottom. I got that much!! So do you guys generally figure a linear relatsionship in between the top and the bottom. I ask because this isn't how the forces work in PCI (5th ed), pg 6-20. Why the difference??

I take it you're using a linear distribution since you're saying there is zero pull-out in the middle of the 8" leg.

I really appreciate your response!

 

[redhead]

Sorry guys, but this is not a problem in statics. The reactions at the bolts are indeterminate. Try modeling it on a simple frame analysis program.
Hinged reaction at the heel and reaction points at the bolt lines with "y" rollers. The resulting forces may surprise you.

 

[DaveAtkins]

Here is how I analyze this common situation:
Assume a trianglar shaped bearing stress at the bottom of the 8" leg, with the maximum stress equal to the allowable stress in the concrete (or CMU). Assume a pullout force occurs in the uppermost bolt. Then the pullout force is equal to the volume of the bearing stress "triangle". The depth of the triangle is a variable (call it "x&quot, and the moment arm between the centroid of the "triangle" and the pullout force, in this case, is 5 - x/3. Equating the 48 kip-inch moment to the volume of the bearing stress triangle times (5 - x/3) results in an easy to solve quadratic equation. Once you know x, you can solve for the pullout force.

 

[Ron]

Redhead is right...statically indeterminant. If you want to make it determinant, ignore the compression below the 2nd fastener and assume rotation about the 2nd fastener. This will give you a conservative value to use for fastener pullout comparison. Remember to use a factor of safety of about 4 for pullout.

 

[trilinga]

This is the normal problem we solve for the design of anchor bolts and base plate at the base of a steel column subjected to bending moments. This case is a specific case of the problem with zero axial force.

As suggested by Dave, we have to assume a compressive stress triangle and a pull on the outer bolt. In addition, we also have to use the linear strain relation in the plane of the moment. There are three unknowns namely, the tensile stress in the bolt fst, extreme compressive stress fc and the neutral axis distance x. The thre equations are

1. Linear strain relation

2. Force eqillibrium

3. Moment equillibrium.

The equations are solved to get the neutral axis distance 'x' and we should verify whether the location of neutral axis is consistent with our assumption of only one row of bolts is in tension. If the neutral axis is below the second row of the bolts, the equations shall be modified to account for tension in the second row of bolts also. The same procedure is followed as above till the results are consistent with the assumption.

 

[jpcp]

Thanks for all the responses!!

I was afraid someone might point out this was an indetermante problem. I was sure that it was but was hoping there was a different way to approach it. And it looks like there is....

I like the procedure that Dave and trilinga talk about. Although, in the case I intially outlined, the results I'm getting indicate the compression zone is small which means the bottom bolt is in the tension zone. It's stated that if this is the case, one has to consider the second bolts tension resistance.....won't this add another term that makes the problem indeterminate? This puts me right back to where I started!!? I can't see a away to add that tension term without making the problem indetermate...am I missing something??

Thanks for all the help!! Does anyone know of a book that has many examples similar to this? I wish they would have taught this stuff in, at least, one of my degrees!! :-(

 

[jpcp]

....OR do you guys solve the the "two bolts in tension" problem by using the "x" that was solved for when you tried it with "one bolt" problem?

I'm really trying to get this down. I sweat the small the stuff!! Anybody have any more advice?

 

[jpcp]

NEVERMIND. I think I got the statics figured out (finally). For the two bolt procedure I'm just going to use what Ron and AJUK suggested (if the second bolt is in the tension zone).

I have three more questions:

1) I'm adding the factor of safety at the end and this is really giving me large pull-outs. For the problem above (FS=4)...~75kips pull-out?? I know I'm not going to find an anchor for that. [] Is that where you guys add the FS?? I just want to make sure before I look to re-dimension the problem and then find an error later!!

2) What do you generally try to acheive for pull-out values when going into a concrete wall?? Masonry wall??

3) In PCA is states bearing is (PHI).85*fc. This is much higher than what I saw for a value in an example problem. What do you guys use for concrete bearing stress?? Masonry bearing stress??

Thanks in advance!!

 

[trilinga]

jpcp

As you have rightly guessed, it IS an indeterminate problem to start with and that is why we seek the help of strain relation to get the additional equation.

However, the second bolt getting into tension does not increase the indeterminacy. The strain diagram relates the strains (and thereby the stresses)in the bolts and the bearing stress at the bottom end linearly. That means any of the three stresses (stresses in the two bolts and the bearing stress) can be expressed in terms of the third stress. The solution is very much similar to the earlier case and no additional indeterminacy is introduced.


Since you have mentioned that the compression triangle is small, you should also ensure that the compressive (bearing)stress at the bottom is within allowable limit.

To make the solution simpler, we solve this using working stress method since we use the relation stres = strain * Young's Modulus. In other words, we use linear stress variation.

Regarding FS, since we use the working stres design, you assume the allowable stresses in the bolts with the relevant FS already included in them. I do not think you need to have any more FS.

The pull out capacity is fixed by the allowable bond stress in conctete, the bolt perimeter and the length of embedment.

Similarly, the bearing stress can be taken as the allowable compressive stress in concrete or masonry. if you are using working stress method of design, the allowable compressive stress for working stress design has to be used.

Regarding the text book dealing with this problem, the book by BLODGET ( I will try to get the tiltle of the book) provides this method for anchor bolt design.

 

I really havent read all the responses but the one from DaveAtkins is what I always follow. Although in your case there are two bolts and aside from the pull out force on the bolt itself there is the question of overlaping shear cones in the concrete. Have you addressed that? ACI 2001 manual for concrete practice books (i dont remember which volume or committee) has anchor bolt pull out examples.

 

[jpcp]

Thanks everyone for the responses!

I apoligize for the "simplicity" of some of my questions (primarily FS) but I was having trouble digesting the information. As I'm sure you can tell, I'm a recent graduate. The current circulum at my school only taught strength design. Therfore, when I have to work with stress design a lot of questions come up!!

Thanks again! Your information gives me a great basis to start learning from about these problems!!

P.S. I will also look into the shear cones.

 

[redhead]

Trilinga:
Your assumption of a linear relationship for the strain with the two bolt problem would be true for a fully rigid base plate, but does not account for bending in the plate for the more usual case.
I believe this problem is much more complex, and most of the responders are not giving it a full measure of rigorous analysis.

 

you are right it is complex but it really does not deserve a rigorous analysis!!!
triangular distribution on concrete equaling tension in the bolt does work!
Off course, satisfiying concrete allowables...etc.
I know HILTI has a software that does all this and you could download it from their site I dont know if you stil can.

 

[trilinga]

I agree with vstr. The solution assuming the base plate as rigid works well. The method is described in 'DESIGN OF WELDED STRUCTURES ' by Omer W. BLODGETT and has been widely used for the design of base plates and the anchor bolts.

 

[redhead]

Trilinga:

Yes. The method you describe is commonly used and gives acceptable results. But it is based on only one row of bolts in tension, not two. With two rows of bolts the properties of the base plate become paramount in the distribution of tension between the bolts and, depending on relative geometry, there may be prying action induced as well. I have never found anything in the literature that offers a general solution to this problem.

 

[curvbridger]

A possible solution in case you are not comfotable with the various approximations:

Weld vertical stiffener plates connecting the angle flanges at a reasonable close spacing (say 6-18&quot. Once that is done, prying forces and flexibility of base plate difficulties can be dispensed with and you can solve the problem assuming the angle is rigid.

This detail can usually accomodate the stiffener plates geometrically, and it is relatively cheap.

Curvbridger