Analyzing Wall Bracket

[jacobd]

I use simple wall brackets to support piping, etc... that usually consist of a rectangular tube welded between (2)lengths of angle (somewhat like a gusset connection on each side). The other toe of each angle (the one not welded to the tube) is drilled with 2 holes for mounting to the wall with concrete anchors, so all together there are 4 anchors holding it to the wall.

My question is how should I analyze this statically? I usually just take a look at the rect. tube like a beam and check the moment, deflection and shear. I know the anchors are rated for 5000# tensile (for pull-out), with what I know about statics I don't really know how to check the loads that my anchors actually see, can anyone help out?

Much appreciated,
JD

...a little more info on the assembly: the angles run vertically when mounted to the wall, so the anchors are going to be some distance above and below the rect. tube.

 

[Neilmo]

Hello Jacobd,

The top 2 bolts will be the most critical, because they are subject to both tension and shear forces.

Take the total load on the bracket and multiply it by the outstand (horizontal distance) from the wall. Divide this by the vertical distance between bolts, and then by 2 (2-bolts at top of bracket), to get the tension (pull-out) for each of the top bolts. The shear on each bolt is just, Total load / 4-bolts. Don't forget to multiply both of these by whatever safety factor you wish to use.

Now select an anchor from your literature which is capable of taking both the above tension and shear at the same time. When making your selection, be sure to allow reduction factors for, `close anchor spacing`, `close distance to edge of wall`, etc, etc, which should also be given in the literature.

Hope this helps.

Regards,
Neilmo

 

[jacobd]

Thanks for the quick reply. After reading your solution, it became clear that this is nothing more than a 90º lever problem as far as tension is concerned.

Thanks for making me see the light.

JD

 

[chicopee]

I would analyze the problem a little differently than the above suggestion. After calculating the external moment from pipe weight on the bracket, I would use the bottom portion of the bracket as the fulcrum and assume a linearly distributed force along the length of the bracket. The force on the lower row of bolts will be lower than the force on the upper row of bolts. This higher force woulb be the focus of my attention and I would try to determine if the wall structure could sustain this higher force.

For shear thru the bolts I would use the same approach as above.

 

[Neilmo]

Yes Chicopee, I agree. I have taken the simple (conservative) approach, yours is more exact. But it all depends on how stiff the bracket actually is. My approach assumes a relatively `flexible` bracket, while your approach assumes a relatively `stiff` bracket. In reality no doubt, the answer lies somewhere in between.

Try this (ignoring weight of bracket) -

Load on bracket = W = 10.0kN
Outstand from wall = L = 300mm
Distance from bottom of bracket to lower bolts = E = 100mm
Distance from bottom of bracket to upper bolts = D = 600mm
2 - vertical rows of bolts

My approach -
Moment on bracket = W*L = 10.0*300 = 3000Nm
Tension force upper bolts = W*L/2*(D-E) = 3000/2*500 = 3.0Kn each

Your approach -
Modulus of upper bolts = (E^2+D^2)/D^2 = (100^2+600^2)/600 = 616.67mm
Tension force upper bolts = W*L/2*616.67 = 3000/2*616.67 = 2.43Kn each (a small saving over my 3.0kN)
Modulus of lower bolts = (E^2+D^2)/D^2 = (100^2+600^2)/100 = 3700mm
Tension force lower bolts = W*L/2*3700 = 3000/2*3700 = 0.41Kn each

From the figures you can see that, the greater the distance from the bottom of the bracket to the lower bolts, the less will be the tension in the upper bolts. But there will now be a bending in the lower part of the bracket which must be accounted for, with possibly a larger section for the bracket.

Regards,
Neilmo

 

[chicopee]

Neilmo-From your calculations my design approach of 2.43 KN would have incoorperated a factor of safety and would have approached your 3.0 KN value. Which proves that there is more than one way to skin a cat.

 

[desertfox]

Hi to All

I would use the same method of analysis as chicopee
on this bracket because if additional fixings were added then Neilmo's simple approach could not be used.
In regard to the stiffness of the bracket it seems to me that both methods assume rigid brackets ie:- imagine if each bracket were made from plasticine then both brackets
would distort irrespective of how the bolt loads were analysed or if you take the example bracket calculated by
Neilmo where he states that there is a bending moment in the
lower part of that bracket which has to be accounted for;suppose that those dimensions of the bracket, are
those of the bracket that jacobd is using then the bending moment is within the lower part of the bracket irrespective of either bolt analysis.
If there was any doubt about the strength of the bracket then that would presumbly be subject to an analysis of its own however as we have no physical dimensions of the bracket
we can only speculate.

regards
desertfox

 

[Neilmo]

Your right of course desertfox, with more bolts the way to analyse the problem is by chicopee's method. The simple solution only works for 2-bolts in a vertical line. But then jacobd's question only had 2-bolts in a vertical line!

Ive just noticed a `deliberate mistake` in my formulas for the bolt modulus -
Modulus of upper bolts = (E^2+D^2)/D
Modulus of lower bolts = (E^2+D^2)/E
The calculated values are correct, only the formulas are wrong.

Neilmo