How do I calculate the bending moment and maximum load for a cantilevered stud?

[3thanol]

Hello I hope you can help me and give me some guidance, hopefully I have posted this in the correct section of the forum.

I need to calculate the moment on the attached drawing, and the loads then transferred to the base material, if it is shear, tensile or an oblique/combined load. some guidance would be much appreciated. Ultimately how would I calculate the maximum load the stud can take before flexing/deforming.

I am hoping for a formula that should any variables change like length, diameter, steel strength or yield etc, I can change them on the relevant parts of the formula.

I am not sure how to calculate this as you can see.

some details that I know that might be required.

Length of of stand off = 98mm
Load (Vsd) 2kN or 2000 N shear
Anchor embedment = 125mm
Anchor dia = M16
Yield Strength = 420
Stressed cross section = 157
Elastic section modules = 277.5
Characteristic bending moment = 200
Recommended bending moment = 81.6

the only thing I can see and tried to calculate is the moment itself, again I am not sure if this is correct or even coming out right because I cannot find any working examples.

Mt = (length/moments without restraint) x Vsd = (98/1) x 2000 N = 196000 Nm or 19.6kNm

I don't know if this is correct or if I am starting of in the right direction, or where to go next with it? any help really appreciated...

 

[sardonicus]

It usually helps if you carry the units of the numbers you are combining. You have the moment but it in Newtonmeters (or some multiple) S

 

[3thanol]

Sorry that is true the moment would be Nm or kNm. But is the way I calculated the moment correct? and how do I move on to calculate the rest of the above?

 

[Studiot]

Mt = (length/moments without restraint) x Vsd = (98/1) x 2000 N = 196000 Nm or 19.6kNm

Do you realize that the (bending) moment varies along the length of the bar, from zero at the point of application of the load to a maximum at the face of the wall?

What do you mean by 'without restraint' ?

 

[tvavanasd]

I need to calculate the moment on the attached drawing, and the loads then transferred to the base material, if it is shear, tensile or an oblique/combined load. some guidance would be much appreciated. Ultimately how would I calculate the maximum load the stud can take before flexing/deforming.

I am hoping for a formula that should any variables change like length, diameter, steel strength or yield etc, I can change them on the relevant parts of the formula.

Mt = (length/moments without restraint) x Vsd = (98/1) x 2000 N = 196000 Nm or 19.6kNm

I don't know if this is correct or if I am starting of in the right direction, or where to go next with it? any help really appreciated...

Your units are incorrect.
The maximum bending moment is 196 N*m
It appears that you are cantilevering a threaded rod from a concrete wall. This may not be a good idea (specifically the connection). I would shy away from applying a bending load to a hole drilled in concrete (I am not a concrete expert).
Consider instead clamping a bracket to the wall using several fasteners in tension (if tightened properly).

 

[sardonicus]

You have it already, if your moment is 19.6 kNm and the recommended maximum is 81.6 kNm you are done right? If you want to check the concrete capacity you'll need a strength for that. Whether the concrete might be cracked, edge distances, confining reinforcement and other factors affect that answer. google aci appendix d, that is the relevant code in the US. S

 

[3thanol]

You have it already, if your moment is 19.6 kNm and the recommended maximum is 81.6 kNm you are done right? If you want to check the concrete capacity you'll need a strength for that. Whether the concrete might be cracked, edge distances, confining reinforcement and other factors affect that answer. google aci appendix d, that is the relevant code in the US. S

It's always so simple when someone else says it back to you thanks, I understand the factors you are talking about but for ease there are no edge, spacing factors, non cracked concrete etc. the next part is what would the load be in the concrete in order to calculate the concrete capacity I would need to convert the 19.6kNm into either a shear or tensile load?

I know how to convert a hand rail with a base plate moment into a tensile load. i.e dividing the moment by the distance from the fulcrum to the rarest anchor bolt.

but would this be calculated the same 19.6kNm/0.098 = 200kN or 19.6kNm x 0.098 = 1.92KN
or would it just be a 2kN shear load??

the numbers don't seem right so any help would be appreciated to finish this. "Many thanks to the above for inputting your time".

 

[sardonicus]

I see what you are after now. If the rod bends over it will go into tension, if the rod is stiff enough it will pry a chunk of concrete off* and ultimately bend over and go into tension so 2kN tension. If stiffer yet and the lever arm is short enough it's just shear.

* The compression of the concrete at the outer surface is magnified so you would, in affect, have a magnified shear until the rod bends. You would have to do a more in depth analysis to find out what the affects are. Look at sheet pile bending, it's like a post embedded in a very rigid soil. S