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How to apply shear load and moment on thin-walled cylinder FEM

Sleight (Aerospace) (OP)
14 Apr 09 16:23
How do I apply a shear load, V, and bending moment, M on a thin-walled cylindrical shell FEM to capture the correct bending stresses and shear stresses according to beam theory? According to beam theory, the bending stress is a function of sine, fb = M*Sin(theta)/(Pi*r^2*t) and the shear stress is a function of cosine, fv = V*Cos(theta)/(Pi*r*t) where theta is the angle above the neutral axis.

GregLocock (Automotive)
14 Apr 09 19:49
How would you do it in real life?


Greg Locock

SIG:Please see FAQ731-376: Forum Policies for tips on how to make the best use of Eng-Tips.

rb1957 (Aerospace)
15 Apr 09 7:46
you know where your nodes are ?

(hint, as a function of theta)

depending on your FEA code, there may be a built-in function.

i'll give you another hint for free, i think your expressions will not give you the answer you desire.  think in terms of shear flow (it'll be easier to apply shear force to your model (rather than shear stress) ... derive the shear flow around the open end of the tube (i think your expression for shear stress is the vertical component of the shear stress, but i could be wrong ... on the face of it, it doesn't look right) ... the FEA should solve the moment stress based on the applied shear forces
GregLocock (Automotive)
15 Apr 09 8:19
Take a coke can. Cut the base off. Now apply a shear load to it.

Model that.


Greg Locock

SIG:Please see FAQ731-376: Forum Policies for tips on how to make the best use of Eng-Tips.

rb1957 (Aerospace)
15 Apr 09 8:53
one "dumbed down" apporach the FEA allows is to apply the shear load at one point (the center of the tube) and allow the FEA to distribute the load through rigid beams.

seriously, i'd suggest reading primers on FEA or the manual for your code (it should have good examples to show the features of the code and how to apply them).

it may be a flash of the blindingly obvious, but you are modelling a tube (rather than a section of the tube) and you know that M = V*d (and this time (only, maybe) i'm not trying to be sarcastic).
corus (Mechanical)
15 Apr 09 10:05
This problem probably relates to nozzle loads, which are often supplied from 'outside' software-output as shear, direct, and moment loads. The shear load direction may not be in the same plane as the moment and so the simple expression of V*d might not apply in this case.
Probably the best way is to apply rigid links to the free end of the nozzle as rb1957 says. and apply your loads to the central node that connects to the nodes onto the cylinder/nozzle. I guess you'd have to apply a counter moment to offset the moment you were applying from the shear load if that wasn't in the direction of the actual moment you require. The problem then is the distance you need to apply these rigid links and forces from the area of interest at the connection so they don't have a localised effect which wouldn't be seen in real life. The norm is to take six times the wavelength of the shell, or about 4.5 x sqrt(rt) for axisymmetric forces, so I'd double that for asymmetric loads applied to the cylinder.  


Sleight (Aerospace) (OP)
16 Apr 09 16:08
I am applying a shear load, axial load, and moment from a beam (stick) loads model at a specified station (location)to a more refined cylindrical shell model. I originally applied the axial load, shear load, and moment at a center node at the top of the cylinder by means of a NASTRAN RBE3 which distributes the loads equally among all the nodes around the circumference at the top of the cylinder. This method should work for the axial loads, but I don't think it will work for the applied shear load and moment.

Therefore, I was looking for a good way to apply the shear load and moment to the cylinder such that I would get the correct bending stress due to the applied moment and shear stress due to the applied shear load.

GregLocock (Automotive)
16 Apr 09 19:08
Good, I agree, an RBE3 spider will give hopeless results for most loads on this structure.

Are you interested in the stresses near the point of application of the loads? If not then you can afford to be a bit crude. Otherwise you'll need to apply them element by element.  


Greg Locock

SIG:Please see FAQ731-376: Forum Policies for tips on how to make the best use of Eng-Tips.

rb1957 (Aerospace)
17 Apr 09 7:47
ok, you've got a coarse grid model, giving you Fx, Fy, Fz, Mx, My, Mz at each grid; and now you want to apply them to a fine grid model.  as opposed to greg, i would've thought that the RBE3s would have yielded a satisfactory answer, why do you think it would work for shear ?

have you asked the help desk ... they usually are very helpful.

if you for another approach to apply the loads then calc the grid forces ... work from shear flow to distribute the shear forces and torque, work from areas (and 2nd MoI) to distribute axail force and moments (remember, plane sections remain plane).

your detailed structure must be very complicated, that you can't apply hand methods ...
GregLocock (Automotive)
17 Apr 09 21:13
Sorry, i was assuming the RBEs all joined in the middle with the forces applied at that central node If each RBE is separate and is used to apply a load to each element that'd be OK, but then I'm confused as to how that is simpler than applying the load directly to the element.



Greg Locock

SIG:Please see FAQ731-376: Forum Policies for tips on how to make the best use of Eng-Tips.

rb1957 (Aerospace)
18 Apr 09 13:34
no, you've right, i had in mind a radial web of RBEs.  i'd've thought that it would've kept plane sections plane (for bending) and so distributed the shear correctly.  
femarie (Marine/Ocean)
22 Apr 09 8:58
I would fit RBE-type  elements as well.Have done this various times to apply crane loads to cylindrical pedestals.

rb1957 (Aerospace)
22 Apr 09 9:03
looks like Sleight has gotten bored with this discussion, he hasn't ticked the "notify me" box ...
Sleight (Aerospace) (OP)
27 Apr 09 19:10
Sorry I haven't checked the threads in a while. I found a solution to determine the equivalent running loads (Nx, Nxtheta)on a cylinder from the beam loads and moments. The equivalent nodal forces around the circumference of the cylinder can be determined from the equivalent running loads.  The running loads, Nx and Nxtheta, are functions of the angular position around the circumference of the cylinder.

For example, you have a beam axial load, Fx, an applied shear load, Vy, and an applied beam moment Mz. The x-axis is down the length of the cylinder. The equivalent running load, Nx = Fx/(2Pi*R)- Mz*sin(theta)/(Pi*R^2), where R is the radius and t is the thickness. The shear running load, Nxtheta = Vycos(theta)/(Pi*R). The forces can be determined by Fx = Nx*dl = Nx*R*theta*dtheta and Fxtheta = Nxtheta*dl = Nxtheta*R*theta*dtheta. The Y and Z components can then be determined from Fxtheta by mulitplying by Rsin(theta) or Rcos(theta).

Therefore, instead of applying point loads and moments at a center nodes and using RBE2 elements to spider out the loads around the circumference of the cylinder, I have calculated the equivalent nodal forces around the circumference of the cylinder. It should be OK to apply an axial load, Fx, using the RBE3 method, but applying the shear load and moment using the RBE3 method will not give the correct stresses in cylinder as those predicted by beam theory.

Thanks all to those who replied to my question.
Sleight (Aerospace) (OP)
27 Apr 09 19:13
I meant instead of using RBE3 elements to spider out the loads from a central node location on top of the cylinder.
johnhors (Aerospace)
28 Apr 09 2:43
Sleight, your method is probably alright if you are using linear elements only. To apply forces and moments correctly to a model as a series of nodal point loads you should be honouring the underlying element shape/displacement functions. For higher order elements this is no trivial task. If your elements have mid side nodes then whilst your total load and moments applied may sum correctly, your method will not result in the smooth application you desired, and will probably result in fictitious stress peaks, so you may as well use a RBE3 !!
Onda (Marine/Ocean)
28 Apr 09 6:26
Could you use a RBE3 with different weight on different grid points depending on location on tube?
Although very tricky to set could bring to a better load distribution.

johnhors (Aerospace)
28 Apr 09 6:56
Onda, its not only grid point location that determines what load to apply, but also connectivity (corner nodes are shared by more elements than mid-side nodes) and also element size and shape. Thus nodal loading has to be worked out on an element by element basis and the sum of all element contributions is what has to be applied at each grid point. So the short answer is no.
rb1957 (Aerospace)
28 Apr 09 7:46
it's a good point to mention mid-side nodes, 'cause i believe most practitioners of the FE art don't appreciate the different weighting.  although we don't know it applicable here ('cause the OP hasn't mentioned that detail).

in any case, wouldn't the RBE3 web detect the different stiffness at the mid-side, and proportion the load correctly ?   
johnhors (Aerospace)
28 Apr 09 8:28

An RBE3 element cannot detect stiffness at a node, as this is a function of the overall model stiffness, an unknown before the model is solved.

Consider a face of a twenty noded brick (with 90 degree corners and straight sides - no curvature) , then for a uniform pressure the equivalent nodal forces are as follows:-

At each mid-side node one third of the total load is applied (in the direction of the applied force).

At each corner node one twelfth of the total load is applied in the opposite direction.

This pattern of loading is determined entirely by the element formulation, of which a RBE3 element would know nothing.
Onda (Marine/Ocean)
28 Apr 09 8:37
Johnhors, I understand your point, but, to avoid the problem you mention, the tube could be meshed with a regular pattern of CQUAD4 elements, without mid-side node and with all grid point aligned.
In this case You could apply the shear load with a RBE3 with a weight function of the location.
rb1957 (Aerospace)
28 Apr 09 8:57
yeah, i can see your point john ... it's more to do with the weighting function than the stiffness of the structure (isn't it).

of couse, you could mesh with CQUAD4s ... but where'e the fun in that ;)
johnhors (Aerospace)
28 Apr 09 9:58
Yep, a regular mesh of 4 node quads may work fine with a RBE3. The point is not to assume a RBE3 has any intelligence, without linear elements or uniform mesh it won't give you a uniform or realistic load distribution.
GregLocock (Automotive)
28 Apr 09 19:56
This is sort of getting away from any area of expertise I have, but one way I've applied complex loadings to a structure without upsetting it is to use an intermediate layer of 'soft' elements and apply the loads to them. These then distribute the load smoothly into the structure of interest.

This is somewhat equivalent to an impedance matching problem.



Greg Locock

SIG:Please see FAQ731-376: Forum Policies for tips on how to make the best use of Eng-Tips.

Sleight (Aerospace) (OP)
7 May 09 14:35
I did a comparison of methods to apply loading (axial, shear, and moment) on a cylinder example for RBE2, RBE3, and the statically equivalent loading methods.

The statically equivalent loading method was the best overall in comparsion with beam theory results. The results show that the RBE3 method for applying the loads is very good for applying axial forces and moments, but does poorly for applied shear forces. For shear forces, the results show that the RBE3 elements produce a rigid-body like(sliding) motion with a corresponding high Ny force at the top of the cylinder. The results also show that RBE2 method for applying loads is good for shear forces, but introduces high Ny forces at the load application point for applied axial forces and moments.


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