Just to simplify things, here's a two pager showing the results for a single point load at the free end, based on an assumed forced displacement and at varying contact angles.
Just thought I'd post this last adjusted calculation. By altering the forced displacement, the polar method now calculates a maximum bending stress of 212.3 MPa and an initial contact load of 14.47 N. This compares well to the posted FEA results. Attached is the adjusted file.
Out of curiosity, I revisited the original method and updated it to be in-line with the polar method (same assumed forced radial displacement, point loading at start of contact not in middle of angular increment, etc). The result gives a bending stress of 196.7 MPa. Although it hasn't been...
Just did an update to the polar clip calculation. I changed the forced displacement values. The 1st point load is set to be at the tip of the clip, not in the middle of the 1st angular increment. I also took the opportunity to increase the number of increments. The contact point loads are seen...
I noted that the first method previously posted needed some adjustments. In addition, I concluded a polar coordinate method would be more appropriate. I attach both methods. If others have had a go, it would be interesting to see their results. Although the attachments haven't been checked, I...
I found this problem quite interesting, so I gave it a go from first principals. I've assumed the forced displacement and included ''contact''. The results show only a few points are in contact, and the level of forces needed to make the clip take the desired shape is quite low. You'll probably...
Just posting an updated version of the analysis. This version has introduced an additional boundary condition, requiring the beam to have a zero gradient partially through the supporting ground reaction. Again, these boundary conditions are probably not those traditionally used, but it shows how...
Attached is an attempt to model the pile and solving the unknowns by strain energy, and what look to be different (incorrect) boundary conditions. Although the boundary conditions need to change, the example may give you some ideas. I did find the case an interesting one!
I’m interested to see how the shear force and bending moment equations are derived. The approach I’ve used in the past is by strain energy (SE). I’m wondering if the method can be used in this case. Differentiating the SE w.r.t a point load / moment gives you the deflection / rotation at that...
To understand the problem more clearly, could you give all your used inputs, namely lengths between pile reactions, loading, section properties, etc. Knowing all used inputs, gradient and deflection equations can then be derived and boundary conditions applied.
Just out of interest, I find myself trying to think of possible loading cases. I've never done anything like this, so my brain-storming could be completely wrong! I start to think, is there any possibility of conditions like 'irregular fuel burn' within the exhaust chamber. I'm wondering if some...
Just brain-storming! A scenario ...
You have an I beam. You want to attach two side plates to the web.
Case 1) You put in two rows of pins evenly pitched (say 2in) 1/2in from the top and bottom edges of the side plates. The holes are slotted longitudinally. Outcome ... when the I beam is loaded...
You could look at the joint as a socket.
Example of a loaded socket. The inner and outer parts will experience shear and bending due to the distributed contact load. The max distributed load can be used to derive hoop stress. I suggest having a look at the subject.
Just thinking allowed. Immediately below the top flange, there will be a shear flow in the web. Progressing down the web, the shear flow will increase. As you get to the top of the two side plates, the shear flow will suddenly be confronted with three load paths, into the side plates through the...