Another interesting SS beam problem. Out of interest, I looked into the distributed loading and BM. Attached is my investigation into deriving the equations by integration. In situations like this, I would usually get MathCAD to carry out the integration rather than working out the equations...
You can enter the data as two column arrays, one acting as the independent variable ‘x’ and the other as the dependent ‘y’. You can then use something like the ‘cspline’ function and use that with the ‘interp’ function. This basically fits a smooth curve through your data points and permits you...
I believe your question looks similar to the case where you assume the contact for a pin loaded lug is cosine in shape. It may give you some ideas?https://files.engineering.com/getfile.aspx?folder=265adc0c-824f-4c7e-aa0e-7ec6e84d1fe4&file=Pin_Contact.pdf
What would be interesting is to know at what deflected shape would the beam have to be in for non linear effects to start having a significant effect. Knowing that and what change in length is actually needed for the design to function would be interesting.
Just posting a new copy of the calc's, had to correct a typo in one of the equations!https://files.engineering.com/getfile.aspx?folder=18974723-56bb-4609-be8f-48d262f6950a&file=Beam_pin-pin.pdf
Just put some calc's together. It hasn't been checked but I think it's ok. It may be helpful!https://files.engineering.com/getfile.aspx?folder=20f01696-92a7-4b66-a848-ac67ee326732&file=Beam_pin-pin.pdf
It looks like there is concern that the change in length will be small and insufficient. The beam could be modified to magnify the change in length. First thing that comes to mind is to utilise not just the change in length but also the rotation at the end by introducing an arm at 90 degrees to...
If interested, attached is the method based on M/EI. Just to mention, all the integration was done symbolically using Mathcad. It hasn't been checked but it looks a though it's working!https://files.engineering.com/getfile.aspx?folder=c82f8661-3c48-4f32-9d92-5959a2f8e05f&file=beam_sine.pdf
My calculations from 1st principals gives Ra = -3214.9 lbf and Rb = 4849.9 lbf. This is the same as other posted results.
The method was based on M/EI. The boundary conditions were zero gradient at mid point of beam and zero deflection at Rb. Both resulting equations were functions of Ra and...
On the assumption that the screws will be preloaded, approximately 2/3 of the threads will be loaded. The preload will generate thread radial loading, pushing the groove open. The walls of the groove are tapering, the minimum wall thickness being at the base of the groove. You’ll see build...
If interested, attached a a solution to the posted problem by superposition, using two cases from Roark. It hasn't been checked but it does give the same results as previously given.https://files.engineering.com/getfile.aspx?folder=c48240a6-f12b-4ac0-bad6-77269922673c&file=Beam.pdf
If anyone is interested, attached is a solution to the problem using the traditional M/EI method. It hasn't been checked, but it's good when two different methods give the same answers, it gives you that 'good feel...
When I have a problem such as this (indeterminate, changing section / modulus with length, multiple forms of loading, etc), I usually use symbolic solving software and use 1st principals. Set up the BM equation in terms of the unknowns and then generate the equations to solve for the unknowns...
Just out of curiosity, if anyone has taken a copy of the posted analysis template and generated their own version (Excel, SMath, Mathcad, etc), I would be interested to know if you were successful and if you've modified the method in some way.
Allowable buckling stresses include the use of Et. It’s been a while, but if I remember rightly, crippling is based on a section consisting of elements with differing edge support conditions, the individual summation of which gives you an allowable compression stress, at which load...
mfgengger
The original post does state a horizontal load, and in any direction (assuming 360deg rotation about the vertical). If the load is applied in the middle of the horizontal beam, you could be right, as each vertical beam will take 50% of the applied. It all depends on if the applied...
Out of personal interest only, attached is an investigation I conducted into altering the traditional linearly varying socket distribution load, to allow for an unloaded length within a pin loaded socket. It hasn't been checked or validated, but it may give you some...
