Direction cosines

Is there an easy way to get/calculate the direction cosines for two perpendicular rotational restraints where pipe is in full 3D space, e.g. element cosines are for instance -0.212, 0.334 and -0.918? In this case it would be RX(??,??,??) and RY(??,??,??).

Jouko

I know you are looking for easy way. I think this should be more easier.

Do not model the support restraint now. Leave it for later. But do model the piping as per the layout you said.

1st rotate the element/s in Y axis by -13.00372042 degrees.
2nd rotate the element/s in X axis by -19.51964238 degrees.
Now include the restraints you want.
I modelled rigid X Y and Z; RX, RY and RZ.

Now rotate the same elements in reverse order but in positive degree signs.
Refresh model.
here is what I have got.
X (.974355, 0, -.22501434)
Y (.075183, .942527, .325560)
Z (.212082, -.33412, .918356)
RX (.974355, 0, -.22501434)
RY (.075183, .942527, .325560)
RZ (.212082, -.33412, .918356)

I would model the 3D model as it is then rotate it to align perfectly with the X Y Z co-ordinate system and then model the supports as needed and then rotate it back to its original position. This way the rigorous (at least for me!) trignometry calculations in 3D can be left to Caesar II to compute.

Hope this helps.
Regards,
Siddharth.

Dot product for perpendicular lines is zero. A line perpendicular to your line that lies in the horizontal plane (Y is up) would be (0.918,0,-0.212). Take the cross product of these two lines to set a third line perpendicular to both.

Or, more simply, take the cross product of the first restraint's direction cosines and the pipe run axis to generate the second restraint's axis. (Also check the dot product of each restraint against the pipe run axis to make sure they are all mutually perpendicular.)

3D skews are a royal pain.

-0.212, 0.334 and -0.918? In this case it would be RX(??,??,??) and RY(??,??,??).

the XYZ cosines will be same for the RX RY and RZ cosines.

regards,
Siddharth.

Thanks to everybody.

For a person who studied above maths many moons ago on different language not workable.

There is an "easy" solution. Take element delta x, y and z CAESAR II and draw in Cadworx and rotate co-ordinates using AutoCAD/Cadworx. Add both ends elbows and pipes at perpendicular. Export to CAESAR II and read the cosines. Even this is made difficult by COADE (sorry). Co-ordinates do not match between the two programs. If somebody likes to get step by step let me know. After I have done 10 of these I should know them.

Could we have local co-ordinate option for CAESAR II.

You might want to try downloading the "Global to Local" utility program and see if that will work for you. (Its on the CAESAR II download page, in the "utility" section.)

We have never had any luck with the Global to Local utility program for some reason it just never worked, and so we set up a nice little spreadsheet in excel, using basic maths, so if we have 150 pipe supports (we design long cross country pipelines) we just enter the element cosine into the system and then the spreadsheet spits out the support cosine.

This is well worth doing if you deal frequently with lots of skewed supports and it makes your model easier to QA as you can give the checker a copy of the spreadsheet so they can check that the support cosines have been set up correctly.