Unlike normal pipe bends, there are a few more steps to modeling mitered bends in CAESAR II that the user should be aware of.  This solution will go through the process shown on page 25 of the CAESAR II Application guide.  The focus on this solution will be application to B31.3.  


First of all, the user will need to discern whether or not this will be a closely spaced or widely spaced miter bend.  The reason for this distinction is that closely spaced miter bends, regardless of the number of joints, can be defined as a single bend.  Widely spaced miter bends will be made out of multiple elements.


First, you should determine what is the equivalent radius of the Miter.  The formula is as follows:


Req = S / [ 2 tan(σ)]


Where:


Req = Equivalent miter bend radius

S = Spacing of the miter cuts along the centerline.

σ = code-defined half-angle between adjacent miter cuts: σ = α /2N


Where:

α = total bend angle

N = number of cuts.


Second, you should determine if the miter is closely spaced, or widely spaced.  


A miter is closely spaced if:


S < r [1+tan(σ)]


Where:


S = miter spacing

r = average pipe cross section radius: (ri+ro)/2


A miter is widely spaced if:


S^3 * r * [1+tan(σ)]


Where:


S = spacing between miter points along the miter segment centerline

r  = average cross section radius: (ri+ro)/2

σ = one-half angle between adjacent miter cuts.


To model a widely-spaced miter, you have to enter these sections as individual, single-cut miters, each having a bend radius equal to R= r [1 + cot(σ)] / 2


Where:


R = reduced bend radius for widely spaced miters.


Closely-Spaced Miter Example:


The following is an example of the input for a closely-spaced miter.


1. My Req = 40, and my miter points = 3.


2. Open up a new file.  


3. Create an element 3' long, 6" OD, Standard wall.



4. Add in a BEND on that element, with the following properties:




5. Create a second element, going in the direction of the bend. Here, I created an element 20-30 pointing in the Y direction, 3'-0".



6. Miter bend is complete.  Note that the graphics do not display the miter bends for a closely-spaced miter.



Widely-Spaced Miter Example:


1. Follow the example of the closely-spaced miter, except this time use individual sections for each miter portion.  For example, here I have a miter that consists of 3 sections, and the radius is 36".  I've determined the X and Y coordinate of each miter point, and created those elements, each with a "bend" type option selected, the radius of 36", and a miter point of 1 on each element.:

2. Miter is complete.  Again, notice that the graphical engine will not display the actual miter points in your model.