How to find the in-plane/out-plane bending moment.

I am new in piping stress analysis, i am doing manual calculation for bending stress as per ASME B 31.3 code, as per code we are not able to find the formula for bending moment.

Sb=sqrt ((ii*Mi)^2+(io*Mo^2))/(Z)

Where
ii = in-plane stress intensification factor (appendix D)
io = out plane stress intensification factor (appendix D)
Mi = in plane bending moment,
Mo = out plane bending moment,
Z= section modulus of pipe.
We know in-plan SIF and out-plane SIF but only Mi and Mo is unknown.

Kindly advice me how to find the in-plane bending moment (Mi) and out-plane bending moment (Mo).

by

rajiv

Hello,

Equations for getting the Bending moments Mi and Mo cannot be found in Code. These can be found from Strength of Materials book. For simple configurations such as a cantilever you can easily find equations in strength of materials books and do a manual calculation. But for a piping system, it's complicated to do a manual calculations, although in the past where computers are not readily available, there are some simplified equations to calculate different piping configurations. But at present, where computers are available almost everywhere there are many softwares such as Caesar II to calculate the Forces and Moments in the piping system based on different loading conditions such as weight, thermal, seismic, wind etc.

When I was new in Piping Stress Engineering I was also curious how to get these Moments, Forces and Displacements. So what I did is I study a book entitled "Matrix Analysis of Structures" and it so happened that the book has a detailed explanation on the assumptions made to solve for these displacements, Forces and Moments. It has some examples with it where you can try solving. The book is actually for a Structural Engineering but it's good to study it so that you will have you a good feel of how the software is working.

Basically, if you have tackle Beam Equations in your school days, this is the fundamental basis of the beam element softwares. The equations are just formed in matrices so it can be programmed in computers.

I'm open to any comments in the statements I've made above.

Cheers!!!!

Dear Borzki,

I Know very well in ASME B31.3 code book we don't have that formula (bending moment), I studied Strength of Materials books, you know in strength of material book there are 6 type of loading, 6 type of bending moment formula and 6 type of deflections formulas are there,

If you know please explain me, which formula is exactly used in CAESAR II software or give me a sample calculation, i tried all the formulas for bending moment calculation, but i could not get CAESAR II calculated value.

By

Rajiv

The isn't a formula, c2 is a finite element program, implementing a 3D Beam Element. As stated above, the software solves the matrix equation

[K]{x} = {F} for the displacement vector {x}, where {x} and {F} are unique for each load case.

Once {x} is known, the free body loads (forces and moments) at the ends of each element can be determined.

Richard was right. There isn't a straight forward formula for getting these forces & moments especially for a complicated configuration of piping system. You can try a simple cantilever model in Caesar say a 3m 8" std. wt. pipe with fixed on one end and free at the other. Then apply a force say 10KN at free end and check the resulting displacements, forces and moments in the output report. Then grab your strength of material book check the formula for cantilever beam then do a manual calculation comparing the results with Caesar II. At least you will have a feel of how the software works.

Good luck!!

Cheers!!

Alternatively (and this is a really good idea), click the link at the top of the c2 Forum to obtain information on the "Statics Video Training" course. Matrix solutions are discussed in this training.