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# Stress Reduction / combination, calculation of utilization factor

Hi all,

I met some issue with results postporcessing. I need to combine the results in order to obtain the Utilization Factor of the weld at the end.

Let's assume that the formulat is as follows:

factors of: gamma, alpha, alpha_s and fy  are specified in Expressions, so are available.

and now, when I use Multiple Reduction or Reduction in post-processing i get error that operation '-' or '+' is wrong or something with Tsai-Wu coefficient (?).

What is wrong ?

2 REPLIES
Solution
Solution
Accepted by topic author TomekZeWschodu
‎04-13-2017 05:56 AM

## Re: Stress Reduction / combination, calculation of utilization factor

[ Edited ]

The NX expression system is not unitless. When you define an expression variable, you specify a dimensionality and a set of units.

The error message indicates that one of your expression variables is defined with a dimensionality of Tsai-Wu Coeffficient (and associated units of length^4 over force squared). A second expression is defined with dimensionality of Stress Compliance (and associated units of length squared over force).

When you try to add these two variables, you get the error shown because the units are not consistent. You can see the same error by simply trying to add the two expressions in the expression manager:

Going back to Physics 101, you can't add 1 mm^2/mN + 1 mm^4/mN^2

If you are just trying to add magnitudes to come up with some unitless scalar, you can use the remu() function on each of the variables to remove the units and consider only the scalar magnitude:

Alternatively, you could just define the input expressions as unitless constants to begin with.

## Re: Stress Reduction / combination, calculation of utilization factor

Thank you JimB,

I was aware of the fact that the units must be consistent in formulas.

I fugured out the problem, previous formula and the correct one that worked was:

`(((gamma*SXX)/(alpha*fy))^2) + ((gamma*SYY) / ((alpha*fy) ^2)) - ((gamma*SXX*gamma*SYY) / ((alpha*fy)^2)) + (((gamma*SZZ)/(alpha_s_per*fy))^2)`

the problem laid down in the last 'part' of the equation, where the nominator and denominator were not in separate brackets.

Thanks for help