I need to calculate the "GRMS" values in a Random Vibration analysis, but I see no reference to "GRMS" anywhere in ANSYS.

The RMS values are known as "one-sigma" values in ANSYS. Since "G" refers to acceleration in terms of gravitational acceleration, then "GRMS" is the one-sigma value for G acceleration.

In POST1, this can most easily be retrieved by dividing the one-sigma acceleration values on load-step 5 by the gravitational acceleration constant.

set,5,1,1/386.4 ! 1/386.4 converts in/s^2 to G assuming BIN units
plns,u,x ! contour plot of Grms in x direction
plns,u,y ! contour plot of Grms in y direction
plns,u,z ! contour plot of Grms in z direction

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