Converting Beam Forces to Stresses

[vorwald]

Question: What is the formula for calculating combined stress at a point in beam element NASTRAN?

Below is my hand calculation of the combined stress, and it is quite a bit different from the calculation from NASTRAN. I am modeling an angled beam with force in the axial direction. My input NASTRAN deck is listed below. The calculated forces on element one are

Moment Plane 1: -21.239
Moment Plane 2: 21.239
Axial Force: 100

The areas and inertias (from FEMAP) are:

SHAPE Angle (L) Section
Height 0.9 Width 0.9 Thickness 0.08
Area 0.1376
ShearAr 1, K1 0.42814
Shear Ar 2, K2 0.42814
I1 0.010665
I2 0.010665
I12 6.33E-03
J 2.90E-04

The distances relative to the shear center are

Y Z
Neutral Axis -0.21239 0.21239
Pt 1 0.042146 -4.22E-02
Pt 2 0.042146 0.85785
Pt 3 -0.85785 0.037854
Pt 4 -0.85785 -4.22E-02

My calculation of combined stress is

Axial Stress = Axial Force / Area
Bending Stress = Bending Moment * L / I
Comb Stress = Sum of Axial and Bending Stresses

Axial Stress Calculation

Axial
Point Force Area Stress
1 100 0.1376 727
2 100 0.1376 727
3 100 0.1376 727
4 100 0.1376 727

Bending Momentent Stress Calculations

Bending 1
Point M1 z I1 Stress
1 -21 2.55E-01 0.010665 -507
2 -21 -6.45E-01 0.010665 1,285
3 -21 1.75E-01 0.010665 -348
4 -21 2.55E-01 0.010665 -507


Bending 2
Point M2 y I2 Stress
1 21 -2.55E-01 0.010665 -507
2 21 -2.55E-01 0.010665 -507
3 21 6.45E-01 0.010665 1,285
4 21 6.45E-01 0.010665 1,285

Combined Stress Calculation

My Comb NASTRAN Comb
Point Stress Stress
1 -287 3223
2 1,505 -1190
3 1,665 -1582
4 1,505 -1190

The NASTRAN deck is below

ID C:\Docum,FEMAP
SOL SUPERELEMENT STATICS
TIME 10000
CEND
MAXLINES=999999999
ECHO = NONE
DISPLACEMENT = ALL
OLOAD = ALL
SPCFORCE = ALL
FORCE(CORNER) = ALL
STRESS(CORNER) = ALL
SPC = 1
MAXLINES=999999999
SUBCASE 1
LOAD = 1
MAXLINES=999999999
BEGIN BULK
$ ***************************************************************************
$ Written by : FEMAP
$ Version : 8.10
$ Translator : CSA/NASTRAN
$ From Model : C:\Documents and Settings\VorwaldJG\My Documents\h53\mw_060903\ramp 061703\test_beam_angle.MOD
$ Date : Thu Jun 19 09:26:33 2003
$ ***************************************************************************
$
PARAM,POST,-1
PARAM,AUTOSPC,YES
PARAM,GRDPNT,0
CORD2C 1 0 0. 0. 0. 0. 0. 1.+FEMAPC1
+FEMAPC1 1. 0. 1.
CORD2S 2 0 0. 0. 0. 0. 0. 1.+FEMAPC2
+FEMAPC2 1. 0. 1.
$ FEMAP Load Set 1 : Fx
FORCE 1 11 0 1. 100. 0. 0.
$ FEMAP Load Set 2 : My
MOMENT 2 11 0 1. 0. 100. 0.
$ FEMAP Load Set 3 : Fz
FORCE 3 11 0 1. 0. 0. 100.
$ FEMAP Constraint Set 1 : Fixed End
SPC 1 1 123456 0.
$ FEMAP Property 5012 : Blkhd6UpperCap1
PBEAM 5012 123456 0.13760.0106650.0106656.333E-32.903E-4 0.+PR 3V8
+PR 3V80.042146-4.22E-20.042146 0.85785-0.857850.037854-0.85785-4.22E-2+PA 3V8
+PA 3V8 YESA 1. +PC 3V8
+PC 3V8 0.42814 0.42814 +PD 3V8
+PD 3V8 -0.21239 0.21239-0.21239 0.21239
$ FEMAP Material 123456 : 7075-T6 Plate .04-.125
MAT1 123456 1.03E+7 0.33 0. 0. 0. +MT 2N9C
+MT 2N9C 78000. 69000. 47000.
GRID 1 0 0. 0. 0. 0
GRID 2 0 1. 0. 0. 0
GRID 3 0 2. 0. 0. 0
GRID 4 0 3. 0. 0. 0
GRID 5 0 4. 0. 0. 0
GRID 6 0 5. 0. 0. 0
GRID 7 0 6. 0. 0. 0
GRID 8 0 7. 0. 0. 0
GRID 9 0 8. 0. 0. 0
GRID 10 0 9. 0. 0. 0
GRID 11 0 10. 0. 0. 0
CBEAM 1 5012 1 2 0. 1. 0.
CBEAM 2 5012 2 3 0. 1. 0.
CBEAM 3 5012 3 4 0. 1. 0.
CBEAM 4 5012 4 5 0. 1. 0.
CBEAM 5 5012 5 6 0. 1. 0.
CBEAM 6 5012 6 7 0. 1. 0.
CBEAM 7 5012 7 8 0. 1. 0.
CBEAM 8 5012 8 9 0. 1. 0.
CBEAM 9 5012 9 10 0. 1. 0.
CBEAM 10 5012 10 11 0. 1. 0.
ENDDATA

 

[vonlueke]

vorwald: There are multiple ways to work this out; here's one way. From the given data, it can be seen that, from vector addition, you are applying a moment of M = -sqrt(21.239^2 + 21.239^2) = -30.0365 about the weak principal axis. It can also be figured out that the minor principal moment of inertia is I = 0.004332047. And the corresponding extreme fiber distance is c = -0.3599667. So the maximum normal stress on the cross section is sigma = M*c/I + P/A = 2495.85 + 726.74 = 3222.6, occurring at point 1. Similarly, the fiber distance at point 3 is +0.3329980; substituting this for c in the above formula gives sigma = -1582.1. Likewise, the fiber distance at point 2 (and 4) is +0.2764294, giving sigma = -1189.9. Therefore, all four stress values labeled "Nastran Comb Stress" are exactly correct; all four values labeled "My Comb Stress" are incorrect.