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# Converting Beam Forces to Stresses

## Converting Beam Forces to Stresses

(OP)
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
SPCFORCE = ALL
FORCE(CORNER) = ALL
STRESS(CORNER) = ALL
SPC  = 1
MAXLINES=999999999
SUBCASE 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

### RE: Converting Beam Forces to Stresses

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.

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