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Publication Number: FHWA-HRT-04-097
Date: August 2007

Measured Variability Of Southern Yellow Pine - Manual for LS-DYNA Wood Material Model 143

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1.10 MOISTURE EFFECTS

Empirical equations are implemented that specify the clear wood moduli, strengths, and fracture energies as a function of moisture content. The user specifies the percent moisture content and the model uses the appropriate moduli, strengths, and fracture energies. If the user does not specify the moisture content, then a moisture content of 30 percent is used as the default.

1.10.1 Southern Yellow Pine

Moisture content has a significant effect on the measured moduli, strengths, and fracture intensities of southern yellow pine. The effect of moisture content on the elastic moduli was given in table 1. The effect of moisture content on strength was given in table 4. The effect of moisture content on the mode I and mode II fracture intensities was given in table 10. Plots of clear wood measurements versus moisture content are reproduced in appendix B.

The empirical equations implemented for southern yellow pine are given in table 15. Comparisons of the equations with measured data are given in appendix B. They were derived by plotting the moduli, strength, and fracture intensity data as a function of moisture content and then fitting quadratic curves through the data.(14) Note that the data are highly variable. Therefore, the equations represent average clear wood properties. The equations for the moduli were obtained from fits to the tensile data, rather than to the compressive data. The fiber saturation point is reported as 23 percent. This point is the moisture content at which the cell walls are saturated with water, but no water exists in the cell cavities. It is generally assumed that the material properties do not change above this saturation point. Therefore, all material properties are held constant above 23 percent and set equal to those calculated by the empirical equations at 23 percent. The label saturated in plots indicates a moisture content of 23 percent.

Table 15. Equations fit to moisture content data for southern yellow pine.
Parameter
P
P = A(MC)2 + B(MC) + C
A B C
Moduli

EL Parallel Normal (MPa)


-8.50


-45.3


16774
ET Perpendicular Normal (MPa)
-2.06
17.2
944
nLT Parallel Poisson's Ratio
-0.00013
-0.00354
0.307
Fracture Intensities

K|c  (kN/m3/2)


-0.79


10.9


447
K||c  (kN/m3/2)
-4.80
104
1505
Strengths

XT Tension Parallel (MPa)


-0.448


10.51


80.57
YT Tension Perpendicular (MPa)
-0.016
0.33
2.82
XC Compression Parallel (MPa)
0.011
-3.25
90.17
YC Compression Perpendicular (MPa)
0.000
-0.555
16.93
S|| Shear Parallel (MPa)
-0.0226
0.056
19.86

No data are available for parameters not listed in table 15, such as shear moduli and the strength in the isotropic plane. Therefore, the following assumptions are made:

  • The shear modulus parallel to the grain (G12) varies linearly with the normal modulus parallel to the grain (E11), as follows:
    This equation reads Shear moduli of an orthotropic material subscript 12 equals 619 plus the product parenthesis the quotient of the difference of normal moduli subscript 11 minus 6000 divided by 12000 parenthesis times parenthesis 835 minus 619 parenthesis.
    This linear relationship was obtained from the predicted elastic parameters for softwoods found in table 3.3 of Bodig and Jayne for softwoods.(15)
  • Poisson’s ratio perpendicular to the grain (n23) is obtained from a fit to the Douglas fir data (see section 1.10.2).
  • The shear modulus perpendicular to the grain is obtained from the isotropic relationship:
    This equation reads Shear moduli of an orthotropic material subscript 23 equals the quotient of normal moduli subscript 22 divided by the product of 2 times parenthesis1 plus Impact velocity subscript 23 parenthesis.
  • The shear strength perpendicular to the grain (S23) is 140 percent of the shear strength parallel to the grain (S12). This approximate percentage was obtained from measurements for four wood species reported by Goodman and Bodig.(7) Conversely, the USDA Wood Handbook reports that the rolling shear strength is only 18 to 28 percent of the parallel shear strength and is thus quite small.(18) Nevertheless, the larger value of 140 percent is implemented. The effect of large versus small perpendicular shear strength on the shape of the yield surface is evaluated in appendix D.

1.10.2 Douglas Fir

There is a lack of material property data for Douglas fir. The limited data documented by FPL were used, and the missing information was supplemented with handbook values or pine data. The effect of moisture content versus elastic moduli was previously given in section 1. Strength measurements from various sources were given in table 5. Updating of the default properties is suggested as more data become available in the future.

The empirical equations implemented for the Douglas fir moduli are listed in table 16. They were derived by fitting quadratic curves through the data from table 2. The shear modulus parallel to the grain (G12) varies linearly with the normal modulus parallel to the grain (E11), according to equation 92.

Table 16. Equations fit to stiffness moisture content data for Douglas fir.
Parameter
P
P = A(MC)2 + B(MC) + C
A B C
Moduli

EL Parallel Normal (MPa)


-14.3


297.4


14959
ET Perpendicular Normal (MPa)
-5.88
108.5
508
nLT Parallel Poisson's Ratio
-0.0001154
-0.001808
0.375
nTR Perpendicular Poisson's Ratio
-0.0001649
-0.002297
0.376

The equations implemented for the Douglas fir strengths are based on the equations (P) implemented for southern yellow pine and listed in table 16:

This equation reads Douglas fir strength as a function of moisture content equals the product of Douglas fir strength at 20-percent moisture content times parenthesis the quotient of the parameter Capital P as a function of moisture content divided by the parameter Capital P at 20-percent moisture content subscript pine.

Douglas fir strengths vary with moisture content in the same manner as southern yellow pine strengths. The term in brackets on the right of equation 94 is a scale factor with a value of 1.0 at 20-percent moisture content (assumed fiber saturation point). The strengths implemented for Douglas fir at 20-percent moisture content are the green material strengths listed in the USDA Wood Handbook.(18) They were previously listed in table 6. The shear strength perpendicular to the grain (S23) is 140 percent of the shear strength parallel to the grain (S12).

No fracture intensity data are available for Douglas fir, so the same fracture intensity equations and values are used as implemented for southern yellow pine. In addition, all Douglas fir material properties are held constant above 20-percent moisture content. This is because our quadratic fit to the perpendicular modulus drops to zero stiffness just above 22 percent.

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