Douglas-Fir Larch Compression Tests Parallel to the Grain: Strength and Stiffness Analysis.
Wood strength and stiffness vary with the grain direction. Generally, wood has three primary strength directions: parallel to the grain (longitudinal, L), perpendicular to the grain (radial, R), and tangential to the annular rings (tangential, T), see Figure 1.
The strongest and most rigid direction is parallel to the grain (L), the natural growth direction of the wood towards the sky. Nature intuitively crafts wood with optimal strength and stiffness in this direction. The other two directions (R and T) of the wood grain are comparatively weaker (10 to 30 times weaker than L). Structural engineering calculation defines the two primary wood grain directions as parallel and perpendicular to the grain.
Four Douglas-Fir larch samples of different heights - 51 mm (2 in.), 77 mm (3 in.), 102 mm (4 in.), and 177 mm (7 in.) - all having the same cross-sectional areas are compression tested in the following videos:
The load application direction relative to the wood specimen was parallel to the grain. Specimen displacements were recorded using a load cell and an extensometer to ensure experimental precision, where both measurements showed varying stiffness (Young's moduli) values.
All wood samples had a moisture content of approximately 11% (+/- 1%). The average ultimate strength recorded was 50.65 MPa with a standard deviation of 1.68 MPa (7346 psi and SD = 244 psi), corresponding to an average ultimate force of 90.20 kN (20051 lb). These measured strength and force values align with those outlined in ASTM D2915 for unseasoned wood, which reports the average strength of Douglas-Fir larch of 3469 psi with a standard deviation of 602 psi (COV ?= 0.173). The unseasoned wood strength values should be amplified by 75% (or multiplied by 1.75) to adjust the unseasoned wood strength for seasoned wood at 15% moisture, according to ASTM D2555. Additionally, to adjust for 12% moisture content, the unseasoned wood strength should be multiplied by 2.0 for compression parallel to the grain, resulting in 6938 psi (47.83 MPa). The measured experimental strength properties parallel to the grain match those reported in ASTM D2915. Moreover, the Wood Handbook 2021 indicates that Douglas-Fir larch compression strength parallel to the grain is approximately 47.6 MPa at 12% moisture content.
This article includes a brief example and explanation to derive the design strength and stiffness values using experimental results and ASTM standards. Assuming normality, the strength design values of compression parallel to the grain can be obtained accordingly:
As evident, the 5% exclusion value depends on the sample size and the standard deviation of the experimental results. The coefficient of variation for larger sample sizes typically is from 10 to 40%, depending on load application relative to the grain direction.
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The values for compression strength along the grain align with the established standards, yet the experimental results obtained for stiffness using a compression machine and extensometer show inconsistent results.
Young's modulus (E) was determined within the range of 10% to 40% of the ultimate force, corresponding to the material's elastic stage and the limit for serviceability. The testing machine yielded an average Young's modulus of 2383 MPa (345,000 psi) with a standard deviation of 612 MPa (88,500 psi). In contrast, the average Young's moduli through the extensometer measurements were significantly higher at 11814 MPa (1,710,000 psi), with a standard deviation of 2525 MPa (366,000 psi). This difference is partly due to the testing machine measuring strain across the entire height of the specimens, whereas the extensometer measures strain over a specific 10 mm (0.4 inch) section. The National Design Specification (NDS) for the strength calculations of compressed columns and the assessment of buckling strength employs the minimum value of E (Emin). Moreover, Eurocode 5 (EN 1995-1-1) stipulates using the 5% exclusion value of Young's Modulus in strength calculations without any additional modifiers for stiffness.
How is the minimum modulus of elasticity (Emin) calculated?
Emin formula accounts for modifications due to shear, variations in material properties, and safety considerations, as detailed in Appendix D of the NDS. The value representing the lower 5% of the distribution for Young's modulus (E) is determined by presuming that E follows a normal distribution. The safety margin applied to the lower extremity value of E is set at 1.66 and is calculated accordingly:
The difference between the measured values from the testing machine and the calculated Emin is 25% to 40%. The limited number of specimens limits the precise estimation, but the 25% difference is substantial. Although in strength calculations, Young's moduli are typically reduced to Emin (NDS) or 5% percentile (Eurocode 5) to consider the buckling of compressed elements; the concern arises regarding deformations at the serviceability limit state. How will such low values of Young's moduli affect beam deflections and axial compression deformations in columns?
The NDS and Eurocode 5 recommend using the mean Young's modulus values for wood outlined in the NDS supplement and European standards EN 338 and EN 14080. These values derived from experimental data are adjusted according to standards for practical application in assessing the serviceability limit state.
What do you think, and how could these obtained values be further adjusted to decrease the 25% to 40% stiffness difference between testing machine measurements and Emin calculated according to NDS?
In the following article, I will look at the White Pine specimens in compression and derive the design values according to European Standards.
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Dr.-ing. Aivars Vilguts