The bending stiffness of a structural member is the capacity to resist deflection and is represented in equations as EI. The E is the modulus of elasticity of the material making up the structural member and the I is the moment of inertia of the cross section of the structural member.

When determining true (Shear-Free) and apparent modulus of elasticity, what are the differences in the test methods used? And what do the results mean to an engineer?

The difference between apparent modulus of elasticity (E_apparent) and true modulus of elasticity (E_true) is that E_apparent includes both bending deflection and shear deflection, while E_true includes only bending deflection.

The E_true and E_apparent values for engineered wood products are typically determined through full-scale third-point bending tests using a standard test method, such as ASTM D198, Standard Test Methods of Static Tests of Lumber in Structural Sizes. In general, if the mid-span deflection of a bending member is measured at the neutral axis by referencing the reaction points, the modulus of elasticity is an E_apparent due to the fact that the shear deflection is already included in the experimental data. On the other hand, if the mid-span deflection of a bending member is measured at the neutral axis by referencing the load points (between which no shear stresses are induced), the modulus of elasticity is an E_true due to the fact that the deflection is attributed to the bending stress without shear.

The E_true value for engineered wood products can also be determined through shear modulus tests using another standard test method given in ASTM D198. This method involves center-point loading the same specimen with four different span-to-depth ratios. By plotting 1/E_f (where E_f is the E_apparent calculated under center-point loading) versus (h/L)² for each span-to-depth ratio tested and fitting a regression line to the plot, the reciprocal of the intercept from the regression line represents the E_true. Though this method is not as intuitive as the E_true method mentioned above, it does provide a finer result due to ease of the test setup.

For most structural composite lumber (SCL) products marketed in North America, such as laminated veneer lumber (LVL), the values of E_apparent are generally published; however, some SCL manufactures elect to publish E_true. With the increasing number of proprietary SCL products available in North America, if designers fail to realize that the published value is E_true, the design could be non-conservative when deflection governs the structural design.

For more information on E_apparent and E_true, reference APA publications, Technical Topics: True (Shear-Free) and Apparent Moduli of Elasticity, Form TT-082, and Technical Topics: Apparent and Shear-Free Moduli of Elasticity, Form TT-104.