Mechanically graded lumber, such as machine stress rated (MSR) and machine evaluated lumber (MEL), is being used in more applications that traditionally used visually stress rated lumber (VSR). Substitution of MSR and MEL for VSR or MEL for MSR requires more than just determining equivalent or higher published design values. Depending on the application, modulus of elasticity design values (E) also require consideration regarding their use in buckling equations to determine equivalency. Modulus of elasticity design values for lumber are assumed to have a maximum coefficients of variation (COV_E) as follows:
 

Lumber	COVE
VSR	25%
MEL	15%
MSR	11%

The National Design Specification® for Wood Construction (NDS®), 1997 Edition outlines criteria for determining the beam stability factor, C_L and the column stability factor, C_P, both of which are used in buckling calculations. The buckling stiffness factor, C_T, is also calculated per the NDS. Each of these factors includes recognition of different COV_E for different materials. Thus, when lumber is used in applications requiring buckling calculations, like truss chords, load bearing walls, and laterally unsupported columns, differences in COV_E impact the equivalency of the material.

The following effective E adjustment factors are provided to assist in determining equivalent substitutions of MSR, MEL, and VSR lumber:
 

Substitute Material
	Specified Material
	VSR	MEL	MSR
	Multiply E of Substitute Material by
VSR (COVE = 0.25)	1.00	1.28	1.39
MEL (COVE = 0.15)	0.78	1.00	1.09
MSR (COVE = 0.11)	0.72	0.92	1.00

It is important to note that these factors are only applicable to material where buckling is the critical design consideration. Where deflection controls, a straight comparison of E values is necessary to determine equivalency. It is also important to note that straight comparison of other design values such as bending (F_b), tension parallel to grain (F_t), shear parallel to grain (F_v), compression perpendicular to grain (F_c ), and compression parallel to grain (F_c) is necessary to determine equivalency.

The following example illustrates the use of these factors for substitutability:

Assume #2 Southern Pine 2x4 is specified for use in roof truss chords. Roof trusses are typically buckling critical rather than deflection critical between panel points. Therefore, appropriate substitutes would be 1500f-1.3E MSR and M-11 MEL. Design values are tabulated as follows:
 

Material	Fb (psi)	Ft (psi)	Fc (psi)	E(x106) (psi)	Calculation/Verification
VSR #2 Southern Pine 2x4	1500	825	1650	1.6	-
MSR 1500f-1.3E	1500	900	1650	1.3	(1.3x1.39=1.8>1.6 ok)
MEL M-11 2x4	1550	850	1650	1.4	(1.4x1.28=1.8>1.6 ok)

Equation Format - 1997 NDS for Wood Construction One change to the 1997 NDS for Wood Construction is incorporation of equations to calculate stability and stiffness factors as follows:

Beams - used in beam stability calculations in NDS 3.3.3.8

K_bE = 0.744 - 1.225(COV_E)

= 0.439 for VSR

= 0.561 for MEL

= 0.610 for MSR

Columns - used in column stability calculations in NDS 3.7.1.5, 15.2.3, 15.3.2.4, 15.4.1

K_cE = 0.510 - 0.839(COV_E)

= 0.300 for VSR

= 0.384 for MEL

= 0.418 for MSR

Truss Chords - used in buckling stiffness calculations in NDS 4.4.3.1

K_T = 1 - 1.645(COV_E)

= 0.59 for VSR

= 0.75 for MEL

= 0.82 for MSR