NDS 3.9 - Combined Bending and Axial Loading, and Biaxial Bending

In the presence of an axial load WoodWorks Sizer limits bending to just a single axis.

NDS 3.9.1 Bending and axial tension

According to Equation 3.9.1, which applies when axial tension loads and bending loads are present

NDS 3.9-1

and

NDS 3.9-2

where Ft’ = F_t C_M C_t C_D C_F C_Pt,

Fb* = F_b C_M C_t C_D C_r C_v C_Pt (i.e, missing CL) ,

and Fb** =F_b C_M C_t C_D C_r C_L C_Pt (i.e, missing Cv)

Note that the proviso that F_b** is missing C_v applies only to SCL and glulam, as these are the only ones with volume factors.

Note that there is no provision saying that these equations should be applied in the absence of tension loads. Since C_v can be greater than 1 for SCL, in this case it would be equivalent to the bending check without the C_v included, rendering a C_v which is greater than one meaningless. It does mean, however, that the presence of even a tiny tension load negates the effect of a C_v greater than 1.

In Sizer, this currently applies to columns, and wall studs only as there are no axial loads on beams.

For CLT wall panels, the F_b used in determining F_b* and F_b** is for the laminations in the longitudinal (axial) direction. The 0.85 factor for conservatism that is applied to the value of (F_bS)_eff in PRG 320 Table A2 is also applied to F_b* and F_b** for major axis design (wall panels with outer vertical longitudinal layers).

Note that for CLT, F_b* = F_b** = F_b, as the C_v and C_L factors are not applicable to CLT design in Sizer.

NDS 3.9.2 Bending and axial compression

For the case of combined axial compression load and a bending load on the one of the faces of the member

Sizer fully implements this equation and the conditions under "where...", and the appropriate values are used to compute f_cE for the case of loading on the weak axis for anisotropic materials such as glulam and LVL. .

In Sizer, this currently applies to columns and wall studs, and wall panels only as there are no axial loads on beams.

Note that given our assumptions of column bending about one axis only, the equation 3.9-4 is already handled by the condition f_c < F_cE2.

NDS 3.3.3.10 and 3.9.2 Biaxial bending

For the case of biaxial bending in beams, equation 3.9.3 is

NDS 3.9-3

where the subscripts 1 and 2 refer to loading on the narrow and wide face of the member respectively.

Equation 3.9-3 applies to all bending members whether or not axial loads are present, by virtue of 3.3.10.

It is important to note that we assume the anisotropy of the member is always oriented the same way with respect to b and d (i.e. LVL laminations are always parallel to d dimension, and glulam laminations parallel to the b dimension),so that

For d >= b, F_b1 = F_bx

F_b2 = F_by .

for b > d

F_b1 = F_by

F_b2 = F_bx,

The Euler buckling coefficients F_bE are the same ones that are used to compute the beam stability factors.

NDS 3.3-6

where

Appendix D-4 (1.03 replaced by 1.05 for glulam)

and Slenderness ration R_B

NDS 3.3-5

However, in this case the E, b and d values used in the computation are with respect to the load on the longest face of the member, so that d in this formulation is in fact

d = max( d, b)

and b = min( d, b)

and

E = E_x for d >= b

E = E_y for b > d

and le is the effective length defined in NDS 3.3.3.5 .