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3.4.2 Shear Design Equations
The calculation of actual shear stress fv for sawn lumber, glulam and SCL members is given in 3.3.2.2 as
fv = 3V / 2bd,
where V is the shear force at the member section.
The factored shear stress is compared with the factored allowable shear stress.
Refer to NDS 7 - Wood I-Joists for I-Joist shear design and for PRG 320 Table A-2 and O86 8.4.4.2 - Shear Resistance for CLT shear design.
3.4.3-Shear Design
3.4.3.1 Shear near support
Sizer applies the provisions of NDS 3.4.3.1 by adjusting the shear values calculated using the actual loading conditions of the member. For each load combination, the shear value at the support is reduced with the ignored portions of the shear resulted from each load within the distance “d” of the edge of the support.
In other words, Sizer takes literally the provision that loads within a distance d of a support "shall be permitted to be ignored" . This is slightly different than taking the value of the shear a distance d from the support, as the latter approach does not take into account the contribution to the reaction at the other end of the member of the ignored loads.
Because the adjustments are done after the loading analysis, the contribution of each load to be ignored is distributed proportionally only in the two supports enclosing the current span. This provides exact values of the design shear for single span members and exact or slightly conservative values for multi-span members.
WoodWorks SIZER measures the distance d from the inner edge of the support, as per NDS Figure 3C. Sizer performs iterative design , first determining required bearing lengths assuming d is measured from the support point, then using these to establish the point from which to measure d on the next iteration.
Uniform and non-uniform distributed continuous loads are ignored within distance "d". Point loads are factored as per NDS 3.4.3.1.a. Uplift continuous loads are not ignored, and uplift point loads are not factored.
For a particular load combination, the shear near support is reduced only if there is not an uplift reaction at that support.
Point loads applied on top of sloped members have the position along the member bottom calculated according to the load type (see loads on sloped members) and the member’s depth. This position is then and used in conjunction with the distance “d” point load for magnitude factoring.
3.4.3.2-Shear Design for Notched Bending Members
Tension or compression face determination
As the user inputs the value of the unsupported length “e”, Sizer needs to assign this value to the compression face notches.
If a design has not been performed, the program will consider the top of the member to be the compression edge and assign the “e” to the top notches. When a design is performed, Sizer determines if a notch is on the tension edge or the compression edge by checking the bending orientation at the interior end of the notch. For this purpose, Sizer automatically creates points of interest at these locations.
Length restrictions
While all tension face notches are assumed to be the support length, the compression face notches will be the support length plus the unsupported length “e”.
If the “e” value causes any compression face notch to be more that 1/3 the length of the associated span, the program warns you upon designing the beam. It will then simply reset the unsupported notch length “e” to 1/3 the span length and proceed. The notch length will be adjusted for both (if existing) compression face notches.
Sloped members
Sizer assumes that the notch depth entered by the user is always perpendicular to the member, and that the unsupported length “e” is along the horizontal projection of the member.
Notch diagrams
Notches are not shown in the beam diagrams if the member has not yet been designed or if it is a sloped member. Instead, a note below the location mentions the existence of the notch.
Notch Factor Cn
Sizer's output displays a notch factor called Cn. This is a dimensionless value adopted by SIZER to indicate the decrease in allowable shear stress Fv at a notch. You will not find this factor in the NDS document but it is derived from equations in Clause 3.4.3.2 depending upon whether the notch face is in tension or compression.
Shear Strength Reduction - Tension edge notches
NDS equation 3.4-3 gives the shear reduction due to tension edge notches:
( NDS Equation 3.4-3)
Where dn is the depth remaining after a notch is taken out. Given the usual equation for shear, this establishes the following value for the notch factor Cn –
Equation 2 – Tension edge Cn
In NDS 1997, this equation was formulated by factoring Fv rather than Vr, however the equivalent notch factor was the reciprocal of this ratio raised to a power of 2 rather than 3.
Shear Strength Reduction - Compression edge notches
NDS equation 3.4-5 gives the shear reduction due to compression edge notches:
, for e <= dn (NDS Equation 3.4-5)
Shear reduction for compression edge notches , e >dn:
, for e > dn.
Given the usual equation for shear, this establishes the following value for the notch factor Cn –
, for e <= dn
or
, for e > dn
3.4.3.3-Shear Design for Bending Members at Connections
The effect of connections on the shear capacity of bending members has not been implemented in WoodWorks SIZER. The user is advised to use larger sections than those found using WoodWorks SIZER if the ratio of actual to allowable shear stress is close to unity.
Biaxial shear for Glulam and SCL Members
The NDS gives no guidance on how to deal with bending shear for members loaded on both faces when anisotropic materials such as glulam and SCL are used. In Sizer, this currently applies only to beams with an oblique rotation angle.
It is not sufficient in this situation to resolve the shear stress into components perpendicular and parallel to the member sides, and compare these with the strengths in these directions, because in the longitudinal direction, the material is subject to the full shear stress regardless of the rotational angle.
The equation
fvx/Fvx + fvy/Fvy <= 1
is used in Sizer. It was suggested by AITC, the former authority for glulam design.