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Design Equation
The equation implemented is from O86 9.7.1.1 It is
The meaning of the variables is given in the following sub-sections..
The four terms in the equation give the contribution to deflection from the following sources, in order
Seismic Multiplier
For seismic design, the resulting deflection is multiplied by RdRo/Ie, as per NBC 4.1.8.13 for the purpose of checkoing storey drift
Unit shear v
Load Combinations and Factors
For segmented shearwalls, the unit shear v is vertically accumulated serviceability shear force, that is, the shear force per unit foot unfactored by the 1.4 load combination factor for wind design, as per CSA O86 4.2.4.2.
For seismic design, it is the same as the force that is used for shearwall design and which appears in the elevation view at the bottom of the shearwall.
Distribution of v Within Wall
The second and third terms of this equation apply to the sheathing, which can be different for each side of a composite wall.. Both sides require a shear value v (the third term does so indirectly through en.). Refer to Distribution of v to Sides of Composite Wall for an explanation of how shear is apportioned to each side of a composite wall.
Distribution of v to Segments Within Shearlines
The distribution of v within a shearline depends on the selection of Shearwall Rigidity per Unit Length and Distribute Forces to Wall Segments based on Rigidity in the Design Settings. For more details, refer to subsection Distribution to Segments within Shearline
Shearwall height Hs
The shearwall height Hs is the distance from the bottom of the bottom wall plate to the top of the top wall plate, exclusive of floor joists or other building elements not part of the wall.
Segment length Ls
The length Ls is the length of an individual full-height segment between openings, and the calculations are performed for each segment separately.
End Chord Bending Deflection
The first term in the equation relates to the in-plane bending of the shearwall chords, that is, the wall end studs.
Modulus of Elasticity E
An input field has been added to Shearwalls to allow for input of the grade of the wood end studs. The modulus of elasticity is then taken from the WoodWorks database of material properties.
Cross sectional area A
This is the section area end studs, which are typically built-up members. Shearwalls now allows you to input wall end stud thickness, width, and number of end studs (see Hold-down Input), from which the cross-sectional area is calculated.
End Post Composition
Shearwalls does not allow for wall chord posts that are not made up of built-up wall studs but it is possible to model such a situation by typing in a value for the stud thickness, as it has no effect on shearwall design. However you cannot change the wall stud species to the one for the end post without having an effect on shearwall design, which depends on specific gravity. For MSR/MEL you cannot change the grade without having an effect on design.
Panel Shear Deflection
The second term relates to the in-plane shear deformation of the shearwall
Shear Stiffness Bv
The value for shear –through –thickness rigidity Bv is taken from Table 7.3A-C in CSA O86-09, and from the USA Special Design Provisions for Wind and Seismic (SDPWS) Table C4.2.2B for gypsum wallboard..
Shear Value v
Refer to Distribution of v to Sides of Composite Wall in this topic for an explanation of how shear is apportioned to each side of a composite wall.
Nail Slip Deflection
The third term is related to the slippage of nails fastening the sheathing to the top and bottom shearwall chords, i.e top and bottom wall plates.
Fastener Slip en
The fastener slip en is taken from O86 Table A.9.7 for wood panels and for the USA SDPWS Table C4.2.2D for gypsum wallboard. Note that the slip is non-linear with respect to shear-per-fastener Vn for wood structural panels, but does not depend on v at all for gypsum, it is a constant.
Fastener Load Vn
The load per fastener Vn is calculated by dividing the shear-per-unit-length v by the user-input panel edge spacing, yielding the force on each edge fastener.
Composite Walls
Refer to Distribution of v to Sides of Composite Wall in this topic for an explanation of how shear is apportioned to each side of a composite wall.
Interpolation
The deflections are interpolated for loads per nail in between the values listed. It is not interpolated for nail size when non-standard nails are input, it uses the value for the smaller nail.
Maximum Load Per Fastener
The program limits the fastener shear to the maximum in Table A.9.7. If it is exceeded, it uses the maximum deflection and issues a warning under the Deflection table.
We determined that this level of loading always results in shearwall design failure for which a failure message is already output anyway.
Unseasoned lumber
For unseasoned lumber, that is lumber with fabrication moisture content less than 19%, the deflection values are doubled as per note 2.
Unblocked walls
For unblocked walls, a nail spacing of 150mm is used in place of the actual nail spacing to comply with CSA O86 9.7.1.2.
Unblocked Walls
For unblocked walls, the shearwall deflection is divided by the unblocked factor Jub as per CSA O86 9.7.1.2.
Distribution of v to Sides of Composite Wall
For composite walls, the 2nd and 3rd terms of the equation, shear and nail slippage, apply separately to each side of the shearwall, which may have different materials.
Equal Deflections
Shearwalls apportions shear to each side of the wall by adjusting the v value until the deflection due to shear plus nail slippage is the same on both sides of the wall. Note that this equalisation is done regardless of whether equalisation of deflections for all segments along a line is being done according to the selection of force distribution design settings described in subsection
Zero Shear
Slippage to non-wood-panel materials is a constant, which in many cases creates a larger slippage deflection than is possible for shear plus slippage even when all load is placed on the wood panel. In these cases, all the force is placed on the wood panel side. The deflection for that segment is the nail slippage plus shear from the wood panel side, and does not include the constant gypsum slippage.
Note that in this case, despite the fact that the entire load is assigned to the wood side for purposes of deflection analysis and storey drift, the program still uses the sheathing on both sides of the shearwall for shearwall capacity calculations according to the procedures for combining shearwall capacity in the CSA O86.