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The program now implements Cross-Laminated Timber (CLT) design as per NDS 2018 Chapter 10 and APA PRG 320-19. Additional sources for specific design procedures are described below.
CLT wall, roof and floor panels are implemented in Sizer in Beam/Column modes and in Concept Mode. These panels are composed of alternating layers of softwood lumber laminations, with the laminations in one layer at a right angle to those in the adjacent layers.
In what follows, the "longitudinal layers" refers to those CLT layers oriented the same way as the outermost layers, and "the transverse layers" to the other layers internal to the panel. For floor panels, roof panels, and wall panels loaded laterally, loading in the "longitudinal direction" means that support is perpendicular to the longitudinal layers. This is also referred to as loading along the major strength axis. Loading in the "transverse direction" means support is perpendicular to the transverse layers and loading is along the minor strength axis.
Some CLT properties therefore have four values relating to the material used in the longitudinal and transverse layers, and the value of the property when loaded in the longitudinal and transverse directions.
For wall panels loaded axially, layers in the "longitudinal direction" means layers oriented vertically, and the "transverse direction" means those layers oriented horizontally. For lateral loading on wall panels, major axis design occurs when the outermost layers are vertical.
A CLT database file, uclt.cws has been created and added to the installation. This database file can be edited with Database Editor.
The Species corresponding to those described as composing standard layups given in PRG 320 Annex A
Note that all these species correspond to layups with both the transverse and longitudinal layers the same. When making a custom CLT database file with layers of different species, you could create a new species called e.g. S-P-F/Northern.
These are the designations E1, E2, E3, E4, V1, V2, V3, listed as Layups in PRG 320 Annex A, Tables A1 and A2, but are technically CLT grades and appear as such in the CLT grading stamp. They specify the species and grade of lumber used in the alternating transverse and longitudinal CLT layers. Strictly speaking, a layup also specifies the thicknesses of the layers.
All sections are assumed to be 12" wide, corresponding to the arbitrary design width. The depths include are from the following sources:
The sections in PRG 320 Annex A Table A2:
The following sizes produced by major CLT manufacturers are also included to provide a larger array of default choices:
Please note that the strength properties for these sizes do not correspond to those from any manufacturer; they are the strength properties for the PRG 320 grades
The only species property is weight, used for self-weight of the member, in lb/ft3.
The following properties in are defined in psi. for each CLT grade for the materials used in the longitudinal layers and the transverse layers. They can be entered in the Grade dialog of Database Editor:
These properties correspond to those in Table A1 of PRG 320. Sizer uses the Shear Analogy Model to convert them to the design capacities and (FbS)eff, (EI)eff , and Vs shown in Table A2.
Compressive strength perpendicular to the grain Fcp is also defined as a grade property for use in bearing design and is the Fcp from the lumber used in the longitudinal layers.
Section properties include:
Unless otherwise indicated, the following changes have been made to the input of materials and panel configuration in the Beam Input form, Column Input form, and Concept Mode Design Groups
In Beam Mode, the member types Floor panel and Roof panel are added. For Column Mode, Wall panel has been added.
In Concept Mode, the Group Type box in the Joist Design Groups dialog which previously contained buttons for Roof joists and Floor joists now has four choices – Roof, Floor, Joist, Panel, of which you select two.
The Group Type box has been added to the Wall Design Groups and contains Wall panel and Wall joist.
Initial default groups have been created called Wall-Panel1, Roof_Panel1, and Floor_Panel1, and subsequent additions increment the number at the end.
The species and grade come from the database choices described above.
Width input is disabled and set to 1000 mm for metric and 12" for imperial. CLT design assumes a fixed strip of that width.
Depths are from the sections in the database. It is not possible to enter a custom depth; if you wish to have a CLT panel of a different depth than listed, it is necessary to construct a layup in Database editor.
In Beam and Column modes, the Plies input is renamed Layers, is disabled, and shows the number of CLT layers in the layup corresponding to the depth.
A new input Panel orientation includes the choices Longitudinal and Transverse. Longitudinal means that the outermost layers are parallel to the member span; Transverse that they are perpendicular. Design using the major strength axis is performed for Longitudinal, and the minor axis for Transverse.
Only 1 exposed side for fire design is available.
1- or 2-ply 12.7- or 15.9-mm gypsum wallboard fire protection is available.
A checkbox in Beam Input view allows you to apply the 20% vibration span increase for non-structural elements from CSA O86 A.8.5.3. It is available only for multiple spans.
The following pertains to the Supports for bearing design input in Beam and Column Mode,
CLT roof and floor panels can be supported by hangers, sill plates, beams, walls, and CLT wall panels. The bearing width input is disabled and shows the one-meter or one-foot design width. When supported by a wall panel, the list of panel depths is given as the bearing length choices.
CLT wall panels can be supported by sill plates and CLT floor panels. When supported by a sill plate, the bearing length is assumed to be the panel width, i.e. continuous. When supported by a floor panel, the wall panel width or depth an be used as the bearing length. The panel width indicates continuous support.
The following applies to Beam and Column modes. For Concept mode, lateral support checkbox selections have no effect if not relevant to the member type.
Lateral support input is disabled for CLT roof and floor panels, as the panel is self-supporting laterally and there is no CP factor calculation for CLT.
For wall panels, lateral support spacing on the Width b face, i.e. the length of the wall panel, is disabled, along with the associated Ke input, as the panel is self-supporting laterally in that direction. The spacing on the d face remains enabled for calculation of the column stability factor CL.
In Beam mode, the input for oblique angle has been disabled, so that only CLT roof panels supported by beams or walls running parallel to the roof ridge can be modelled directly by Sizer, by using the slope angle.
If the support runs from the roof to the ridge, the one-foot design width is rotated relative to the load, and Sizer’s oblique angle analysis for beams does not apply to planar panels.
If you have such a support condition, is necessary to model the roof panel as a horizontal panel and modify the input loads accordingly. In such a situation, snow loads that are assumed to be oriented vertically over the projected area of the panel should be multiplied by the cosine of the slope squared, and dead loads by the cosine of slope angle. Wind pressures that are assumed to act perpendicular to the surface need not be modified.
The checkbox to indicate that the member is a repetitive member is disabled, as it does not apply to CLT.
In Beam View, all inputs related to Notches are disabled, as there is no design guidance for CLT notches.
The Beam and Column modes, the input for Moisture Conditions is set to Dry and disabled. Refer to Modification Factors, below. In Concept mode, the Dry service checkbox selection has no effect.
In Beam and Column modes, the Inputs for Incising and Fire-retardant treatment are disabled. Refer to Modification Factors, below.
The Width field, when shown, is disabled and shows one foot or one meter, the arbitrary design width of the member.
Area loads are equivalent to line loads, as the line load is assumed to be distributed over the one-foot or one-meter width of the member. The input magnitude can be equally interpreted as a plf line load along the 1-unit width, or a psf area load.
Point loads are assumed to be distributed over the one-foot or one-meter width of the member. You can show the point load as a plf line load using the existing Enter point load as UDL setting.
As for floor joists, the Beam Supports area load setting is disabled.
The Load Face input is disabled and set to Width b, as the assumption is the one-meter or one-foot design width is loaded, and there is no in-plane wall loading.
The default creep factor for long-term deflection is set to 2.0 for CLT design. rather than the usual 1.5, as per NDS 3.5.2.
Bending moment and shear design for standard CLT panels listed in PRG-320 is in accordance with PRG-320 Table A2. For custom panel lay-ups and for reduced sections for fire design, the program uses the Shear Analogy Method given in the following sources
This Shear Analogy Method also yields the results for standard sections that are shown in Table PRG 320 Table A2.
Axial and combined axial and bending design of wall panels, bearing design, and fire design are in accordance with the NDS. Application of axial design procedures from the NDS to fire design is described in the CLT Handbook.
The modification factors applied to CLT design are given in NDS Table 10.3.1 – Load Duration Factor CD, Temperature Factor Ct, Bearing Area Factor Cb, and Column Stability Factor CP
Table 10.3.1 also includes the following factors which have no effect on CLT floor, roof, or wall panel design in Sizer:
NDS 10.3.3 says that information on moisture factors is supplied by manufacturers, and as most manufacturers do not recommend wet service, the program assumes dry moisture conditions and a CM = 1.0.
CLT floor and roof panels are continuously laterally supported on both edges, as the one-foot design width is supported by the rest of the panel. CLT wall panels are also continuously supported. Lateral support spacing is considered on the Depth d face for wall panels for the CP factor for axial compression, but this is not the direction for lateral support for out-of-plane bending design. The one-foot design width on the b face is continuously supported.
Effective stiffness (EI)eff is used bending moment resistance, calculation of panel deflection and vibration. It is calculated using the Shear Analogy Method, given in O86 8.4.3.2 and in the CLT Handbook 3.3.1, Equation 24.
EIeff = b ( ∑ Ei ti3/12 + ∑ Ei ti zi2 ),
where
the summation i is over all the layers for the major strength axis (longitudinal loading), and over all but the outermost layers for the minor strength axis (transverse loading).
ti is the thickness of the layer
For layers parallel to loading, Ei is the modulus of elasticity E as listed in PRG 320 Table A1
For layers transverse to loading, Ei = E /30 (PRG 320, Table A1, Note d)
zi is the distance from the center of the layer to the neutral axis. For symmetric CLT panels, the neutral axis is the mid-point of the panel depth.
For fire-reduced sections, transverse layers that are the final partially charred layer and are thus the outermost layer on the charred side of the panel are not included in the summation.
The calculation of the neutral axis ỹ is given in Equation 8 of Chapter 8 of the CLT Handbook as follows
ỹ = ∑ yi Ei ti / ∑ Ei ti
where yi is the distance from the unexposed side to the centre of the layer.
As Ei in the transverse layers is effectively zero when compared to the longitudinal Ei , this reduces to Equation 9
ỹ = ∑ yi ti / ∑i ti
where the summation is over longitudinal layers only.
Double outermost layers are treated as a single layer in this calculation, on the assumption that the lamination between these layers is at least as strong in bending as the wood itself, and the two layers act as a unit.
The factored bending moment resistance for the major axis strength direction is
M’ = 0.85 CD Ct (FbS)eff,f,0
and for the minor axis direction is
M’ = CD Ct (FbS)eff,f,90,
where the values of (FbS)eff are those listed in table A-2 of the PRG 320. For custom CLT materials, and for fire design, (FbS) eff is calculated using O86 8.4.3.1:
(FbS) eff = α Fb Seff
where
Seff = 2 (EI)eff / E h
and
Note that the CLT Handbook Chapter 3, Section 2.1, Equations 1 and 2 for transverse loading uses the full panel loading depth rather then the reduced depth, and the Fb of the outermost layer rather than the transverse layers. The CSA method was used because that is the approach used to generate (FbS)eff in the current PRG 320.
The depth used in the calculation of effective section modulus Seff does not include the final partially charred layer on the exposed side if is transverse to the axis of loading.
The calculation of Seff considers the change in the location of the neutral axis as follows, from CLT Handbook, chapter 8, section 4.1.4.1, equation 13:
Seff = (EI)eff / E ( hf – ỹ)
where:
The fire adjustment factor of 2.85 from NDS Table 16.2.2 is applied.
The rolling shear resistance Vs is checked:
Vs’ = CD Ct Vs
where the values of Vs are those listed in table A-2 of the PRG. For custom CLT layups, and for fire design, Vs is adapted from O86 8.4.4.2
Vs = 2/3 A Fs
A is the gross cross-sectional area for loading on the major axis, and for the minor axis it is the cross-sectional area minus the area of the outermost layers.
Fs is the rolling shear resistance, which is assumed to be the same for longitudinal and transverse laminations. If you have a custom CLT material with differing Fs for transverse vs. longitudinal layers, it is recommended to use the lower Fs as the material rolling shear resistance.
This method conservatively assumes that the maximum shear in the member cross section occurs in a transverse layer, where rolling shear governs, as rolling shear strength Fs is typically much lower than shear strength Fv. For custom CLT materials with higher Fs than Fv, it is recommended to enter the Fv value in the database as Fs.
The program applies an adjustment factor of 2.75 to the rolling shear strength Fs, from AWC Technical Report 10, Table 1.4.2, as it is not listed in NDS Table 16.2.2.
The calculation of the gross cross-sectional area does not include final partially charred layer if is transverse to the axis of loading.
For the unusual case of design in the transverse direction with double outermost layers, both layers at the top and the bottom of the panel are omitted from the calculation of A.
Axial design for CLT wall panels uses considers only the layers in the longitudinal direction. Note that these layers may be the "transverse layers" in terms of defining the panel layup, if the outermost layers are horizontal. Therefore, in what follows,
Axial design for CLT wall panels uses NDS 3.8.1 with the net section area for calculation of tensile stress ft being the cross-sectional area of the layers in the longitudinal direction multiplied by the one-foot design width.
NDS Eqns. 3.9-1 and 3.9-2 are used for CLT combined axial tension and bending design, with the Fb used in determining Fb* and Fb** being for the laminations in the longitudinal (axial) direction. The 0.85 factor for conservatism that was applied to the value of (FbS)eff in PRG 320 Table A2 is also applied to Fb* and Fb** for major axis design (wall panels with outer vertical longitudinal layers).
Note that for CLT, Fb* = Fb** = Fb, as the Cv and CL factors are not applicable to CLT design in Sizer.
Axial compression is design is as per NDS 3.6 with net section area for calculation of compressive stress ft being the cross-sectional area of the layers in the longitudinal (axial) direction multiplied by the one-foot design width.
The slenderness ratio is calculated as per NDS Appendix H., which says r √12 can be substituted for the depth d, where r is the radius of gyration = √ (I/A), so the slenderness ratio is as given in in CLT Handbook, Chapter 8, Section 4.1.4.1, Equation 16:
Note that this slenderness ratio is used only to determine whether the panel is under the limit of 50 in NDS 3.7.1.4, for CLT it is not used in the calculations for the column or beam stability factors.
The column buckling resistance PcE is required for the alternative formulations from the NDS Commentary for the column stability factor CP and for combined axial and bending design.
PcE = π2 (EI)app-min’ / le2
le is the effective length between lateral supports, which is usually KeL for wall panels, L being the panel height, and (EI) app-min is discussed in the next section.
Stiffness Used for Buckling Calculations (EI) app-min’
(EI) app-min’ is the factored effective stiffness modified for shear deflection. Although the E for pure bending is used to derive Emin for other materials, NDS Commentary C10.3.7 refers to “significant shear deformation that can occur between the parallel and perpendicular CLT laminations”.
EIapp is determined from EIeff using NDS Equation 10.4-1, then the formula from NDS Appendix Eqn. D-4 and Commentary Eqn. C4.2.4-1, is applied to get (EI) app-min. Finally the adjustment factors from NDS Table 10.3.1 ( or Table 16.2.2. for fire design) are applied to get EIapp-min’.
Note that Eqn. D-4 that is ordinarily applied to E to determine Emin includes a 1.03 factor to convert to pure bending, that is, to factor out the decrease in the published E from the true E to account for shear deflection. This factor has been included in (EI)app-min even though it is intended to include shear deflection.
Examples in the CLT Handbook and the AWC Technical Report 10 for fire design include the 1.03 factor, so it is retained in Sizer as well even though it is contrary to the intention of C10.3.7. Note that the lamination E values used to create EIeff include the 1/1.03 factor for shear deflection, so this just serves to eliminate this redundancy for buckling design.
The Ks factor in Table 10.4.1.1 used to determine EIapp for column buckling is derived using the following expression
and then substituting the expression for PcE given earlier; i.e. PcE-app = π2 (EI)app / (KeL) 2 and PcE-eff = π2 (EI)eff. / (KeL) 2 . κ is a standard factor for section shape, which equals 1.2. for rectangles.
If you then isolate EIapp on the left-hand side, and compare with NDS Equation 10.4-1, which is
you find that
Ks = κ ( π / Ke )2
The values 11.8 and 23.7 for Ks in Table 10.4.1.1 are derived using the "recommended design" row from NDS Table G1 for Ke , for pinned-pinned and fixed-fixed columns, respectively.
Sizer allows pinned-fixed, pinned-pinned, and fixed-free columns, and allows you to enter your own Ke value, so Ks is calculated with the above formula and the Ke values that you input. The default values Ke of 0.8, 1.0, and 2.1, respectively, yield Ks values of 18.50, 11.84, and 2.68.
For CLT wall panels, the alternative formulation Eqn. C3.7.1-1 from NDS Commentary C3.7.1, is used instead of Equation 3.7-1. This equation is also given in the CLT Handbook, Chapter 8, Section 4.1.4.1, Equation 16.
where
For combined axial and bending design, the program uses the formula from NDS Commentary C15.4-5, rather than equations 15.4-1 to 15.4-4 that is used for other materials. This equation is also given in CLT Handbook, Chapter 8, Section 4.1.4.1, Equation 18:
where,
From NDS Table 16.2.2, the fire strength adjustment factors of 2.58 for fc and 2.85 for ft are applied.
The effective area used to determine design stresses fc and ft , the slenderness ratio, and axial compressive resistance Pc* is that of the fire-reduced cross section.
The effective stiffness EIeff used in determining the buckling resistance PcE is calculated using the fire-reduced section as described in Effective Stiffness, above.
The effective moment of inertia Ieff used for the slenderness factor is calculated using the reduced section.
The value of the out-of-plane deflection used for combined axial and bending includes the load eccentricity, that is, the distance from the location of the axial load to the centroid of the fire-reduced section. For this reason, combined-axial-and-bending compression design is always calculated for fire design, even when there was initially no load eccentricity or lateral loads.
Bearing design is identical to that for beams or for columns, using the input bearing lengths and widths. The bearing length factor Cb is applied to CLT bearing design as per Table NDS 10.3.1.
For floor and roof panels, this implies a bearing length that is the width of whatever is supporting the member, and the corresponding Cb factor.
For the supporting member it means a bearing length that is the one-meter or one-foot design width, which means Cb = 1.0, as it should be for continuous support. .
For wall panels supported by sill plates, the sill plate bearing length is the one-meter or one-foot design width, so Cb = 1.0.
For wall panels supported by floor panels, you can choose to use the one meter design width for cases that the floor is continuously supported beneath the wall, or you can choose to use the wall depth, for cases that the beam supports the wall without a continuous support below. In this case, a Cb factor is calculated.
Fire design is in accordance with NDS 16.2. Refer to previous sections for changes to specific design procedures for fire design.
The char depth is calculated using Eqn. 16.2-3. then multiplied by 1.2 as per 16.2-4 to get the effective char depth used to reduce the section depth for design.
Equation 16.2-3 calculates the number of layers that will fully burn during the exposure time, using an increased char rate for the fully burned layers to account for the effect of lamination, then adds the char depth of the final partially charred layer using the usual char rate.
For fire-reduced sections, transverse layers that are the final partially charred layer and are thus the outermost layer on the exposed side of the panel are not included in the following calculations
As described in the previous sections, the following values are calculated differently for fire design to account for the modified geometry of the section due to charring:
Refer to the specific procedure, above, for more details.
The "design stress to member strength" factor given in NDS Table 16.2.2. is applied to fire design of CLT panels. The only other applicable factor from this table is the column stability factor CP.
Refer to the specific design criterion, above, for more details.
Double outermost layers are treated as separate layers in the calculation of char rate using Eqn. 16.2-3 but are considered as a single layer of double thickness for bending moment design. The double layer is considered when determining whether the final outermost exposed charred layer is a transverse layer, and in determining cross sectional areas for shear and axial design.
True panel stiffness for deflection calculations is the effective stiffness (EI)eff described in . (EI)eff is used in NDS Equation 10.4-1 for apparent stiffness EIapp that includes an approximation of the effect of shear deflection.
Shear deflection is implemented by applying the uniform loading simple-span equation for apparent stiffness EIapp in NDS 10.4-1 to all loading and span configurations. Research has shown that this can be very inaccurate for unbalanced loading or spans, and we are developing an improved procedure to be implemented in a future version.
In this equation effective shear modulus GAeff is calculated using the Shear Analogy Method, given in O86 8.4.3.2 and. CLT Handbook 3.3.1, Equation 25.
GAeff = a2 / b ∑ α i t i / Gi
where,
Double outermost layers are treated as a single layer in this calculation.
According to NDS Table 10.3-1, only the moisture factor CM and temperature factor Ct are to be applied to the stiffness EIapp to get EIapp’ that is used as the panel stiffness calculations. Sizer assumes dry moisture conditions, so only the Ct factor is applied.
The default creep factor for long-term deflection is 2.0 from NDS 3.5.2.
Allowable span lengths for vibration has been implemented using the procedure in CSA O86-14 A.8.5.3.
A data group in the Design Settings has been added called CLT Vibration allowing you to specify whether vibration design using CSA O86 A.8.5.3 is performed, and to allow you to enter a percentage span adjustment increase for manufacturers performance expectations as allowed by A.8.5.3 Note 3.
The allowable vibration span is calculated as
lv <= 0.11 EIeff0.29 / m0.12
where EIeff is in N-m2 and m is the mass per square meter of the panel.
Although the equation is derived for simple spans, the allowable span is compared with the longest span on a multi-span member, as is allowed by Note 1.
The allowable span is then increased by the largest of the performance increase (Note 3, see a), above) or the non-structural element increase (see ). Both increases are not applied simultaneously.
The non-structural element increase is not applied to spans greater than 8 m (26.25 feet in length) and will increase spans less than 8 m only as far as 8m.
A Vibration line is added to the Analysis vs Allowable Stress table showing the largest center-to-center span on the member Lmax, the maximum allowable vibration span Lv, and the ratio between them.
Inadequate vibration span lengths are indicated by a failure warning message.
A design note appears if the span has been increased either by the performance increase (see a), above) or the non-structural element increase (see c), above).
In the Building Codes box, the source of all CLT analysis and design procedures is given in detail referring to references in the CSA O86-14, the NDS, the FPInnovations CLT Handbook, and AWC Technical report 10. Equation numbers from CLT Handbook provisions are given.
CLT panels in Concept mode are treated as if they were joist areas, with the reactions from the one-unit design strip at each end of the panel used to create line loads on the supporting members.
If the supports for a CLT panel are sloped, such as is the case for rafters or gable end walls, the panel is loaded obliquely and cannot be designed by Sizer (see ).
If the program encounters such a panel, it operates the same way as it does for a non-planar floor or roof area, it is able to transfer the reactions to the supporting members but cannot design the member or the group to which the member belongs.
The Design Summary indicates that the group could not be designed, and the Design by Member results indicate that the panel could not be designed.
The member is specified as e.g.
CLT Floor Panel, Southern Pine, E4, 7 Layers 3-7/16" (12" width)
The Panel orientation, either longitudinal axis or transverse axis, is shown in the information below the member.
Volume is shown as cu. m / m or cu. ft./ ft i.e. indicating the volume of the one-unit design width.
Lateral support information is not shown, except for wall panels.
In the Analysis vs. Allowable Stress table,
The Shear line shows value for shear force V and allowable factored rolling shear Vs’.
The Moment line shows values for moment M and allowable moment M’. M’ is the same as (Fb’S)eff.
The Deflection lines appear as they do for beams and columns.
For wall panels:
The Axial, Axial Bearing and Support Bearing lines appear as they do for columns.
The Combined line refers to Equation C15.4-5.
In the Factors table of the Additional Data,
The shear line shows Fs. The modification factors shown are applied to Vs.
The moment line shows Fb. The modification factors shown are applied to (FbS)eff.
The deflection line shows EIapp’. The unfactored EIapp is shown along with the treatment factor if one exists.
For wall panels, Fc’, Fc’comb, and Fcp support lines appear as they do for columns.
A column called CLT has been added to show the 0.85 (longitudinal) or 1.0 (transverse) for bending moment resistance (see ). The column for notch factor CN has been removed.
The Calculations section of the Additional Data shows the following data
A note appears saying that (EI)app’ is based on the Ks = 11.5 for uniform loading on a simple span and is approximate for other loading conditions.
A design note refers to the sources of the design procedures; NDS Chapters 10, C3, and C5, CSA O86-14 Chapter 8, and the FPInnovations CLT Handbook Chapters 3 and 8.
CLT panels are depicted showing alternating uniform layers and layers composed of repeated end-grain. Longitudinally oriented panels have uniform layers at top and bottom; transverse layers show end grain at top and bottom.
Double outermost layers are shown as two layers at the top and at the bottom which have the same orientation.
For wall panels, the Width b face is shown as the one foot or one-meter design strip. The Depth d face shows the thickness of the panel.
Lateral support is not shown in the drawings, as it does not apply to floor or roof panels or to the Depth d face for wall panels and would be confusing if it appeared on the Width b face, as it is the arbitrary 1-unit wide design strip.