Strong Way Systems Wood Column with SWS Foundation System. Chart 1

Transcription

1 Strong Way Systems Wood Column with SWS Foundation System Chart 1 Allowable Loads For 3 ply 2x6, 4 ply 2x6, 3 ply 2x8 and 4 ply 2x8 Nail-Lam or Glulam Post-Frame Sidewall Columns TTE Project Number E by Dimitry A. Reznik, P.E. Timber Tech Engineering, Inc dar@timbertecheng.com July 18, 2018 East: 22 Denver Road, Suite B Denver, PA West: 406 S. Main St, P.O. Box 509 Kouts, IN Fax: Fax:

2 Strong Way Systems This design is an intellectual property of Timber Tech Engineering, Inc. prepared for use exclusively by Strong Way Systems. Column load rating summarized in Chart 1 is intended for estimate and pricing purposes only. The final column design should include a complete building analysis by a design professional. Timber Tech Engineering, Inc. may not be held liable for any damages in direct or indirect connection with this design. Timber Tech Engineering, Inc Page 1 TTE# E134-18

3 Strong Way Systems 1) DESIGN OVERVIEW The Strong Way Systems (SWS) foundation system is designed for use with mechanically laminated (nail-lam) and glue laminated (glulam) wood columns used in typical post-frame application. The SWS foundation system consists primarily of a steel bracket that provides a semi-rigid, moment-resisting connection between the wood column and the concrete pier. The SWS foundation system is set in place using the built-in elevation-adjusting mechanism which is also designed to temporarily support the self-weight of the wood column before the concrete pier is poured in place. The concrete pier, wet-poured around the SWS foundation system, however, is required to support the final loads on the column and the building. Each column assembly consists of: A reinforced concrete pier below the grade, designed by the building designer according to the provisions of the Building Code Requirements for Structural Concrete (ACI ) by the American Concrete Institute. A SWS moment-resisting column-base bracket designed according to the Specification for Structural Steel Buildings by American Institute of Steel Construction (AISC) A nail-lam or glulam column designed according to the 2015 edition of the National Design Specification for Wood Construction (NDS) by the American Wood Council (AWC) and the 2010 edition of the Design Requirements and Bending Properties for Mechanically-Laminated Wood Assemblies, (EP559.1) by the American Society of Agricultural and Biological Engineers. Having a rotational rigidity and moment-resisting properties, the SWS foundation system allows the column assembly to behave similar to a column that is continuous from footing, below grade, to the eave of the building. The purpose of this report is to describe the calculated rotational stiffness and bending strength of the SWS bracket and to prepare a column chart showing the allowable axial capacities for the 3-ply 2x6, 4-ply 2x6, 3-ply 2x8 and 4-ply 2x8 nail-lam and glulam columns used with the SWS foundation system. The calculations for the nail-lam columns are based on #1 grade Southern Pine lumber using the unadjusted design values shown in Table 1A. The calculations for the glulam columns are based on southern pine glulam column with unadjusted design values shown in Table 1B. The lateral load on the columns is based on 8ft column spacing. The adjustment factors are shown in Tables 1C and 1D. TABLE 1A: UNADJUSTED DESIGN VALUES FOR #1 SP NAIL-LAM COLUMNS 2x6 Nail-Laminated Columns 2x8 Nail-Laminated Columns Fb 1350 psi Fb 1250 psi Fv 175 psi Fv 175 psi Ft 875 psi Ft 800 psi Fc 1550 psi Fc 1500 psi Fcp 565 psi Fcp 565 psi E psi E psi Emin psi Emin psi Timber Tech Engineering, Inc Page 2 TTE# E134-18

4 Strong Way Systems TABLE 1B: UNADJUSTED DESIGN VALUES FOR SP GLULAM COLUMNS 2x6 Glulam Columns 2x8 Glulam Columns Fb 1850 psi Fb 1700 psi Fv 175 psi Fv 175 psi Ft 875 psi Ft 800 psi Fc 1600 psi Fc 1500 psi Fcp 565 psi Fcp 565 psi E psi E psi Emin psi Emin psi TABLE 1C: ADJUSTMENT FACTORS FOR DESIGN VALUES (NAIL-LAM COLUMNS) Load Duration Factor Wet Service Factor Temperature Factor Beam Stability Factor Size Factor Incising Factor Repetitive Member Factor Column Stability Factor CD CM (NDS) Ct CL CF Ci Cr (VG, ASAE EP559.1) CP (NDS) Wet Dry (NDS) (NDS) (NDS) (NDS) 3-ply 4-ply (NDS) Fb' = Fb x Ft' = Ft x The columns in this analysis are not loaded in tension, this section does not apply Fv' = Fv x Fcp' = Fcp x Fc' = Fc x Varies E' = E x Emin' = Emin x TABLE 1D: ADJUSTMENT FACTORS FOR DESIGN VALUES (GLULAM COLUMNS) Load Duration Factor Wet Service Factor Temperature Factor Beam Stability Factor Volume Factor Stress Interaction Factor Flat Use Factor Shear Reduction Factor Column Stability Factor CD CM (NDS) Ct CL CF CI Cfu Cvr CP (NDS) Wet Dry (NDS) (NDS) (NDS) (NDS) (NDS) (NDS) (NDS) Fb' = Fb x Varies Ft' = Ft x The columns in this analysis are not loaded in tension, this section does not apply Fv' = Fv x Fcp' = Fcp x Fc' = Fc x Varies E' = E x Emin' = Emin x Timber Tech Engineering, Inc Page 3 TTE# E134-18

5 Strong Way Systems 2) SWS FOUNDATION SYSTEM The SWS foundation system consists primarily of a moment-resisting bracket made of two 1/4 thick vertical steel plates (ASTM A36) and four #5 (5/8 ) grade 60 weldable rebar. All other steel components are responsible for secondary functions such as keeping the bracket together, providing bearing surface for the wood column, providing attachment for the skirt board, enabling elevation adjustability and providing temporary support to wood column (self-weight of wood column) during the installation and other similar functions (see Figures 2A, 2B and 2C)). The bending and shear forces from the wood column are transferred into the vertical steel plates using (16) 1/4 x2-1/2 SDS Simpson screws. The vertical steel plates transfer these forces into the rebar and then into the concrete pier. The rebar that is welded to the steel bracket may not replace the main vertical rebar in the concrete pier as required by the design. The design of the concrete pier is excluded from this report and is the responsibility of others. Figure 2A: SWS Foundation System Timber Tech Engineering, Inc Page 4 TTE# E134-18

6 Strong Way Systems Figure 2B: SWS Foundation System 326 and 426 models Timber Tech Engineering, Inc Page 5 TTE# E134-18

7 Strong Way Systems Figure 2C: SWS Foundation System 328 and 428 models Timber Tech Engineering, Inc Page 6 TTE# E134-18

8 Strong Way Systems 3) SWS FOUNDATION SYSTEM: ROTATIONAL STIFFNESS The effective rotational stiffness, (M/θ) e, of the connection between the wood column and the concrete pier is calculated using the analogy of 3 springs arranged in series: Spring 1, (M/θ) f, represents the rotational stiffness of the steel-to-wood connection, which is defined by the slip-modulus of the SDS fasteners (see calculations) Spring 2, (M/θ) s, represents the rotational stiffness of the steel plates Spring 3, (M/θ) r, represents the rotational stiffness resulting from the axial deformation of the compression and tension rebar The effective rotational stiffness is calculated using the effective spring constant equation for springs arranged in series: Effective Rotational Stiffness: (M/θ) e = [1 / (M/θ) f + 1 / (M/θ) s + 1 / (M/θ) r] -1 The calculated effective rotational stiffness values for all models of the SWS foundation system are provided in Table 3A. Table 3A: Effective Rotational Stiffness of SWS Foundation System, (M/θ) e Model (lb-in) / deg (lb-in) / radians ,500 3,465, ,500 3,465, ,300 5,575, ,300 5,575,600 Alternatively, the semi-rigid joint may be modeled as a vertical member, a segment between the wood column and the concrete pier. Because this member will also replace a portion of the wood column, the effective rotational stiffness calculations should include a 4 th spring component, Spring 4, (M/θ) w, that represents the rotational stiffness of the wood column segment that is being replaced. The geometric and material properties of the joint member are defined in the following expression: EI = (M/θ) e L Where, E = elastic modulus of the joint member I = moment of inertia of the joint member s profile (M/θ) e = rotational stiffness of the joint consisting of 4 parts ((lb-in) / radians) L = length of the joint member Table 3B shows the properties of the vertical joint member that is 1 long and is made of steel (E=29,000,000 psi). For example, the semi-rigid joint between the wood column and the concrete pier with SWS 326 bracket may be modeled as a 1 long, wide and deep vertical member, made of steel material (for ex. ASTM A36), rigidly connected to the concrete column and the concrete pier. The joint in this example will produce the same results as the joint that is assigned a rotational stiffness value of 60,500 (lb-in) /deg from Table 4A. The steel material for the joint member is a good choice as the elastic modulus for all steel is constant. Timber Tech Engineering, Inc Page 7 TTE# E134-18

9 Strong Way Systems Model Table 3B: Properties of the Joint Member Between Wood Column and Concrete Pier Joint Effective Flexural Modulus of Calculated Side dimension of Member Rotational Rigidity, EI Elasticity, E Moment of joint member, b Length, L Stiffness, (M/θ) e Inertia, I (in) (lb-in) / radians (lb/in 2 ) in 4 (lb/in 2 ) in 4 in ,325,300 3,325,300 29,000, ,360,800 3,360,800 29,000, ,420,100 5,420,100 29,000, ,459,900 5,459,900 29,000, ) SWS FOUNDATION SYSTEM: SHEAR, BENDING & UPLIFT The shear, bending and uplift (tensile) strength of the SWS foundation system is controlled by the steel-to-wood connection (SDS screws). The shear force through the steel-to-wood connection is not an independent quantity but is a function of the bending moments just above and below the steel bracket: V = V T = V B = (M B M T) / x, where V T and M T are the shear moment forces just above the top fastener group, T B and M B are the shear and moment forces just below the bottom fastener group, and x is the distance between the centroids of the top and bottom fastener groups (see the free body diagram). It is, therefore, true that, when the bending strength requirements are satisfied, the shear strength requirements are also satisfied and do not require separate calculations. The allowable bending strengths (ASD) and the design bending strengths (LRFD) for each of the SWS models is shown in Table 4. The values in Table 4 assume a short load duration (wind) where the load-duration factor for ASD design is C D =1.6, and time effect factor for LRFD design is λ = 1.0. The SWS foundation system is intended for use with columns that are protected from moisture (enclosed buildings); the wet service reductions are not applied. Model Table 4: Bending and Tensile Strength of SWS Foundation System Allowable Bending Strength, M a Design Bending Strength, φm n Allowable Tensile Strength, T a Design Tensile Strength, φt n (lb-in) (lb-in) (lb) (lb) ,700 65, ,700 65, ,700 65, ,700 65, ) CHART 1: DESIGN OF NAIL-LAM AND GLULAM COLUMNS The laminations are continuous from the bottom to the top of the column. The certified structural glued end joints are allowed. In a nail-laminated column, a construction structural adhesive may be applied between the laminations on each face but is not required as ASABE EP559 and the calculations in this report do not consider the effect of the adhesive on strong axis bending and interlayer shear capacity. That is, the mechanical fasteners alone are required to resist the interlayer shear. The fastener schedule is to be specified by the column manufacturer (example: x4 nails 9 o/c, staggered from side to side). All fasteners to be electro-coated Timber Tech Engineering, Inc Page 8 TTE# E134-18

10 Strong Way Systems galvanized as per ASTM A653, type G185 or AISI type 304 or 316 stainless steel. The allowable loads contained in Chart 1 are to be used in normal post-frame buildings enclosed on all four sides and supported at the top by a diaphragm action of the building. 6) CHART 1: LOAD CALCULATION ON COLUMNS Columns in Chart 1 were designed for wind load of 96 lb/ft and 160 lb/ft using 90 mph and 115 mph wind speeds calculated per ASCE 7-05 and 7-10, respectively. Additional wind load criteria are summarized below: Building Category (Risk Category) II Exposure Category C Maximum Building Mid-Height 29ft Maximum Roof Pitch 4:12 Envelope: Enclosed Building Topographic Factor, K zt 1.0 Higher wind loads could be required for columns in buildings with Building Category (Risk Category) III and IV, Exposure Category D, and wall edge zone locations. The vertical loads consist of Dead Load and Snow Load. The Snow Load may also be called Roof Live Load for regions where Roof Live Load controls the design. In this report, the assumed Snow Load to Dead Load ratio is 3 to 1, that is, the Dead Load comprises 25% of the total load, while the Snow Load (Roof Live Load) accounts for the remaining 75%. In most cases, the design was controlled by the combined axial compression and bending loading which applies dead, wind and snow loads simultaneously according to the load combinations listed in ASCE 7-05 and ASCE ) CHART 1: STRUCTURAL ANALOG MODELS The computer models were analyzed for each column size and eave height using Visual Analysis software by Integrated Engineering Software, Inc. The restraint conditions at the grade level and at the top of a post-frame column are most similar to a propped cantilever. However, the analysis is modified to account for some rotational displacement at grade and a controlled lateral displacement at the top of the column. Column deflections are limited to L/120 ratio (IBC, Table ), measured at the most extreme point of the deflected column curvature. The L/120 deflection limit is not suitable for walls with brittle finishes. The strength and stiffness of a roof diaphragm depend on many factors: building configuration, roof and wall sheathing material (corrugated metal, OSB, plywood), presence or absence of stitch screws at panel overlap seams, size and pattern of fasteners through the sheathing and other factors. It is the responsibility of the building designer to ensure that building diaphragm design is suitable for the building and for use of these columns and SWS column-base brackets. The effective length coefficient, K e, a quantity related to the buckling characteristics of a compression member (column), is determined while column is in pure axial-compression mode (external bending forces are not present). When lateral forces are not present, a post-frame column with moment-resisting SWS column-base bracket is expected to exhibit a buckling behavior specific to a propped cantilever. The recommended effective length coefficient for a propped cantilever is 0.8 (Table G1, NDS 2015). The nail-laminated columns with SWS columnbase brackets are not designed for flag pole installations where no lateral support at the top of the post can be expected. Columns are semi-rigidly connected to the concrete pier using the SWS moment-resisting steel bracket. In the computer structural design program, the joint between the wood column and the concrete pier is assigned a rotational stiffness value as determined in Section 4. If a computer program of choice does not have such Timber Tech Engineering, Inc Page 9 TTE# E134-18

11 Strong Way Systems capability, the semi-rigid joint may be modeled as a member segment with geometric and material properties carefully selected to produce the desired results (Section 4). Each column assembly is analyzed using the base restraints of the universal method for a constrained and nonconstrained shallow post foundation in accordance with the EP The concrete pier is assumed to be 48 inch deep measured from grade to bottom of the pier. The pier is laterally restrained by a series of spring supports, each representing the lateral stiffness relationship between the pier and the soil at the respective spring location. The springs are spaced at 6 inches on center and are assigned a varying degree of stiffness based on medium to dense consistency of silty or clayey fine to coarse sand (SM, SC, SP-SM, SP-SC, SW-SM, SW-SC). The increase in Young s Modulus per unit depth below grade, A E, is assumed to be 110 (lbf/in 2 )/in, which is double the value in Table 1 of EP486.3 as the water table is assumed to be below the foundation. The springs with the resulting forces greater than forces defined by the ultimate lateral strength of soil, F ult, are replaced by F ult and F ult/0.6 using LRFD and ASD (ASCE 7-10) methodologies respectively. 8) CHART 1: ALLOWABLE AXIAL CAPACITIES The SWS foundation system is designed for use with and without the concrete slab. When a concrete slab is installed, the axial compression forces from the column are transferred into the concrete pier via direct bearing, as all surfaces are in direct contact with one another. When the concrete slab is not installed, there may be a 4 gap between the bottom of the wood column and the top of the concrete pier. In such application, the axial compression forces are transferred into the concrete pier via the steel plates and the rebar. Because the rebar are also transferring tension and compression forces from the bending moments at the joint, the axial compression strength of the steel bracket is diminished such that the net compression load on the rebar does not exceeds the design compressive strength of the rebar. For example, if the bending moment from the governing ASD load combination on the 326 or 426 SWS bracket is 40,000 in-lb, the load on each compression rebar is calculated by dividing the bending moment by the spacing between the tension and compression rebar and by the quantity of compression rebar: (40,000 in-lb) / (4.125 in) / (2 compression rebar) = 4,849 lb. The allowable axial strength of one #5, 60 grade rebar is 10,846 lb (see calculations in Appendix A). The remaining axial strength in each rebar is therefore 10,846 lbs 4,849 lbs = 5,997 lb. The allowable axial strength of the 326 and 426 SWS bracket that is also subjected to a 40,000 in-lb bending force is then calculated as (5,997 lb/rebar)(4 rebar) = 24,000 lb (rounded up). The axial and combined axial and bending strength of SWS column-base brackets, however, does not control the design for columns in Chart 1. This is because (1) the largest axial forces on the bracket are found in shortest columns which also produce the smallest internal bending forces at the SWS bracket, and (2) the governing load combination is such that either axial forces are reduced, bending forces are reduced, or both, further reducing the effects of the combined bending and compression loading on the bracket. The allowable axial capacities specified in Chart 1 are controlled by the design of wood columns, not the SWS bracket. This behavior is expected to hold true for most columns used in typical post-frame applications. The specified allowable axial capacities in Chart 1 are contingent on structural performance of the roof diaphragm at the top of the column and the shallow post foundation at bottom of the column. A roof diaphragm that is more flexible than what is assumed in this design, or a foundation with other lateral properties may significantly affect the allowable axial capacities reported in Chart 1. Hence, the allowable axial capacities of columns are variables not constants. Chart 1 is merely a mid-field representative of how these columns and the SWS semi-rigid column base brackets are expected to perform in most common post-frame structures. Chart 1 is intended for preliminary design and pricing purposes only. The final column design should be provided by a building designer and should include a complete building analysis. Timber Tech Engineering, Inc Page 10 TTE# E134-18

12 Strong Way Systems 9) CALCULATIONS The design calculations for the SWS column-base bracket are provided in Appendix A. The wind loading calculations and design calculations for the wood columns are included in Appendix B. The Visual Analysis reports in Appendix C show the post computer models, load combinations and member unity checks for all column sizes and heights contained in Chart 1. Timber Tech Engineering, Inc Page 11 TTE# E134-18

13 Strong Way Systems ALLOWABLE VERTICAL LOAD (LB) FOR NAIL-LAM OR GLULAM COLUMNS WITH SWS BASE BRACKET 8FT O/C UNDER CONSTANT WIND LOAD OF 160 LB/FT USING ASCE 7-10 LOAD COMBINATIONS AND 96 LB/FT USING ASCE 7-05 LOAD COMBINATIONS Sidewall Height (ft) ply 2x6 16,880 11,480 8,000 n/a n/a n/a 4 ply 2x6 24,920 17,740 12,780 9,440 n/a n/a 3 ply 2x8 38,320 28,680 21,240 15,720 11,740 n/a 4 ply 2x8 51,880 43,960 33,700 25,860 20,000 n/a Chart Notes: This chart is for #1SYP nail-laminated (nail-lam) columns or equal glulam columns with SWS semi-rigid column base brackets (at grade/floor level) in a normal post-frame building (enclosed on all four sides), supported at the top by diaphragm action of the building. All members and connections are designed using Allowable Stress Design (ASD) as per IBC 2009, 2012, 2015, and 2018 (NDS 2015 and ASAE EP ) Columns are #1 SYP using design values per NDS 2015 Table 4B or glulam columns with following minimum design values: 3-ply and 4-ply 2x6, F b = 1850 psi, F c = 1600 psi; 3-ply and 4-ply 2x8, F b = 1700 psi, F c = 1500 psi No splices Columns are not exposed to moisture Dead Load to Total Load ratio = 0.25 ASCE 7 Wind design criteria: Building (Risk) Category II, Wind Exposure C, Enclosed Building, 28ft max midheight, 4:12 roof pitch, ASCE 7-05 wind speed 90 mph, ASCE 7-10 wind speed 115 mph, ASCE 7-05 Wind Load = 96 lb/ft, ASCE 7-10 Wind Load= 160 lb/ft Wind load is calculated for 8ft o/c column spacing Repetitive member factor for nail-lam columns, C r, is 1.35 for 3-ply columns and 1.40 for 4-ply columns, per ASAE EP559 All posts are roller or spring supported at top to simulate resistance from diaphragm action of roof and shearwalls Horizontal deflection limit of L/120 is not suitable for walls with brittle finishes (where L is the building height); actual deflections are based on larger of sidesway at the building eave or curvature of the column. Effective length factor, K e, is 0.8 ASCE 7-05 Load combinations: 1) Dead+Snow 2) Dead+.75(Wind+Snow) 3) Dead+Wind; ASCE 7-10 Load combinations: 1) Dead+Snow 2) Dead+.75(0.6Wind+Snow) 3) Dead+0.6Wind Wood columns are semi-rigidly attached to the foundation (concrete pier) at floor/grade level using SWS column-base bracket Constrained or non-constrained shallow post foundation (concrete pier) per ASABE EP486.3 Full lateral bracing and major axis bending only, no loads acting on weak axis Exterior sidewall post with lateral loading from wind only; loads from knee braces, stored materials, Bi-fold and Hi-fold doors, machinery or other impact loads are not considered in this chart Values for 22ft tall columns are not provided as bending forces at the bracket level exceed the allowable bending strength of the bracket This chart is intended only for preliminary sizing and cost estimates purposes only (not for construction); final column design should include a complete building analysis by a design professional Combination 3-ply 2x6 4-ply 2x6 3-ply 2x8 4-ply 2x8 COLUMN SECTION DIMENSIONS Width (in) x Depth (in) 4-1/2 x 5-1/2 6 x 5-1/2 4-1/2 x 7-1/4 6 x 7-1/4 Revised 7/18/2018 Timber Tech Engineering, Inc Page 12 TTE# E134-18

14 APPENDIX A Structural Design Calculations for the Strong Way Systems (SWS) Steel Bracket Timber Tech Engineering, Inc. Appendices, Page 1 of 127 TTE #E134-18

15 EFFECTIVE ROTATIONAL STIFFNESS OF THE SWS STEEL BRACKET The rotational stiffness of the steel bracket can be separated into three parts: (1) rotational stiffness of the steel-to-wood connection (slip modulus of the dowel fastener connection between steel plates and wood column), (2) rotational stiffness of the steel plates, and (3) rotational stiffness resulting from axial deformation in the compression and tension rebar (in concrete). For the alternative bracket modeling method, where the rotational stiffness is modeled as a member segment (as oposed to the node/joint), the effective rotational stiffness calculations should include a fourth component, the segment of the wood column that is being replaced by the bracket segment. The effective rotational stiffness is calculated using the effective spring constant equation for springs in series. The Wood Handbook (FPL, 2010) provides fastener slip-modulus equation for dowels in single shear in steel-to-wood and wood-to-wood applications. The slip-modulus is higher for dowels in steel-to-wood applications as the movement between the steel plate and the dowel is asumed to be insignificant. Some play between the steel plates and the SDS screws in this application is expectred however, and a more conservative slip-modulus, one based on dowels in wood-to-wood application, is used in these calculations: k = 180,000 D 1.5 = 180,000 (0.242) 1.5 = 21,430 lb/in, round down to 21,000 lb/in. There are (8) screws in each fastener group: (4) screwes on each side of column, (16) screws total per bracket. The slip modulus of each fastener group is (8 screws)(21,000 lb/in per screw) = 168,000 lb/in. The distance between the centroids of the top and bottom fastener groups is 10 inches for all models. The rotational stiffness of the steel bracket (vertical steel plates) is determined by dividing the flexural rigidity, EI, by the effective length L e, which is measured from the top of concrete to the centroid of the top fastener group. The rotational stiffness of the steel bracket below the top of the concrete pier is attributed mostly to the axial deformation of the compression and tension rebar. Because the axial forces in rebar are linearly dicreasing from maxium to zero along the length L d, the effective length used in calculating axial rebar stiffness is equal to L d /2. The calculations are completed in Microsoft Excel (2016) using the listed equations. GOVERNING EQUATIONS: Effective Rotational Stiffness (M/θ) e = [1 / (M/θ) f + 1 / (M/θ) s + 1 / (M/θ) w + 1 / (M/θ) r ] -1 Rotational Stiffness of Fastener Slippage (M/θ) f = k x 2 / 2 Rotational Stiffness of Steel Bracket (M/θ) s = (EI) s / L e Rotational Stiffness of Wood Segment (M/θ) w = (EI) w / L Rotational Stiffness due to Rebar Elongation (M/θ) r = [(EA) r / (L d / 2)] s 2 / 2 k = slip modulus for a fastener group = 168,000 lb/in L = bracket segment replacing wood column in the alternative method E = elastic modulus I = moment of inertia L e = effective length of vertical steel plates as measured from top of concrete to centroid of top fastener group L d = rebar development length (ACI 318, Equation a), round up to 15.4 inches A = combined area of tension or compression rebar s = distance between tension and compression rebar Timber Tech Engineering, Inc. Appendices, Page 2 of 127 TTE #E134-18

16 ROTATIONAL STIFFNESS (1) Fastener Slippage (2) Steel Bracket k x (M/θ) f t d I E L e Model (lb/in) (in) (lb-in/deg) (in) (in) (in 4 ) (lb/in 2 ) (in) (M/θ) s (lb-in/deg) ROTATIONAL STIFFNESS (Continuation) (3) Rotational Stiffness due to Rebar Elongation s A L d E (M/θ) r Model (in) (in 2 ) (in) (lb/in 2 ) (lb-in/deg) ROTATIONAL STIFFNESS - ALTERNATIVE METHOD (VERTICAL SEGMENT) (4) Wood Column Segmen Effective Rotational Segment Properties L I E (M/θ) w Stiffness (M/θ) e EI E (steel) I b Model (in) (in 4 ) (lb/in 2 ) (lb-in/deg) (lb-in/rad) (lb/in 2 ) in 4 (lb/in 2 ) in 4 in b is the dimension of the square profile (lb-in/deg) Effective Rotational Stiffness (M/θ) e (lb-in/rad) Timber Tech Engineering, Inc. Appendices, Page 3 of 127 TTE #E134-18

17 BENDING STRENGTH OF STEEL-TO-WOOD CONNECTION The shear and bending forces are transferred from the wood column into the steel bracket via 1/4"x2.5" SDS screws by Simpson Strong Tie. The holes in the steel bracket are 17/64" (diameter). The calculations below are for wood columns with specific gravity, SG, of 0.55 and higher. The distance between the centroids of the top and bottom fastener groups is measured as 10 inches for all brackets. Note that the strength of the connection is defined only in terms of the allowable bending strength. This is because the shear force through the connection is not an independent quantity, but is rather a function of the bending moments just above and below the steel bracket: V T = V B = V = (M B - M T ) / x, see a free body diagram in Figure A. The allowable bending strength is calculated using the shear strength of the top fastener group, which controls the design, and is expressed as the sum of the lower fastener group, F B, and the shear force V: NZ' = F B + V. It is, therefore, true that, when the bending strength requirements are satisfied, the shear strength requirements are also satisfied. Only the applicable NDS adjustment factors are included in this report. The calculations are completed in Microsoft Excel (2016) using the listed equations. GOVERNING CODE: Figure A: Free body diagram National Design Specification for Wood Construction, NDS GOVERNING EQUATIONS: Allowable Lateral Strength of Screws Z' ASD N = N Z C D C NDS Table Design Lateral Strength of Screws Z' LRFD N = φ N Z λ C K F NDS Table Z = Unadjusted reference lateral (shear) design value for one fastener NDS Table A Z' = Adjusted lateral design value for one fastener NDS Table C D = ASD load duration factor NDS Table C Δ = Geometry factor NDS N = total quantity of fasteners in (1) fastener group φ = LRFD resistance factor NDS Table N2 λ = LRFD time effect factor NDS Table N3 K F = ASD to LRFD format conversion factor NDS Table N1 Allowable Bending Strength of Connection Design Bending Strength of Connection M a = x NZ' ASD φm n = x NZ' LRFD x = distance between the centroids of the fastener groups CALCULATIONS: ADJUSTED LATERAL DESIGN VALUE OF ONE FASTENER: NDS Table A (Yield Limit Equations) Screw Size SDS F yb R e 1.1 θ 0 Screw Diameter (in) D F em, par R e 2.1 I m Screw Length (in) L 2.5 F em, perp 5526 k I s Thickness of Steel Plate Member (in) l s 0.25 F em 5526 k II Thickness of Wood Member (in) l m 4.5 R e k III m Screw Penetration into main member (in p 2.25 R t F es, par III s Minimum Allowed Penetration, p min = 6D p min 1.5 K o F es, perp IV Specific Gravity of Wood Member G 0.55 p 2.3 F es D r Lateral Design Value (lbs) Z 380 LRFD resistance factor φ 0.65 ASD Load Duration Factor C D 1.6 LRFD time effect factor λ 1 Geometry Factor C Δ 1 ASD to LRFD format conversion factor K F 3.32 ASD Adjusted Lateral Design Value (lbs) Z' ASD 609 LRFD Adjusted Lateral Design Value (lbs) Z' LRFD 821 BENDING STRENGTH OF CONNECTION x N Z' ASD Z' LRFD M a φm n Model (in) (lbf) (lbf) (lb-in) (lb-in) Timber Tech Engineering, Inc. Appendices, Page 4 of 127 TTE #E134-18

18 GOVERNING CODE: Specification for Structural Steel Buildings ANSI/AISC 360 Building Code Requirements for Structural Concrete, ACI 318 GOVERNING EQUATIONS: BENDING AND AXIAL STRENGTH OF SWS POST-FRAME BRACKET The bending and axial strength calculations for the SWS Post-Frame bracket are presented in both the LRFD and ASD formats in accordance with the provisions of the governing code (AISC 360). The calculations for the rebar development into the concrete pier are pepared using ACI 318. The calculations are completed in Microsoft Excel (2016) using the listed equations. When concrete slab is not installed, the vertical steel plates and the rebar are responsible for transferring bending, shear, and axial forces into the concrete pier, 4" below the bottom of the wood column. This diminishes the axial strength of the bracket as the compression rebar is carrying compression forces due to axial and bending forces in the column. In the calculations below, the axial strength of the bracket that does not have direct bearing between column plate and concrete, is calculated such that the combined compression force in the rebar does not exceed the compressive strength of the rebar. REBAR TENSILE STRENGTH: AISC 360, SECTION D2 Design Tensile Strength φp n = φf y A g φ = 0.90 (D2-1) Allowable Tensile Strength P n / = F y A g / = 1.67 (D2-1) REBAR COMPRESSION STRENGTH: AISC 360, SECTION E3 Design Compressive Strength φp n = φf cr A g φ = 0.90 (E3-1) Allowable Compressive Strength P n / = F cr A g / = 1.67 (E3-1) F cr = (0.658 Fy/Fe )F y F e = π 2 E / (KL/r) 2 WELDS: AISC 360, SECTION J2 Design Strength φr n = φf w A w φ = 0.75 (J2-3) Allowable Strength R n / = F w A w / = 2.00 (J2-3) F w = 0.60F EXX A w = Lt e, where L = length of weld, t e = effective weld thickness) (E3-2) (E3-4) (T. J2.5) BENDING IN VERTICAL STEEL PLATES: AISC 360, SECTIONS F1 & F11 Design Bending Strength φm n = φf y Z φ = 0.90 (F1, F11) Allowable Bending Strength M n / = M n Z / = 1.67 (F1, F11) REBAR DEVELOPMENT REQUIREMENTS, ACI 318, Equation a Development Length L d = [(3/40)(f y / f' c ) (Ψ t Ψ e Ψ s ) / c b ] d b 2 Timber Tech Engineering, Inc. Appendices, Page 5 of 127 TTE #E134-18

19 CALCULATIONS: REBAR PROPERTIES WELD PROPERTIES Rebar Diameter, D r in Fillet Weld Leg Size, t 0.25 in Rebar Yield Strength, F y 60 ksi Effective Weld Thickness (throat), t e 0.18 in Rebar Section Area, A s 0.31 in 2 Total Weld Length, L 4.00 in/bar STEEL PLATE PROPERTIES Minimum Tensile Strength, F u Minimum Yield Strength, Fy Thickness of steel, t 58 ksi 36 ksi in Effective Weld Area, A w = Lt e Electrode Classification Number Nominal Strength of Weld Metal, F w 0.71 in 2 /bar 70 ksi 42 ksi AXIAL STRENGTH AND WELD STRENGTH OF SINGLE REBAR (1) Rebar Tensile Strength (1 Rebar Compressive Strength (1) Rebar Weld Strength (1) A s φp n P n / K L r F e F cr φp n P n / A w φr n R n / Model ID (in 2 ) (lbf) (lbf) (in) (in) ksi ksi (lbf) (lbf) (in 2 ) (lbf) (lbf) BENDING STRENGTH OF SWS BRACKET Bending Strength of Vertical Plates Bending Strength Based on Rebar t d Z φm n M n / s N φm n M n / Model ID (in) (in) (in 3 ) (in-lb) (in-lb) (in) (in-lb) (in-lb) N = number of compression rebar s = spacing between tension and compression rebar N Model ID AXIAL (COMPRESSION) STRENGTH OF SWS BRACKET - NO CONCRETE SLAB All Rebar in Compression Combined Compression and Bending 1.2D+1.6S D+S 1.2D+1.6S+0.5W φp n P n / φm n M a φp n (lbf) (lbf) (in-lb) (in-lb) (lbf) N = number of compression rebar s = spacing between tension and compression rebar φm n and M a in this table are steel-to-wood connection bending strengths D+0.75(S+0.6W) P n / (lbf) REBAR DEVELOPMENT LENGTH # d b f y f' c Ψ t Ψ e Ψ s c b (in) (ksi) (ksi) L d (in) 15.4 Timber Tech Engineering, Inc. Appendices, Page 6 of 127 TTE #E134-18

20 TENSILE STRENGTH OF SWS POST-FRAME BRACKET The tension strength calculations for the SWS Post-Frame bracket are presented in both the LRFD and ASD formats in accordance with the provisions of the governing code (AISC , NDS 2015). The calculations are completed in Microsoft Excel (2016) using the listed equations. GOVERNING CODE: Specification for Structural Steel Buildings ANSI/AISC National Design Specification for Wood Construction, NDS (2015) GOVERNING EQUATIONS: REBAR AND STEEL PLATES: AISC 360, SECTION D2 φp n = φf y A g (tensile yielding) φ = 0.90 (D2-1) Design Tensile Strength φp n = φf u A e (tensile rupture) φ = 0.75 (D2-2) Allowable Tensile Strength P n / = F y A g / (tensile yielding) = 1.67 (D2-1) P n / = F u A e / (tensile rupture) = 2.00 (D2-2) WELDS: AISC 360, SECTION J2 Design Strength φr n = φf w A w φ = 0.75 (J2-3) Allowable Strength R n / = F w A w / = 2.00 (J2-3) F w = 0.60F EXX A w = Lt e, where L = length of weld, t e = effective weld thickness) STEEL-TO-WOOD CONNECTION: NDS Allowable Lateral Strength of Screws Z' ASD N = N Z C D C NDS Table Design Lateral Strength of Screws Z' LRFD N = φ N Z λ C K F NDS Table Z = Unadjusted reference lateral (shear) design value for one fastener NDS Table A Z' = Adjusted lateral design value for one fastener NDS Table C D = ASD load duration factor NDS Table C Δ = Geometry factor NDS N = total quantity of fasteners φ = LRFD resistance factor NDS Table N2 λ = LRFD time effect factor NDS Table N3 K F = ASD to LRFD format conversion factor NDS Table N1 (T. J2.5) Timber Tech Engineering, Inc. Appendices, Page 7 of 127 TTE #E134-18

21 CALCULATIONS: REBAR PROPERTIES WELD PROPERTIES Rebar Diameter, D r in Fillet Weld Leg Size, t 0.25 in Rebar Yield Strength, F y 60 ksi Effective Weld Thickness (throat), t e 0.18 in Rebar Rupture Strength, F u 90 ksi Total Weld Length, L in Rebar Section Area, A s 0.31 in 2 Effective Weld Area, A w = Lt e 2.83 in 2 STEELPLATE PROPERTIES Minimum Tensile Strength, F u Minimum Yield Strength, Fy Thickness of steel, t 58 ksi 36 ksi in Electrode Classification Number Nominal Strength of Weld Metal, F w 70 ksi 42 ksi TENSILE STRENGTH OF REBAR AND WELDS Rebar Tensile Strength Weld Strength Yielding Rupture (1) A s φr n R n / φr n R n / A w φr n R n / Model ID (in 2 ) (lbf) (lbf) (lbf) (lbf) (in 2 ) (lbf) (lbf) TENSILE STRENGTH OF STEEL PLATES Yielding Rupture A g φr n R n / A e φr n R n / Model ID (in 2 ) (lbf) (lbf) (in 2 ) (lbf) (lbf) ADJUSTED LATERAL DESIGN VALUE OF ONE FASTENER: NDS Table A (Yield Limit Equations) Screw Size SDS F yb R e 1.1 θ 0 Screw Diameter (in) D F em, par R e 2.1 I m Screw Length (in) L 2.5 F em, perp 5526 k I s Thickness of Steel Plate Member (in) l s 0.25 F em 5526 k II Thickness of Wood Member (in) l m 4.5 R e k III m Screw Penetration into main membe p 2.25 R t F es, par III s Minimum Allowed Penetration, p min = 6D p min 1.5 K o F es, perp IV Specific Gravity of Wood Member G 0.55 p 2.3 F es D r Lateral Design Value (lbs) Z 380 LRFD resistance factor φ 0.65 ASD Load Duration Factor C D 1.6 LRFD time effect factor λ 1 Geometry Factor C Δ 1 ASD to LRFD format conversion factor K F 3.32 ASD Adjusted Lateral Design Value (lbs) Z' ASD 609 LRFD Adjusted Lateral Design Value (lbs) Z' LRFD 821 TENSILE STRENGTH OF STEEL-TO-WOOD CONNECTION N Model ID Z' ASD (lb) Z' LRFD (lb) Timber Tech Engineering, Inc. Appendices, Page 8 of 127 TTE #E134-18

22 APPENDIX B Wind Loading Calculations Interlayer Shear Calculations for Nail- Laminated Columns Concrete Foundation Calculations (EP486.3) Timber Tech Engineering, Inc. Appendices, Page 9 of 127 TTE #E134-18

23 ASCE 7-05 Load Calculations WIND LOAD: Method 2 - Analytical Procedure - Low-Rise Building Building Inputs: Length Parallel to Ridge, B (length, typ) Length Normal to Ridge, L (width, typ) Wall Height, z Building Midheight, h Roof Pitch (rise per 12 units of run) Building Category Exposure Category Definitions: Calculation Inputs: n/a ft Basic Wind Speed, V 90 mph n/a ft Topographic Factor, K zt ft, max 29 ft Envelope: Enclosed Building 4 Wind Directionality Factor 0.85 II Roof Overhang (ft) 1 C Case A - Wind Direction Normal to Roof Ridge, Pressure Coefficients Vary With Roof Angle. Case B - Wind Direction Parallel to Ridge, Pressure Coefficients are Constant for all Roof Angles. Intermediate Calculations: Importance Factor, I 1.00 Table 6-1 Calculated Roof Angle deg Nom. Height of Atmospheric Boundary (z g ) 900 Internal Press. Coefficient, Gc pi Vel. Press. Exp. Coefficient, K z 0.98 Table 6-3, Note 2 3-s Gust Speed Power Law Exponent (α) 9.5 Velocity Pressure, q h 17.2 psf Wind Load Results: A. Main Wind Force Resisting System: ASCE7-05, Figure 6-10 Equation: p = q h [(GC pf -(Gc pi )] Case A Case B P (psf) P (psf) Gcpf I* II** III ~ Gcpf I* II** III ~ Zone 1: Windward Side Wall Zone 4: Leeward Side Wall Zone 5: Windward Gable Wall Zone 6: Leeward Gable Wall * Internal Pressure Positive ** Internal Pressure Negative ~ Internal Pressure Zero VERTICAL LOAD Roof Dead Load = 25% of Total Load Roof Snow Load = 75% of Total Load Timber Tech Engineering, Inc. Appendices, Page 10 of 127 TTE #E134-18

24 Envelope Procedure for Low-Rise Buildings Building Inputs: Calculation Inputs: Length Parallel to Ridge, B (length, typ) n/a ft Basic Wind Speed, V 115 mph Length Normal to Ridge, L (width, typ) n/a ft Topographic Factor, K zt 1.00 Wall Height, z Building Midheight, h Roof Pitch (rise per 12 units of run) Risk Category Exposure Category Definitions: ASCE 7-10 and 7-16 Load Calculations 24 ft Wind Directionality Factor, K d ft Enclosure Classification: Enclosed Building 4 II Roof Overhang (ft) 1 C Case A - Wind Direction Normal to Roof Ridge, Pressure Coefficients Vary With Roof Angle. Case B - Wind Direction Parallel to Ridge, Pressure Coefficients are Constant for all Roof Angles. Intermediate Calculations: Calculated Roof Angle deg Nom. Height of Atmospheric Boundary (z g ) 900 (Table ) Internal Press. Coefficient, Gc pi Vel. Press. Exp. Coefficient, K z 0.98 (Table ) 3-s Gust Speed Power Law Exponent (α) 9.5 (Table ) Velocity Pressure, q h 28.1 psf Wind Load Discussion: The ASCE 7-10 load combinations attach a 0.6 coefficient in front of all wind loads, while the ASCE 7-05 load combinations do not. In this design, wind load is applied to columns using ASCE 7-10/16 standard. However, to ensure this design also satisfies ASCE 7-05 standard, the wind loading is calculated as the greater of: (1) the pressures calculated using 7-10/16 methods or (2) the pressures calculated using 7-05 methods divided by 0.6 coefficient: (7-05) (7-10) q h (psf) Gc pf Gc pi P (psf) P (psf) ASCE ASCE 7-10/ n/a 19.5 USE (with 7-16 load combinations) 20.0 VERTICAL LOAD Roof Dead Load = 25% of Total Load Roof Snow Load = 75% of Total Load Timber Tech Engineering, Inc. Appendices, Page 11 of 127 TTE #E134-18

25 NAIL CONNECTION BETWEEN LAMINATIONS: 2X6 LAMINATIONS - DRY Nail Spacing (in) s 9 Interlayer Shear Capacity (lbf/in) ISC 12.0 (EP 559, Table 4) Total Shear Load per Interface, lbf V 108 V = (ISC)s Shear Load Taken by Glue, lbf 0 0% (Percentage of Load Taken by Glue) Net Shear Load per Interface, lbf V 108 Includes Effect of Glue if applicable NAILS - WOOD TO WOOD - SHEAR - NDS, ASD Nail Size n/a Intermediate Calculations Number of nails per interface N 1 K D 2.2 Nail Diameter (in) D (or larger) F yb (psi) Nail Length (in) L n/a 2+R e = 3.0 Width of Side Member (in) l s R e = 3.0 Width of Main Member (in) l m 1.5 k 1 = 1.15 Nail Penetration into main member (in) p 1 k 2 = 1.07 Minimum Allowed Penetration, p min = 6D p min 0.8 F em = 5526 Specific Gravity of Side Member G s 0.55 F es = 5526 Specific Gravity of Main Member G m 0.55 R e = 1.0 Lateral Design Value (lbs) Z 106 (controlling yield value) p = 1.00 Duration Factor C D R e = 2.0 Wet Service Factor C M 1 I s 494 Temperature Factor C t 1 III m 126 Toe Nail Factor C tn 1 III s 176 End Grain Factor C eg 1 IV 106 Total Allowable Lateral Capacity (lbs) Z' 169 Z'=N x Z x C D x C eg x C tn x C M x C t Actual/Allowable = = 0.64 < 1.0 PASS NAIL CONNECTION BETWEEN LAMINATIONS: 2X8 LAMINATIONS - DRY Nail Spacing (in) s 9 Interlayer Shear Capacity (lbf/in) ISC 15.0 (EP 559, Table 4) Total Shear Load per Interface, lbf V 135 V = (ISC)s Shear Load Taken by Glue, lbf 0 0% (Percentage of Load Taken by Glue) Net Shear Load per Interface, lbf V 135 Includes Effect of Glue NAILS - WOOD TO WOOD - SHEAR - NDS, ASD Nail Size n/a Intermediate Calculations Number of nails per interface N 1 K D 2.2 Nail Diameter (in) D F yb (psi) Nail Length (in) L n/a 2+R e = 3.0 Width of Side Member (in) l s R e = 3.0 Width of Main Member (in) l m 1.5 k 1 = 1.15 Nail Penetration into main member (in) p 1 k 2 = 1.07 Minimum Allowed Penetration, p min = 6D p min 0.8 F em = 5526 Specific Gravity of Side Member G s 0.55 F es = 5526 Specific Gravity of Main Member G m 0.55 R e = 1.0 Lateral Design Value (lbs) Z 106 (controlling yield value) p = 1.00 Duration Factor C D R e = 2.0 Wet Service Factor C M 1 I s 494 Temperature Factor C t 1 III m 126 Toe Nail Factor C tn 1 III s 176 End Grain Factor C eg 1 IV 106 Total Allowable Lateral Capacity (lbs) Z' 169 Z'=N x Z x C D x C eg x C tn x C M x C t Actual/Allowable = = 0.80 < 1.0 PASS Timber Tech Engineering, Inc. Appendices, Page 12 of 127 TTE #E134-18

26 SHALLOW POST FOUNDATION 16" Concrete Pier: EP LATERAL SOIL PRESSURES - UNIVERSIAL METHOD, ALLOWABLE STRESS DESIGN [Water table is below the bottom of the footer (pore water pressure, u z = 0), cohesionless soils] Adjustments : Risk Category, I Not Low 1.0 (EP486.3, Sect. 9.2) BACKFILL SOIL: Increase in Young's Modulus per Unit Depth, A E 110 (lbf/in 2 )/in, See EP486.3, Table 1 UNDISTURBED SOIL: Increase in Young's Modulus per Unit Depth, A E 110 (lbf/in 2 )/in, See EP486.3, Table 1 Unit weight of soil around post/footing, γ 110 pcf Angle of internal friction for soil around post/footing, φ 35 deg Coefficient of passive earth pressure, K p = 3.69 K p = (1 + sinφ) / (1 - sinφ) Safety factor for lateral strength assessment, f L 2.98 f L = 1.4 / ( φ)(I) 1.5 Thickness of soil level, t 6.00 in (NOTE: A E is doubled since water table is assumed to be below the bottom of the footer) z t J b E S,B E S,U I S E SE k K H σ' v,z p U,z F ult F ult / 0.6* (in) (in) (in) (in) lbf/in 2 lbf/in 2 lbf/in 2 lbf/in 3 lbf/in psf psf lbf lbf N/A N/A N/A N/A N/A N/A N/A N/A When the lateral pressure against pier exceeds the ultimate lateral strength of soil (soil response is in plastic region), the spring is replaced by ultimate soil force, F ult. * For use in Visual Analysis using ASD design methodology with ASCE 7-10 load combinations NOTES: z t is depth below the ground surface is thickness of a soil spring, t 2w w is face width of rectangular post/pier E S,B is Young's modulus for backfill soil E S,U is Young's modulus for unexcavated soil E SE is Effective Young's modulus I S is strain influence factor, dimensionless k is the modulus of horizontal subgrade reaction K H is stiffness of a horizontal spring F S is a force in a horizontal spring σ' v,z is effective vertical stress at depth z, if u z =0, then σ' v,z = σ v,z p U,z is the ultimate lateral resistance at depth z p z is lateral soil resistance at depth z J is the distance between the edge of the backfill and the face of the post/footing/collar b is the width of the face of the post/pier, footing, or collar that applies load to the soil f L is ASD factor of safety for lateral strength assessment F ult is the soil spring ultimate strength NOTE: The purpose of these calculations is to create a mathematical basis for the selection of the lateral post/pier restraints below the grade consistent with a typical shallow post foundation. The application of the universal method of the EP486.3 is separated into two stages: the analysis stage and the design stage. In the analysis stage, the overloaded spring forces are replaced with un-adjusted F ult and F ult /0.6 forces using LRFD and ASD (ASCE 7-10) design methodologies respectively. In the design stage, the overloaded springs are replaced by adjusted (reduced) forces as described in the EP The scope of these calculations are limited to the analysis stage. During the design stage, it may be determined that the width of the concrete collars specified in these calculations is insufficient and wider concrete collars may be required to satisfy the equilibrium between the loading the lateral strength of the supporting soils. Because the spring stiffness, K H, is not a function of the post/pier width dimension (is not affected by width of post or concrete collar), the selection of the concrete collar width that is different than specified in these calculations does not change the analysis of the foundation. Timber Tech Engineering, Inc. Appendices, Page 13 of 127 TTE #E134-18