NFBA Design Tool for Design of Post-Frame Building Systems

Transcription

1 NFBA Design Tool for Design of Post-Frame Building Systems Part 1: Lateral Design of a 72 x120 x16 Post-Frame Building Wind-Governed Design Example Introduction Design professionals can use this document to learn how to conduct the structural design of a post-frame building system for lateral loading. Architects or engineers can use this document to walk through the unique features of diaphragm design of post-frame building systems and the detailed engineering calculations for the structural design of a typical post-frame building. This document Part 1: Lateral Design of a 72 ft. x 120 ft. x 16 ft Post-Frame Building, Wind- Governed Design Example contains the engineering design procedures and detailed calculations to conduct the structural design of a single story post-frame building located on a site where lateral design wind loads exceed lateral design seismic loads. It begins with a general description of the post-frame building to be designed, followed by detailed descriptions and calculations of design loads, roof diaphragm panel in-plane shear strength and stiffness, shearwall panel in-plane shear strength and stiffness, the portion of the lateral wind load carried to ground by the post-frame, and the portion carried to ground by the roof diaphragm and shearwalls using an on-line computer program, the Diaphragm and Frame Interaction (DAFI) Calculator. The structure has a 72 ft. clear span, is 120 ft. long, and has a 16 ft. eave height. The building has post-frames spaced 8 ft. on center along both sidewalls. Each post frame consists of wood sidewall columns attached directly to engineered, 2x metal-plate connected wood gable trusses with flat lower chords, and two equally sloped upper chords. The roof and walls are sheathed with 29 ga corrugated steel sheathing. Preservative treated laminated wood sidewall columns embedded directly into the ground provide the building foundation.

2 The design example continues with the structural design of the unique structural elements of the post-frame system, including the nail-laminated wood sidewall columns, the shallow embedded post foundation system, the wood sidewall girts, and the wood roof purlins. The document also includes the detailed procedures and calculations to determine the adequacy of the roof diaphragm panels and all the shearwall panels to carry the design in-plane shear loads. The key structural connections required to ensure continuous load paths to ground are identified and detailed procedures and calculations for designing each of the key connections are provided. Finally, the document details the lateral and longitudinal bracing requirements for the building system. The design example follows provisions of the 2009 International Building Code, the 2005 National Design Specification for Wood Construction, ASCE 7-05: Minimum Design Loads for Buildings and Other Structures, and the Post-Frame Building Design Manual. The appropriate sections of these design references are cited throughout the design example. This design tool was developed by Timber Tech Engineering, Inc. located in Kouts, Indiana. Timber Tech Engineering s assistance in developing the calculations and solution presentation is hereby acknowledged. The truss design was provided by Lumber Specialties of Dyersville, Iowa and their contribution is also acknowledged. How to Use This Design Tool This example is divided into two parts. Part 1 is written as a teaching tool for designers not familiar with post-frame building design in that it explains each step of the lateral design process for a post-frame building and summarizes the results of the calculations. Part 2 is a comprehensive calculation package that gives the background design calculations for each step and is a much longer document. The reader is referred to the Part 2 comprehensive calculation package through hyperlinks, placed at critical locations throughout the report, if more information is desired. Both Part 1 and Part 2 can be used as stand alone documents. Part 1 Wind-Governed Design Example 2

3 TABLE OF CONTENTS Section 1: Building Description 4 Section 2: ASCE 7-05 Load Calculations 7 Section 3: Diaphragm Design 10 Section 4: Post Design 21 Section 5: Post Foundation Design 23 Section 6: Purlin & Girt Design 27 Section 7: Connection Design 28 Section 8: Truss Bracing Details 33 Section 9: Design Summary 40 Part 1 Wind-Governed Design Example 3

4 Section 1: Building Description This is a design example in which a 72' wide x 120' long x 16' high Post-Frame building's lateral force resisting system is analyzed and designed for wind and seismic loading. The roof is gable framed with a 3.5:12 pitch on each side. The building is located in Dane County, Wisconsin where, surrounded by closely spaced wind obstructions, it qualifies for surface roughness category B as defined in ASCE This commercial building is comprised of the following structural members: Structural Component Description Spacing Sidewall Posts 3-ply 2x8 nail-laminated column 8 ft o/c Endwall Posts 3-ply 2x8 nail-laminated column 8 ft o/c Foundation 24 Ø x 8 concrete footing with 24 Ø concrete 8 ft o/c collar poured around post Wall Girts 2x4 #2 SYP, each continuous over 2 spans 24 in o/c Roof Purlins 2x4 #2 SYP, on edge 24 in o/c and 16 in o/c in unbalanced snow area Roof Trusses Metal plate connected wood truss, 3.5/12 pitch, 8 ft o/c 0/12 pitch bottom chord Roof/Wall Sheathing 29 gage Grandrib 3 metal sheathing by Fabral n/a Figure 1A shows the exterior elevations, and Figure 1B is a sketch of the plan view of the building. There are (4) 36"x60" windows equally spaced on one endwall and (1) 24'Wx14'H overhead door in the opposite endwall; there are (2) 36"x60" windows and (2) 16'Wx14'H overhead doors and (1) 36"x80" man door in the rear sidewall and (2) 36"x80" man doors and (2) 16'Wx14'H overhead doors in the front sidewall. The exterior walls and roof are sheathed with Grandrib 3, 29 gage structural metal sheathing manufactured by Fabral. On the interior, the walls and ceiling are also sheathed with Grandrib 3, 29 gage structural metal sheathing by Fabral (see Figure 3A and 3B for panel profile and fastener pattern, test panel size and configuration, and in-plane shear strength and stiffness data). The ceiling is framed with 2x4 #2 SYP ceiling joists 24" o/c between the trusses. The ceiling sheathing and roof sheathing have the same orientation. The building is heated and insulated with R-19 insulation in walls and R-30 insulation in the ceiling. There is a 12" roof overhang on the gable ends and 24" overhang on the sidewalls. Part 1 Wind-Governed Design Example 4

5 Figure P5.1. Building Footprint Figure P5.3. Cross section of office area Figure 1A. Exterior Elevations Part 1 Wind-Governed Design Example 5

6 Figure 1B. Floor Plan Part 1 Wind-Governed Design Example 6

7 Section 2: ASCE 7-05 Load Calculations The design dead loads, snow loads, minimum roof live loads, wind loads and seismic loads are all taken from ASCE 7-05, Minimum Design Loads for Buildings and Other Structures per IBC The design loads and the ASCE 7-05 section reference for each are given in Table 1. Link to Part 2 Section 2.1 Wind Load Calculations > Link to Part 2 Section 2.4 Snow Load Calculations > Link to Part 2 Section 2.5 Seismic Load Calculations > TABLE 1 DESIGN LOAD REQUIREMENTS Dead Loads: (Dead: ASCE 7-05 Section 3.1) Steel Roofing (psf surface area ) 1 psf Purlins (psf surface area ) 1.25 psf Bracing/Hardware (psf surface area ) 1.5 psf Total Top Chord [D r (surface area)] 3.75 psf Top Chord [D r = D r (surface area)/cos(16.26)] 4 psf Bottom Chord 5 psf Truss Loads: (Dead: ASCE 7-05 Section 3.1)(Live: ASCE 7-05 Section 4) A. Top Chord Live 25 psf B. Top Chord Dead 4 psf C. Bottom Chord Live 0 psf D. Bottom Chord Dead 5 psf Snow Loads: (ASCE 7-05 Section 7) A. Ground Snow (P g ) 30 psf B. Flat Roof Snow (P f ) 23.1 psf C. Snow Exposure Factor (C e ) 1.0 D. Snow Load Importance Factor (I) 1.0 E. Sloped Roof Snow (P s ) 23.1 psf F. Unbalanced Snow i. Windward roof 7 psf ii. Leeward roof (for first 10.5 ft. from ridge) 44 psf iii. Leeward roof (from 10.5 ft. from ridge to eave) 23.1 psf Wind Loads: (ASCE 7-05 Section 6) A. Basic Wind Speed (V) 90 mph B. Wind Load Importance Factor (I) 1.0 C. Wind Exposure Category B D. Internal Pressure Coefficient +/ E. Components and Cladding per ASCE 7 Figure 6-11 Part 1 Wind-Governed Design Example 7

8 Wind Pressures Main Wind Force Resisting System Wall Windward End Zone psf Windward Interior Zone psf Leeward End Zone psf Leeward Interior Zone psf Roof End Zone - +10/-14 psf Interior Zone - +/-10 psf End Zone psf Interior Zone psf Components and Cladding (1) Roof Interior Zones - +10/-11.7 psf (2) Roof End Zones - +10/-19.2 psf (3) Roof Corner Zones - +10/-29 psf (4) Wall Interior Zones - +10/-13.7 psf (5) Wall End Zones - +10/-16.4 psf Seismic Loads: (ASCE 7-05 Section 12) A. Analysis Procedure Used: i. Equivalent Lateral Force Procedure B. Basic Seismic Force Resisting System: i. Light-framed walls sheathed with steel sheets C. Mapped Spectral Response Coefficients i. At Short Periods, S S 0.15 ii. At 1 Second, S D. Occupancy Category II E. Seismic Importance Factor (I) 1.0 F. Site Class (Assumed) D G. Design Spectral Response Coefficients i. At Short Periods, S DS 0.16 ii. At 1 Second, S D H. Seismic Design Category D I. Response Modification Factor, R 7 J. Redundancy Factor, r 1.0 K. Seismic Response Coefficient, C s L. Design Base Shear, V (for one 8 bay) 143 lbs The design roof dead load is 4 psf and the design ceiling dead load is 5 psf. The dead loads of the different materials for the roof plane are listed based on surface area and then converted to the horizontal projection to give the top chord dead load. Part 1 Wind-Governed Design Example 8

9 The design snow load is 23.1 psf which is greater than the minimum roof live load of 20 psf and therefore controls. Unbalanced snow load is calculated based upon the windward roof slope projection (greater than 20 ft.) and the roof slope (less than 20 degrees as per ASCE 7-05, Section 7.6.1). Snow load and unbalanced snow load are calculated for a heated building with insulated ceiling and the roof is considered to be partially exposed. The Design Main Wind Force Resisting System (MWFRS) and Components and Cladding (C&C) wind pressures and suctions were calculated for positive, negative and zero internal pressure conditions. Footnote 6 of Figure 6-10 in ASCE 7-05 specifies that if the roof wind loads act to decrease the magnitude of the wall framing shear, that maximum post shear shall be determined by neglecting the lateral forces acting on the roof. The controlling lateral wind force to be resisted by the MWFRS was found by considering wind applied to roof and walls, wind applied to walls only, and 10 psf wind pressure applied to the vertical projection. The lateral force from seismic load was also calculated and compared to the wind force. The response modification factor, R, and deflection amplification factor, C d, were chosen from ASCE 7-05 Table The comparison between wind and seismic was performed for both strength and serviceability criterion using forces generated from the critical load combinations. It was found that wind loading controls for strength design and serviceability requirements. The allowable lateral deflection at the eave was found by taking the eave height divided by 120 (L/120 limit). The actual deflection comes from the DAFI analysis in the Diaphragm Design section. ASCE 7-05, Section lists six design load combinations for allowable strength design. Of these the controlling combinations for this building design are: Wall posts D (S + W) Roof diaphragm D + W and 0.6D + W Endwall shearwalls D + W and 0.6D + W Roof Truss D + S Post foundation (Lateral) D + W and 0.6D + W Post foundation (Uplift) 0.6D + W Wall girts D + W and 0.6D + W Purlins 0.6D + W or D + S The 10 psf minimum wind load applied to the vertical projection (per ASCE 7-05 Section ) controls the design of the MWFRS for this building as shown in Part 2 Section However, many individual building components are controlled by wind pressures derived from coefficients. The purpose of this design example is to illustrate how wind pressures are applied to each individual building surface, how they translate into shear and bending forces in the diaphragm, and what affect these pressures have on individual building components. This example will present the lateral design process for a post-frame building using wind pressures and suctions from coefficients, and the effects of the 10 psf minimum wind load on the MWFRS will be shown separately in Part 2 Appendix E. The MWFRS is a combination of the roof diaphragm, shearwalls, and the post-frame. Part 2 Appendix E shows the adequacy of the roof diaphragm, shearwalls, and post-frame for the 10 psf minimum wind load requirement. Part 1 Wind-Governed Design Example 9

10 Section 3: Diaphragm Design The roof diaphragm, ceiling diaphragm and shearwalls (including inside and outside faces of endwalls and sidewalls) will be sheathed with 29 gage Fabral Grandrib 3 structural steel sheathing panels with the profile and fastener pattern shown in Figure 3A. Figure 3A. Sheathing profiles and fastener patterns for the roof and wall panels The primary dimensions of the diaphragm test panel used to determine the in-plane shear strength and stiffness are shown in Figure 3B. The overall test panel dimensions are a = 9 ft and b = 12 ft. The panel fastener schedule is (1) #10-1 ½ inch long screw at each corrugation/framing intersection. The exception is that (2) screws are used per connection along the diaphragm boundary. Purlins (2x4) on edge and spaced 2 ft. on center are attached to the Part 1 Wind-Governed Design Example 10

11 chords/rafters with (1) 60d spike and (2) 10d toenails. The species and lumber grade for the panel framing was No. 2 Douglas-fir for the purlins and No. 2 Douglas-fir for the rafters. The in-plane structural properties of the Grandrib 3 test panels as provided in Table 6.1 (Test Assembly #6) of the "Post-Frame Building Design Manual" (PFBDM) by the National Frame Building Association (NFBA) are shown below. Ulitimate Strength, P u, (lb f ) 3300 Allowable Shear Strength, v a, (lb f /ft) 110 Effective In-Plane Stiffness, c, (lb f /in) 2920 Effective Shear Modulus, G, (lb f /in) 2190 Figure 3B. Test panel arrangement for determining in-plane shear strength and stiffness of diaphragm test panels. The maximum in-plane shear force cannot exceed the allowable unit shear strength, v a, multiplied by the diaphragm length. The PFBDM is silent on the controlling failure mode for the different test series' conducted. If the failure was in the wood portion of the test assembly, a load duration factor of 1.6 could be applied; however, if the failure was in the steel panels, then no increase can be taken. We will use the conservative approach and assume steel failure. The total in-plane shear strength of an individual diaphragm is calculated by multiplying the allowable design shear strength, v a, by the slope length of the diaphragm. The horizontal shear stiffness of an individual diaphragm, c h, is obtained by adjusting the model diaphragm in-plane shear stiffness, c, for the actual building size and roof slope as described in Section 6.4 of the PFBDM and as shown in the following calculations. Part 1 Wind-Governed Design Example 11

12 3 C h ch, i I 1 b ch, 1 roof ch,2 roof G cos a G c b lb c 2920 in a 9 ft b 12 ft h,1 s lb 9 ft lb G in 12 ft in 72 ft b h, 1 2 ft 38 ft 2 s 8 ft lb 38 ft lb ch, 1 ch, cos in 8 ft in lb 72 ft lb ch, 3 ceiling 2190 cos in 8 ft in c h, 1 roof = 9,986 lb/in c h, 2 roof = 9,986 lb/in c h, 3 ceiling = 19,710 lb/in Link to Part 2 Section 3.1 Horizontal Roof Stiffness Calculations > 3.1 Total Diaphragm Horizontal Roof Stiffness, C h The total horizontal shear stiffness, C h, of the roof assembly is calculated by summing the horizontal shear stiffness values of the individual roof diaphragms including both roof slopes, c h,1 and c h,2 as well as the ceiling, c h,3. C h,total = 39,683 lb/in Part 1 Wind-Governed Design Example 12

13 3.2 Frame Stiffness, k The stiffness of the bare frame, k, is the ratio of an applied horizontal eave load divided by the resulting calculated horizontal eave deflection. A computer analog of the frame consisting of two posts and the truss has been used to calculate this term. The post to soil interface is assumed to be a non-constrained post as defined in the PFBDM, Page 8-2; the structural analog of this interface is shown in Figure 4A on page 22. p lbs k in P horizontal load frame displacement Link to Part 2 Appendix Section A.1 Frame Stiffness Calculations > 3.3 Endwall Stiffness, k e The endwall stiffness, k e, is calculated by summing the horizontal shear stiffness of the endwall diaphragm and the sum of the bending stiffness of all the endwall posts. The horizontal shear stiffness of the endwall diaphragm is deduced from the test panel shear stiffness using the same equations as used to determine the roof diaphragm panel. The interior liner attached to the endwalls is constructed the same as the exterior siding and is included by doubling the endwall sheathing shear stiffness. k e, 1 = 17,117 lb/in (stiffness of endwall with 4 windows) k e, 2 = 13,693 lb/in (stiffness of endwall with 24 ft door) Link to Part 2 Section 3.3 Endwall Stiffness Calculations > 3.4 Eave Load The eave load, P i, used in this analysis is the resultant lateral load from the controlling combination of design loads acting over the tributary area of the eave, and is applied as a concentrated load at the eave of each frame. The eave load is calculated by using either Frame- Base Fixity Factors or Plane-Frame Structural Analysis. The standard method of fixity factors typically assumes that a post is simply supported with zero rotational resistance at ground level, or is fully fixed with zero rotation at ground level. Most often neither of these assumptions is completely accurate. In the case of a non-constrained post foundation, the top horizontal support of the foundation system is located a distance below ground level. This means that there are some lateral and rotational deflections at the ground line. Part 1 Wind-Governed Design Example 13

14 As a result, the standard fixity factor for a rigidly supported column is a rough approximation. Assuming a pinned base condition for the post yields a higher eave load and is conservative for the diaphragm design; conversely, assuming a perfectly fixed base condition yields a lower eave load and is conservative for the post design. We have chosen to use a fixity factor of 0.42 which is a little more toward fixed than pinned. It was found that the wall wind loads without the roof wind loads (ASCE 7-05, Fig 6-10, Note #6) control the eave load calculation. Eave Load Calculation by Frame Base Fixity Factors: P i s h r q q h f q q wr lr w ww lw f f pin fixed f new ft 0 psf 0 psf 16 ft psf 2.4 psf lbs P i 8 ft 538 Link to Part 2 Section 3.4 Eave Load Calculations > 3.5 DAFI Inputs DAFI (Diaphragm and Frame Interaction) is a computer program for calculating the distribution of horizontal loads among the individual post-frames and roof diaphragm sections of a building. It can be used to analyze diaphragm action in buildings in which bay spacings vary, the stiffness of individual post-frames differ, endwalls are not assumed infinitely rigid, and/or the stiffness of individual diaphragms are not the same. A Windows version of this program is available as a free download from the National Frame Building Association website (nfba.org). It allows data to be entered using a special screen editor. The data can be saved to and later recalled from an input data file. For the example building and design loads, the DAFI inputs are: Number of Bays = 15 Roof Diaphragm Shear Stiffness = lb f /in Endwall 1 Shear Stiffness = lb f /in Endwall 2 Shear Stiffness = lb f /in Interior Frame Stiffness = lb f /in Eave Load on an Interior Frame = 538 lb f Input this information in the DAFI Default Values screen. Use the shear stiffness for Endwall 1 as the default value and then adjust the shear stiffness for Endwall 2 within the Specific Values table. Part 1 Wind-Governed Design Example 14

15 DAFI Input Screen Bay Number Diaphragm Stiffness Frame Number Frame Stiffness Eave Load DAFI Outputs The DAFI outputs are found on the Frame Analysis and Diaphragm Analysis tabs in the program. These tables are shown here and interpreted in the next section. Frame Number Frame Stiffness Applied Load Horizontal Displacement Load Resisted by Frame Fraction of Applied Load Part 1 Wind-Governed Design Example 15

16 Diaphragm Number Diaphragm Stiffness Shear Displacement Shear Load Interpretation of DAFI Outputs From the DAFI Frame Analysis screen, frame 9 is the most highly loaded frame. Frame 9 carries 76 lbs (Figure 3C), or 14% of the applied eave load. The horizontal deflection at the eave of frame 9 is 0.57 inches. Figure 3C. FBD of Frame 9 Part 1 Wind-Governed Design Example 16

17 Thus, the restraining force, Q, provided by the diaphragm is 538 lbs 76 lbs = 462 lbs (Figure 3D). Figure 3D. FBD of Frame 9 with Restraining force Q From the DAFI Diaphragm Analysis screen, diaphragm 1 has the highest shear load. This shear load of 3432 pounds plus the eave load of 269 pounds (shown on the Specific Values tab in DAFI) makes up the total load resisted by Endwall 1 (DAFI Frame 1). Similarly, the total load resisted by Endwall 2 (3487 lbs) is the sum of the applicable shear load (3218 lbs) and eave load (269 lbs) from the DAFI analysis. Total Load Resisted by Endwall 1 = 3701 lbs (DAFI Frame 1) Total Load Resisted by Endwall 2 = 3487 lbs (DAFI Frame 16) Maximum Horizontal Diaphragm Shear = 3432 lbs (Shear in DAFI Diaphragm 1) 3.8 Endwall Shear Strength Check (Wind Acting Perpendicular to Ridge) The endwalls are sheathed inside and out with structural steel panels and the allowable shear strength, v a, is 110 lb/ft for each layer, 220 lb/ft total. These steel panels are the primary component of the lateral force resisting system for this building. The panels are fastened to 2x4 girts with #10x1" screws 6" o/c at edges and 12" o/c at all intermediate framing. Though the testing was done with purlins placed on edge, it is a reasonable assumption that the purlins with flat orientation will yield equal or better results. The shear load in the each endwall is resisted by the two layers of structural steel panels and the wood columns in the endwall. The amount of load carried by each component can be calculated according to the stiffness of each component. It was found that the exterior and interior panels each carry 48% of the load and the wood columns carry 4%. The calculations in Part 2 show that Part 1 Wind-Governed Design Example 17

18 each layer of Endwall 1 carries a unit shear of 30 lb/ft for a total of 60 lb/ft, and each layer of Endwall 2 carries a unit shear of 35 lb/ft for a total of 70 lb/ft. The unit shear load for Endwall 1 is 60 lb/ft: The unit shear load for Endwall 2 is 70 lb/ft: 60 lb/ft < 220 lb/ft OK 70 lb/ft < 220 lb/ft OK The shear strength of the steel panels is sufficient, no additional wood or metal strap bracing is required. Link to Part 2 Section 3.8 Endwall Shear Strength Calculations > 3.9 Sidewall Shear Strength Check (Wind Acting Parallel to Ridge) The construction of the sidewall is identical to that of the endwall. Thus, the shear strength of the sidewall is the same as the endwall, 220 lb/ft. The controlling load combination for wind loads parallel to ridge is D+W, where windward and leeward pressures are applied to the tributary area of the endwall. For simplicity, the columns are assumed to be fully rigid at ground level with a fixity factor of 3/8. This means that 5/8 of the wind pressure on the endwalls will be taken directly into the foundation by the columns. The sidewall shear forces are based upon wind acting parallel with the ridge and the shear load on the sidewall is calculated by using 3/8 of the wall height plus the roof gable. The sidewall shear equals 51 lb/ft: 51 lb/ft < 220 lb/ft OK Typically the endwalls in a post-frame building are the controlling shear walls. There are cases, however, when sidewalls are the critical shear walls, especially in wide buildings that are short in length. In those situations a more thorough analysis is required, in which a roof and sidewall stiffness and possibly torsional effects on the overall building envelope are considered. An analytical model of each column height with proper base conditions may also be required to calculate loads on the diaphragm more accurately. Link to Part 2 Section 3.9 Sidewall Shear Strength Calculations > Part 1 Wind-Governed Design Example 18

19 3.10 Roof Diaphragm Shear Strength Check The roof and ceiling are also sheathed with structural steel panels. The panels are fastened to 2x4 purlins with #10x1" screws 6" o/c at edges and 12" o/c at all intermediate framing. The shear load in the diaphragm is resisted by the one layer of structural steel panels on the sloping roof plane, and one layer on the flat ceiling plane. The amount of load carried by each component can be calculated according to the stiffness of each component as shown below. It was found that the roof and ceiling diaphragms each carry 50% of the load. Load ratio to each diaphragm, p = c h,i /C h Load ratio to roof diaphragm, p roof = (c h,1 + c h,2 )/C h =19,973/39,683 =0.503 Load ratio to ceiling diaphragm, p ceiling = c h,3 /C h =19,710/39,683 =0.497 The maximum unit shear load for roof or ceiling panels is 24 lb/ft: 24 lb/ft < 110 lb/ft OK Link to Part 2 Section 3.10 Roof Diaphragm Shear Strength Calculations > 3.11 Roof Diaphragm Chord Forces The roof diaphragm acts like a deep beam where the ends of the beam are assumed to be fixed. The diaphragm of this building consists of two individual roof diaphragms, one on each side of the ridge, and one ceiling diaphragm. The bending forces in each diaphragm are resisted by roof purlins and ceiling joists. Because only the edge purlins and ceiling joists are fastened together in this building to provide continuous tensile resistance to tension chord forces, it is conservatively assumed that the intermediate purlins and ceiling joists provide zero contribution to the diaphragm bending resistance (Design equations for inclusion of all purlins are provided in the PFBDM.). The individual (sixteen ft long typical) edge purlin members are fastened together at splices with a single HTP37Z Simpson plate fastened to the side with 10dx1-1/2 nails (tabulated capacity = 1600 lbs); the ceiling joists are spliced together with a single MSTA21 Simpson strap, fastened to the bottom edge with 10dx3" nails (tabulated capacity = 1505). The design eave load (67.3 lbs/ft) is applied to the diaphragm at the eave, and redistributed to individual diaphragms according to their stiffness. It was found that the individual roof diaphragms each take 25% of the load, and the ceiling diaphragm carries the remaining 50%. For simplicity, the load resistance contribution of the frame is ignored. Using these assumptions the maximum chord force in the edge purlins of each diaphragm panel are: Part 1 Wind-Governed Design Example 19

20 Maximum chord force in each roof diaphragm is 535 lbs: 535 lbs < 1600 lbs OK Maximum chord force in ceiling diaphragm is 557 lbs: 557 lbs < 1505 lbs OK It should be noted that typical roof diaphragm deflection consists of bending deflection, shear deflection of sheathing panel, deflection due to nail slip, and deflection due to slip in chord connection splices. Because the diaphragm stiffness in this example is based on a sample test, it can be assumed that all of these deflection contributors, with exception of the deflection due to slip in chord connection splices, are accounted for. It is further assumed that the deflection due to slip in chord connection splices is minimal and is an insignificant contributor to the overall diaphragm deflection. Link to Part 2 Section 3.11 Roof Diaphragm Chord Force Calculations > Part 1 Wind-Governed Design Example 20

21 Section 4: Post Design Figure 4A shows the structural analog of the post-frame consisting of the truss, a windward column and a leeward column. The post to soil interface is modeled with a pin and a roller, and all the loads are shown including the horizontal restraining force, Q = 462 lbs (From Section 3.7). The loads shown in Figure 4A are individual load cases which will be used in the ASCE 7-05 load combinations. Wind loading on the roof is not shown because, in this example building, it tends reduce the total lateral shear load. Visual Analysis 7.0 by IES, Inc. was used for the column design. From the Visual Analysis output, we are able to determine that a 3 ply 2x8 #1 SYP naillaminated (nail-lam) post is adequate for the applied loads (See Visual Analysis Report in Part 2 Appendix A). All applicable load combinations from ASCE 7-05 for combined axial and bending stresses were checked, the controlling combination was D (S+W), and combined stress index (unity check) was 0.5. Nail-lam posts were chosen because they are pressure preservative treated only at the embedded end, they can be easily notched at the top for a good truss connection, and they are readily available in 3 ply 2x6, 3 ply 2x8, 4 ply 2x6 and 4 ply 2x8 sizes. The post design values (F b = 1725 psi, F c = 1650 psi, E = 1.7E6 psi, bxd = 4.31 x 7.19 in 2, S X = in 3, and I X = in 4 ) used in this design assume that the splice between the treated and untreated plies is made with a structural finger joint (certified by a third party inspection agency). If nail-lam columns with butt joints at the splice are used, they should be designed as per ANSI/ASAE EP 559 using reduced strength and stiffness in the butt-spliced joint region. The maximum post moment, M a, maximum post shear, V max, and ground line shear, V a, from the Visual Analysis computer program are: M max = 1850 lb-ft V max = 602 lbs V a =602 lbs Post unity check = 0.5: 0.5 < 1.0 OK Link to Part 2 Appendix Section A.2 Post Design Calculations > Part 1 Wind-Governed Design Example 21

22 Figure 4A. Structural analog of post-frame with non-constrained foundation Deflection Results The maximum horizontal displacement from the DAFI output is 0.57 inches at frame 9. Allowable displacement as per Table from IBC 2009 is L/120 or 1.6 inches for a 16 ft. high wall with flexible finishes. Post deflection = 0.57 inches: 0.57 in < 1.6 in OK Part 1 Wind-Governed Design Example 22

23 Section 5: Post Foundation Design The post foundation is designed as a non-constrained post with a partial concrete collar located at the bottom of the post. The post foundation depth calculation is iterative in that the designer must assume a depth and check the outcome using design equations. We will assume 4 ft. embedment below grade and a 24 inch high concrete collar attached to the post at the bottom (Figure 5A). Please note, a collar that is less than 24 inches high is often satisfactory and may be so for this example. The axial, shear and moment reactions on the foundation are imposed from the column at ground level. The allowable lateral bearing soil pressure, S', is assumed to be 200 psf/ft of depth, and the initial allowable vertical bearing soil pressure is assumed to be 2000 psf (ANSI/ASAE EP486.1, Table 1 for sandy gravel and/or gravel (GW and GP) soils). The governing design equations for lateral design of the non-constrained case with a concrete collar at the bottom are from Section in ANSI/ ASAE EP 486. The adjusted allowable vertical soil pressures along with controlling load combinations for gravity, lateral and uplift loads, and other calculations are provided in Part 2 Appendix B. Figure 5A. Post Foundation Sketch Link to Part 2 Appendix B Post Foundation Design Calculations > Post Foundation Footing Design A f = Maximum post gravity load/soil bearing resistance From Table 1, ANSI/ ASAE EP and Footnote 4, Soil bearing resistance = 2000[ (ftg depth ft - 1ft) + 0.2(ftg width ft - 1ft)] = 2000[ (4.67ft - 1ft) + 0.2(2ft - 1ft)] = 3868 psf Part 1 Wind-Governed Design Example 23

24 A f =post reaction / soil bearing resistance = 9872/3868 = 2.55 ft 2 D f = [4A f /π] 1/2 = 1.8 ft Use a 2 ft. diameter footing pad S a = Actual vertical soil pressure = 3142 psf 3142 psf < 3868 psf OK Post Foundation Design for Lateral Load Resistance The lateral design criteria for shear and moment resistance, from ANSI/ASAE EP 486, Section are, respectively, V a V r = S b/2(2d 3 /d 0 3d 2 ) + S (w-b)/2[2(d 3 -d 3 1 )/d 0 3(d 2 d 2 1 )] V a d + M a M r = -S b/4(d 4 /d 0-2d 3 ) - S (w-b)/4{[d 4-3dd d 1 4 ]/d 0-2d 3-6dd d 1 3 } where d = minimum post embedment depth (ft) t c = collar dimension in vertical direction = 2.0 ft. w = collar dimension in horizontal direction = 2 ft. d 0 = depth to rotation axis (>0.67d when Va=0;>0.75d when Ma=0; (Sections 6.5 and 6.5.2, ANSI/ASABE EP 486) d 1 = distance from ground surface to top of collar (d t c = d 2.0) b = 1.41(B) = 1.41(4.31/12) = 0.51 ft. (Section 7.7.1, ANSI/ASABE EP 486) B = post dimension bearing on soil = 4.5 in. M a = post frame ground line moment from PF analysis = 1,850 lb-ft. V a = post-frame ground line shear from PF analysis = 602 lbs. S = allowable lateral soil bearing strength, including increases, psf M r = resisting moment of the soil profile (lb-ft). V r = resisting shear of the soil profile (lbs). Allowable Lateral Soil Bearing Strength Calculation From (ASAE EP 486, Table 1; Sections and ) S = S(Isolated post factor)(short duration load factor) S = 200(Isolated post foundation factor)(short term load factor) Isolated post foundation factor = 2 Short term load factor = 1.33 S = 200(2)(1.33) = 532 psf Part 1 Wind-Governed Design Example 24

25 S = 200 psf is conservatively used in this case because this is a design example that may be applied to many different buildings in many different locations. The designer need not be hesitant to use the increases to allowable lateral soil strength for actual designs. Check both equations for an embedment depth of 4.0 ft to see if it provides adequate lateral load resistance: V a V r (0.51)/2{2(4.0) 3 /[(0.68)(4.0)] 3(4.0) 2 } + 200( )/2{2( )/[0.68(4.0)] 3( )} = 723 lbs V a d + M a M r 602(4.0) =4258 = -[200(0.51)/4]{4.0 4 /[(0.68)(4.0)] 2(4.0 3 )} - [200( )/4]{[ (4.0)(2.0 3 ) + 3(2.0 4 )]/[0.68(4.0)] 2(4.0 3 ) - 6(4.0)(2.0 2 ) + 4(2.0 3 )} = ft post embedment OK The required embedment depth is the larger of the required depths from both the shear and moment criterion. Both design equations require an iterative solution. These iterative calculations, performed in a spreadsheet shown in Part 2 Appendix B, show that an embedment depth of 3.27 ft provides adequate lateral load resistance. We will keep the embedment depth of 4 ft because it is widely accepted in the industry. The designer could decide to use a more shallow embedment depth provided the lateral load criterion is satisfied and minimum frost depth conditions for the building site are met. Post Foundation Design for Uplift Resistance The uplift design criterion is: U Truss Uplift Reaction = Calculated Uplift Calculated Uplift = 1153 lb f Soil Properties (ANSI/ASAE EP 486, Table 1; PFBDM, Table 8-1) Angle of internal friction: φ = 26 Soil density: w s = 105 pcf Concrete density: w c = 150 pcf U = g(m F + w s V s ) Part 1 Wind-Governed Design Example 25

26 M F = M collar : mass of foundation elements attached to the post M collar = [(πw 2 /4)(t c ) (A p )(t c )](w c ) = [π(2) 2 (2)/4 (4.31)(7.19)/144(2)](150) = 878 lb m V s : mass of truncated cone of soil above the attached collar V s = πd T [r 2 + d T rtanφ + d T 2 tan 2 Φ/3] d T A p (PFBDM Section 8.9.4) d T = distance from ground surface to top of collar or footing, ft r = radius of collar or footing, ft Φ = angle of internal friction of soil A p = post/pier cross-sectional area, ft 2 Substituting terms into the equation (Tan 26 = 0.49; A p =.310 ft 2 ) V s = π(2)[(1) 2 + 2(1)(0.49) +(2) 2 (0.49) 2 /3] - (.310)(2) V s = 6.283(2.3) 0.62 V s = ft 3 Substituting in to the equation for U: U = (1)[ (105)] = 2330 lb f 1153 lbs < 2330 lbs 4 ft post embedment OK Link to Part 2 Appendix B Post Foundation Design Calculations > Use an 8 in. x 24 in. diameter footing with a 24 in. high x 24 in. diameter concrete collar and 4 ft. post embedment. Part 1 Wind-Governed Design Example 26

27 Section 6: Purlin & Girt Design 6.1 Purlin Design Purlins are positioned on edge on top of top chord of truss and typically span over two spans for the total length of 16 ft. Due to the sloping roof, the gravity loads are not aligned with the strong axis of the purlin. At the same time, the purlin can only move about its strong axis as the movement about the weak axis is restricted by the attached rigid roof panels. Thus, the gravity loads on the purlin should be broken down into strong axis and weak axis components, or 'y' and 'x' components on the sloping coordinate system. Purlins must be designed for three wind load areas: interior purlins, edge purlins, and corner purlins. The design calculations are provided in Part 2 Appendix C. 2x4 #2 S. Pine on 24" on center except 16" on center in unbalanced snow area 10.5 ft. each side of ridge. Link to Part 2 Appendix C Purlin and Girt Design Calculations > The maximum CSI value for the interior purlins is 0.97 for 2x4 purlins spaced 16 inches on center for the D + S unbalanced load combination. The maximum CSI value for the edge and corner purlins spaced 24 inches on center for the load combinations with dead and wind loading is Girt Design Girts must be designed for two wind load areas: interior girts and edge girts. All analyses assume the purlins are loaded flatwise and are spaced 24 inches on center. The calculations show that No. 2 SYP 2x4 girts spaced 24 inches on center are satisfactory in all wall sections. The maximum CSI value for girts located at the edge is The design calculations are provided in Appendix C. 2x4 #2 S. Pine flat against 24" on center continuous over two spans. Link to Part 2 Appendix C Purlin and Girt Design Calculations > Part 1 Wind-Governed Design Example 27

28 Section 7: Connection Design Only connections critical to the lateral force resisting system are included in this section. Connection details are presented in Section 9: Design Summary. The key connections presented, in order, and identified in Figure 7A are: 7.1 Truss-to-Post Connection Vertical shear due to truss uplift 7.2 Truss-to-Post Connection Horizontal shear due to post top end reactions 7.3 Truss-to-Glulam Header Connection Truss uplift 7.4 Endwall Ceiling Ledger -to- Post Connection Shear between ceiling diaphragm and end shear wall 7.5 Skirt Board-to-Post Connection Shear between shear wall and posts at grade level 7.6 Purlin-to-Purlin at Splice Connection Tension load at diaphragm tension chords 7.7 Ceiling Joist-to-Ceiling Joist at Splice Connection Tension load at diaphragm tension chords 7.8 Post-to-Concrete Collar Connection Vertical shear due to post uplift Figure 7A. Critical connection locations Part 1 Wind-Governed Design Example 28

29 7.1 Truss -to-post Connection (Vertical) Trusses are placed in a pocket created by notching the center lamination at top of post. The exterior laminations are then extended to the top of top chord of truss, and fastened to truss with (5) 16d common wire nails on each side. This connection is designed to resist vertical and horizontal shear loads. The vertical shear load, or load from truss uplift, can be calculated using tributary areas and roof wind pressures, or can be provided by a truss designer. In this example the uplift loads are calculated using tributary areas and wind pressures. Link to Part 2 Appendix D Page 2 of 8 > 7.2 Truss -to-post Connection (Horizontal) The horizontal shear load at top of post can be approximated using tributary area and wind pressures, which is a product of (fixity factor)(column height)(column spacing)(controlling wind pressure), assuming that the column is pinned or fixed at bottom (grade level) and has a horizontal roller support at top. The fixity factor is 0.5 for a pinned base and for a fixed base. For non-constrained columns that fall between fixed and pinned, see discussion in Section 3.4. A more accurate horizontal shear load can be determined by modeling the critical frame, the frame closest to the more rigid endwall, in a computer program, or by using DAFI result outputs. This example utilizes results from DAFI. Link to Part 2 Appendix D Page 3 of 8 > 7.3 Truss -to-glulam Header Connection The truss is fastened to a glulam header over the 16 ft. sidewall door opening with (2) H10A Simpson hurricane ties, one tie on each side of beam. The specific gravities of truss and beam are assumed to be Link to Part 2 Appendix D Page 4 of 8 > Part 1 Wind-Governed Design Example 29

30 7.4 Endwall Ceiling Ledger -to- Post Connection The shear load from the roof diaphragm is transferred to the endwall truss and then to wall sheathing. This load path does not directly rely on the truss to post connection. The shear forces from the ceiling diaphragm, however, are transferred to the endwall posts first and then to girts and sheathing. There are 10 posts in endwall 1, the endwall with largest shear loads, to which the ceiling ledger is fastened. The endwall ceiling ledger is fastened to each post with (4) 16d nails. Link to Part 2 Appendix D Page 4 of 8 > 7.5 Skirt Board-to-Post Connection There is a 2x8 #2 SYP skirt board on the exterior side of the end wall, and a 2x4 #2 SYP bottom girt on the interior side of the end wall. The skirt board and bottom girt to post connection is the last connection in the load path of the lateral force resisting system before the lateral loads are transferred to the ground. The skirt board and the bottom girt are fastened to each post with (4) 16d galvanized common wire nails. Link to Part 2 Appendix D Page 5 of 8 > 7.6 Edge Purlin-to-Purlin at Splice and to Endwall Truss Connection The edge purlins serve as tension and compression chords of the roof diaphragm. In order to provide continuity in tensile resistance in the tension chord of the diaphragm, the purlins must be fastened together at each splice. In this design an HTP37Z Simpson strap is used at each purlin splice (the designer may choose to try a 2x4 splice block with nailed connection as an alternative). The edge purlin must also be fastened to the endwall truss to transfer loads into sidewall sheathing. To accommodate this connection, a 2x8x10 inch wood block is attached to truss and purlin as shown in the Connection Detail (Edge Purlin to Truss Connection) in Section 9 (the designer may choose to use a Simpson hanger or strap as an alternative). To provide adequate withdrawal capacity, the block is attached to truss with (8) #8x3" wood screws, four (4) screws at top of top chord of truss and four (4) screws at bottom of top chord. The purlin is fastened to the block with (5) 16d nails. This connection must be at all edge purlins for each roof diaphragm; there are the total of four (4) purlins and eight (8) such connections in the building. Link to Part 2 Appendix D Page 6 of 8 > Part 1 Wind-Governed Design Example 30

31 7.7 Edge Ceiling Joist-to-Ceiling Joist at Splice and to Corner Post Connection The edge ceiling joists serve as tension and compression chords of the ceiling diaphragm. In order to provide continuity in tensile resistance in the tension chord of the diaphragm, the edge ceiling joists must be fastened together at each splice. In this design an MSTA21 Simpson strap is used at each purlin splice. The edge ceiling joists must also be fastened to corner posts to transfer loads into sidewall sheathing. This connection is made with (6) 16d nails. Link to Part 2 Appendix D Page 6 of 8 > 7.8 Post-to-Concrete Collar Connection Each post is connected below grade to a concrete collar (backfill) with (1) #4 x 16 inch hot dipped galvanized rebar. This connection is checked using the provisions of the 2005 National Design Specification for Wood Construction (NDS) by AF&PA for a 1/2 inch diameter bolt in high moisture conditions. Link to Part 2 Section 7.8 > The design loads for each of cases 7.1 to 7.8 are given in the immediately following table. These design loads are taken from the load calculations in Section 2 and the diaphragm analysis results in Section 3. Case 7.1 & 7.2 Maximum Uplift/ Withdrawal Load (lb) Maximum Lateral/Shear Load (lb) Comments Uplift calculated from A trib of the connection, Lateral calculated from diaphragm analysis. Uplift calculated from A trib of the connection, Lateral calculated from diaphragm analysis. 7.4 NA 1704 Lateral calculated from diaphragm analysis 7.5 NA 1776 Lateral calculated from shearwall analysis 7.6 NA 535 Lateral calculated from diaphragm chord anal. 7.7 NA 557 Lateral calculated from diaphragm chord anal NA Uplift calculated from A trib of the connection Part 1 Wind-Governed Design Example 31

32 The following table summarizes the schedule of fasteners for each case. The connection details are presented in Section 9: Design Summary. Case Fastener Schedule Descriptor 7.1 & d common nails Truss-to-Post Connection 7.3 (2) H10A Hangers-Simpson Truss-to-Glulam Beam Strong-Tie Connection d common nails 2x6 Endwall Ceiling Ledger- to- Post Connection d galvanized nails 2x8 Endwall Skirt Board- to- Post Connection 7.6a (1) HTP37Z Simpson strap Purlin- to-purlin at Splice Edge 7.6b 1-60d R.S. nail into truss & 5-16d common nails into block 7.7a (1) MSTA21 Simpson strap 7.7b 6-16d common nails into corner post No. 4 x 16 in. rebar Purlins Only at Eave and Ridge Purlin-to-Endwall Truss Connection Edge Purlins Only at Eave and Ridge Ceiling Joist-to-Ceiling Joist at Splice Connection Edges Ceiling Joists Only Ceiling Joist-to-Corner Post Connection Edges Ceiling Joists Only Post-to-Concrete Collar Connection - Uplift This design example is focused on resistance to lateral loads and the connections related to these loads only; however, some other important connections that should be addressed in a complete building design include: Girt-to-Post Connection Withdrawal due to wind suction Wall Sheathing-to-Girt Connection Withdrawal due to wind suction Purlin-to-Truss Connection Withdrawal (uplift) due to wind suction Roof Sheathing-to-Purlin Connection Withdrawal (uplift) due to wind suction Overhead Door Headers -to-post Connection Vertical and horizontal shear Part 1 Wind-Governed Design Example 32

33 Section 8: Truss Bracing Details Permanent truss bracing details must be specified for the following: 1. Bottom chord continuous lateral restraint 2. Web member restraint 3. X-bracing 4. Corner Bracing Guidelines for handling, bracing and installing metal plate connected wood trusses are contained in the Building Component Safety Information (BCSI) booklet published jointly by TPI and WTCA. Also work is currently underway on a new ANSI/TPI 3 standard dealing with temporary and permanent bracing of metal plate connected wood trusses. 8.1 Bottom Chord Lateral Restraint and Web Member Restraint The bottom chord continuous lateral restraint and web member restraint are specified on the truss manufacturer s design drawing. Figure 8A is the truss design drawing for this building and it shows six webs, designated by bolder lines, which are to receive T-brace reinforcement. T-brace reinforcement is being used here as opposed to continuous web lateral restraints because of the wide spacing of the trusses. The truss drawing also indicates that the bottom chord lateral restraints are to be spaced no more than 10 ft. on center unless a rigid ceiling is directly applied. In this example building, there is a ceiling constructed with steel panels. However, we have elected to keep the bottom chord lateral restraints in the design since they will likely already have been installed as part of the temporary bracing scheme. L-Reinforcement is used with the lateral restraints based upon Table 2 of BCSI B10 Post Frame Truss Installation, Restraint and Bracing. 8.2 X-Bracing Truss members that are braced with continuous lateral restraints can all buckle in the same direction if sufficient diagonal or X-bracing is not provided. The main purpose of the diagonal bracing is to create a triangle with the continuous lateral restraints and direct axial forces into the sidewalls. This type of bracing is considered part of the permanent building stability bracing scheme and is not shown on the truss design drawing. X-bracing is used at each bottom chord lateral restraint to brace it off to the roof and ceiling planes. This is designed to resist a force in the lateral restraint equal to 5% of the max compression force in the bottom chord times the number of trusses between brace locations divided by the number of lateral restraints. The ceiling was ignored in this calculation. Lateral Restraint Force, LRF = [0.05(C max )(No. Trusses)]/(No. Restraints) = [0.05(858)(7)]/6 = 50 lbs Part 1 Wind-Governed Design Example 33

34 X-bracing is also used as sway bracing between the roof diaphragm and ceiling diaphragm. The intent is to prevent truss rollover or rotation as the roof and ceiling diaphragms are resisting wind load from any direction. Currently, the specification of sway bracing is a matter of engineering judgment as there is no published design reference that contains specific guidance or recommendations for this type of bracing. 8.3 Bottom Chord Diagonal Bracing Bottom chord diagonal bracing has not been used in this plan. The ceiling diaphragm serves to distribute wind and bracing loads to the bearing walls, and the X-bracing diagonally braces the lateral restraints. Therefore, bottom chord diagonals are not needed. If the building had no ceiling, bottom chord diagonal bracing would have been used to help distribute loads from the X- bracing to the bearing walls. Corner bracing is used on the bottom side of the top chord at each corner of the building. 8.4 Truss Design Truss design is usually conducted by the truss manufacturer using the provisions of ANSI/TPI 1, National Design Standard for Metal Plate Connected Wood Truss Construction with the top chord live or snow load, the top chord dead load, the bottom chord live load, and the bottom chord dead load specified by the building designer. In this design example, the designer would specify the following loads for the truss design: Top chord live load 25 psf Top chord dead load 4 psf Bottom chord live load 0 psf Bottom chord dead load 5 psf Figure 8B is a truss bracing plan for the roof system. The blue lines show the bottom chord continuous lateral restraint running continuously from endwall to endwall. The green lines show the corner bracing, and the cyan lines show the X bracing. Figure 8C is Cross Section A/1 taken at the location indicated on the Truss Bracing Plan. The roof and ceiling diaphragms are shown on this figure and the truss webs that receive a T-brace and/or an X-brace. The bottom chord continuous lateral restraint is also identified. Figure 8D shows how the X bracing should be applied when running across 3 trusses, while Figure 8E shows an X brace detail across 2 trusses. Figure 8F is an end lap detail for the lateral restraints. Figure 8G details the connection of T-Reinforcement to a truss web and L-Reinforcement to a lateral restraint. Part 1 Wind-Governed Design Example 34

35 Figure 8A. Truss Design Drawing by Lumber Specialties, Dyersville, IA Part 1 Wind-Governed Design Example 35

36 Figure 8B. Truss Bracing Plan Part 1 Wind-Governed Design Example 36

37 Figure 8C. Cross Section Part 1 Wind-Governed Design Example 37

38 Figure 8D. X Brace Across 3 Trusses Figure 8E. X Brace Across 2 Trusses Part 1 Wind-Governed Design Example 38

39 Figure 8F. End Lap Detail Figure 8G. Reinforcement Details Part 1 Wind-Governed Design Example 39

40 Section 9: Design Summary The post-frame design is summarized in the following series of design drawings by Timber Tech Engineering, Inc. Part 1 Wind-Governed Design Example 40

41 Part 1 Wind-Governed Design Example 41

42 Part 1 Wind-Governed Design Example 42

43 Part 1 Wind-Governed Design Example 43

44 Part 1 Wind-Governed Design Example 44

45 Part 1 Wind-Governed Design Example 45

46 NFBA Design Tool for Design of Post-Frame Building Systems PART 2: LATERAL DESIGN OF A 72'X120'X16' POST-FRAME BUILDING COM PREHENSI VE CAL CUL ATI ON PACK AGE Wind-Governed Design Example NOTE: This design example is divided into two parts. Part 1 is written as a teaching tool for designers not familiar with post-frame building design in that it explains each step of the lateral design process for a post-frame building and summarizes the results of the calculations. Part 2 is a comprehensive calculation package that gives the background design calculations for each step and is a much longer document. Both Part 1 and Part 2 can be used as stand alone documents.

47 TABLE OF CONTENTS SECTI ON PAGE SECTION 1: BUILDING DESCRIPTION 3 SECTION 2: ASCE 7-05 LOADING CALCULATIONS 6 SECTION 3: DIAPHRAGM DESIGN 10 SECTION 4: POST DESIGN 19 SECTION 5: FOUNDATION DESIGN 20 SECTION 6: CONNECTIONS 21 SECTION 7: PURLIN AND GIRT DESIGN 27 SECTION 8: OTHER DESIGN CONSIDERATIONS 28 APPENDIX APPENDIX PAGE APPENDIX A A1: FRAME STIFFNESS 2 A2: EAVE LOAD 3 A3: POST DESIGN 4 APPENDIX B: FOUNDATION DESIGN 1 APPENDIX C: DESIGN OF CRITICAL CONNECTIONS 1 APPENDIX D PURLIN DESIGIN 2 GIRT DESIGN 9 APPENDIX E: DIAPHRAGM DESIGN WITH MINIMUM 10 PSF WIND REQUIREMENT ASCE 7-05 LOADING 2 DIAPHRAGM DESIGN 5 CONNECTIONS 11 NOTE: ASCE 7-05 Section requires the main wind force resisting system (MWFRS) be designed for a horizontal wind pressure of 10 psf multiplied by the area of the building projected onto a vertical plane normal to the assumed wind direction. The MWFRS for this building is the roof diaphragm, shearwalls and post-frame. The 10 psf minimum wind load requirement controls the design of the MWFRS for this building as shown in section of this report. However, individual building components are controlled by wind pressures derived from coefficients. This design example is a detailed look at the lateral design of a post-frame building using wind pressures and suctions from coefficients, and Appendix E is included to show that the MWFRS is adequate for the 10 psf minimum wind load requirement.

48 Section 1: Building Description Wind-Governed Design Example This is a design example in which a 72' wide x 120' long x 16' high Post-Frame building's lateral force resisting system isanalyzed and designed for wind and seismic loading. The building islocated in Dane County, Wisconsin where, surrounded by closely spaced wind obstructions, it qualifies for surface roughness category B as defined in ASCE This commercial building is comprised of the following structural members: Str uctur al Component Sidewall Posts Endwall Posts Foundation Wall Girts Roof Purlins Roof Trusses Roof/ Wall Sheathing Description 3-ply 2x8 nail laminated column with structural finger joints; posts are embedded into ground; bottom treated for direct ground contact, top notched to accept truss 3-ply 2x8 nail laminated column with structural finger joints; posts are embedded into ground; bottom treated for direct ground contact 24"Ø x 8" concrete footing with 24"Ø concrete collar poured around post, (1) #4x16" long rebar thru post at 8" above top of footing 2x4 #2 SYP, each continuous over 2 spans, fastened to side of post with (2) 16d nails 2x4 #2 SYP, on edge, fastened to truss with (1) 60d R.S. nail and (2) 16d toenails, each Metal plate connected wood trusses, 3.5/12 pitch top chord, 0/12 pitch bottom chord, attached to post directly 29 gage Grandrib 3 metal sheathing by Fabral, fasten to girts/purlins with #10x1" screws as per manufacturer's recommendations, no stitch screws Spacing 8 ft o/c 8 ft o/c 8 ft o/c 24 in o/c 24 in o/c and 16 in o/c in unbalanced snow area 8 ft o/c n/a There are (4) 36"x60" windows equally spaced on one endwall and (1) 24'Wx14'H overhead door on opposite endwall; there are (2) 36"x60" windows and (2) 16'Wx14'H overhead doors and (1) 36"x80" man door in rear sidewall and (2) 36"x80" man doors and (2) 16'Wx14'H overhead doors in front sidewall. The exterior walls and roof are sheathed with Grandrib 3, 29 gage structural metal sheathing manufactured by Fabral. On the interior, the wallsand ceiling are also sheathed with Grandrib 3, 29 gage structural metal sheathing by Fabral (see Figure 3A and 3B for panel profile and fastener pattern, test panel size and configuration, and in-plane shear strength and stiffness data). The ceiling is framed with 2x4 #2 SYP ceiling joists 24" o/c in between the trusses. The ceiling sheathing and roof sheathing have the same orientation. The building is heated and insulated with R-19 insulation in walls and R-30 insulation in the ceiling. There is a 12" roof overhang on the gable ends and 24" overhang on the sidewalls.

49

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51 The wind load calculations, including main wind force resisting system (MWFRS) and components and cladding (C& C) loads, are presented first; followed by dead, live and snow load calculations. Seismic loading is then calculated and compared to wind to see which controls the lateral design for strength and deflection. This section concludes with allowable lateral deflection criterion and controlling load combinations for various components. 2.1 Wind Design M ethod 2 - Analytical Pr ocedur e - L ow-rise Building (ASCE 7-05, 6.5, ) Building I nputs: Calculation I nputs: Length Parallel to Ridge, B 120 ft Basic Wind Speed, V 90 mph Length Normal to Ridge, L 72 ft Topographic Factor, K zt 1.00 Wall Height, z 16 ft Post Sidewall Spacing, s 8 ft Post Endwall Spacing, s 8 ft Envelope: Enclosed Building Building Midheight, h ft Wind Directionality Factor 0.85 Roof Pitch (rise per 12 units of run) 3.5 Building Category II Eave Overhang 2 ft Exposure Category B Definitions: 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. Interior Zones - Zones 1-6 Below Edge Zones - Zones 1E - 6E Below I nter mediate Calculations: Importance Factor, I 1.00 Table 6-1 Calculated Roof Angle 16.3 deg Nom. Height of Atmospheric Boundary (z g ) 1200 Internal Press. Coefficient, Gc pi Vel. Press. Exp. Coefficient, K z s Gust Speed Power Law Exponent (α) 7 Velocity Pressure, q h 11.2 psf M ain Wind For ce Resisting System: ASCE 7-05, Figur e 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 2: Windward Roof Zone 3: Leeward Roof Zone 4: Leeward Side Wall Zone 5: Gable Wall Zone 6: Gable Wall Zone 1E: Windward Side Wall Edge Zone 2E: Windward Roof Edge Zone 3E: Leeward Roof Edge Zone 4E: Leeward Side Wall Edge Wind load should not be less than 10 psf on vertical projection. (ASCE 7-05, ) Because the structure is less than 30ft high, the torsional cases 1T, 2T, 3T and 4T do not apply. (ASCE 7-05, Fig. 6-10, note 5) Components and Cladding: ASCE 7-05, Figur e 6-11 Equation: p = qh[(gcp)-(gcpi)] Note: Only negative loads are shown because they are larger than positive and so control the design. Effective Wind Ar ea: span length multiplied by an effective width that need not be less than one-third the span length. Component: Wall Girts Section 2: ASCE 7-05 L oad Calculations Component: Roof Purlins Effective Area: ft 2 Effective Area: ft 2 Zone Gc p P (psf) Zone Gc p P (psf) I* II** III ~ I* II** III ~ 4: Wall Interior : Roof Interior : Wall Edge : Roof Edge : Roof Corners * Internal Pressure Positive * * Internal Pressure Negative ~ Internal Pressure Zero Back

52 2.2 Dead L oad Calculations Wall Dead L oad 3 psf Roof Dead L oad TOP CHORD BOTTOM CHORD Steel Roofing 1 psf surf ace area Bottom Chord Load 5 psf Purlins 1.25 psf surf ace area Bracing/Hardware 1.5 psf surf ace area Total Top Chord 3.75 psf surf ace area Top Chord Load On Horizontal Projection 3.91 psf horizontal projection TOTAL ROOF LOAD 9 psf 2.3 L ive L oad Calculations Floor L ive L oad Minimum Floor Live Load = n/a psf (ASCE 7-05, Table 4-1) M inimum Roof L ive L oad Top Chord 20 psf 2.4 Snow L oad Calculations Bottom Chord 0 psf Total (on horizontal projection) 20 psf (ASCE 7-05, Table 4-1) Flat-Roof Snow L oad, pf Equation: p f = 0.7(C e )(C t )(I)(p g ) Notes Ground Snow Load, pg: 30 psf Figure 7-1 Exposure Factor, C e : 1.0 Table 7-2 Partially exposed roof Thermal Factor, C t : 1.1 Table 7-3 Heated building Importance Factor, I: 1.0 Table 7-4 p f 23.1 psf Sloped-Roof Snow L oad, ps Equation: p s = (C s )(p f ) Notes Roof Slope Factor, Cs: 1.00 Figure 7-2 p s 23.1 psf Unbalanced Roof Snow L oad Hip and Gable Roofs 1) Required for Hip and Gable Roofs with a slope less than 70/W and exceeding 70 degrees 2) The unbalanced snow load is applied to the leeward roof and windward roof as indicated Inputs: Horizontal Distance Eave to Ridge, W 38 ft Equations: W 20 ft. (ASCE 7-05, Figure 7-5) 0 Windward Unbalanced (p g )(I) Leeward Unbalanced W > 20 ft 0.3*p s Windward Unbalanced p s + h d (γ)/( (S)) Leeward Unbalanced, the latter extended from the ridge a distance of [8( (S))(hd)]/3 I nter mediate Calculations: Roof Angle = degrees h d = 2.13 ft g = 17.9 pcf S = Roof slope run for a rise of 1 = p unbal, leeward = 43.7 psf for a distance of 10.5 ft from the ridge, then 23.1 psf to eaves p unbal, windward = 6.9 psf Back

53 2.5 Seismic L oad Calculations Calculation I nputs: Building and Site Inputs: Spectral Response Acceleration, S Site Class D Spectral Response Acceleration, S S 0.15 Basic Structural System: Response Modification Factor, R 7 All other structural systems: Height to Highest Level (ft), h n 16 Light-framed walls sheathed w/ steel sheets Weight of Structure (lbs), W 6240 Seismic Design Category: D (ASCE 7-05, 11.6) (9 psf)( ft)(8 ft)+2(3 psf)(16 ft)(8 ft) Effective Weight of Structure (lbs), W e 5760 (9 psf)( ft)(8 ft)+2(3 psf)(16 ft)(8 ft)(3/8) I nter mediate Seismic Calculations Wind Resolved to Hor izontal Point L oad at Eave, F w Seismic Use Group II Building Inputs: Load from Roof Occupancy Importance Factor, I E 1 Fixity Factor (lbs) S ms Wind Force with 10 psf min, F w = 1320 lbs 840 S Ds Wind Force with Roof and Walls, F w = 256 lbs -223 S m Wind Force with Walls only, F w = 479 lbs 0 S D NOTE: The 10 psf minimum requirement of ASCE 7-05, C T 0.02 controls the design of the main wind force resisting system C u 1.7 (MWFRS). The MWFRS for this building is the roof diaphragm and Acceleration Site Coefficient, F a 1.6 shearwalls, and the post-frame. This example will proceed with Velocity Site Coefficient, F v 2.4 building component design using wind pressures from coefficients, and then show that MWFRS is adequate for 10 psf minimum load in App. Fund. Period, T a 0.16 Appendix E at the end of this report. Fundamental Period, T 0.27 Seismic Coefficient, C s C s min C s max Seismic Base Shear, V = 143 lbs Controlling Wind Load: Lateral Seismic Force at Roof, F R = 132 lbs Wind Force per Frame, F w = 479 lbs [F R = 143 x 5760 / 6240 ] Seismic vs. Wind Compar ison Controlling Load Combination D+W 479 lbs D+0.7E 92.2 lbs 2.6 Stor y Dr ift and Wind Deflections Strength Comparison Serviceability Comparison Wind Controls the Strength Design (D+0.7E)C d < D+ W: Wind Controls Serviceability Requirements Allowable Story Drift = 0.02 h s1 (ASCE 7-05, Table ) Story Height, h s1 = 192 in Allowable Story Drift = 3.84 in Other Deflection Criterion = l/120 (ASCE 7-05, Section and IBC 2009, Table ) Allowable Deflection at Eave = 1.6 in (controlling deflection criterion) Actual Calculated Deflection = 0.57 in (see DAFI outputs) Story Drift from Elastic Analysis, δ 1e = n/a in (seismic does not control the strength or serviceability design) Deflection Amplification Factor, C d = 4.5 Calculated Stor y Dr ift at Eave, δ 1 = n/a in Story drift requirements are satisfied - calculated story drift is less than controlling allowable story drift Back

54 2.7 Contr olling L oad Combinations Wall Posts D+0.75(S+W) Post Foundation (Lateral Loading) D+W and 0.6D+W Roof Diaphragm D+W and 0.6D+W Post Foundation (Uplift) 0.6D+W Endwall Shearwalls D+W and 0.6D+W Wall Girts D+W and 0.6D+W Roof Truss D+S Purlins 0.6D+W or D+S 2.8 L oad Calculations Summar y Design MWFRS and C&C wind pressures and suctions were calculated for positive, negative and zero internal pressure conditions. The controlling lateral wind force to be resisted by the MWFRS was found by considering wind applied to roof and walls, wind applied to walls only, and 10 psf wind pressure applied to the vertical projection. The lateral force from seismic load was also calculated and compared to the wind force. The response modification factor, R, and deflection amplification factor, Cd, were chosen from ASCE 7-05 Table The comparison between wind and seismic was performed for both strength and serviceability criterion using forces generated from the critical load combinations. The allowable lateral deflection at the eave was found by taking the eave height divided by 120 (L/120 limit). The actual deflection comes from the DAFI analysis in the Diaphragm Design section. The dead load of the different materials for the roof plane are listed based on surface area and then converted to the horizontal projection to give the top chord dead load. Snow load and unbalanced snow load is calculated for a heated building with insulated ceiling and the roof is considered to be partially exposed.

55 Section 3: Diaphr agm Design Wallsand roof are sheathed with Grandrib 3, 29 gage structural metal sheathing manufactured by Fabral. Below are the properties of Grandrib 3 panels as provided in Table 6.1 of the "Post-Frame Building Design Manual" (PFBDM) by the National Frame Building Association (NFBA). The panel dimensions and fastening pattern are shown in Figure 3A. The panel properties were obtained using a cantilever test procedure as shown in Figure 3B. Ultimate Strength, P u, lbf 3300 Allowable Shear Strength, v a, lbf/ft 110 Effective In-Plane Stiffness, c, lbf/in 2920 Effective Shear Modulus, G, lbf/in 2190 Reference: Lukens & Bundy, 1987 Figure 3A. Sheathing profiles and fastener patterns for the roof and wall panels. Figure 3B. Test panel arrangement for determining in-plane shear strength and stiffness of diaphragm test panels. 3.1 Diaphr agm Hor izontal Roof Stiffness, C h The total horizontal shear stiffness, C h, of the roof assembly iscalculated by summing the horizontal shear stiffness values, ch,1 and ch,2, of the individual roof diaphragms including both roof slopes. The horizontal shear stiffness of an individual diaphragm, c h, is obtained by adjusting the model diaphragm in-plane shear stiffness, c, for actual building size and roof slope. C h = c h,1 roof +c h,2 roof +c h,3 ceiling c h,1 roof = c h,2 roof = G(cosθ roof )(b h,1 roof /s) c h,3 ceiling = G(cosθ ceiling )(b h,1 ceiling /s) b h,1 roof = 38 ft (half of the building's width+overhang) b h, ceiling = 72 ft (building's width) s= 8 ft (column spacing) θ roof θ ceiling degrees Back

56 c h,1 roof = 9986 lbf/in c h,2 roof = 9986 lbf/in c h,3 ceiling = #### lbf/in C h = lbf/in (The total horizontal shear stiffness of roof diaphragm) 3.2 Frame Stiffness, k (See Visual Analysis Results in Appendix A) The stiffness of the bare frame, k, is the ratio of the applied horizontal eave load divided by the resulting horizontal eave deflection. A computer analog of the frame consisting of two posts and the truss has been used to calculate this term. The post to soil interface of this structural analog is shown in Figure 4A. k = p/δ p = horizontal load at eave Δ = frame displacement at eave p = 100 lbf (applied to eave in Visual Analysis Model) Δ = 0.75 in (resulting truss displacement in Visual Analysis Model) k = lbf/in (bare frame stiffness)

57 3.3 Endwall Stiffness, k e The endwall stiffness, k e, is calculated by summing the horizontal shear stiffness of the wall diaphragm and the bending stiffness of the endwall posts. The horizontal shear stiffness of the wall diaphragm isfound by adjusting the model diaphragm shear stiffness for the actual size of endwall. The interior liner is constructed the same as the exterior siding and is included in the endwall calculations. 3.4 Eave L oad k e = G(cosθ exterior )(b h,exterior /s) + G(cosθ interior )(b h, interior /s) + n(6ei/l 3 ) θ exterior = θ interior = G= 2190 lbf/in 0.0 degrees 0.0 degrees b h1, exterior = b h1, interior = 60 ft (length of endwall 1 minus door/window openings) b h2, exterior = b h2, interior = 48 ft (length of endwall 2 minus door/window openings) s = 16 ft (s=length perpendicular to loading = wall height) n 1 = 10 columns (n 1 =number of columns in endwall 1) n 2 = 8 columns (n 2 =number of columns in endwall 2) E= psi I= 48 in 4 (moment of inertia about weak axis of each individual endwall column) L= 16 ft (column height) k e1 = lbf/in (stiffness of endwall with four windows) k e2 = lbf/in (stiffness of endwall with 24ft door) The eave load, Pi, used in this analysis is the resultant lateral load from the controlling combination of design loads acting over the tributary area of the eave, and is applied as a concentrated load at the eave of each frame. The eave load is calculated using Frame- Base Fixity Factors or by Plane-Frame Structural Analysis. The standard method of fixity factors typically assumes that a post is simply supported with zero rotational resistance at ground level, or is fully fixed with zero rotation at ground level. Sometimes neither of these assumptions are completely accurate. In the case of a non-constrained post foundation, the top horizontal support of the foundation system islocated a distance below ground level. This means that there are some lateral and rotational deflections at the ground line. As a result, the standard fixity factor for a rigidly supported column isa rough approximation. Assuming a pinned base condition for the post yieldsa higher eave load and is conservative for the diaphragm design; conversely, assuming a perfectly fixed base condition yields a lower eave load and is conservative for the post design. We have chosen to use a fixity factor of 0.42 which is a little more toward fixed than pinned. Eave Load by Frame-Base Fixity Factors: P i = s[h r (q wr - q lr ) + h w f (q ww - q lw )] s= 8 ft h r = 10.5 ft h w = 16 q ww = 7.6 q lw = -2.4 q wr = 0.0 (load with roof loads did not control) q lr = 0.0 (load with roof loads did not control) Back

58 f pin = 0.5 (fixity factor for a pin post base support) f ixed= (fixity factor for a fixed post base support) P i, pin = 639 (Eave Reaction With Pinned Column Base) P i, fixed = 479 (Eave Reaction With Fixed Column Base) f new = 0.42 P i = 538 lbs P i = s[ h r (q wr - q lr ) + h w f new (q ww - q lw )] 3.5 Summar y of DAFI I nputs DAFI (Diaphragm and Frame Interaction) is a computer program for calculating the distribution of horizontal loads among the individual post-frames and roof diaphragm sections of a building. It can be used to analyze diaphragm action in buildings in which bay spacings vary, the stiffness of individual post-frames differ, endwalls are not assumed infinitely rigid, and/or the stiffness of individual diaphragms are not the same. A windows version of this program is available as a free download from the National Frame Building Association website (nfba.org). It allows data to be entered using a special screen editor. The data can be saved to and later recalled from an input data file. Roof Diaphragm Shear Stiffness: lbf/in (C 1 = C 2 = C 3 = = C 15 ) Endwall 1 Shear Stiffness: lbf/in Endwall 2 Shear Stiffness: lbf/in Interior Frame Stiffness: lbf/in (k 2 = k 3 = k 4 = = k 14 ) Eave Load on Interior Frame: 538 lbf

59 3.6 Summar y of DAFI Outputs Frame Number Frame Stiffness Diaphr agm Number DAFI FRAM E ANALYSIS OUTPUTS Applied Hor izontal Load Resisted L oad Displacement Fr ame DAFI DIAPHRAGM ANALYSIS OUTPUTS Diaphr agm Shear Displacement Stiffness Shear L oad by Fraction of Applied L oad

60 3.7 Interpretation of DAFI Outputs Controlling Frame Number = 9 (Resists the most load compared to other frames) Deflection of Frame = 0.57 in Load Resistance by Frame = 75.7 lbf Resisting Force by Diaphragm, Q = lbf (Eave Load Minus Load Resistance by Frame) Shear Load in Endwall 1 = 3701 lbf DAFI Output: Load Resisted by Frame 1 Shear Load in Endwall 2 = 3487 lbf DAFI Output: Load Resisted by Frame 16; Wall with 20' Door Horizontal Diaphragm Shear = 3432 lbf DAFI Output: Largest Diaphragm Shear Load 3.8 Endwall Shear Strength Check The endwalls are sheathed inside and out with Grandrib 3, 29 gage structural metal sheathing manufactured by Fabral. The sheathing is fastened to 2x4 girts with #10x1" screws 6" o/c at edges and 12" o/c at all intermediate framing. Though the testing was done with purlins placed on edge, it is a reasonable assumption that the purlins with flat orientation will yield equal or better results. The testing was done with 2x4 No.2 DFL purlins, fastened to rafters with (1) 60d spike and (2) 10d toenails. Table 6.1 of the PFBDM issilent on the controlling failure mode, whether it was in the wood portion of the test assembly or the steel panels. To be conservative, it is assumed that the failure isin the steel panels and the load duration factor, C D = 1.0 is applied in the calculations. Ref: Lukens & Bundy, 1987, as presented in Table 6.1 (Test Assembly #6) of the PFBDM by NFBA. k e = G(cosθ exterior )(b h,exterior /s) + G(cosθ interior )(b h, interior /s) + n(6ei/l 3 ) (endwall stiffness) G(cosθ exterior )(b h1,exterior /s) = 8213 lbf/in (stiffness provided by exterior sheathing of endwall 1) G(cosθ interior )(b h1, interior /s) = 8213 lbf/in (stiffness provided by interior sheathing of endwall 1) n(6ei/l 3 ) = lbf/in (stiffness provided by columns of endwall 1) G(cosθ exterior )(b h2,exterior /s) = 6570 lbf/in (stiffness provided by exterior sheathing of endwall 2) G(cosθ interior )(b h2, interior /s) = 6570 lbf/in (stiffness provided by interior sheathing of endwall 2) n(6ei/l 3 ) = lbf/in (stiffness provided by columns of endwall 2) Shear Load in Endwall 1, V max, 1 = 3701 lbf DAFI Output: Load Resisted by Frame 1 Shear Load in Endwall 2, V max, 2 = 3487 lbf DAFI Output: Load Resisted by Frame 16; Wall with 24' Door Allowable Shear Strength, v a = 110 lbf/ft (from Table 6.1 test assembly #6 of PFBDM) Endwall Wall Component Stiffness of Wall Component Total Stiffness of Endwall L oad Ratio Total L oad on Component Shear L oad on Component, v max Allowable L oad on Component, v a (lbf/in) (lbf/in) (lbs) (lb/ft) 1 Exterior Sheathing Interior Sheathing Bare Frame n/a (lb/ft) n/a 2 Exterior Sheathing Interior Sheathing Bare Frame n/a n/a v max v a <ok> (actual shear in endwalls is less than allowable shear) Back

61 3.9 Sidewall Shear Str ength Check Wind Parallel To Ridge The controlling load combination for wind loads parallel to ridge is D+W, where windward and leeward pressures are applied to the tributary area of the endwall. For simplicity the columns are assumed to be fully rigid at ground level with a fixity factor of 3/8. Typically the endwalls in a post-frame building are the controlling shear walls. There are cases, however, when sidewalls are the critical shear walls, especially in wide buildings that are short in length. In those situations a more thorough analysis is required, in which a roof and sidewall stiffness and possibly torsional effects on the overall building envelope are considered. An analytical model of each column height with proper base conditions may also be required to calculate loads on the diaphragm more accurately. Allowable Shear Strength, v a = 220 lbf/ft (Exterior Sheathing and Interior Liner) Fixity Factor, f ixed = (assume zero column rotation at ground level) Tributary Area, A t = 810 ft 2 (see sketch above) Length of Wall, L sidewall = 79 ft (length of sidewall minus all door and window openings) q ww = 10.0 psf (10 psf minimum requirement controls the design) q lw = 0.0 psf (10 psf minimum requirement controls the design) Maximum Shear Load, V max = 8100 lbs Actual Shear Load, v sidewall = 51 lbf/ft V max /L sidewall /2walls v sidewall v a <ok> (actual shear in sidewall is less than allowable shear) 3.10 Roof Diaphr agm Shear Str ength Check The roof is also sheathed with Grandrib 3, 29 gage structural metal sheathing manufactured by Fabral. The sheathing is fastened to 2x4 purlins with #10x1" screws 6" o/c at edges and 12" o/c at all intermediate framing. The testing was done with 2x4 No.2 DFL purlins, fastened to rafters with (1) 60d spike and (2) 10d toenails. Ref: Lukens & Bundy, 1987, as presented in Table 6.1 (Test Assembly #6) of the PFBDM by NFBA. Allowable Shear Strength, v a = 110 lbf/ft M ax Shear, V max, hor izontal = 3432 lbf DAFI Diaphragm Analysis Output C h, roof = c h,1 roof + c h2, roof = lbf/in C h, ceiling = lbf/in (horizontal stiffness provided by roof sheathing) (horizontal stiffness provided by ceiling sheathing) L s, roof = ft (width of building plus overhangs divided by cosine of roof angle) L s, ceiling = 72 ft (width of building) v max, in-plane = V max, in-plane / L s (shear load in plane of the roof or ceiling sheathing) Back

62 Roof Component Hor izontal Stiffness of Component Total Hor izontal Stiffness of Diaphr agm L oad Ratio M ax Horizontal L oad on Component, V max, hor izontal θ M ax L oad in Plane of Component, V max, in-plane Shear L oad in Plane of Component, v a Allowable Shear L oad, v a (lbf/in) (lbf/in) (lbs) (deg) (lbs) Roof Sheathing (lb/ft) 23 (lb/ft) 110 Ceiling Sheathing v max v a <ok> (actual shear in diaphragm is less than allowable shear)

63 3.11 Roof Diaphr agm Chor d For ces The roof diaphragm acts like a deep beam where the ends of the beam are assumed to be fixed. The diaphragm of this building consists of two individual roof diaphragms, one on each side of ridge, and of one ceiling diaphragm. The bending forces in each diaphragm are resisted by roof purlins and ceiling joists. Because only the edge purlins and ceiling joists are fastened together to provide a continuous tensile resistance to tension chord of diaphragms, it can be conservatively assumed that the intermediate purlins and ceiling joists provide zero contribution to the bending resistance of diaphragms. The load is applied to the diaphragm at eave, and redistributed to individual diaphragms according to their stiffness. For simplicity, the load resistance contribution of frames is ignored. The purlins are fastened together at spliceswith a single HTP37Z Simpson plate fastened to the side with 10dx1-1/2 nails; the ceiling joists are fastened together at splice with a single MSTA21 Simpson strap, fastened to the bottom edge with 10dx3" nails. It should be noted that typical roof diaphragm deflection consists of bending deflection, shear deflection of sheathing panel, deflection due to nail slip, and deflection due to slip in chord connection splices. Because the diaphragm stiffness in this example is based on a sample test, it can be assumed that all of these deflection contributors, with exception of the deflection due to slip in chord connection splices, are accounted for. It isfurther assumed that the deflection due to slip in chord connection splicesis minimal and is an insignificant contributor to the overall diaphragm deflection. c h,1 roof = 9986 lbf/in (horizontal stiffness of roof diaphragm 1) c h,2 roof = 9986 lbf/in (horizontal stiffness of roof diaphragm 2) c h,3 ceiling = lbf/in (horizontal stiffness of ceiling diaphragm) C h = lbf/in (total combined horizontal stiffness diaphragm) Load Ratio to Each Diaphragm, p = c h,x /C h (individual diaphragm stiffness divided by total diaphragm stiffness) Load on Roof Diaphragm, w = lbf/ft (eave load, P i, divided by column spacing, s) End Moment, M ex = w x L x 2 /12 Midspan Moment, M mx = w x L x 2 /24* Tension/ Compression Force, T x = M ex /b x (controls the design) (moment equation for a beam with fixed end supports) (controlling moment divided by depth of individual diaphragm) * A moment is generated in the diaphragm as the diaphram deflects lateraly under horizontal wind or seismic loads. The resulting bending forces travel along the length of the buidling through the edge ceiling joists and purlins which are restricted from moving longitudinaly by rigid sidewalls; hence, the diaphragm is assumed to be rigidly fixed at the endwalls. HTP37z Simpson Strap = 1600 lbs (allowable tension capacity as specified by the manufacturer) MSTA21 Simpson Strap = 1505 lbs (allowable tension capacity as specified by the manufacturer) Diaphr agm Component (dec.) Roof Diaphragm Roof Diaphragm Ceiling Diaphragm L oad Diaphr agm Ratio, Length, L x p Diaphr agm Depth, b x (ft) (ft) (lb/ft) (lb-ft) (lbs) (lbs) L oad on Diaphr agm, w x 33.4 M oment in Diaphr agm, M x Tension/ Compression For ce, T x 557 Allowable Tension L oad T a 1505 P x P a <ok> (actual tension load is less than allowable tension load) Back

64 Section 4: Post Design 4.1 L oads Dead Load, DL = 9 psf Roof Live Load, LL r = 20 psf Snow Load, SL balanced = 23.1 psf Snow Load, SL unbalanced, windward = 6.9 psf Snow Load, SL unbalanced,leeward = 43.7 psf, for a distance of 10.5 ft from ridge, then 23.1 psf Windward Post Wind Load, q ww = 7.6 psf or 3.6 Leeward Post Wind Load, q lw = -2.4 psf or -6.4 Diaphragm Restraining Force, Q = lbs (applied at eave of frame) Figure 4A. Structural analog of post-frame with non-constrained foundation. 4.2 Results Detailed post design calculations are provided in Appendix A Post Size = 3-ply 2x8, nail laminated post with structural glued finger joints Grade = #1 southern yellow pine, pressure preservative treated at the embedded end V max, dry = 602 lb (at grade) M max, dry = 1850 lb-ft (at grade) V max, wet = 1191 lb (below grade) M max, wet = 2395 lb-ft (below grade) P max = 9872 lb (D+S) Actual/Allowable Unity = 0.50 (controlling combined axial and bending load combination: D+.75(S+W) The post is sized adequately for the required loading

65 Section 5: Foundation Design ANSI/ASAE EP486.1 Defines non-constrained foundation as a case in which "Post foundation rotation and horizontal displacement (horizontal movement of entire foundation) is resisted by reactive soil pressures only " If the post is horizontally supported by a concrete slab or concrete collar at ground level, the foundation is designed as a constrained foundation. In this example the concrete floor serves as a horizontal support at ground level only for windward wind loads. Because the post is not attached to concrete slab and is free to move outward under leeward wind loads, the foundation is conservatively designed as a non-constrained foundation. The design procedures and equations are outlined in ANSI/ASAE EP486.1; the design equations are also shown in Appendix B. The structural analog in Figure 4A shows a vertical roller support at 0.33d (16 inches) below grade and a pin at 0.1d (5 inches) up from the bottom. The post embedment below grade is 4 ft; a 24" diameter x 24" high concrete collar is poured around the post, on top of an 8" thick concrete footing. The reactions on the foundation are imposed from the column at ground level, as shown in Figure 5A below. The allowable lateral bearing soil pressure, S', is assumed to be 200 psf/ft of depth, and the initial allowable vertical bearing soil pressures are assumed to be 2000 psf (EP486.1, Table 1). Per Footnote 4 of the EP486.1 Table 1, the vertical allowable foundation pressures "are for footings at least 300 mm (1 ft) wide and 300 mm (1 ft) deep into natural grade. Pressure may be increased 20% for each additional 300 mm (1 ft) of width and/or depth to a maximum of three times the tabulated value. Source: Table 18-1-A UBC." The adjusted allowable vertical soil pressures along with controlling load combinations for gravity, lateral and uplift loads, and other calculations are provided in Appendix B. Figure 5A. FBD of non-constrained post foundation with concrete collar from ANSI/ASAE EP Post Reactions at Gr ade L evel P D = 3010 lbs (Vertical dead load reaction from Visual Analysis model) P Lr = 6080 lbs (Vertical roof live load reaction from Visual Analysis model) P S = 6862 lbs (Vertical snow load reaction from Visual Analysis model) Q uplift = 2959 lbs (Wind service load on footing calculated using tributary area) V a = V max, dry = 602 lbs (Shear force applied at grade level, from Visual Analysis model) M a = M max, dry = 1850 lb-ft (Moment reaction applied at grade level, from Visual Analysis model) P = P max = 9872 lb (Vertical foundation load, D+S) Q net = 1153 lb (Net uplift load on foundation, 0.6D+W) 5.2 Results Detailed foundation calculations are provided in Appendix B Minimum Post Embedment, d = 3.3 ft (minimum calculated embedment depth) Actual Post Embedment, d a = 4.0 ft Applied Vertical Soil Pressure, S a = 3142 psf (calculated) Allowable Soil Pressure, S v = 3867 psf, ( % increases are applied per EP486.1, Table 1, Footnote 4) Calculated Uplift Resistance, U = 2395 lbs (resistance consists of weight of concrete collar + weight of soil cone) d d a <ok> (required post embedment is less than actual post embedment) S a S v <ok> (actual vertical soil bearing pressure is less than the allowable) Q net U <ok> (net uplift load is less than the calculated footing uplift resistance)

66 6.1 Pur lin Design 2x4 #2 S. Pine on 24" on center except 16" on center in unbalanced snow area 10.5 ft. each side of ridge (Design details are provided in Appendix C). Dead Load, DL = 2.5 psf (on surface area, see Roof Dead Load Section) Roof Live Load, LL r = 20 psf (on horizontal projection, does not control) Snow Load, SL balanced = 23.1 psf (on horizontal projection) Snow Load, SL unbalanced, windward = 6.9 psf (on horizontal projection) Snow Load, SL unbalanced,leeward = 43.7 psf, for a distance of 10.5 ft from ridge, then 23.1 psf Interior Roof Wind Load, q interior = psf (component and cladding) Edge Roof Wind Load, q edge = psf (component and cladding) Corner Roof Wind Load, q corner = psf (component and cladding) Deflection Criterion = l/150 and l/120 for Live and Dead + Live Loads Roof angle, θ r = 16.3 degrees STRONG AXIS LOADING ON PURLIN Purlin θ r Spacing Roof Dead Balanced Unbalanced L ive L oad Snow L oad Snow L oad L oad Corner Wind L oad (deg) (ft) (lb/ft) (lb/ft) (lb/ft) (lb/ft) (lb/ft) (lb/ft) (lb/ft) Typical Purlin Purlin in Unbalanced Snow Area Girt Design Section 6: Purlin & Girt Design Purlins are positioned on edge on top of top chord of truss and typically span over two spans for the total length of 16ft. Due to the 2x4 #2 S. Pine flat against 24" on center continuous over two spans (Design details are provided in Appendix C). Interior Wall Wind Load, q interior = psf (component and cladding) Edge Wall Wind Load, q edge = psf (component and cladding) Deflection Criterion = l/90 (IBC 2009, , Footnote a) Interior Wind L oad Edge Wind L oad

67 Section 7: Connections Detailed Connection Calculations Are Provided In Appendix D 7.1 L ist of Cr itical Connections In this example only connections critical to the lateral force resistance system are analyzed: Truss to Post Connection - Vertical shear due to truss uplift Truss to Post Connection - Horizontal shear due to post top end reactions Truss to Glulam Header Over Sidewall Door Connection -Truss uplift Endwall Ceiling Ledger to Posts Connection - Shear between ceiling diaphragm and end shear wall Skirt Board to Posts Connection - Shear between shear wall and posts at grade level Purlin to Purlin at Splice Connection - Tension load between diaphragm tension chords Ceiling Joist to Ceiling Joist at Splice Connection - Tension load between diaphragm tension chords Post to Concrete Collar Connection - Vertical shear due to post uplift Figure 6A. Critical connection locations. 7.2 Truss to Post Connection Trusses are placed in a pocket created by notching the center lamination at top of post. The exterior laminationsare then extended to the top of top chord of truss, and fastened to truss with (5) 16d common wire nailson each side. This connection isdesigned to resist vertical and horizontal shear loads. The vertical shear load, or load from truss uplift, can be calculated using tributary areas and roof wind pressures, or can be provided by a truss designer. In this example the uplift loads are calculated using tributary areas and wind pressures. The horizontal shear load at top of post can be conservatively approximated using tributary area and wind pressures, which isa product of (3/8)(column height)(column spacing)(controlling wind pressure), assuming that the column isfixed at bottom (grade level) and has a horizontal roller support at top. The more accurate horizontal shear load can be determined by modeling the critical frame, the frame closest to the more rigid endwall, in a computer program, or by using DAFI results outputs. This example utilizes the latter of these three methods.

68 Vertical Shear Load and Design: Tributary Width = 304 ft 2 Roof Wind Pressures, q wr = -9.7 psf Effective Dead Load = 4.5 psf (50% of design dead load) Net Uplift Force = lbs (0.6D+W) Allowable Shear Capacity = 2275 lbs (Detailed connection calculations are provided in Appendix D) Horizontal Shear Load and Design: The end shear at top of post equals the calculated horizontal reaction of the critical frame. This reaction is the sum of three (3) components: Horizontal Roof Load, F r = 0 lbs (1) (roof component of calculated eave load divided by 2 posts) Resisting Force by Diaphragm, R d = lbs (2) F d = [ (eave load)-(load resisted by Frame 2)] [ q ww /(q ww +q lw )] Resistance by Opposite Post, R 2 = lbs (3) R 2 = Δ 2 (k)q lw /(q ww -q lw ), where k = frame stiffness Shear at Top of Post, V 2 = -387 lbs (V 2 = F r + R d + R 2 ) Allowable Shear Capacity = 2275 lbs (Detailed connection calculations are provided in Appendix D) 7.3 Tr uss to Glulam Header Connection Truss isfastened to glulam header over 16 ft. door with (2) H10A Simpson hurricane ties, one tie on each side of beam. The specific gravities of truss and beam are assumed to be Tributary Width = 304 ft 2 Roof Wind Pressures, q wr = -9.7 psf Effective Dead Load = 4.5 psf (50% of design dead load) Net Uplift Force = lbs (0.6D+W) Allowable Shear Capacity = 2280 lbs (Detailed connection calculations are provided in Appendix D) 7.4 Endwall Ceiling L edger to Posts Connection The shear load from roof diaphragm is transferred to endwall truss and then to wall sheathing. This load path does not directly rely on truss to post connection. The shear forces from ceiling diaphragm, however, are transferred to endwall posts first and then to girts and sheathing. There are 10 posts in endwall 1, the endwall with largest shear loads. The ceiling ledger is fastened to each post with (4) 16d nails. Number of Posts = 10 Number of 16d Nails per Post = 4 M aximum Shear, V max, hor izontal = 1704 lbs (V max, horiz. from Section 3.10 Roof Diaphragm Shear Strength Check) Allowable Shear Capacity = 9830 lbs (Detailed connection calculations are provided in Appendix D) 7.5 Endwall Skir t Boar d to Post Connection There is a #2 SYP skirt board on the exterior side of end wall, and a 2x4 #2 SYP bottom girt on the interior side of end wall. The skirt board and bottom girt to post connection isthe last connection in the load path of the lateral force resisting system before the lateral loads are transferred to the ground. The skirt board and the bottom girt are each fastened to each post with (4) 16d galvanized common wire nails. Number of Posts = 10 Number of 16d Nails per Post = 4 M aximum Shear, V max, exter ior = 1776 lbs (V max from Section 3.8 Endwall Shear Strength Check) M aximum Shear, V max, inter ior = 1776 lbs (V max from Section 3.8 Endwall Shear Strength Check) Allowable Shear Capacity, V a = 6881 lbs (Detailed connection calculations are provided in Appendix D)

69 7.6 Purlin to Purlin at Splice and to Endwall Truss Connection The edge purlins serve as tension and compression chords of the roof diaphragm. In order to provide a continuity in tensile resistance in the tension chord of the diaphragm, the purlins must be fastened together at each splice. In this design a HTP37Z Simpson strap is used at each purlin splice. The edge purlin must also be fastened to endwall truss to transfer loads into sidewall sheathing. In addition to (1) 60d R.S. nail, a 2x8x10 inch wood block is attached to truss and purlin. To provide adequate withdrawal capacity, the block is attached to truss with (8) #8x3" wood screws, four (4) screws at top of top chord of truss and four (4) screws at bottom of top chord. The purlin isfastened to the block with (5) 16d nails. This connection must be at all edge purlins on each side of the ridge line; there are the total of four (4) purlins and eight (8) of such connections in the building. M aximum Tension For ce, T max = 535 lbs (T x from Section 3.11 Roof Diaphragm Chord Forces) Allowable Tension Capacity, T a = 1850 lbs (Detailed connection calculations are provided in Appendix D) Allowable Tension Capacity, T a = 1513 lbs 7.7 Ceiling Joist to Ceiling Joist Splice and to Cor ner Post Connection The edge ceiling joists serve as tension and compression chords of the ceiling diaphragm. In order to provide a continuity in tensile resistance in the tension chord of the diaphragm, the ceiling joists must be fastened together at each splice. In this design a MSTA21 Simpson strap is used at each purlin splice. The edge ceiling joists must also be fastened to corner posts to transfer loads into sidewall sheathing. M aximum Tension For ce, T max = 557 lbs (T x from Section 3.11 Roof Diaphragm Chord Forces) Allowable Tension Capacity, T a = 1505 lbs (Detailed connection calculations are provided in Appendix D) Allowable Tension Capacity, T a = 1474 lbs 7.8 Post to Concr ete Collar Connection Each post is connected below grade to a concrete collar (backfill) with (1) #4 x 16 inch hot dipped galvanized rebar. This connection ischecked using the provisions of the 2005 National Design Specification for Wood Construction (NDS) by AF& PA for a 1/2 inch diameter bolt in high moisture conditions. Net Uplift Force, Q net = 1153 lbs (from Section 5.1 Post Reactions at Grade Level) Number of Reinfor cing Bar s = 1 Allowable Shear Capacity, Z' = Z(C D )(C M ) = 1720(1.6)(0.7) = 1926 lbs Back

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73 Section 8: Other Design Consider ations This design example focused on resistance to lateral loads. Some other important connections not contained in this example, may include: Overhead Door Header(s) to Post Connection - Vertical and Horizontal shear Girt to Post Connection - Withdrawal due to wind suction Purlin to Truss Connection -Withdrawal (uplift) due to wind suction Roof Sheathing to Purlins Connection -Withdrawal (uplift) due to wind suction Wall Sheathing to Girts Connection - Withdrawal due to wind suction It is also important to note that the truss design will be performed by the truss designer using the loading and geometry provided by the building designer. Guidelines for handling, bracing, and installing metal plate connected wood trusses are contained in the Building Component Safety Information (BCSI) booklet published jointly by TPI and WTCA. The truss bracing design for this building should take into account the bottom chord and compression web lateral restraint requirements shown on the truss design drawings, as well as the on center spacing of the trusses.

74 APPENDIX A FRAME STIFFNESS FRAME EAVE REACTION POST DESIGN

75 A.1 Fr ame Stiffness LOADING ON FRAME FRAME DEFLECTION FROM THE APPLIED 100 LB HORIZONTAL EAVE LOAD (Eave Deflection = in) Back