The Wood Products Council is a Registered Provider with The American Institute of Architects Continuing Education Systems (AIA/CES). Credit(s) earned on completion of this program will be reported to AIA/CES for AIA members. Certificates of Completion for both AIA members and non-aia members are available upon request. High Load Diaphragm Design for Panelized Roofs A Cost Effective Solution for Large Low Slope Roofs Lisa Podesto, PE Technical Director This program is registered with AIA/CES for continuing professional education. As such, it does not include content that may be deemed or construed to be an approval or endorsement by the AIA of any material of construction ti or any method or manner of handling, using, distributing, or dealing in any material or product. Questions related to specific materials, methods, and services will be addressed at the conclusion of this presentation. Learning Objectives Copyright Materials This presentation is protected by US and International Copyright laws. Reproduction, distribution, display and use of the presentation without written permission of the speaker is prohibited. At the end of this program, participants will be able to: 1. Highlight ht important t high h load diaphragm detialing. Explore sub diaphragm design techniques 3. Introduce the collective chord modification theory 4. Discover high load effects on diaphragm deflection The Wood Products Council 010
Overview Rigid vs. Flexible Wood Diaphragms Calculation l Methods Rigid vs. Flexible High Load Diaphragm Table Sub-diaphragms Collective Chord design Diaphragm Deflection Diaphragm Design Example Flexible, Rigid and Semi-Rigid Diaphragms Diaphragm (Plan View) Flexible Diaphragm load is distributed to shear walls by tributary area Rigid Diaphragm load is distributed to shear walls by wall stiffness and torsion Semi-rigid Between flexible and rigid, dependent on stiffness w L/ L/
Flexible Diaphragm Rigid All walls Identical w w sw sw Flexible.5wL.50wL.5wL Rigid (no Torsion).333wL.333wL.333wL di L/ L/ L/ L/ Flexible vs. Rigid Flexible, Rigid or Semi-Rigid w Which do you have? Stiffness K K K Prescribed flexible Calculated flexible Flexible.5wL.50wL.5wL Prescribed rigid Rigid (no Torsion).40wL.0wL.40wL Else, semi-rigid L/ L/
Prescribed Flexible Diaphragm Prescribed Flexible Diaphragm In many cases wood diaphragms are permitted to be idealized as flexible ASCE 7-05 Sec. 1.3.1.1 exempts one- and two-family dwellings from rigid diaphragm analysis. CBC 007 Sec. 1613.6.1 Diaphragms constructed of wood structural panels. Shall also be permitted to be idealized as flexible, provided all of the following conditions are met: CBC 007 Sec 1613.6.1 adds following text to the ASCE provisions. Prescribed Flexible Diaphragm Calculated Flexible Diaphragm 1. Concrete topping is non-structural t and is less than 1.5 in.. Each line of vertical elements of LFRS complies with allowable story drift of ASCE7-05 Table 1.1-1 3. Vertical elements of LFRS are light framed walls sheathed with wood structural panels or steel sheets 4. Cantilever portions of the diaphragm designed in accordance with Sec. 305..5 ASCE 7-05 Sec. 1.3.1.3 Diaphragms are permitted to be idealized as flexible when: The diaphragm deflection is more than two times the average story drift of adjoining shear walls DIAPHRAGM x SHEARWALLS
Calculated Flexible Diaphragm Prescribed Rigid Wood Diaphragms (CBC 305..5) (Average Deflection) SHEARWALLS DIAPHRAGM Open front Cantilevered diaphragms The longer the diaphragm the more likely it is to calculate as flexible Semi-Rigid Diaphragm Deflections (4-term eqn s) Semi-rigid results in force distribution somewhere between rigid and flexible Thus, an envelope approach can be used where the both rigid and flexible models are used and the highest forces from each are selected Shear Wall (IBC 305.3.) 8 3 vh vh 0. 75he EAb G t v v n h b Diaphragm (IBC 305..) 3 5vL vl ( cx ) 0.188Len 8 EAb 4 G t b da v v APA L350 (www.apawood.org) has comprehensive listing of input parameters and examples
Deflections (4-term equations) Diaphragm (CBC 305..) Total b v n c bending shear nail slip chord connection slip 3 5vL vl ( cx ) 0.188Len 8 EAb 4 G t b v v 0.5 v L 1000Ga SDPWS unblocked and blocked Deflections (4-term equations) Shear Wall (CBC 305.3.) Total b v n a bending shear nail slip anchorage slip 8vh 3 vh 0. 75 he EAb G t v v v h 1000Ga h d b n SPDWS APA L350 (www.apawood.org) has comprehensive listing of input parameters and examples a Deflection (3-term eqn.) Diaphragms and Shear Walls Diaphragm (SDPWS 4..) Deflection of Unblocked Diaphragms is.5 times the deflection of blocked diaphragm. 5 3 vl 0.5 vl ( c X ) 8EAW 1000G W a If framing members are spaced more than 4 o.c., testing indicates further deflection increase of about 0%, or 3 times the deflection of a comparable blocked diaphragm. (This is based on limited testing of the diaphragm by APA) G a values for blocked and unblocked diaphragms
Large & High Load Diaphragms How to design for lateral loads High Load Diaphragm Design Table 4.B in SDPWS referenced in 009 IBC Based on APA full scale testing APA report 138 ES 195 now incorporated in code 3x normal diaphragm shear values 1800 plf ASD for seismic 50 plf - ASD for wind 40% increase for wind loads All edges are blocked 8-10 panel width with purlins at each end Utilizes multiple rows of nails Fastener Pattern Figure 4C in 008 SDPWS for use with High-Load Diaphragm Table 4 nominal three lines 3 nominal two lines
Avoid Nail Splitting 4..7.1 notes High-Load Diaphragm Table Loads were limited by lumber splitting. x4 X4 3X4 Slide provided by John Lawson, S.E., Kramer and Lawson Clarification to High Load Diaphragm Table Notes to High Load Diaphragm Table Intermediate Nailing Maximum spacing 1 o.c. Exception: 6 ocfor o.c spans greater than 3 o.c. Intermediate Member Size x framing allowed at intermediate framing members where fasteners are 1 or 6 oc o.c. The shear values in the table are for cases 1 and The shear values are applicable to cases345 3,4,5 and 6 provided fasteners at all continuous edges are spaced in accordance with the boundary fastener spacing
Diaphragm Layout Cases Clarification to High Load Diaphragm Table Load Perpendicular to Cont. Edge Boundary Nailing Intermediate Nailing Boundary, edge and intermediate nailing (case 1 and ) Continuous Panel Edge Nailing (Panel Edge Nailing- for case 1, Boundary Nailing - for case 3,4,5 and 6) Panel Edge Nailing Note: Framing omitted for clarity Load Parallel to Cont. Edge Clarification to High Load Diaphragm Table Seismic Diaphragm-to-Wall Anchorage Forces Boundary, edge and intermediate t nailing (case 3,4,5,6) Boundary Nailing Field Nailing Edge Nailing (use boundary nailing at continuous edge per note d.) Note: Framing omitted for clarity
Sub-diaphragm Concept Advantages Sub-diaphragm is a portion of a larger wood diaphragm designed to anchor and transfer local forces to primary diaphragm struts and main diaphragm (006 IBC 30.1) Eliminates the need for long-span design of walls for out-of-plane bending Transfers anchorage forces to main members, thus reducing the number of connections required to fulfill continuous cross tie requirements. Members used as cross-ties are typically better suited for accommodating the necessary connections Reduces cost the larger the roof the greater are the savings provided by the use of sub-diaphragms. How to design for lateral loads Normal Diaphragm Design Connections required for each line of sub-purlins How to design for lateral loads Sub-Diaphragm Design Typical load transfer Lateral Load = 1800 connections Lateral Load = 10 connections Aspect ratio.5:1 max.
How to design for lateral loads Normal Diaphragm Design Typical Load Transfer Lateral Load Connections required for each line of purlins Subdiaphragm (Typical) max aspect ratio =.5:1 Subdiaphragm is designed the same as a diaphragm Sub-diaphragm Summary Reference Use of the the subdiaphragm concept often reduces number of connections Reduces cost of wood roofs APA document (Z350) provides connection details and has tables to aid the designer Examples: Sub-diaphragms Continuous cross-ties Anchorage details APA Publication Z350
Reference Examples: Diaphragms Design Sub-diaphragm Design Deflection Calculations APA Publication L350 How to design for lateral loads Traditional Chord Design Works well on small and moderate size buildings Lateral Load How to design for lateral loads Collective Chord Design More economical on large buildings Realistic way to model chord action Lateral Load X How to design for lateral loads Traditional Chord vs. Collective Chord Based on 8 oc tie spacing Y X Y Traditional Collective 10 160 19 kips 400 400 40 kips 750 1100 11 kips 6kips 6. max 4.5 kips max 9.0 kips max Results of Example done by Kramer and Lawson
How to design for lateral loads Multiple Nailing Zones Economizes on material and time Less nails Less nailing time 1 4 3 1 How to design for lateral loads Diaphragm Deflection Calculations Two Equations to choose from 006 IBC traditional equation 005 AF&PA NDS simplified equation **suggested you use this equation** Collective Chord Modification Reduces diaphragm deflection calculations Complicates equation for moment of inertia See John Lawson s s paper for resulting equation Multiple nailing zones More accurate deflections when taken into account Using virtual work method, equation is derived for you in John Lawson s paper
How to design for lateral loads High Load Diaphragm Design Example Calculation Methods Resources/Examples High hload ddiaphragm CBC table 306.3.3 & Diaphragms and Shear Walls Design/Construction Guide -APA form L350A Sub-Diaphragm Diaphragms and Shear Walls Design/Construction Guide -APA form L350A Lateral Load Connections for Low-Slope Roof Diaphragms APA Form No. Z350A Collective Chord Thinking Outside the Box: New approaches to very large flexible diaphragm by John Lawson Diaphragm Deflection Thinking Outside the Box: New approaches to very large flexible diaphragm by John Lawson Design Criteria 19 x 10 tilt-up building Panelized Roof System 8 30 ft high wall with 4 ft parapet Check for seismic load only Importance Factor 1.0 Seismic Category D(S S = 168 1.68, S 1 = 06) 0.6) NOTE: The example is simplified to illustrate specific points and does not include all load combinations and all design checks otherwise required. Design Process Part A. Diaphragm Design Diaphragm Loads (Seismic only) Diaphragm Analysis (Transverse) Structural Panel and Fastener Pattern Selection (Transverse) Diaphragm Analysis (Longitudinal) Structural Panel and Fastener Pattern Selection (Longitudinal) Diaphragm Loads Vertical Loads DL Roof = 10 psf LL Roof = 30 psf DL Wall = 100 psf Seismic Loads C S = S DS /(R/I) C S max = S D1 /T(R/I) C S min = 0.5S 1 /T(R/I) S DS = 1.1 S D1 = 0.6 R = 4, I = 1 SDC Category D C S =1.1/(4/1) = 0.8 > 0.01 C S max =0.6/.3(4/1) = 0.50>0.8 C Smin =0.5x0.6/(4/1) = 0.075<0.8 W ROOF = 19 x 10 x 10 = 30,400 lbs (16.3%) W WALL = (30/+4) x 100 x x (19 +10) = 1,185,600 lbs (83.7%) W TOTAL = 30,400 + 1,185,600, = 1,416,000, lbs V TOTAL = 0.8 x 1,416,000 = 396,480 lbs V TRANSVERSE = (10 x 10 + 19 x 100 x ) x 0.8 = 1,400 lbs (plf) V LONGITUDINAL = (19 x 10 + 19 x 100 x ) x 0.8 = 1,600 lbs (plf) V = C S W=0.8W
Diaphragm Loads (Transverse) Diaphragm Layout Cases case 4 w = 1,400 plf case 1 A B C D 48 19 48 48 48 E Sub-purlin Purlin 3 Girder N 4 Diaphragm Analysis (Transverse) (Case 4) Load w: w = 1400 plf x 19 CASE 4 Shear V: CASE V 400 10 max = 1,400 x 19 / = 134,400 lbs v max = 1,10 plf v max = 134,400 / 10 = 1,10 plf v 40 = (134,400 40x1,400)/10 = 653 plf v 40 = 653 plf v 7 = (134,400 7x1,400)/10 = 80 plf = 80 plf v 7
1,10 plf 653 plf @ 40 80 plf @ 7 High Load Diaphragm Table (Case 4) v = 1,10plf 10 (case 4) 1 A B C D E 19 48 48 48 48 A D C D A 640/=130 3 N 4 High Load Diaphragm Table (306.3.) v = 653 plf (case 4) Panel and Nailing Pattern Selection A v max = 134,400 / 10 = 1,10 plf v max = 1,10 plf < 130 plf case and 4 19/3 Rated Sheathing Exposure 1 4x Framing 3 rows of 10d Common Nails @ 4, 4, 1 1340/ = 670 The table gives shear values for Case 1 and. For cases 3,4,5,6 values are applicable providing fasteners at all continuous edges are spaced in accordance with boundary fastening spacing. B v 40 = (134,400 40x1,400)/10 = 653 plf case D adjust edge spacing to 4 o.c. case 4 C v 7 = (134,400 7x1,400)/10 = 80 plf case and 4 v 40 = 653 plf > 670 plf 19/3 Rated Sheathing Exposure 1 3x Framing rows of 10d Common Nails @ 4, 6, 1 (adjusted 4,4,1 ) v 7 = 80 plf < 30 plf 19/3 Rated Sheathing Exposure 1 x Framing 1 row of 10d Common Nails @ 6, 6, 1
Panel and Nailing Pattern Selection (Transverse) Diaphragm Loading (Longitudinal) 1 A B C D 48 19 48 48 48 A D C D A E case 1 A B C D E 19 48 48 48 48 W= 1,600 plf N 3 4 4x Fram ming 3 rows of 10d Comm mon Nails @ 4, 4, 1, 4, 1 3x Fra aming rows of 10d @ 4 x Framing 1 rows of 1 0d @ 6, 6, 1, 4, 1 3x Fra aming rows of 10d @ 4 4x Fram ming 3 rows of 10d Comm mon Nails @ 4, 4, 1 N 3 4 Capacity 1,90 plf 650 plf 30 plf 650 plf 1,90 plf Diaphragm Analysis (Longitudinal) Panel & Fastener Pattern Selection Load w: x w = 1600 plf 10 B v max = 96,000 / 19 = 500 plf v max = 500 < 650 < 1,90 plf 19/3 Rated Sheathing Exposure 1 3x Framing rows of 10d Common Nails @ 4, 6, 1 Shear V: C v 3 = (96,000 3x1,600)/19 = 33 plf v 7 = 33 plf < 30 plf 19/3 Rated Sheathing Exposure 1 x Framing 1 row of 10d Common Nails @ 6, 6, 1 V max v max = 1,600 x 10 / = 96,000 lbs v max = 500 plf = 96,000 / 19 = 500 plf v 3 = (96,000 3x1,600)/19 = 33 plf v 3 = 33 plf
Panel & Fastener Pattern Selection Panel & Fastener Pattern Selection (Combined) 1 A B C D 48 19 48 48 48 B E 1 A B C D 19 48 48 48 48 E 3 4 3x Framing rows of 10d @ 4, 6, 1 C x Framing 1 rows of 10d @ 6, 6, 1 3x Framing rows of 10d @ 4, 6, 1 B Capacity 30 plf 650 plf N 3 4 4x Framing Nails 0d Common v 3 rows of 1 @ 4, 4, 1 A g 3x Framing rows of 10d @ 4, 6, 1 1 D C x Framing 1 rows of 10d @ 6, 6, 1 0d @ 4, 4, 3x Framing rows of 1 3x Framing rows of 10d @ 4, 6, 1 B D n Nails 4x Framing 3 rows of 10d Common @ 4, 4, 1 v A N High Load Diaphragm Fastener Pattern High Load Diaphragm Fastener Pattern D B 4 or 6 3 nominal two lines A Boundaries Intermediate 4 Other edges 4 nominal three lines
Design Example (Continued) Wall Anchorage Force Part B. Wall to Diaphragm Anchorage Anchorage Forces (Seismic only) Sub-diaphragm Analysis and Design (E- W) Wall anchorage to Sub-purlin (E-W) W ll h t S b li (E W) Cross-tie Load Transfer (E-W) Cross-tie Load Transfer (N-S) F P = 0.8 I S DS w p (ASCE 7-05 equation 1.11-1 ) F P = 0.80 x 1.0 x 1.1 x w p =.90 w p = 100 x 34 x 17/30 = 1,97plf F P = 0.90 x (100 x 19) = 1,734 plf > 400x1.1 > 80 plf Sub-diaphragm Depth L SUB E-W = 1,734 x 0/190 = 7 ft L SUB E-W = 1,734 x 8/190= 11 ft L SUB E-W = 1,734 x 4/190= 5.4 ft L SUB N-S = 1,734 x 8/650 = ft < 40 ft (girder spacing) E-W USE: 3 ft wide sub-diaphragm F TIE = 1,734x 4 = 6,940 lbs F TIE = 1,734 x 8 = 13,87 lbs F TIE = 1,734 x 40 = 69,360 lbs Sub-diaphragm Design (E-W) w = 1,734 plf Sub-diaphragm Design (E-W) 1 3 w = 1,734 plf Wall load for anchorage force = 1, 734 plf Length-to-width to = 40/3 = 1.5 < ½ (o.k.) Subdiaphragm Shear 1,084 plf < 1,90 plf (v=(wl/)/width =1,734x0/3 = 1,084) main diaphragm sheathing/nailing is adequate for subdiaphragm 4 48 48 48 48 19 A B C D E N Maximum chord force = 10,834 lb (T = wl /8x3 = 1,734 x 40 /(8x3), important to check combined tension-bending)
Wall Subpurlin Anchorage (E-W) Continuous Cross Ties 1 Subpurlins @ oc, use every other subpurlin to transfer wall forces into the sub-diaphragm (wall need not be checked for bending between anchors) 3 Large number of connections are required for just one line of sub-purlins 6,940 lb per subpurlin anchor F TIE = 1,734x 4 = 6,940 lbs 4 Fewer connections are required for one line of purlins. 48 48 48 48 19 A B C D E Sub-diaphragm Load Transfer (E-W) Sub-diaphragm Load Transfer (E-W) Continuity Ties 6,940 lbs 1,734x18/3=976 plf Typical Sub-diaphragm lf 1,734 pl 40' Subdiaphragm (Case E-W direction) 48 48 48 48 6,940 lbs 19 A B C D E 3'
Sub-diaphragm Load Transfer (E-W) Wall-to-Subpurlin Connection (Design for 7,000 lbs) Ties at 4-0 o.c. APA wood structural panel sheathing Tack weld hanger or provide Pneutek pins. Subpurlin Sub-purlin to Wall Connection Sub-purlin to Sub-purlin connection Diaphragm to wall anchorage using embedded straps shall be attached to or hooked around the reinforcing steel or terminated so as to directly transfer force to the reinforcing steel. (ASCE 7-05 1.11...5) Add steel box to hanger for compressive stress Steel channel Conc crete or CMU wall Anchorage Element Design Subpurlin-to-Subpurlin Continuity Tie Connection Strength design forces for steel elements of the wall anchorage system shall be 1.4 times the force otherwise required by this section Strap installed over sheathing (not shown) Purlin Subpurlin (ASCE 7-05 1.11...) Plan
Anchorage (E-W) Wall-to-Girder 4 tributary area, same force as wall-tosubpurlin connection 6,940 lb per subpurlin anchor Wall-to-Girder Connection Ledger/diaphragm chord (shown behind) Design for 7,000 lbs APA wood structural panel sheathing Concrete or CMU wall Girder (glulam shown) Wall-to-Girder Connection Design for 7,000 lbs APA Wood Structural Panel Sheathing Continuous Girder Ties (E-W) Continuity Ties Typical Sub-diaphragm Top mounted Girder hanger (glulam shown) 48 48 48 48 19 A B C D E
Continuous Girder Ties (E-W) Continuous Girder Ties (E-W) 6,940 lbs 976 plf f,734 plf 1 40' 69,400 lbs 1,734x18/4=976 plf Subdiaphragm (Case E-W direction) As load is transferred into the girder from the subdiaphragm, the axial load in the girder increase from 6,940 lb to 69,400 lb The girder-to-girder connection must resist 69,400 lb 6,940 lb 976 x 3 = 7,360 69,400 lb 69,400 lbs 976 x 3 = 7,360 6,940 lbs 976 plf 3' 6,940 lb 69,400 lb Girder-to-Girder Connection Design for 70,000 lbs Continuous Purlin Ties (N-S) 8 typical N-S continuity ties located at each purlin line (Typ.) Wood structural panel sheathing not shown for clarity Girder (glulam beam shown) Hanger Tension ties on both sides of girder 50,000 lbs. Use (10) 3/4" diameter bolts 75,000 lbs. Use (1) 1" diameter bolts 13,900 lb 1,734x8 =13,87 lb
Wall-to-Purlin Connection Design for 14,000 lbs Purlin-to-Purlin Continuity Tie Connection APA wood structural panel sheathing Inserts to provide approx. 1K 6" wide tension tie embossed to go over hanger APA wood structural panel sheathing Elevation Purlin (Typ.) Top-mount hanger Full length steel channel Glulam purlin Elevation Plan Wood structural panel sheathing not shown for clarity Course Evaluations In order to maintain high-quality learning experiences, please access the evaluation for this course by logging into CES Discovery and clicking on the Course Evaluation link on the left side of the page. We re here to answer your questions. This concludes The American Institute of Architects Continuing Education Systems Course WoodWorks! Lisa Podesto, P.E. Office: 530.596.4031 Cell: 530.50.7966 lisa@woodworks.org www.woodworks.orgwoodworks org