The Analysis of Offset Diaphragms and Shear Walls

Transcription

1 Presentation based on: Webinar Presentation, June 5, 2014: The nalysis of Offset Diaphragms and Shear Walls Presentation updated to 2012 I, SE 7-10 opyright McGraw-Hill, I and the Wood Products ouncil y: R. Terry Malone, PE, SE Senior Technical Director rchitectural & Engineering Solutions terrym@woodworks.org

2 Outline / Learning Objectives asic Information Discuss boundary elements, complete lateral resisting load path requirements, related code sections, and how to establish complete lateral load paths across areas of discontinuity. Discuss an analytical method used for the analysis Discuss an analytical method used for solving complex diaphragms and shear walls using Transfer Diaphragms and the Visual Shear Transfer Method. Horizontally offset Diaphragms Review the analysis of flexible offset diaphragms consisting of structural wood panel sheathing or un-topped steel decking. In-plane and out-of-plane offset shear walls Review the analysis and effects of horizontally out-of-plane and in-plane offset shear walls.

3 omplete Example with narrative and calculations

4 Mid-rise Multi-family Marselle ondominiums 5 stories of wood over 6 stories concrete Structural Engineer engineer: Yu & Trochalakis, PLL (podium) 2 above grade Photographer: Matt Todd Photographer

5 Mid-rise Multi-family Lds. Discontinuous struts Longitudinal ant. SW SW SW Lds. Discontinuous chords Transverse SW SW SW SW SW SW SW No exterior Shear walls Flexible, semi-rigid, or rigid???

6 Vertically offset Diaphragms? Openings in diaphragm Offsets in the diaphragm and walls Harrington Recovery enter Structural engineer: Pujara Wirth Torke, Inc. Photographer: urtis Walz

7 Presentation ssumptions Flexible wood sheathed or un-topped steel deck diaphragms (an also apply to semi-rigid and rigid diaphragms) Loads to diaphragms and shear walls Strength level or allowable stress design Wind or seismic forces. The loads are already factored for the appropriate load combination. ode and Standards: SE 7-10 Minimum Design Loads for uildings and Other Structures 2012 I 2008 SDPWS- Special Design Provisions for Wind and Seismic nalysis and Design references: The nalysis of Irregular Shaped Structures: Diaphragms and Shear Walls- Malone, Rice Woodworks-The nalysis of Irregular Shaped Diaphragms Design of Wood Structures- reyer, Fridley, Pollock, obeen SEO Seismic Design Manual, Volume 2 Wood Engineering and onstruction Handbook-Faherty, Williamson Guide to the Design of Diaphragms, hords and ollectors-nse

8 asic Information oundary Elements omplete Load Paths Method of nalysis

9 Diaphragm oundary Elements Fundamental Principles: shear wall is a location where diaphragm forces are resisted (supported), and therefore defines a diaphragm boundary location. Note: ll edges of a diaphragm shall be supported by a boundary element. 1 2 Strut SW1 Strut Diaphragm 1 oundary (typical) hord Diaphragm 2 oundary (typical) Diaphragm 1 Diaphragm 2 hord SW3 ollector Diaphragm oundary Elements: hords, drag struts, collectors, Shear walls, frames oundary member locations: Diaphragm and shear wall perimeters Interior openings reas of discontinuities Re-entrant corners. Diaphragm and shear wall sheathing shall not be used to splice boundary elements. ollector elements shall be provided that are capable of transferring forces originating in other portions of the structure to the element providing resistance to those forces. 3 Note: Interior shear walls without a collector or a complete alternate load path are NOT LLOWED! hord SW2 Strut Required for Seismic and wind

10 Strut SW1 1 Support Multiple offset diaphragm What does this mean? Strut/chord Strut /chord E ollector Strut (typ.) 2 SW5 Strut 3 ollector (typ.) ollector (typ.) Open 4 Strut SW2 Strut chord Strut/chord F SW6 ollector (typ.) Strut/chord Strut/chord ollector Offset SW3 strut SW4 omplete ontinuous Lateral Load Paths ollector (typ.) Strut chord D MRF1 Support nalysis: SE7-10 Sections: Design shall be based on a rational analysis t diaphragm discontinuities such as openings and re-entrant corners, the design shall assure that the dissipation or transfer of edge (chord) forces combined with other forces in the diaphragm is within shear and tension capacity of the diaphragm.

11 Strut SW1 1 Strut/chord Strut /chord Discont. diaph. chord Support ollector Strut (typ.) 2 SW5 ollector (typ.) Discontinuous diaphragm 5 chord 3 Strut ollector (typ.) Open Strut SW2 Strut chord E Strut/chord F Discont. diaphragm 4 chord SW6 Strut/chord ollector SW3 ollector (typ.) ollector (typ.) Strut/chord SW4 Strut chord D MRF1 Discont. diaphragm chord Support Discontinuous diaphragm chord/strut SE7-10 Section 1.4-omplete load paths are required including members and their splice connections omplete ontinuous Lateral Load Paths

12 Strut SW1 1 Support Offset shear walls 2 Strut/chord E ollector Strut /chord Strut (typ.) SW5 Strut 3 ollector (typ.) ollector (typ.) Open 5 Strut SW2 Strut chord Strut/chord F SW6 Strut/chord ollector SW3 ollector (typ.) ollector (typ.) Strut/chord SW4 Strut chord D MRF1 Support 4 Offset shear walls and struts SE7-10 Section 1.4-omplete load paths are required including member and their splice connections omplete ontinuous Lateral Load Paths

13 Strut SW1 1 Support Strut/chord E ollector Strut /chord Strut (typ.) 2 SW5 Strut 3 ollector (typ.) ollector (typ.) Open 5 Strut SW2 Strut chord Strut/chord F Opening in diaph SW6 Strut/chord ollector SW3 ollector (typ.) Vertical offset in diaphragm ollector (typ.) Strut/chord SW4 Strut chord D MRF1 Support 4 Design: I Openings in shear panels that materially effect their strength shall be fully detailed on the plans and shall have their edges adequately reinforced to transfer all shear stresses. omplete ontinuous Lateral Load Paths

14 asic Information oundary Elements omplete Load Paths Method of nalysis

15 Method of nalysis The Visual Shear Transfer Method + Symbol for 1 ft x 1 ft square piece of sheathing in static equilibrium (typ.) FY Lds. +M + - FX Positive Direction + - Transverse Direction (shown) Shears pplied to Sheathing Elements Unit shear acting on sheathing element (plf) Unit shear transferred from the sheathing element into the boundary element (plf) Shears Transferred Into oundary Elements

16 + - T Resisting wall (+) shears Strut in comp. Strut Forces Strut in tension Resisting wall (+) shears Positive sign convention Support Positive diaph. shear elements SW (-) SW 2 Pos. Diaphragm.L. w=uniform load 1 2 (-) SW + Diaphragm shear transferred into boundary element (typ.) + - Maximum moment 1 ft. x 1 ft. square sheathing element symbol at any location in the diaphragm. T SW asic Shear Diagram - SW (-) (-) Neg. Shear Distribution Into a Simple Diaphragm The Visual Shear Transfer Method Strut in ompr. Resisting wall shears (+) Strut in tension Support T Strut Forces Negative diaph. shear elements ll edges of a diaphragm shall be supported by a boundary element (chord, strut, collector) or other vertical lateral force resisting element (shear wall, frame).

17 Introduction to Transfer Diaphragms and Transfer reas Transfer Diaphragm hord (support) sub-diaphragm Transfers local forces out to primary chords/struts of the main diaphragm. T ollector TD1 TD Ratio=4:1 Maximum ollector ollector Framing members, blocking, and connections shall extend into the diaphragm a sufficient distance to develop the force transferred into the diaphragm. What does this mean? hord (support) T

18 1 2 3 Diaph..L. W ( plf) 4 Diaphragm chord SW Discontinuous diaphragm chord Diaphragm chord Diaphragm support Transfer rea The length of the collector is often determined by dividing the collector force by the diaphragm nailing capacity. (Wrong!) The collector is often checked for tension only. (Wrong!) ompression is rarely checked. Diaphragm chord Longitudinal ollector Typical callout MST14 tie strap x 10-0 with (xx) 10d nails over 2x flat blocking. Lap 2-8 onto wall. Transfer Diaphragm Members and Elements SW Drag strut Diaphragm support

19 SW Support SW Main chord This force must be transferred out to the main chords. complete load path is required. Disrupted chord Transfer area 1 2 Resisting forces ollector Rotation of section Resisting forces Transfer area without transverse collectors Transfer Mechanism 3 Disrupted chord Discontinuous diaphragm chord hord T Strut hord/ollector Transfer Diaphragm ( eam) TD1 ollector Full depth Support SW 2 3 hord/ollector NOTE: ollector must extend the full depth of the transfer diaphragm Main chord Transfer using beam concept

20 1 hord 2 (TD support) 3 Main chord T(a) V=, Shear = V LTD DTD -75 plf - SW vnet=+300-(75)= +225 plf vnet =+225 (75)= +150 plf The transfer diaph. aspect Ratio should be similar to the main diaphragm. hord force at discontinuity Disrupted chord vnet=+300+(250)= +550 plf No outside force is changing the basic diaphragm shear in this area T ollector +500 plf TD1 vnet =+225 +(250) = +475 plf ollector (TD support) TD depth DTD ollector Transfer diaphragm length Main chord +300 plf plf plf asic Shear Diagram at transfer diaphragm LTD asic Procedure Method by Edward F. Diekmann T T No outside force is changing the basic diaphragm shear in this area + Subtract from basic shears +250 plf a b dd to basic diaphragm shears T(b), Shear = V V= LTD LTD DTD Transfer Diaphragm Shears nalogous to a beam with a concentrated Load. vnet= (250) = 550 plf Net shear asic diaph. shear TD shears

21 Direction of shear transferred into collector plf +150 plf + + ollector plf +475 plf Net shear Net direction of shears acting on collector Place the net diaphragm shear on each side of the collector Place the transfer shears on each side of the collector Sum shears on collector (based upon direction of shears transferred onto collector). Shear left= = +325 plf 325 plf 325 plf Lcollector Note: The net shears will not always be equal. Dir. of force on collector Shear right= =+325 plf ollector force=area of shear diagram Fcollector=( )(Lcollector) 2 Resulting net shear diagram on collector Shear Distribution Into The ollector

22 1 Transfer Diaph. depth hord, strut or shear wall 2 F( a) R L Support R 1 Transfer Diaph. depth hord, strut or shear wall 2 F( a) R b Support R F Transfer Diaphragm TD1 Discont. ollector hord / strut hord, strut or shear wall Support F( b) R L a b L Transfer Diaph. length F R Discont. F hord / strut Transfer Diaphragm TD1 hord, strut or shear wall a b Support F( L) R b L Transfer Diaph. length R F Simple Span Transfer Diaphragm nalogous to a simple span beam with a concentrated load Propped antilever Transfer Diaphragm nalogous to a propped cantilever beam with a concentrated load Simple Span and Propped antilever Transfer Diaphragms

23 Diaphragms with Horizontal Offsets

24 Example 1-Diaphragm with Horizontal End Offset Transverse Loading w=200 plf Support Diaph..L. Diaph. chord 35 SW 1 ollector TD chords TD1 ollector TD chords plf F2 M=0 35 SW 2 50 M2 ft.-lb F2 lb /R=2.5:1 25 RL lb F2 Diaph. chord ollector Free body for F2 15 Support Support RL lb Discontinuous diaphragm chord V2 lb V3 lb Diaph. chord Sign onvention Support RR lb

25 Transfer Diaphragm and Net Diaphragm Shear v1 plf v2l plf v2r plf asic shear diagram v3 plf Diaph..L. V lb V v= plf DTD SW 1 35 V=asic shear - TD shear plf (Net shear) 15 F2 RL lb v= Net shear> 2x asic shear No net change Net change occurs in TD F Pos. Neg. TD shear diagram v4 plf SW 2 Vc v= plf DTD V lb + - Sign onvention RR lb 80 No net change 4 Net TD shears (basic shear +/- transfer diaph. shears)

26 F2 +v2 +F lb x1 x2 -v3 -F lb v1 v2l F3 FL 0 plf SW 1 SW 2 F2 F2 T FL Support 15 F F T 0 plf Diaph..L. Longitudinal hord Force Diagrams + - Sign onvention Support 4

27 Net shear Net shear SW 1 F=6000 lb T F Sign onvention F=6000 lb (this is not an insignificant force.) F Transverse ollector Force Diagrams

28 357.2 plf x1 x2 x3 x4 Special nailing along 320 plf 285 plf plf 42.9 plf 37.1 plf 70 plf collectors Sum of shears to collector or highest boundary nailinggreater of plf plf 150 plf asic shear diagram 70 plf Transfer diaphragm oundary (Typ.) 4/6/12 6/6/12 6/12 U ase I 6/12 U ase I 6/12 U ase I allout all nailing on drawings: Standard diaphragm nailing oundary nailing ollector nailing Diaphragm boundary heck the shear capacity of the nailing along the collector /6/12 Transfer area oundary (High shear area) oundary locations Diaphragm Nailing allouts

29 Example 2-Diaphragm with Horizontal End Offset Longitudinal Loading 5 SW 2 10 Diaph..L. Drag strut 40 plf 160 plf plf 35 hord Diaphragm 1 Discontinuous Drag strut ollector and TD chords Transfer diaphragm TD1 ollector ollector and TD chords Diaphragm 2 50 hord plf Discontinuous Drag strut 200 plf Drag strut SW Pos. direction + - 4

30 V Vnet=vsw-vdiaph SW 2 10 v - 35 Diaphragm 1 (Net shear) Diaphragm 2 Neg. Diaph..L. 1 V 15 (Net shear) 2 3 V 2 Pos. v + v Transfer area Vnet=vsw-vdiaph 15 SW 1 4 Transfer Diaphragm and Net Diaphragm Shear Pos. direction + -

31 F2 SW SW 2 Fend Fstart 35 F2 Long F2 Trans F2 Long F F3 SW 15 SW 1 F2 Trans HEK: Fstrut Fchord Pos. direction Longitudinal and Transverse ollector/strut Force Diagrams

32 Offset Shear Walls SW 1 ollector ollector ollector SW 2 Out-of-plane Offsets In-plane Offsets

33 Out-of-Plane Offset Shear Walls ssumed to act in the Same Line of Resistance Drag strut SW ollector Transfer area ollector ollector Offset walls are often assumed to act in the same line of lateral-force-resistance. alculations are seldom provided showing how the walls are interconnected to act as a unit, or to verify that a complete lateral load path has been provided. Discont. drag strut Offset SW Loads ollectors are required to be installed to transfer the disrupted forces across the offsets. Discont. drag strut SW Drag strut ollector ollector ollector Where offset walls occur in the wall line, the shear walls on each side of the offset should be considered as separate shear walls unless provisions for force transfer around the offset are provided. Typical mid-rise multi-family structure at exterior wall line heck for Type 2 horizontal irregularity Re-entrant corner irregularity

34 Longitudinal Loading Offset transverse walls In-line transverse walls ant. No exterior Shear walls?? Flexible, semi-rigid, or rigid???

35 Loads 1 SW3 2 SW1 TD1 TD2 3 SW4 SW2 TD3 Higher shears and nailing requirements SW5 Multi Story, Multi-family Wood Structure Diaphragm stiffness changes I1 I2 I3

36 Example 3-Diaphragm with Horizontal End Offset Longitudinal Loading-Offset Shear Walls 200 plf hord 35 SW 1 8 Drag strut SW Offset SW Drag strut 200 plf Drag strut is discontinuous hord collectors TD1 ollector Drag strut hord collectors 12 Drag strut 80 ssumptions: 1. ssume shear walls at grid lines and act along the same line of lateral-forceresistance. 2. ssume the total load distributed to grid lines and /= wl/2. Offset SW 50 hord SW 3 Drag strut SW Support Pos. direction + - Support

37 Total Shear to Shear Walls (ssumed) Vsw2=wL/2 plf Vsw1, sw3, sw4=wl/2, vsw= V1,3,4/(Lsw1+Lsw3+Lsw4) plf V SW 2 10 V V 40 plf 160 plf 200 plf 35 Pos. Fend F2 50 SW 1 8 V 17 Vnet=Vsw-Vdiaph F2 200 plf 200 plf F2 SW 3 8 Neg. V V V SW Determine Force transferred Into Transfer Diaphragm Pos. direction + - asic Diaphragm Shears and Transfer Diaphragm Shear

38 Vnet sw SW 2 V V 35 V=asic shear - TD shear plf (Net shear) Pos SW 1 Vnet sw 15 V=asic shear - TD shear plf (Net shear) No net change Net change in TD 1 2 Net Diaphragm Shears 3 No net change Neg. 8 SW 3 15 SW 4 Vnet sw V 80 V V Pos. direction + - Vnet sw 4

39 SW 2 - Net shear Net shear (TD tension chord and Diaph.2 compression hord) F2 Special nailing F3 Diaphragm 2 F3 8 SW SW3 15 SW 4 F2 -v 2 3 Net shear x2 -F +F +v x1 So far, so good Transverse ollector Force Diagrams Pos. direction + -

40 F2 Fend 5 SW F3 80 F4=+xxx lb (Error) Fstart Vnet sw Fend F2 F= F2 Note: Neither force diagram closes to zero, therefore error. Notice that they do not close by the same amount. 8 SW 1 Vnet sw Vnet sw SW SW 4 Vnet sw F3 Fstart Fend 80 Fstart F4 = -xxx lb (Error) Longitudinal Strut Force Diagrams Pos. direction + -

41 SW 2 Revised forces alculated forces 4600 lb The shear wall shears needs to be lower in order to move the force diagram in this direction Line needs to move in this direction The shear wall shears need to be higher in order to move the force diagram in this direction Load distribution needs to increase towards line /. Increase the load to / by the amount off +/-. SW 1 Line needs to move in this direction 15 SW 3 SW lb Pos. direction + - djusted Longitudinal Strut Force Diagrams (8% increase to /) [mount shifted to / depends on the offset to span ratio of the transfer diaphragm]

42 In-plane Offset Shear Walls

43 Example 4-In-plane Offset Segmented Shear Wall -with Gravity Loads VHdr=450 lb DL=150 plf 2000 lb Hdr lb No hold down (option 1) Hold-down (option 2) 4 ollector lk g. or rim joist Nail shtg. To each 2x stud 12 SW1 DL=250 plf SW2 8 Wd VHdr=960 lb Sill Hdr/collector Wd Sill D 6 1 Section does not comply with the required aspect ratio for a perforated or FTO shear wall. SE 7 Table Type 4 vertical irreg.- in-plane discontinuity in the LFRS

44 Ends of wall panels do not line up. Requires special nailing of sheathing into stud below. Requires same number of studs above and below with boundary nailing each stud Solid blocking required Hold down Nailing found in field was 12 o.c. No hold-down below Photo-In-plane Offset Segmented Shear Walls Hold down

45 2000 lb w=230 plf (incl. wall DL) VHdr=450 lb 5000 lb lb Rim joist lb 1080 lb 330 plf (incl. wall DL) ver.=250 plf lb 8 Pos. direction lb +450 lb 3370 lb 5000 lb Wall and Transfer Diaphragm Shears SW1 Upper Shear Wall Sign onvention plf 1260 lb (-157.5) 1260 (-157.5) (+7.5) (-127.5) TD shears-lbs. (plf) 1080 ollector SW Lower Shear Wall (+202) + shears lb 9700 lb 1620 lb (+202) - shears 8 VHdr=960 lb plf asic Shear

46 2000 lb Roof 2000 lb Roof SW (8)+450= SW lb 1 T 8 2 nd floor Rim joist VHdr=990 lb 3000 lb 8 2 nd floor Rim joist 1 + T SW Depth TD SW Depth TD T T lb 9700 lb 2490 lb lb Vertical ollector Forces Horizontal ollector Forces ollector Force Diagrams Pos. direction + - Sign onvention

47 Questions? This concludes The National ouncil of Structural Engineers ssociation Webinar Presentation-June 5, 2014 The nalysis of Offset Diaphragms and Shear Walls R. Terry Malone, P.E., S.E. Senior Technical Director WoodWorks.org Prescott Valley, rizona ontact Information: Technical or design assistance - terrym@woodworks.org ook related questions - malone.rice.book@gmail.com WoodWorks woodworks.org