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Specifications OFFICE COPY 11IIIIIJY EiMmIzazimmannaniiiiimemimiin STRUCTURAL CALCULATIONS FOR ALDERBROOK APARTMENTS DECK REPLACEMENT C 13070 SW ASH AVE. W� TIGARD, OREGON .CIr U hi CC I o January 24, 2019 2VALIDITY OF PERMIT 4 Y THE ISSUANCE OF PERMIT 0 > � 3 _ BASED ON C;ON;sTRUCTJON 0 3 o DOCUMENTS AND OTHER (,) Q c u_ .74 S'`���D I p�t�Ffs�� ' DATA SHALL NOT PREVENT �. O o v; �G��� FF 0y ,,,,pig GC�DE-©F-FECI, ,..4FROM -0 >,z ` e •g, - EQUIR1NGrH CO' REC1fON 1.._ > 0 C I-- = 'D Ir F}RJ�. CAS f 2 t O 'S J -. a CIc ccQ OREGON v cD f 9' .W SpT21. �9 Q V L.L. a. � m � -tiq£1cep L. 4, IRENEWS: 12 31-2QI9 :. A►- DESIGN PARAMETERS: 2014 Oregon Structural Specialty Code DECK LOAD 7 psf DL 40 psf LL CONTENTS: _ _ SKETCHES SK-1 STRUCTURAL NOTES SN-1 — DECK FRAMING l to 7 • 6443 SW Beaverton-Hillsdale Hwy,suite 210•Portland,OR 97221 •ph:503203.8111 •fx:503.203.8122•www.wdyi.com (3) 0.22" DIA LEDGERLOK SCREWS AT 16" O.C. TO (E) RIM JOIST SISTER TO (E) FLOOR JOIST P.T. 2x10 WI 0.22" II DIA LEDGERLOK m SCREWS AT 16" 0 O.C. STAGGERED _N o TO (E) RIM JOIST x ao i I co (3) 0.22" DIA SIMPSON LUS26 c' LEDGERLOK I HANGER TYP SCREWS AT 16" 0.\-:_174 a TO (E) RIM JOIST _ __ __ __ __ \ , 1 ) I I I J AI16„ OC I o P. T. 3 1/8x12 GLB I I I I I I I IL _ TREX DECKING P.T. 3 1/8x12 GLB * \ SIMPSON ML26Z SIMPSON ML26Z TRANSFER ANGLE TRANSFER ANGLE 14' 6" 2ND FLR DECK FRAMING PLAN SCALE: 1/4"=1'-0" ,,c� D PROFFsnn QS+ I N F�v/9 Job Name: ALDERBROOK APARTMENTS .842 Date: 01/23/2019 ink o no Job No.: 19018 Drawn: GBB SOREGO 9� �v Client: T&H HOMEBUILDERS Sheet: Cyq£ z,, ‘o�a� SK-1 '7 t C rihrim y Structural -Civil Engineers 6443 SW Beaverton-Hillsdale Hwy,suite 210 Portland,OR 97221 RENEWS: 12-31-2019 ph:503.203.8111 fx:503.203.8122 www.wdyl.com (f-:)9rna 1Nhv STRUCTURAL NOTES • 01.0 GENERAL NOTES 1. These notes set minimum standards for construction. The drawings govern over the .-truct�lral 1`'ote3 to the extent shown. 2. Contractor shall verify all dimensions and conditions on drawings and in field. Norify owne's representative of any discrepancies. 3. Construction means, methods and all necessary temporary support prior to completion of vertical and lateral load systems is the sole responsibility of the contractor, 4. Compliance with all safety and OSHA requirements is the sole responsibility of the contractor. 5. All work shall be in compliance with 2014 edition of the"Oregon Structural Specialty Code" (OSSC) as amended by all other local codes, permits, and building department requirements that apply. 6. Where reference is made to ASTM,AISC,ACI or other standards,the referenced issue shall apply. 7. Details shown on the drawings are intended to apply at all similar conditions and locations. 8. Do not scale information from drawings. 06.0 WOOD FRAMING 1. All glue-laminated beams (GLB) shall be Douglas Fir 24F-V4 for simple span beams and 24F-V8 for beams with cantilevers. Beams shall be treated for exterior use. Beam appearance grade shall be industrial, except beams exposed to view shall be architectural. 2. All lumber species and grade to be as follows: Joists, beams and stringers (2x&4x) Pressure treated, Hem Fir#2 1AWPA UC2 3. Framing anchors,joist hangers, post caps, etc., shall be by'Simpson Strong-Tie'. Install per manufacturer's recommendations for tabulated maximum capacities with fasteners installed in all holes. Framing anchors attaching to pressure treated lumber shall be Z Max coated or hot dipped galvanized and attached with hot dipped galvanized (2.0 oz per square foot) or stainless steel nails or screws. Framing anchors installed at exterior locations exposed to weather are to be stainless steel with stainless steel fasteners. 4. All bolts for wood to steel or wood to wood connections and in manufactured connectors shall be ASTM A307, Grade A unless otherwise noted. Provide standard plate washers under all bolt heads and nuts in contact with wood. Use hot dipped galvanized washers in contact with pressure treated lumber. 5. All bolt holes in wood to be 1/16 inch larger than the bolt. Do not ream or oversize bolt holes. 6. Do not recess bolt heads or nuts unless shown on drawings. 7. Nails, bolts or lags in pressure treated lumber shall be hot dipped galvanized or stainless steel. tIIPROiFstt c� �,� o ���, Job Name: ALDERBROOK APARTMENTS Date: 01/23/2019 Q 1,6842 alb Job No.: 19018 Drawn: GBB •1GO Client: T&H HOMEBUILDERS Sheet: `4/ SN-1 -�y21. ,��o� qFL CO fl W D Y Structural -Civil Engineers 6443 SW Beaverton-Hillsdale Hwy,suite 210 Portland,OR 97221 RENEWS: 12-31-2019 ( oh:503.203.8111 fx:503.203.8122 www.wdvi.com nW110 umv rilWDY Structural . Civil Engineers Job Name: Alderbrook Apartments-Deck Replacement Job No: 19018 _ Sheet No: 1 Client: T+H Homebuilders Date: Jan 2049- B_Zr._ MC _ 2nd Floor Deck Replacement Plan I I I I 0 1 ' i 1 I l '4 i : J I 1— ; I e1-01,11 I I I I l 1 .ioisr 1 1 1 q I 7 ir''97----4 :t. , D cia,- 4,r:-A7`- • 14'-6" / y' Deck Loading: Trex Decking 4.0 psf Joists 2.8 Misc 0.2 DL= 7.0 psf LL= 40.0 psf (Residential) COMPANY PRO-JeG WDY, Inc Aldei brook Apartments %VoodVVorks® Portland, OR Job No. 19018 SOFIWARFFOR WOOD DIMON Jan.21,2019 13:30 Deck Joist.wwb Design Check Calculation Sheet Wood Works Sizer 10.4 Loads: • Load Type Distribution Pat- Location [ft] Magnitude Unit tern Start End Start End Loadl Dead Full Area 7.00(16.0") psf Load2 Live Full Area 40.00(16.0") psf Self-weight Dead Full UDL 2.2 pif Maximum Reactions (Ibs), Bearing Capacities (Ibs) and Bearing Lengths (in) : i I I Unfactored: Dead 24 24 Live 109 109 Factored: Total 132 132 Bearing: Capacity Joist 204 204 Anal/Des Joist 0.65 0.65 Load comb #2 #2 Length 0.50* 0.50* Min req'd 0.50* 0.50* Cb 1.00 1.00 Cb min 1.00 1.00 *Minimum bearing length setting used: 1/2"for end supports Deck Joist Lumber-soft, Hem-Fir, No.2, 2x8 (1-1/2"x7-1/4") Supports:All-Hanger Floor joist spaced at 16.0"c/c;Total length:4'-1.0';volume=0.3 cu.ft.; Service:wet; Lateral support:top=full, bottom=at supports; Repetitive factor:applied where permitted(refer to online help); Analysis vs. Allowable Stress and Deflection using NDS 2012 : Criterion Analysis Value Design Value Unit Analysis/Design Shear fv = 12 Fv' = 145 psi fv/Fv' = 0.09 Bending(±) fb = 121 Fb' = 1173 psi fb/Fb' = 0.10 Live Defl'n 0.01 = <L/999 0.13 = L/360 in 0.04 Total Defl'n 0.01 = <L/999 0.20 = L/240 in 0.04 WoodWorks® Sizer SOFTWARE FOR:WCOD DES' N Deck Joistwwb WoodWorks®Sizer 10.4 Additional Data: — —— FACTORS: F/E(psi)CD CM Ct CL OF Cfu Cr Cfrt C Fv' 150 1.00 0.97 1.00 _ - 1 L2 Fbp 950 1_00 1.00 1.00 1.000 1.200 1.00 1.15 1.001 .0000 00- 2 Fc0.67 1.00 - - - - 1.00 1.00 E' 1.3 million 0.90 1.00 - - - 1.00 1.00 - 2 Emir_' 0.47 million 0.90 1.00 - - - - 1.00 1.00 2 CRITICAL LOAD COMBINATIONS: Shear LC 02 = D+L, V = 13i, V design = 91 lbs Bending(+) : LC 02 = D+L, M = 133 lbs-ft Deflection: LC 02 = D+L (live) LC 02 = D+L (total) D=dead L=live S=snow W=wind I=impact Lr=roof live Lc=concentrated E=earthquake All LC's are listed in the Analysis output Load combinations: ASCE 7-10 / IBC 2012 CALCULATIONS: Deflection: EI = 61.9e06 lb-in2 "Live" deflection = Deflection from ail non-dead loads (live, wind, snow...) Total Deflection = 2.00(Dead Load Deflection) + Live Load Deflection. Design Notes: 1.WoodWorks analysis and design are in accordance with the ICC International Building Code(IBC 2012),the National Design Specification (NDS 2012),and NDS Design Supplement. 2. Please verify that the default deflection limits are appropriate for your application. 3. Sawn lumber bending members shall be laterally supported according to the provisions of NDS Clause 4.4.1. • COMPANY PROJa,T _ 4 •%VOOd\/VorkS Portland, OR Job No. 19018 SORWARE FOR WOOD 04310y Jan.21,2019 13:31 Deck Beam 1_.wwb Design Check Calculation Sheet WoodWorks Sizer 10.4 Loads: Load Type Distribution Pat- Location [ft] Magnitude Loadl tern Start End Start End Dead Full UDL 65.0 Load2 Live Full UDL plf 80.0 plf Self-weight Dead Full UDL 8.6 plf Maximum Reactions (Ibs), Bearing Capacities (lbs) and Bearing Lengths (in) : 14'-6" 4 0' x 14'-5" Unfactored: Dead 533 53Live 580 580 Factored: 580 Total 1113 Bearing: 1113 Capacity Beam 1113 1113 Anal/Des Beam 1.00 00 Load comb #2 1'#2 Length 1.03 1.03 Min req'd 1.03 1.03 Cb 1.00 1.00 Cb min 1.00 1.00 Deck Beam 1 Giulam-Bal., West Species,24F-1.8E WS, 3-1/8"x12" 8 laminations, 3-1/8"maximum width, Supports:All-Non-wood Total length: 14'-6.0";volume= 3.8 cu.ft.; Service:wet; Lateral support:top=full, bottom=at supports; Analysis vs. Allowable Stress and Deflection using NDS 2012: Criterion Analysis Value Design Value Unit Analysis/Design Shear fv = 38 Fv' = 232 psi fv/Fv' = 0.16 Bending(±) fb = 638 Fb' = 1920 psi fb/Fb' = 0.33 Live Defl'n 0.12 = <L/999 0.48 = L/360 in 0.24 Total Defl'n 0.33 = L/528 0.72 = L/240 in 0.45 WoodWorks® Sizer SOFTWARE FORW'COD DESIGN Deck Beam 1.wwb WoodWorks®Sizer 10.4 Additional Data: FACTORS: F/E(psi)CD CM Ct CL CV Cfu Cr Cfrt Notes- Cr.*''vr LC4 Fv' 265 1.00 0.88 1.00 - - - - 1.00 1.00 1.00 2 Fb'+ 2400 1.00 0.80 1.00 1.000 1.000 1.00 1.00 1.00 1.00 - 2 Fcp 650 - 0.53 1.00 - - - - 1.00 - • - E' 1.8 million 0.83 1.00 - - - - 1.00 - - 2 Eminy' 0.85 million 0.83 1.00 - - - - 1.00 - - 2- CRITICAL LOAD COMBINATIONS: Shear : LC #2 = D+L, V = 1107, V design = 947 lbs Bending(+) : LC #2 = D+L, M = 3990 lbs-ft Deflection: LC #2 = D+L -(live) LC #2 = D+L (total) D=dead L=live S=snow W=wind I=impact Lr=roof live Lc=concentrated E=earthquake All LC's are listed in the Analysis output Load combinations: ASCE 7-10 / IBC 2012 CALCULATIONS: Deflection: EI = 810e06 lb-in2 "Live" deflection = Deflection from all non-dead loads (live, wind, snow...) Total Deflection = 2.00(Dead Load Deflection) + Live Load Deflection. Design Notes: 1.WoodWorks analysis and design are in-accordance with the ICC International Building Code(IBC 2012),the National Design Specification(NDS 2012), and NDS Design Supplement. 2. Please verify that the default deflection limits are appropriate for your application. 3.Glulam design values are for materials conforming to ANSI 117-2010 and manufactured in accordance with ANSI A190.1-2007 4. GLULAM:bxd=actual breadth x actual depth. 5.Glulam Beams shall be laterally supported according to the provisions of NDS Clause 3.3.3. 6. GLULAM:bearing length based on smaller of Fcp(tension), Fcp(comp'n). 1111111111111111111111111111164 /` COMPANY PRO:EST {�' WDY, Inc Alderbrcok Apa amen:s � ' %Vood\jVorks® Portland, OR Job No. 19018 SOFTWARE FOR WOOD DSIGA Jan.21,2019 13:31 Deck Beam 2.wwb Design Check Calculation Sheet WoodWorks Sizer 10.4 Loads: Load Type Distribution Pat- Location [ft] Magnitude . Uuit 1 tern Start End Start En4 ' Load1 • Dead Full UDL No 15.0 ply Load2 Dead Point No 12.00 533 lbs Load3 Live Point Yes 12.00 580 lbs Self-weight Dead Full UDL No 8.6 plf Maximum Reactions (Ibs), Bearing Capacities (Ibs) and Bearing Lengths (in) : 12' 0' 7'-11.8" 11-11.8" Unfactored: Dead 26 1013 Live -291 871 Factored: Uplift 487 Total 26 1883 Bearing: Capacity Beam 538 1883 Anal/Des Beam 0.05 1.00 Load comb #1 T2 Length 0.50* 1.37 Min req'd 0.50* 1,37 Cb 1.00 1.27 Cb min 1.00 1.27 `Minimum bearing length setting used: 1/2"for end supports Maximum reaction on at least one support is from a different load combination than the critical one for bearing design, shown here, due to Kd factor. See Analysis results for reaction from critical load combination. Deck Beam 2 Glulam-Bal.,West Species,24F-1.8E WS, 3-1/8"x12" 8 laminations, 3-1/8"maximum width, Supports:All-Non-wood Total length: 12';volume= 3.1 cu.ft.; Service:wet; Lateral support:top=at supports, bottom=at supports; Analysis vs. Allowable Stress and Deflection using NOS 2012 : Criterion Analysis Value Design Value Unit Analysis/Design Shear fv = 47 Fv' = 232 psi fv/Fv' = 0.20 Bending(-) fb = 743 Fb' = 1841 psi fb/Fb' = 0.40 Deflection: Interior Live -0.02 = <L/999 0.27 = L/360 in 0.09 Total -0.07 = <L/999 0.40 = L/240 in 0.17 Cantil. Live 0.09 = L/505 0.27 = L/180 in 0.36 Total 0.27 = L/175 0.40 = L/120 in 0.68 WoodWorks® Sizer SOFTWARE FOR-WO3D DESIGN -7 _ Deck Beam 2.wwb WoodWorks®Sizer 10.4 Additional Data: . • 1 FACTORS: F/E(psi)CD CM Ct CL CV Cfu Cr Cfrt Notes. Cnx ;rr LC-1 Fv 265 1.00 0.88 1.00 - - - - 1.00 1.00 1.00 2 Fb'- 2400 1.00 0.80 1.00 0.959 1.000 1.00 1 .00 1.00 1.00 - 2 Fcp' 650 - 0.53 1.00 - - - - 1.00 - - - • - E' 1.8 million 0.83 1.00 - - - - 1.00 - - - 2 Eminy' 0.85 million 0.83 1.00 - - - - 1.00 - - z- - - CRITICAL LOAD COMBINATIONS: - Shear : LC #2 = D+L, V = 1208, V design = 1185 lbs Bending(-) : LC #2 = D+L, N = 4641 lbs-ft Deflection: LC #2 = D+L (live) LC #2 = D+L (total) D=dead L=live S=sncw W=wind 1=impact Lr=roof live Lc=concentrated _=earthauake All LC's are listed in the Analysis output Load Patterns: s=S/2, X=L+S or L+Lr, _=no pattern load in this scan Load combinations: ASCE 7-10 / IBC 2012 CALCULATIONS: Deflection: El' = 810e06 lb-in2 "Live" deflection = Deflection from all non-dead loads (live, wind, snow...) Total Deflection = 2.00 (Dead Load Deflection) + Live Load Deflection. Lateral stability (-) : Lu = 7'-11.75" Le = 14'-5.86" RB = 14.62 Design Notes: 1.WoodWorks analysis and design are in accordance with the ICC International Building Code(IBC 2012),the National Design Specification (NDS 2012), and NDS Design Supplement. 2. Please verify that the default deflection limits are appropriate for your application. 3. Glulam design values are for materials corrming to ANSI 117-2010 and manufactured in accordance with ANSI A190.1-2007 4. Grades with equal bending capacity in the top and bottom edges of the beam cross-section are recommended for continuous beams. 5. GLULAM:bxd=actual breadth x actual depth. 6. Glulam Beams shall be laterally supported according to the provisions of NDS Clause 3.3.3. 7. GLULAM:bearing length based on smaller of Fcp(tension), Fcp(comp'n). 8.The critical deflection value has been determined using maximum back-span deflection. Cantilever deflections do not govern design. -�. �- Jr site. OFFICE COPY_ InW D-Y Structural • Civil Engineers _ „ STRUCTURAL CALCULATIONS FOR ALDERBROOK APARTMENTS DECK GUARDRAIL REPLACEMENT 13070 SW ASH AVE. TIGARD, OREGON November 25, 2019 �14D PROFics .� _ \Cj� G l N / i of T+`- ,ard' Q E. g. •' _ 14 _ 7 _ ` ! I- OREGON • 9 4C/ sFAP 1 21. 9y yq FL COR RENEWS: 12-31-2019 DESIGN PARAMETERS: 2014 Oregon Structural Specialty Code GUARDRAIL UNIFORM 50 p1f _ CONCENTRA I ED 200 lbs VA m!D f. lam`F- -_ THE ISSUANC` OF A PE=;; BASED ON r-sa' S3=. C-- CONTENTS: DOCL.; - GUARDRAIL FRAMING GR-1 to GR-6 :j,SH',J THE i E _ : . OF ERRORS, OS IF' f r 6443 SW Beaverton-Hillsdale Hwy,suite 210•Portland,OR 97221 •ph:503.203.8111 •fx:503.203.8122•www.wdyi.com _ _ , , , , inWDY Structural . Civil Engineers ••• •• • • Job Name: Alderbrook Apartments Job No: 19018 Sheet No: GR-1 Client: T&H Homebuilders Date: Nov 2019: - - - By: -, : - SAC General Layout - - - - . - - - - Ts • a so . a a a a a -r A a a A _LI 'I'4 u a o Q r a a a St0 6— g f a C,i n a a e 3 a a at a a rn kj ies s=nt=.gym' =w t , r,K _ ..'... . .>. .ter= �Z•� ii s i L 9e ss k s '- : is § - yc , g m si $ a$ yes VC.or=.tar 4 7- sue=a->-ur 5 Na q'A S.a.�' t' I ' Design Criteria Guards/Handrail Loading per 2014 OSSC, 1607.8.1: Uniform Load: 50 plf (applied at top) or Concentrated Load: 200 lbs (applied at any point) Intermediate Component Loading per 2014 OSSC, 1607.8.1.2: Concentrated Load: 50 lbs (applied at any point) rOWDY Structural . Civil Engineers ••••• ••• ••• Job Name: Alderbrook Apartments Job No: 19018 Sheet No: GR-2 Client: T&H Homebuilders Date: Nov 2019 By: irIC Vertical Post l Si ram =yr.j_R'._ It . !, is $e 4 E § +g il ;11g '`11 s; "h is it x ES, 1 k ; 1 ;11 11 8 IL mes cr.x._ur ;l S1 --- ea Or.ar...aa- Hm av=a'_.uc Selected piece: HSS 1 1/2 x 1 1/2 x 0.12" Height= 36.0 in M (Uniform load) = 8406.0 in-lbs . M (Conc load) = 7200.0 in-lbs D= 1.50 in t= 0.12 in D/t= 12.5 OK, Compact: < 1.12 [E/Fyj12 Z= 0.309 in3 I = 0.188 in4 Mn = Fy*Z 14214.0 in-lbs Mn/S2b= 8511.4 > MMAx OK Use: HSS 1 1/2 x 1 1/2 x 0.12" aWOY . . .. . : • . . - Structural . Civil Engineers ••• •• • • • Job Name: Alderbrook Apartments Job No: 19018 Sheet No: GR-3 Client: T&H Homebuilders Date: Nov 201R - ,By: , dv1C Top Horizontal Rail a k k 1 li ; - W 1 ; baR i s , 4 s s § 1 ''"-- 3 ;sit � g 1. k g k u g ss 4 ;4 1.0 u ..uP - Si o a•.a... . Selected piece: HSS 1 1/2 x 1 1/2 x 0.12" Max span = 56.0 in MMax(Uniform load) = 1633.3 in-lbs MMAx(Conc load) = 2800.0 in-lbs D = 1.50 in t= 0.12 in D/t= 12.5 OK, Compact: < 1.12 [E/Fyj112 Z= 0.309 in3 = 0.188 in4 Mn= Fy*Z 14214.0 in-lbs MIQb= 8511.4 ' Mnnax OK Use: HSS 1 1/2 x 1 1/2 x 0.12" InIWDY Structural . Civil Engineers 1 • .. . . Job Name: Alderbrook Apartments Job No: 19018 Sheet No: GR-4 Client: T&H Homebuilders Date: Nov 2019 By: = -AriC Bottom Horizontal Rail/Intermediate Rail —7 Iiris At' W.?� _ - `J t 111 I . - _ i It it to s la g la � I '$ a it '< S1 a er k ie ; ig$ $ ( II El. ; 1 III It . li kki KZm.r..vr tl 1tam a,+A,,..r r- -S wssu t Or.asA Selected piece: HSS 1 1/4 x 1 1/4 x 0.12" Max span = 56.0 in M<(Conc load) = 700.0 in-lbs D = 1.25 in t= 0.12 in D/t= 10.4 OK, Compact: < 1.12 [E/Fyf 12 Z= 0.204 in3 1 = 0.101 in4 Mn = Fy*Z 9384.0 in-lbs Mn/c2b= 5619.2 > MMAx OK Use: HSS 1 1/4 x 1 1/4 x 0.12" � 1NDY :• :• • • Structural . Civil Engineers ..•. •. •. • Job Name: Alderbrook Apartments Job No: 19018 Sheet No: GR-5 Client: T&H Homebuilders Date: Nov 2019 ; By: - _MC _ Infill Pickets _ _ .V-..e� A E - I - 1 " is *FA - 11 ` la b ' apt ;i1 i` Y1 1 - Se . Y k 4 . le. le p 9 ilY� ll - - - - R - 11 1f Selected piece: HSS 5/8 x 5/8 x .065" Max span = 32.0 in MMAx(Conc load)= 400.0 in-lbs D = 0.63 in t= 0.07 in D/t= 9.6 OK, Compact: < 1.12 [E./Fy]112 Z= 0.031 in3 I = 0.008 in4 M„ = Fy*Z 1116.0 in-lbs Mn/Qb= 668.3 > MMAx OK Use: HSS 5/8 x 5/8 x.065" 1 I • nWDY Structural • Civil Engineers • • •• •• • •• • Job Name: Alderbrook Apartments Job No: 19018 Sheet No: GR-6 Client: T&H Homebuilders Date: Nov 2019 `By: "`MC Vertical Post Connection + ‘12. 44.fr, POST I 11 3 ? 5A-S T. V1- vJ fi C�) vAr-i-GocDsS 4S- l' 31I2`/LIZ GLA)-t 4M 4 P = (sow%)&,;z07 ) = 2'2O 15 „ M = p ( 3,0') = (,9-0 Fr' M cAW-. C4.) 1/Y\)7VDtJ 114 ` 7,0 ,f5 cam-`��. .J5 "P-- - - `f- MA,OuJ . 5 c-F - ( - o), ( Z.o) = _to . > (P0 Arkit,p u.) vJ IT1-.0 R - ' (5(00) (7.0) _ 1 ) L i t7 b�` S°lo ( III o) 640 • _ ( ( 19 * Z [ (p024- I)30Z] '1z I I2O cos (87)+ 40 11nz('�1) ' t t2 $`f z' 10 O '- I