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.- 2c g - 6 7 ?ozro stt) Western Wood Structures, Inc. . ECEVE PO Box 130 egif Tualatin, Oregon 97062 ;v1 1 1 Voice: (503) 692 -6900 OITYOFTIGN O Fax: (503) 692 -6434 BUILDINGDIVISION Structural Design Calculations For: BEAM POST- TENSION REPAIR PITCHED & TAPERED CURVED BEAM(S) Designer: BAM Tigard High Beam Repairs Tigard, Oregon WWSI Job No. 088003 March 10, 2008 3 Mofo$ :. F`O PROFE 44,. • jOR n N.f 4 E1' ti `\ EXPIRES: 1 Z 0 10 J The attached calculations ( 30 Sheets) show the span and loading conditions and product design /selection for the above referenced project. r' • Western Wood Structures, Inc. P.O. Box 130 - Tualatin. Oregon 97062 March 7, 2008 (503) 692 - 6900 Page 1 of Tigard High Beam Repairs Tigard, Oregon . Job Number: 088003 Pitched and Tapered Curved Beam - Radial Reinforcement 6 E"` At- Beam Properties • Slope of top of beam - d- = 9.46 Deg Species = D.F. Slope of bottom of beam - 4 >B = 7.89 Deg Fb = 2400 psi Width - b = 9.00 in. Note: Beam made prior to 1971 have no dedicated tension laminations. Depth @ bearing - d brg = 27.625 in. Therefor the bending stress allowable must be multiplied by 0.75. Depth @ tangent point - d, = 34.375 in. Fb = 1800 psi Depth @ centerline - d = 51.00 in. F„ = 265 psi Beam Spacing = 20.50 ft. F, = 1650 psi Beam Length = 69.33 ft. Fcperp = 560 psi • Radius = 100.00 ft. F 1100 psi Thickness of Beam Lams = 1.625 in. E = 1800000 psi F = 15 psi Loading • Roof Dead Load Bulit -up Roofing: 3.50 psf 5/8" plywood: 1.90 psf 2x12 @ 16" o /c: 3.20 psf Accoustical Ceiling: 3.00 psf Batt Insulation: 3.00 psf Miscellaneous: 1.50 psf Total Roof DL = 16.10 psf - -- -Use 17 psf + Beam Self- Weight Beam Self Weight Beam Average Depth = 37.67 in. Density of Glulam = 35 pcf Beam Average Weight = 82 plf Total Beam Dead Load: Roof Dead Load = 349 plf Beam Self Weight = 82 plf DL = 431 plf Roof Snow Load Roof Snow Load = 25.00 psf • Total Beam Snow Load: SL = 513 plf 1I Western Wood Structures, Inc. P.O. Box 130 - Tualatin. Oregon 97062 March 7, 2008 (503) 692 -6900 Page of Tigard High Beam Repairs Tigard, Oregon Job Number: 088003 Design Check Check Depth at Centerline for Bending M = WL /8 = 566,876 ft -lb Bending Stress Coefficient - K Coefficients from AITC Timber Construction Manual Table 4.11 D= 1.311 E = 0.219 F = 0.631 R = Radius + d = 1226 in. K = D + E(d + F(d = 1.3212 Bending Stress f = 6M /bd = 1743.6 psi f = Kolb = 2304 psi Allowable Stress Factors CD = 1.15 C = (5.125/b) ° '(12/d) 01 (21/L) °1 = 0.7258 C� = 1- 2000(t /R) = 0.9963 F' = FbCDC„ CC = 1497 psi Bending Stress Check f = 154% NG Check Depth at Tangent Point for Bending Reaction = WL /2 = 32704 lb Distance from bearing to tangent point: x = 20.91 ft. M = Reaction(x) - Wx /2 = 477,609 ft-lb • • Bending Stress f = 6M /bd = 3234 psi Allowable Stress Factors CD = 1.15 C,, = (5.1 251b) 1 (21 /L) 1 = 0.7550 C, = 1- 2000(t/R) = 0.9963 C, = [1 /1 +(F tan 8 /F„) + Fb tan b /Fcperp)211Q = 0.6610 F' = F of C & C,)C = 1363 psi Bending Stress Check f = 237% NG 1' • Western Wood Structures, Inc. P.O. Box 130 - Tualatin. Oregon 97062 March 7, 2008 (503) 692 -6900 Page '6 of Tigard High Beam Repairs Tigard Oregon Job Number: 088003 Check Depth at three points between Tangent Point and Bearing for Bending Section ,A (B IC x (ft.) 5.25 10.5 15.75 d' (in.) 29.250 31.000 32.750 M (ft-lb) 158,697 291,391 398,083 S (in 1,283 1,442 1,609 f (Psi) 1,484 2,426 2,969 Co 1.15 1.15 1.15 C� 0.7673 0.7629 0.7587 C, 0.6610 0.6610 0.6610 Fb (psi) 1,368 1,368 1,368 f 108.46% 177.29% 217.01% NG NG NG Check Radial Tension Stress at Centerline Coefficient for the Determination of K Coefficients from AITC Timber Construction Manual Table 4.7 A = 0.0367 B = 0.0793 C = 0.2128 R = Radius + d /2 = 1226 in. K = A + B(d + C(d = 0.0404 Shape Reduction Factors from AITC Timber Construction Manual Table 4.8 l = 27.4635 ft. Ul = 2.5 a= 0.750 R = -0.675 C c3 + d = 0.722 f = K = 51 psi F' = F„ C 17 psi Note: f must not exceed 1/3 the of the allowable shear stress. Note: Multiply F. by 0.72 for radial tension values. (0.72 *F. /3)C 73 psi Radial Tension Stress Check Radial reinforcement required Western Wood Structures, Inc. P.O. Box 130 - Tualatin. Oregon 97062 March 7, 2008 (503) 692 -6900 Page "I of Tigard High Beam Repairs Tigard. Oregon Job Number: 088003 Radial Reinforcement Design Using 3/4" diameter grade 60 rebar in 1" diameter epoxy - filled holes: Effective depth at centerline: d /2 - 2" = 23.50 in. Allowable wood withdrawal: 1455 lb / 2.5 = 582 pli Max tension for wood withdrawal = 13677 lb Area of 3/4" diameter rebar = 0.4418 in Fy for grade 60 rebar = 60,000 psi Allowable tension for steel: 0.5Fy = 30,000 psi Max tension for steel rebar = 13254 lb Controls Radial Tension Force per in of length: f b = 457 pli Maximum Rod Spacing = 28.98 in. Use 28" maximum rebar spacing • Western Wood Structures, Inc. N.O. Box 130 - Tualatin Oregon 97062 March 7, 2008 (503) 692 -6900 Page 5 of Tigard High Beam Repairs Tigard, Oregon Job Number: 088003 Pitched and Tapered Curved Beam - Cable Repair BsAtek Beam Properties Slope of top of beam - 4 T = 9.46 Deg Species = D.F. Slope of bottom of beam - (kg = 7.89 Deg Fb. = 2400 psi Fb = 1450 psi Width - b = 9.00 in. Note: Beam made prior to 1971 have no dedicated tension laminations. Depth @ bearing - d brg = 27.625 in. Therefor the bending stress allowable must be multiplied by 0.75. Depth @ tangent point - d = 34.375 in. Fb = 1800 psi Depth @ centerline - d = 51.00 in. F„ = 265 psi Beam Spacing = 20.50 ft. F = 1650 psi Beam Length = 69.33 ft. F cpefp = 560 psi Radius = 100.00 ft. F = 1100 psi Thickness of Beam Lams = 1.625 in. E = 1800000 psi F = 15 psi Loading Roof Dead Load Bulit -up Roofing: 3.50 psf 5/8" plywood: 1.90 psf 2x12 @ 16" o /c: 3.20 psf • Accoustical Ceiling: 3.00 psf Batt Insulation: 3.00 psf Miscellaneous: 1.50 psf Total Roof DL = 16.10 psf - -- -Use 17 psf + Beam Self- Weight Beam Self Weight Beam Average Depth = 37.67 in. Density of Glulam = 35 pcf Beam Average Weight = 82 plf Total Beam Dead Load: Roof Dead Load = 349 plf Beam Self Weight = 82 plf DL = 431 plf Roof Snow Load Roof Snow Load = 25.00 psf Total Beam Snow Load: SL = 513 plf Western Wood Structures, Inc. P.O. Box 130 - Tualatin, Oregon 97062 //� March 7, 2008 (503) 692 -6900 Page �O of Tigard High Beam Repairs Tigard, Oregon .lob Number: 088003 Beam Stresses Worst case overstress at tangent point from radial tension analysis Distance from bearing to tangent point: x = 20.91 ft. DL Reaction = WDLU2 = 14938 lb TL Reaction = W = 32704 lb Bending Stress Mp = Reaction(x) - WDLx2 /2 = 218,148 ft-lb fbpL = 6MoL/bd 2 = 1477 psi MTV = Reaction(x) - WTLX2 /2 = 477,609 ft -lb fbTL = 6MTL/bd; = 3234 psi Allowable Stress Factors CD = 1.15 C„ = (5.125/b) = 0.7550 C = 1- 2000(t/R) = 0.9963 C, = [1 /1 +(F, tan fi /F„) + Fb tan .0 /Fcperp)2]v2 = 0.6610 Fb = F of C„ & C,)C = 1363 psi • Bending Stress Check f = 108% NG f = 237% NG Cable Tension Beam "e" at tangent point: e = 35.00 in. Beam Area at tangent point: A = 309.38 in Beam Section Modulus at tangent point: S = 1772.46 in f b= fb- F' T /A +Te /S Therefor: T = f - Fb / (1 /A + e /S) = 81,393 lb Number of cables = 4 • Tension on each cable = 20,348 lb Use Tension = 20,400 lb Western Wood Structures, Inc. P.O. Box 130 - Tualatin. Oregon 97062 March 7, 2008 (503) 692 -6900 Page 1 of Tigard Hieh Beam Repairs Tigard, Oregon Job Number: 088003 Check beam at other points Section A IB IC (Centerline Dist. from Bearing to Section x (ft.) 5.250 10.500 15.750 34.667 Depth at Section d' (in.) 29.250 31.000 32.750 51.000 • Dead Load Moment MDL (ft-lb) 72,485 133,093 181,824 258,920 Total Load Moment MTV (ft-lb) 158,697 291,391 398,083 566,876 Area at Section A (in 263 279 295 459 Section Modulus at Section S (in 1,283 1,442 1,609 3,902 Dead Load Bending Stress fbDL (psi) 678 1,108 1,356 796 Total Load Bending Stress f (psi) 1,484 2,426 2,969 1,744 Duration or Load Factor CD 1.15 1.15 1.15 1.15 Volume Factor C„ 0.7673 0.7629 0.7587 0.7258 Stress Interaction Factor C 0.6610 0.6610 0.6610 0.6610 Curvature Factor Cc 1.0000 1.0000 1.0000 0.9963 Allow. Pos. Bending Stress F' (psi) 1,368 1,368 1,368 1,363 Amount of overstress in beam f -F' (psi) 116 1,058 1,601 380 Cable Ecc. to Beam N.A. e (in.) 6.2500 16.0000 25.5000 54.8125 Allow. Pos. Bending Stress from Cables f b (psi) 707 1,198 1,570 1,324 Negative Bending Stress fb (psi) 592 141 944 Allow. Neg. Bending Stress F (psi) 1,102 1,102 1,102 1,102 Neg. Bending Stress Check f bOF'e 53.68% 12.76% 85.63% OK OK OK os. Bending Stress Check with Cables TensionedlfblF'b + f b 71.49% 94.52% 101.05% 64.88% OK OK ok OK Final cable loads When the cables are initially tensioned, the beam is loaded with dead load only and when live load is applied, the tension in each cable increases by the amount determined on the next sheet. Tension Reduction Worksheet Amount of reduction in tension = 3,000 lb Reduced tension = 17,400 lb When the second cable is tensioned, it reduces the load in the first cable. Change in cable load: Avg f in 3rd cycle = 489 psi A at 1 cable = (Avg f 3 cycle)' 30,970 / 1.8E6' 0.007 = 1,202 lb Increase in tension at cable #1 = 1,200 lb Final Cable Loads: Tension at Cable #1 = 18,600 lb Tension at Cable #2 = 17,400 lb The difference between the average stress under total load and the average stress at dead load only is a measure in the change in fiber length in the wood at the bottom of the member. The change of cable length must equal the change in fiber length from total load condition of loading and dead load only. Field measurements indicate the change in length of the cable is equal to 0.7% of its length under 30,970 lb. for 1/2" diameter grade 270 cable. Cable increase (lbs.) = «= • P, / E„, ' e, CABLE BEAM POINT OF BEAM BEAM AREA SECTION LOAD MOMENT IN- fb "e" "T" fb' PSI fb -fb' PSI fb -fb' AT "e" INCREASE MARK REVIEW WIDTH DEPTH MODULUS CASE LBS PSI IN. LBS TOP BOTTOM TOP BOTTOM MEAN TOTAL LBS B1 A 9 29.25 263.3 1283.3 TL 158,697 1,484 6.25 81,600 87 707 1,396 777 B 9 31 279.0 1441.5 TL 291,391 2,426 16 81,600 613 1,198 1,812 1,228 C 9 32.75 294.8 1608.8 TL 398,083 2.969 25.5 81,600 1,017 1,570 1,953 1,399 T.P. 9 34.375 309.4 1772.5 TL 477,609 3,234 35 81,600 1,348 1,875 1,886 1,358 MIDSPAN 9 51 459.0 3901.5 TL 566,876 1,744 54.8125 81,600 969 1,324 775 419 1,036 B1 A 9 29.25 263.3 1283.3 DL 72,485 678 6.25 81,600 87 707 590 -30 B 9 31 279.0 1441.5 DL 133,093 1,108 16 81,600 613 1,198 495 -90 C 9 32.75 294.8 1608.8 DL 181,824 1,356 25.5 81,600 1,017 1,570 340 -214 T.P. 9 34.375 309.4 1772.5 DL 218,148 1,477 35 81,600 1,348 1,875 129 -398 MIDSPAN 9 51 459.0 3901.5 DL 258,920 796 54.8125 81,600 969 1,324 -172 -528 -252 1,288 3,166 61 A 9 29.25 263.3 1283.3 DL 72,485 678 6.25 78,434 84 680 594 -2 B 9 31 279.0 1441.5 DL 133,093 1,108 16 78,434 589 1,152 518 -44 C 9 32.75 294.8 1608.8 DL 181,824 1,356 25.5 78,434 977 1,509 379 -153 T.P. 9 34.375 309.4 1772.5 DL 218,148 1,477 35 78,434 1,295 1,802 182 -325 MIDSPAN 9 51 459.0 3901.5 DL 258,920 796 54.8125 78,434 931 • 1,273 -135 -476 -200 1,236 3,039 B1 A 9 29.25 263.3 1283.3 DL 72,485 678 6.25 78,561 84 681 594 -3 B 9 31 279.0 . 1441.5 DL 133,093 1,108 16 78,561 590 1,154 518 -46 C 9 32.75 294.8 1608.8 DL 181,824 1,356 25.5 78,561 979 1,512 378 -156 T.P. 9 34.375 309.4 1772.5 DL 218,148 1,477 35 78,561 1,297 1,805 180 -328 MIDSPAN 9 51 459.0 _ 3901.5 DL 258,920 796 54.8125 78,561 933 1,275 -136 -478 -202 1,238 3,044 Reduce Cable Tension by • / A _ DATE P ROJECT TI `1 4 - , 0-1 C IA 1 'EA' 1 R - f'A'�Z O WESTERN WOOD STRUCTURES, INC. /�.� /� /�� 31�/0� LOCATION 4e--1. I 0 (2 -E-4 - wow P.O. BOX 130, TUALATIN, OREGON 97062 SHEET • �DRV!!I9\ ,�}/�' 503/692 -6900 • FAX 503/692 -6434 JOB NO.. ©® BY OF PIT A A 3L. B o — GA-13 Ar-NLt-voI°� 3' -O" PIPE COLUMN I I I MOM. I I 3y - a / I TO 4 OF 6EAu". '--1-1" To ct PIPS c oz_vm .1 Pr V5E ( 6) S 1 6vc_rs L 0 514-m— - C}ti-P = Si, 930 L 3s, A • ID Western Wood Structures, Inc. — Computer Analysis Systems P.O. Box 130, 20675 S.W. 105th, Tualatin, OR 97062 -0130 - 503/692 -6900 or 800/547 -5411 Fax: 503/692 -6434 Tigard High Beam Repairs - Tigard, Oregon - Job # 088003 7- Mar -08 Shear Plate(s) in side grain loading Joint Description: 4" Shear Plate w/ 7/8" Bolts # of bolts: 6 # of fasteners /face: 2 CD = 1.15 P = 4320 lbs C = 0.98 Q = 3000 lbs CA = 1.00 C = 1.00 P' = P * (CD) * (CO * (CA) * (Cst) P' = 4868.64 lbs = Q * (CD) * ( Cg) * ( CA) Q' = 3381 lbs 8 = 0.0447 radians = 8.00 degrees P Q 4828 lbs . P' sin 'e +Q'cos' Capacity of (12) 4" Shear Plate w/ 7/8" Bolts = 57,930 lbs • • Western Wood Structures, Inc. P.O. Box 130 - Tualatin, Oregon 97062 March 7, 2008 (503) 692 - 6900 Page 11 of Tigard High Beam Repairs Tigard, Oregon Job Number: 088003 Pitched and Tapered Curved Beam - Radial Reinforcement 6 B • Beam Properties Slope of top of beam - dr = 9.46 Deg Species = D.F. Slope of bottom of beam - (k = 7.58 Deg Fb = 2400 psi Width - b = 9.00 in. Note: Beam made prior to 1971 have no dedicated tension laminations. Depth @ bearing - d brg = 24.375 in. Therefor the bending stress allowable must be multiplied by 0.75. Depth @ tangent point - d, = 30.50 in. Fb = 1800 psi Depth @ centerline - d = 46.75 in. = 265 psi Beam Spacing = 20.50 ft. F, = 1650 psi Beam Length = 58.00 ft. Fcperp = 560 psi Radius = 100.00 ft. F, = 1100 psi Thickness of Beam Lams = 1.625 in. E = 1800000 psi F = 15 psi Loading Roof Dead Load Bulit -up Roofing: 3.50 psf 5/8" plywood: 1.90 psf 2x12 @ 16" o /c: 3.20 psf Accoustical Ceiling: 3.00 psf Batt Insulation: 3.00 psf Miscellaneous: 1.50 psf Total Roof DL = 16.10 psf - -- -Use 17 psf + Beam Self- Weight Beam Self Weight Beam Average Depth = 33.88 in. Density of Glulam = 35 pcf Beam Average Weight = 74 plf Total Beam Dead Load: Roof Dead Load = 349 plf Beam Self Weight = 74 plf DL = 423 plf Roof Snow Load Roof Snow Load = 25.00 psf Total Beam Snow Load: SL = 513 plf • Western Wood Structures, Inc. P.O. Boa 130 - Tualatin. Oregon 97062 March 7, 2008 (503) 692 - 6900 Page 11, of Tigard High Beam Repairs Tigard, Oregon Job Number: 088003 Design Check Check Depth at Centerline for Bending M = WL /8 = 393,210 ft -lb Bending Stress Coefficient - Kb Coefficients from AITC Timber Construction Manual Table 4.11 D = 1.311 E = 0.219 F = 0.631 R = Radius + d = 1223 in. K = D + E(d + F(d = 1.3203 Bending Stress f = 6M /bd = 1439.3 psi f = K = 1900 psi Allowable Stress Factors CD = 1.15 • C„ = (5.125/b) 1 (21 /L) 1 = 0.7454 C. = 1- 2000(t/R) = 0.9963 F = FbCDC = 1537 psi Bending Stress Check f /F' = 124% NG Check Depth at Tangent Point for Bending Reaction = WL /2 = 27118 lb Distance from bearing to tangent point: x = 15.80 ft. M = Reaction(x) - Wx /2 = 311,744 ft-lb Bending Stress f = 6M /bd = 2681 psi Allowable Stress Factors CD = 1.15 C,, = (5.125/b) = 0.7779 C = 1- 2000(t/R) = 0.9963 C = [1 /1 +(F tan -6/F0 + Fb tan 0 /Fcperp)2]112 = 0.6610 F = F of C„ & C = 1363 psi Bending Stress Check fb/Fb = 197% NG Western Wood Structures, Inc. P.O. Box 130 - Tualatin. Oregon 97062 March 7, 2008 (503) 692 - 6900 Page ` of Tigard High Beam Repairs Tigard, Oregon Job Number: 088003 Check Depth at three points between Tangent Point and Bearing for Bending Section A IB IC x (ft.) 4 • 8 12 d' (in.) 25.750 27.375 29.000 M (ft-lb) 100,991 187,020 258,088 S (in 995 1,124 1,262 f (psi) 1,218 1,997 2,455 C 1.15 1.15 1.15 C , 0.7912 0.7863 0.7818 C 0.6610 0.6610 0.6610 F'b (psi) 1,368. 1,368 1,368 f 89.06% 145.92% 179.43% OK NG NG Check Radial Tension Stress at Centerline Coefficient for the Determination of K Coefficients from AITC Timber Construction Manual Table 4.7 A = 0.0367 B = 0.0793 C = 0.2128 R = Radius + d = 1223 in. K = A + B(d + C(d = 0.0400 Shape Reduction Factors from AITC Timber Construction Manual Table 4.8 I, = 26.3958 ft. Ul,= 2.2 a = 0.708 3 = -0.660 C,= a +pd /R 0.683 f = K = 39 psi F = F „C 17 psi Note: f must not exceed 1/3 the of the allowable shear stress. Note: Multiply F, by 0.72 for radial tension values. (0.72 *F„ /3)C 73 psi Radial Tension Stress Check Radial reinforcement required Western Wood Structures, Inc. P.O. Box 130 - Tualatin. Oregon 97062 • March 7, 2008 (503) 692 - 6900 Page 19 of Tigard High Beam Repairs Tigard, Oregon Job Number: 088003 Radial Reinforcement Design Using 3/4" diameter grade 60 rebar in 1" diameter epoxy - filled holes: Effective depth at centerline: d /2 - 2" = 21.38 in. Allowable wood withdrawal: 1455 lb / 2.5 = 582 pli Max tension for wood withdrawal = 12440 lb Controls Area of 3/4" diameter rebar = 0.4418 in Fy for grade 60 rebar = 60,000 psi • Allowable tension for steel: 0.5Fy = 30,000 psi Max tension for steel rebar = 13254 lb Radial Tension Force per in of length: . 1 0 * b = 354 pli Maximum Rod Spacing = 35.13 in. Use 35" maximum rebar spacing Western Wood Structures, Inc.. P.O. Box 130 - Tualatin. Oregon 97062 March 7, 2008 (503) 692 -6900 Page , J ol_ Tigard Hieh Beam Repairs Tigard, Oregon Job Number: 088003 Pitched and Tapered Curved Beam - Cable Repair Pte\ a • Beam Properties Slope of top of beam - 4'T = 9.46 Deg Species = D.F. Slope of bottom of beam - 4)B = 7.58 Deg Fb, = 2400 psi Fb = 1450 psi Width - b = 9.00 in. Note: Beam made prior to 1971 have no dedicated tension laminations. Depth @ bearing - dbrg = 24.375 in. Therefor the bending stress allowable must be multiplied by 0.75. Depth @ tangent point - d, = 30.50 in. Fb = 1800 psi Depth @ centerline - d = 46.75 in. F„ = 265 psi Beam Spacing = 20.50 ft. F, = 1650 psi Beam Length = 58.00 ft. Fcperp = 560 psi Radius = 100.00 ft. F, = 1100 psi Thickness of Beam Lams = 1.625 in. E = 1800000 psi F 15 psi Loading Roof Dead Load Bulit -up Roofing: 3.50 psf 5/8" plywood: 1.90 psf 2x12 @ 16" o /c: 3.20 psf Accoustical Ceiling: 3.00 psf Batt Insulation: 3.00 psf Miscellaneous: 1.50 psf Total Roof DL = 16.10 psf - -- -Use 17 psf + Beam Self- Weight Beam Self Weight Beam Average Depth = 33.88 in. Density of Glulam = 35 pcf Beam Average Weight = 74 plf Total Beam Dead Load: Roof Dead Load = 349 plf Beam Self Weight = 74 plf DL = 423 plf Roof Snow Load Roof Snow Load = 25.00 psf Total Beam Snow Load: SL = 513 plf Western Wood Structures, Inc. P.O. Box 130 - Tualatin. Oregon 97062 March 7, 2008 (503) 692 -6900 Page t ( e01_ Tigard High Beam Repairs Tigard, Oregon Job Number: 088003 Beam Stresses Worst case overstress at tangent point from radial tension analysis Distance from bearing to tangent point: x = 15.80 ft. DL Reaction = W = 12255 lb TL Reaction = W = 27118 lb Bending Stress Mop = Reaction(x) - WDLx2 /2 = 140,887 ft -lb f = 6MDL/bd 2 = 1212 psi MTV = Reaction(x) - WTLx2 /2 = 311,744 ft -lb fbTL = 6M = 2681 psi Allowable Stress Factors CD = 1.15 C. = (5.125/b) ° ''(21/L) 01 = 0.7779 C = 1- 2000(t/R) = 0.9963 C, = [1 /1 +(F tan -8/F,) + Fb tan b /FCperp)2]1n = 0.6610 F' = F of C & C,)C = 1363 psi Bending Stress Check fboL /F'b = 89% - - -OK fbTL /F = 197% NG • Cable Tension Beam "e" at tangent point: e = 23.50 in. Beam Area at tangent point: A = 274.50 in Beam Section Modulus at tangent point: S = 1395.38 in' rb= fb- F' T /A +Te /S Therefor: T = f - F'b / (1 /A + e, /S) = 64,330 lb Number of cables = 4 Tension on each cable = 16,082 lb Use Tension = 16,100 lb Western Wood Structures, Inc. P.O. BON ISO - Tualatin. Oregon 97062 March 7, 2008 (503) 692 -6900 Paee 1' of Tigard 1 -ligh Beam Repairs Tigard, Oregon Job Number: 088003 Check beam at other points Section A IB IC (Centerline Dist. from Bearing to Section x (ft.) 4.000 8.000 12.000 29.000 Depth at Section d' (in.) 25.750 27.375 29.000 46.750 Dead Load Moment MDR (ft -lb) 45,641 84,520 116,638 177,704 Total Load Moment Mrs (ft -lb) 100,991 187,020 258,088 393,210 Area at Section A (in 232 246 261 421 Section Modulus at Section S (in 995 1,124 1,262 3,278 Dead Load Bending Stress foci_ (Psi) 551 902 1,110 650 Total Load Bending Stress f (Psi) 1,218 1,997 2,455 1,439 Duration or Load Factor CD 1.15 1.15 1.15 1.15 Volume Factor C„ 0.7912 0.7863 0.7818 0.7454 Stress Interaction Factor C 0.6610 0.6610 0.6610 0.6610 Curvature Factor Cc 1.0000 1.0000 1.0000 0.9963 Allow. Pos. Bending Stress F (psi) 1,368 1,368 1,368 1,363 Amount of overstress in beam f -F' (psi) -150 628 1,087 76 Cable Ecc. to Beam N.A. e (in.) 2.2500 9.3750 16.5000 42.2500 Allow. Pos. Bending Stress from Cables f (psi) 424 798 1,089 983 Negative Bending Stress fb (psi) 573 170 2 907 Allow. Neg. Bending Stress F (Psi) 1,102 1,102 1,102 1,102 Neg. Bending Stress Check f /F'b 52.02% 15.44% 0.20% 82.28% OK OK OK OK os. Bending Stress Check with Cables Tensioned f /F' + f 68.00% 92.14% 99.91% 61.35% OK OK OK OK Final cable loads When the cables are initially tensioned, the beam is loaded with dead load only and when live load is applied, the tension in each cable increases by the amount determined on the next sheet. Tension Reduction Worksheet Amount of reduction in tension = 2,500 lb Reduced tension = 13,600 lb When the second cable is tensioned, it reduces the load in the first cable. Change in cable load: Avg f in 3rd cycle = 338 psi A at 1 cable = (Avg f 3 cycle) ' 30,970 / 1.8E6 * 0.007 = 831 lb Increase in tension at cable #1 = 800 lb • Final Cable Loads: • Tension at Cable #1 = 14,400 lb Tension at Cable #2 = 13,600 lb The difference between the average stress under total load and the average stress at dead load only is a measure in the change in fiber length in the wood at the bottom of the member. The change of cable length must equal the change in fiber length from total load condition of loading and dead load only. Field measurements indicate the change in length of the cable is equal to 0.7% of its length under 30,970 lb. for 1/2" diameter grade 270 cable. Cable increase (lbs.) = iy„, • P / E„, • e, CABLE BEAM POINT OF BEAM BEAM AREA SECTION LOAD MOMENT IN- fb "e" "T" fb' PSI fb -fb' PSI fb-fb' AT "e" INCREASE MARK REVIEW WIDTH DEPTH MODULUS CASE LBS PSI IN. LBS TOP BOTTOM TOP BOTTOM MEAD TOTAL LBS B1 A 9 25.75 231.8 994.6 TL 100,991 1,218 2.25 64,400 -132 424 1,351 795 B 9 27.375 246.4 1124.1 TL 187,020 1,997 9.375 64,400 276 798 1,721 1,198 C 9 29 261.0 1261.5 TL 258,088 2,455 16.5 64,400 596 1,089 1.859 1,366 T.P. 9 30.5 274.5 1395.4 TL 311,744 2,681 23.5 64,400 850 1,319 1,831 1,362 MIDSPAN 9 46.75 420.8 3278.3 TL 393,210 1,439 42.25 64,400 677 983 762 456 1,035 B1 A 9 25.75 231.8 994.6 DL 45,641 • 551 2.25 64,400 -132 424 683 127 B 9 27.375 246.4 1124.1 DL 84,520 902 9.375 64,400 276 798 627 104 C 9 29 261.0 1261.5 DL 116,638 1,110 16.5 64,400 596 1,089 514 20 T.P. 9 30.5 274.5 1395.4 DL 140,887 1,212 23.5 64,400 850 1,319 362 -108 MIDSPAN 9 46.75 420.8 3278.3 DL 177,704. 650 42.25 64,400 677 983 -26 -333 -38 1,073 2,638 B1 A ' 9 25.75 231.8 994.6 DL 45,641 551 2.25 61,762 -127 406 677 144 B 9 27.375 246.4 1124.1 DL 84,520 902 9.375 61,762 264 766 638 136 C 9 29 261.0. 1261.5 DL 116,638 1,110 16.5 61,762 571 1,044 538 65 T.P. 9 30.5 274.5 1395.4 DL 140,887 1,212 23.5 61,762 815 1,265 396 -54 MIDSPAN 9 46.75 420.8 3278.3 DL 177,704 650 42.25 61,762 649 943 1 -292 0 1,035 2,545 B1 A 9 25.75 231.8 994.6 DL 45,641 551 2.25 61,855 -127 407 678 144 B 9 27.375 246.4 1124.1 DL 84,520 902 9.375 61,855 265 767 637 135 C 9 29 261.0 1261.5 DL 116,638 1,110 16.5 61,855 572 1,046 537 63 T.P. 9 30.5 274.5 1395.4 DL 140,887 1,212 23.5 61,855 816 1,267 395 -55 MIDSPAN 9 46.75 420.8 3278.3 DL 177,704 650 42.25 61,855 650 944 0 -294 -1 1,037 2,548 Reduce Cable Tension by GO DATE WESTERN WOOD STRUCTURES, INC. PROJECT 11 61A-1 1 +1(.(k 6 LAr l e- E-k-I. 3 / 1"1(1 00--E4(.70 LOCATION P.O. BOX 130, TUALATIN, OREGON 97062 ��.y� n SHEET 503/692 -6900 • FAX 503/692 -6434 JOB NO. di J t7� -'-�3 By 0, , ' OF • P I iZ't AI ,A ! T 'ERJP_Z G02VE 0 6FA •'\ - kr-! U!}o (Lr o NN ' 1. 1 $ � 2' -44" y 3' -0" PI ?E COL MN I I 32. t-4. P€AZ o � I I A -ni'[. -#x•02 !� c�Ttl? cri •I a z m • � us ( �� 3o u3 4t s N la — CAP SZ l 66 N 1— a J O co co O O 0 J W _ LL CO CO O _ O N • Western Wood Structures, Inc. — Computer Analysis Systems • P.O. Box 130, 20675 S.W. 105th, Tualatin, OR 97062 -0130 — 503/692 -6900 or 800/547 -5411 Fax: 503/692 -6434 Tigard High Beam Repairs - Tigard, Oregon - Job # 088003 7- Mar -08 Shear Plate(s) in side grain loading Joint Description: 4" Shear Plate w/ 7/8" Bolts # of bolts: 4 # of fasteners /face: 2 CD = 1.15 P = 4320 lbs C 9 = 0.98 Q = 3000 lbs C = 1.00 C = 1.00 P' = P * (C * ( C g ) * (C,) * (Cst) P' = 4868.64 lbs = Q * (CD) * ( Cg) * ( CA) Q' = 3381 lbs O = 0.0427 radians = 7.60 degrees P Q 4831 lbs P' sin 9 +Q'cos 6 Capacity of (8) 4" Shear Plate w/ 7/8" Bolts = 38,652 lbs • Western Wood Structures, Inc. P.O. Box 130 - Tualatin. Oregon 97062 March 10, 2008 (503) 692 - 6900 Paue ( Z 1 of Tigard High Beam Repairs Tigard, Oregon • Job Number: 088003 Pitched and Tapered Curved Beam - Radial Reinforcement 13 c_ Beam Properties Slope of top of beam - cl)T = 9.46 Deg Species = D.F. Slope of bottom of beam - ci, = 7.10 Deg Fb = 2400 psi Width - b = 9.00 in. Note: Beam made prior to 1971 have no dedicated tension laminations. Depth @ bearing - d brg = 17.625 in. Therefor the bending stress allowable must be multiplied by 0.75. Depth @ tangent point - d = 23.00 in. Fb = 1800 psi Depth @ centerline - d 38.875 in. F„ = 265 psi Beam Spacing = 20.50 ft. F = 1650 psi Beam Length = 46.67 ft. F cpe r p = 560 psi Radius = 100.00 ft. F = 1100 psi Thickness of Beam Lams = 1.625 in. E = 1800000 psi F„ = 15 psi Loading Roof Dead Load Bulit -up Roofing: 3.50 psf 5/8" plywood: 1.90 psf • 2x12 @ 16" o /c: 3.20 psf Accoustical Ceiling: 3.00 psf Batt Insulation: 3.00 psf Miscellaneous: 1.50 psf • Total Roof DL = 16.10 psf - -- -Use 17 psf + Beam Self- Weight Beam Self Weight • Beam Average Depth = 26.50 in. Density of Glulam = 35 pcf Beam Average Weight = 58 plf Total Beam Dead Load: Roof Dead Load = 349 plf Beam Self Weight = 58 plf DL = 406 plf • Roof Snow Load Roof Snow Load = 25.00 psf Total Beam Snow Load: SL = 513 plf • Western Wood Structures, Inc. P.O. Box 130 - Tualatin, Oregon 97062 March 10, 2008 (503) 692 - 6900 Page a of Tigard High Beam Repairs Tigard. Oregon Job Number: 088003 Design Check Check Depth at Centerline for Bending M = WL /8 = 250,164 ft -lb Bending Stress Coefficient - Kb Coefficients from AITC Timber Construction Manual Table 4.11 D = 1.311 E = 0.219 F = 0.631 R = Radius + d = 1219 in. K = D + E(d /R + F(d /R = 1.3186 Bending Stress f = 6M /bd = 1324.3 psi f = K = 1746 psi Allowable Stress Factors CD = 1.15 C„ = (5.125/b) (12 /d) (21 /L) l = 0.7759 C, = 1- 2000(t /R) = 0.9963 F'b = FbCDC = 1600 psi Bending Stress Check f /F' = 109% NG Check Depth at Tangent Point for Bending Reaction = WLJ2 = 21443 lb Distance from bearing to tangent point: x = 11.00 ft. M, = Reaction(x) - Wx /2 = 180,271 ft-lb Bending Stress f = 6M /bd 2 = 2726 psi Allowable Stress Factors CD = 1.15 C, = (5.125/b) 1 = 0.8177 C = 1- 2000(t/R) = 0.9963 C, = [1 /1 +(F tan ,0 /F„) + F tan - 0/Fcperp) 2 ] 112 = 0.6610 F'b = F of C,, & C,)C = 1363 psi Bending Stress Check f /F' = 200% NG Western Wood Structures, Inc. P.O. Box 130 - Tualatin. Oregon 97062 March 10, 2008 (503) 692 - 6900 Page 13 of Tigard High Beam Repairs Tigard, Oregon Job Number: 088003 Check Depth at three points between Tangent Point and Bearing for Bending Section A IC x (ft.) 2.75 5.5 8.25 d' (in.) 19.000 20.375 21.750 M (ft-lb) 55,492 104,035 145,628 S (in 542 623 710 f (psi) 1,230 2,005 2,463 Co 1.15 1.15 1.15 C, 0.8335 0.8277 0.8223 C 0.6610 0.6610 0.6610 F'b (psi) 1,368 1,368 1,368 f /F' 89.88% 146.53% 180.00% OK NG NG Check Radial Tension Stress at Centerline Coefficient for the Determination of K, Coefficients from AITC Timber Construction Manual Table 4.7 A = 0.0367 B = 0.0793 C = 0.2128 R = Radius + d = 1219 in. K = A + B(d + C(d = 0.0394 Shape Reduction Factors from AITC Timber Construction Manual Table 4.8 l = 24.6406 ft. L /I, = 1.9 = 0.656 R= -0.640 C = a +13 d = 0.636 = K = 33 psi F'„ = F 17 psi Note: f„ must not exceed 1/3 the of the allowable shear stress. Note: Multiply F„ by 0.72 for radial tension values. (0.72 *F„ /3)C 73 psi Radial Tension Stress Check Radial reinforcement required Western Wood Structures, Inc. P.O. Box 130 - Tualatin, Oregon 97062 - 7} - t March 10, 2008 (503) 692 -6900 Page of Tigard High Beam Repairs Tigard, Oregon Job Number: 088003 Radial Reinforcement Design Using 3/4" diameter grade 60 rebar in 1" diameter epoxy - filled holes: Effective depth at centerline: d - 2" = 17.44 in. Allowable wood withdrawal: 1455 lb / 2.5 = 582 pli Max tension for wood withdrawal = 10149 lb Controls Area of 3/4" diameter rebar = 0.4418 in Fy for grade 60 rebar = 60,000 psi Allowable tension for steel: 0.5Fy = 30,000 psi Max tension for steel rebar = 13254 lb • Radial Tension Force per in of length: f * b = 299 pli Maximum Rod Spacing = 33.96 in. Use 33" maximum rebar spacing Western Wood Structures, Inc. P.O. Box 130 - Tualatin, Oregon 97062 March 7, 2008. (503) 692 -6900 Page ! of Tigard High Beam Repairs Tigard, Oregon Job Number: 088003 Pitched and Tapered Curved Beam - Cable Repair ('SF- ''' Beam Properties Slope of top of beam - d) = 9.46 Deg Species = D.F. Slope of bottom of beam - (0e = 7.10 Deg F = 2400 psi Fe = 1450 psi Width - b = 9.00 in. Note: Beam made prior to 1971 have no dedicated tension laminations. Depth @ bearing - d brg = 17.625 in. Therefor the bending stress allowable must be multiplied by 0.75. Depth @ tangent point - d = 23.00 in. Fb = 1800 psi Depth @ centerline - d = 38.875 in. F„ = 265 psi Beam Spacing = 20.50 ft. F = 1650 psi Beam Length = 46.67 ft. Fcpem = 560 psi Radius = 100.00 ft. F = 1100 psi Thickness of Beam Lams = 1.625 in. E = 1800000 psi F = 15 psi Loadin Roof Dead Load Bulit -up Roofing: 3.50 psf 5/8" plywood: 1.90 psf 2x12 @ 16" o /c: 3.20 psf Accoustical Ceiling: 3.00 psf Batt Insulation: 3.00 psf Miscellaneous: 1.50 psf Total Roof DL = 16.10 psf - -- -Use 17 psf + Beam Self- Weight Beam Self Weight Beam Average Depth = 26.50 in. • Density of Glulam = 35 pcf Beam Average Weight = 58 plf Total Beam Dead Load: Roof Dead Load = 349 plf Beam Self Weight = 58 plf DL = 406 plf Roof Snow Load Roof Snow Load = 25.00 psf Total Beam Snow Load: SL = 513 plf • Western Wood Structures, Inc. P.O. Box 130 - Tualatin, Oregon 97062 March 7, 2008 (503) 692 -6900 I'ageol_ Tigard High Beam Repairs Tigard, Oregon Job Number: 088003 Beam Stresses Worst case overstress at tangent point from radial tension analysis Distance from bearing to tangent point: x = 11.00 ft. DL Reaction = W /2 = 9484 lb TL Reaction = W = 21443 lb Bending Stress Mpg = Reaction(x) - W /2 = 79,736 ft -lb fbo1_ = 6MDL/bdt = 1206 psi MTL = Reaction(x) - WTLx2 /2 = 180,271 ft -lb fon = 6M = 2726 psi Allowable Stress Factors Co= 1.15 C„ = (5.125/b) 1 = 0.8177 C = 1- 2000(t/R) = 0.9963 C, = [1 /1 +(F tan T9 /F + Fb tan WFCpefp)2)1rz = 0.6610 • F = F of C„ & C,)C = 1363 psi Bending Stress Check • fboL /F'b = 88% - - -OK f bTL /F' = 200% NG Cable Tension Beam "e" at tangent point: e 15.75 in. Beam Area at tangent point: A = 207.00 in Beam Section Modulus at tangent point: S = 793.50 in f b= fb- F'b= T /A +Te /S Therefor: T = f - F / (1 /A + e, /S) = 55,228 lb Number of cables = 4 Tension on each cable = 13,807 lb Use Tension = 13,800 lb Western Wood Structures, Inc. P.O. Box 130 - Tualatin, Oregon 97062 ` March 7, 2008 (503) 692 -6900 Pagel/ of Tigard High Beam Repairs Tigard, Oregon Job Number: 088003 Check beam at other points Section A IB IC ICenterline Dist. from Bearing to Section X (ft.) 2.750 5.500 8.250 23.333 Depth at Section d' (in.) 19.000 20.375 21.750 38.875 Dead Load Moment Mph (ft -lb) 24,545 46,016 64,413 110,650 Total Load Moment MTV (ft -lb) 55,492 104,035 145,628 250,164 Area at Section A (in 171 183 196 350 Section Modulus at Section S (in 542 623 710 2,267 Dead Load Bending Stress fbpL (Psi) 544 887 1,089 586 Total Load Bending Stress fbTL (Psi) 1,230 2,005 2,463 1,324 Duration or Load Factor C 1.15 1.15 1.15 1.15 Volume Factor C„ 0.8335 0.8277 0.8223 0.7759 Stress Interaction Factor C 0.6610 0.6610 0.6610 0.6610 Curvature Factor Cc 1.0000 1.0000 1.0000 0.9963 Allow. Pos. Bending Stress F'b (psi) 1,368 .1,368 1,368 1,363 Amount of overstress in beam f -F' (psi) -138 637 1,095 -39 Cable Ecc. to Beam N.A. e (in.) 1.7500 6.5000 11.2500 37.5000 Allow. Pos. Bending Stress from Cables f b (psi) 251 877 1,157 1,071 Negative Bending Stress fb (psi) 389 241 63 1,110 Allow. Neg. Bending Stress Ft; (psi) 1,102 1,102 1,102 1,102 Neg. Bending Stress Check 35.30% 21.83% 5.68% 100.70% OK OK OK ok os. Bending Stress Check with Cables Tensionedlfb /Fb + f b 75.97% 89.28% 97.52% 54.40% OK OK OK OK Final cable loads When the cables are initially tensioned, the beam is loaded with dead load only and when live load is applied, the tension in each cable increases by the amount determined on the next sheet. Tension Reduction Worksheet Amount of reduction in tension = 3,500 lb Reduced tension = 10,300 lb " When the second cable is tensioned, it reduces the load in the first cable. Change in cable load: Avg f in 3rd cycle = 398 psi A at 1 cable = (Avg f 3 cycle) ' 30,970 / 1.8E6 * 0.007 = 978 lb Increase in tension at cable #1 = 1,000 lb Final Cable Loads: Tension at Cable #1 = 11,300 lb Tension at Cable #2 = 10,300 lb The difference between the average stress under total load and the average stress at dead load only is a measure in the change in fiber length in the wood at the bottom of the member. The change of cable length must equal the change in fiber length from total load condition of loading and dead load only. Field measurements indicate the change in length of the cable is equal to 0.7% of its length under 30,970 lb. for 1/2" diameter grade 270 cable. Cable increase (lbs.) = v„,' P 1 E„.' e CABLE BEAM POINT OF BEAM BEAM AREA SECTION LOAD MOMENT IN- fb "e" "T" fb' PSI fb -fb' PSI fb -fb' AT "e" INCREASE MARK REVIEW WIDTH DEPTH MODULUS CASE LBS. PSI IN. LBS TOP BOTTOM TOP BOTTOM MEAN TOTAL LBS 81 A 9 19 171.0 541.5 TL 55,492 1,230 1.75 27,600 -72 251 1,302 979 8 9 20.375 183.4 622.7 TL 104,035 2,005 6.5 55,200 275 877 1,730 1,128 C 9 21.75 195.8 709.6 TL 145,628 2,463 11.25 55,200 593 1,157 1,870 1,306 T.P. 9 23 207.0 793.5 TL 180,271 2,726 15.75 55,200 829 1,362 1,897 1,364 MIDSPAN 9 38.875 349.9 2266.9 TL 250,164 1,324 37.5 55,200 755 1,071 569 253 1,013 B1 A 9 19 171.0 541.5 DL 24,545 544 1.75 27,600 -72 251 616 293 B 9 20.375 183.4 622.7 DL 46,016 887 6.5 55,200 275 877 612 10 C 9 21.75 195.8 709.6 DL 64,413 1,089 11.25 55,200 593 1,157 496 -68 T.P. 9 23 207.0 793.5 DL 79,736 1,206 15.75 55,200 829 1,362 377 -156 MIDSPAN 9 38.875 349.9 2266.9 DL 110,650 586 37.5 55,200 755 1,071 -170 -485 -175 1,188 2,919 B1 A 9 19 171.0 541.5 DL 24,545 544 2.25 24,681 -42 247 586 297 8 9 20.375 183.4 622.7 DL 46,016 887 9.375 52,281 502 1,072 385 -185 C 9 21.75 195.8 709.6 DL 64,413 1,089 16.5 52,281 949 1,483 141 -393 T.P. 9 23 207.0 793.5 DL 79,736 1,206 23.5 52,281 1,296 1,801 -90 -595 MIDSPAN 9 38.875 349.9 2266.9 DL 110,650 586 42.25 52,281 825 1,124 -239 -538 -428 1,441 3,541 B1 A 9 19 171.0 541.5 DL 24,545 544 2.25 24,059 -41 241 585 303 B 9 20.375 183.4 622.7 DL 46,016 887 9.375 51,659 496 1,059 391 -173 C 9 21.75 195.8 709.6 DL 64,413 1,089 16.5 51,659 937 1,465 152 -376 T.P. 9 23 207.0 793.5 DL 79,736 1,206 23.5 51,659 1,280 1,779 -75 -574 _ MIDSPAN _ 9 38.875 349.9 2266.9 DL 110,650 586 _ 42.25 51,659 815 1,110 -229 -525 _ -412 1,424 3,501 Reduce Cable Tension by DATE WESTERN WOOD STRUCTURES INC PROJECT 1 /14 Ni 4711- t J1lr\ (aF qA 3 / 7 I B LOCATION 1-16 /41 2 -b + 01 ✓G P.O. BOX 130, TUALATIN, OREGON 97062 gia&Y) BY 2 p ,� � 503/692 -6900 • FAX 503/692 -6434 JOB NO. P � 1 , ' Z ' 1 OF V PI "1" A- S T'Rl' E, JRx/ FAD t? EAel, - GA-BL-�_A-,4C-H' (2_ GOt IJ E -1 o!J aSPeN c.- 101" 3' -0" )' • PIPE COLIJMN 1 ii I lio ! �� Z - 7 bm ut3 . P ,'- {�— . I ' I I I , Pyw)c,OC L I-OCA-T (Ofi I (V I� • a I 23 ! 4 �� To 4_ of (31X'1 v- • I- �� I-- -g To L e► u�L L. 0..- z in o U s e C3) g�� eoL- it' 0 6 .- ..eLA '.S - -P= z9, 01 Lt S. co O O (., (0 M) 0 N O M) 0 O co co O ND O 0 CO CO 0 0_ i O 0 J W _ IL co co • _O O O rI Western Wood Structures, Inc. - Computer Analysis Systems • P.O. Box 130, 20675 S.W. 105th, Tualatin, OR 97062 -0130 — 503/692 -6900 or 800/547 -5411 Fax: 503/692 -6434 Tigard High Beam Repairs - Tigard, Oregon - Job # 088003 10- Mar -08 Shear Plate(s) in side grain loading Joint Description: 4" Shear Plate w/ 7/8" Bolts # of bolts: 3 # of fasteners /face: 2 CD = 1.15 • • P = 4320 lbs C = 0.98 Q = 3000 lbs CA = 1.00 C 1.00 P' = P * (C * (CO * (C * (Cst) P' = 4868.64 lbs = Q * (CD) * ( Cg) * ( CA) Q' = 3381 lbs A = 0.039u radians = 7.10 degrees P Q' • 4836 lbs P' sin 2 e + Q'cos'e Capacity of (6) 4" Shear Plate w/ 7/8" Bolts = 29,017 lbs