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""-\' '/R;;i;vV ispnl)i ,or canforrnance'wlth tile design cons;ept of tile f!roject . anckcGlmplloPCB 􀁾􀀬􀁩􀁴􀁨 theinformation, givet;l in the COJ1tract Dpcuments. : ApprovaldOes net aUlhcrize an¥ deviation from the Contract Documents I " I􀁡􀁮􀁾􀁤􀁡􀁮􀁹􀀮􀁣􀁨􀁡􀁮􀁧􀁾 fr-om tile Gontract !)O'cL\mMts 􀁭􀁬􀁪􀁳􀁴􀁢􀁥􀁰􀁲􀁑􀁃􀁥􀁳􀁾􀁥􀁑􀁢􀁻 I,j: 􀁾􀀹􀁉􀀱􀁡􀁊􀀱􀁧􀁥􀁄􀁩􀁤􀁾􀁲􀀬 􀁃􀁯􀁲􀁴􀁴􀁡􀁣􀁴􀁏􀁦􀁪􀁳􀁊􀁾􀁳􀁲􀀱􀀿􀁮􀁳􀁩􀁢􀁬􀁅􀀺􀀬􀁦􀀹􀁴􀀬􀁤􀁩􀁭􀁥􀁮􀁓􀁩􀀶􀀱􀀱􀁓􀁽􀀨􀀩􀀩􀁢􀁾􀀺􀁃􀁏􀁑􀁦􀁩􀁲􀁮􀀺􀀢􀁤􀀬 land 􀁣􀁯􀀨􀁛􀁥􀁩􀁾􀁬􀁥􀁤􀁡􀁦􀁴􀁮􀁥 Job;;lte', :for mrQrmatlon that pellqlnssale!yto 􀀬􀁬􀁾􀁥􀀻 'I' faJjricatibn 􀁰􀁲􀁯􀁣􀁾􀁳􀁳􀁥􀁳 arlo ,technfques,:,of corrstr't1Ction; and fDr ,cr)ordii'ouon ofthe\'ljor(ofallfi'adas, ';"," " " 􀀬􀀮􀀬􀁾 . "'c, 􀀭􀁾 '.. _.,.... 􀁾 􀁾 , 􀂷􀂷􀀧􀁉􀁾􀁷 􀁦􀁬􀀧􀁬􀁾􀁲􀀴􀁱􀁾 -, '--' -' ,< • JJ\ :1r"'" .1 ,! I!. i . i ARAPAHO RD. STEP-BY-STEP CONSTRUCTION ANALYSIS WITH DEFLECTIONS AND CABLE FORCES August 15, 2005 TABLE OF CONTENTS ! SUMMARY The enclosed calculations are for the step-by-step longitudinal construction analysis oftheArapaho Road steel arch bridge. BRUeO, a two-dimensional finite element analysis program that considers time dependent losses, was used for the step-bystep analysis. Stardyne, a three-dimensional finite element analysis program, was used to verify the load distribution to the north and south arches and the BRueo deck deflections. A step-by-step check ofthe stresses in the superstructure will follow in a separate submittal. The step-by-step construction analysis follows the construction sequence shown in the contract plans, with the exception ofthe steel arch being erected prior to erecting the precast u-beams. This change in the construction sequence was chosen by the contractor and does not effect the stresses in structure in any way. The hangers were stressed to the forces shown in table 1 ofthe contract plans. The BRueo step-by-step cable force table shows the comparison between plan cable forces and BRUeO cable forces at bridge opening. The results show that the majority of the cable forces are within a reasonable tolerance to contract plans, with the exception of cables 2 and 8, which are vary from contract plans by approximately 15%. However, the maximum final cable force (north cable 9) is. within 1% ofplan and . therefore, none ofthe cable are overstressed. The comparison ofBRUeO and Stardyne cable forces and support reactions verifies the assumed distribution ofloads in the two-dimensional BRueo analysis. The Stardyne deflections at bridge completion are approximately W' upwards on the north edge ofdeck and 3/8" upwards on the south edge of deck. These deflections are similar to BRUeO, however, the BRueo deflections also consider the creep ofthe prestressed concrete u-beams. I· II iiII . II BRUCO MODEL LAYOUT z. BRUCO MODEL LAYOUT NORTH AND SOUTH LAYOUTS IDENTICAL 404 403 402 401 409 408 407 406 414 413 411 412 5 6 3 2 8 9 \13 n4 11 116 117 118 119 120 12\ 123 124 1 .4 4 1 152 10 11 12 13 14 IS 16 17 18 19 20 21 22 23 24 2526 2728 29 30 .31 32 33 34 3S 36 37 38 39 40 41 42 43 44 45 46 47 ELEMENT 􀁾 NODE EXAMPLE: MEMBER 7 BEGINS AT NODE 7 AND ENDS AT NODE 8 (TYP.) NODE 7 fEL7EM.t NODE 8 313 314 312 311 "11 JJ􀁾 J1'I ] -""1:1 'I􀁾1I -1J 304 309 J 303 308 302 307 301 306 I 'i 1 11IIIIIII I -II .1IIII STARDYNE MODEL LAYOUT N N ,....,,..0.., ,...., U 7 N .-D Stardyne Model: Beam Element Designation (West End) VI l10 Cl G3 2.. ,2102 2103 21M ,2105 2106 ,2107 ,2108 2109 2110 2111 T' 211'1-2115 2116 ,2117 ·"1'19"'0 2121 ·"11'"'112 􀀱􀁾 1 1212. 'IT 2205,2206, '11'"['''19" 2212 2213 221'1-2215 2216 "'fE'f20 2221. 2222 2223 2224.'122 􀀮􀁺􀁾 􀀲􀁾􀀧􀁬􀀲􀀲 'm2-IT 2307 2308 2309 .. 2310 2311 2312 .2313 2314 2315 .2316 : 2317 2318 2319 2320 2321 2322 2323 2324 '132 3 3 '32 " .. .. 2 2402 .2403. ,2404 2W'/"+'" 2408. 2409. , 2410 2411 2412. 2413 2414 2415 2416 , 2417 2418 2419 2420 2421 2422 2423 "'n'.. . .. 4 􀁾􀀴􀀲􀀮 .. 1 . Stardyne Model: Beam Element Designation (East End) VI LlO Cl G3ntrl'+130 22" 22" 22" .22" 22". 􀀲􀀲􀀳􀀶􀁾2137t'138 2139. mo .22" . 2242 . '143. 22" 22" 2246. 􀁭􀁴􀁾􀁾 􀁭􀀹􀁾 􀀢􀀧􀁾􀀢􀀧􀁾􀀧 ,􀀧􀁾􀀧􀁾􀀲􀀲􀁾􀀲􀀲􀀺22"􀁾2230I22"r'"B:tJJ􀁾􀀲􀀳􀀷􀁴􀀲􀀳􀀸􀀱􀀲􀀲􀀢􀁉􀀲􀀲􀁗l224212242.1. 2243 I 2244j ""1 "46.1. "421 ""1 "46 I 2250j225m" :d"TI' I 􀀳􀁾􀀬􀁾􀀬􀁭􀁅231ftl'l'" 2336 '1:" 1339 23W 234'=r111ll'''' 2'1-'1-91. 2If50 􀀱􀀮􀀲􀀧􀀱􀀭􀀵􀁾􀁙􀁴􀁰􀀲 """>42 "",,2430. ''''I''31!""!"1=."36,"" "" "", 'T'r"'['['["[']']':, " 1 o -VI llO CI Glf. !:,11t1 Stardyne Model: North Arch Element Designation L f"J VI LlO CI G5 ,"1 􀂢􀀱􀀭􀁙􀁾􀀲􀁾􀁾􀀧 72'v-L Stardyne Model: South Arch Element Designation ,<.",..,'.:.:. "' I .1I1I .JIIII I BRUCO CONSTRUCTION SEQUENCE I I! I ARAPAHO RD -BRUCO ERECTION SEQUENCE STEP ERECTION DAY CASTING DAY DESCRIPTION 1 30 0 ERECT PIERS 9 AND 10 2 90 ERECT STEEL ARCH 3 120 90 ERECT PRECAST BEAMS ON TEMPORARY BENT 4 130 CAST U-BEAM SPLICE AND TRANSVERSE DIAPHRAGMS 5 160 POUR DECK (ADD DECK WEIGHT TO PRECAST U-BEAMS) 6 160 130 DECK HARDENED (ERECT WEIGHTLESS DECK ELEMENTS) 7 190 STRESS CABLE 5 TO 5 KIPS 8 190 STRESS CABLE 6 TO 5 KIPS 9 190 STRESS CABLE 4 TO 5 KIPS 10 190 STRESS CABLE 7 TO 5 KIPS 11 190 STRESS CABLE 3 TO 5 KIPS 12 190 STRESS CABLE 8 TO 5 KIPS 13 190 STRESS CABLE 2 TO 5 KIPS 14 190 STRESS CABLE 9 TO 5 KIPS 15 190 STRESS CABLE 1 TO 5 KIPS 16 -20 190 STRESS CABLE 5 TO 238.1 KIPS 21 -24 190 STRESS CABLE 6 TO 146.2 KIPS 25 -28 190 STRESS CABLE 4 TO 159.0 KIPS 29 -32 190 STRESS CABLE 7 TO 162.4 KIPS 33 -36 190 STRESS CABLE 3 TO 192.6 KIPS 37 -39 190 STRESS CABLE 8 TO 158.9 KIPS 40 -42 190 STRESS CABLE 2 TO 171.1 KIPS 43 -44 190 STRESS CABLE 9 TO 142.1 KIPS 45 -46 190 STRESS CABLE 1 TO 146.1 KIPS 47 220 ADD BARRIER WEIGHT NOTE: CABLES WERE STRESSED IN MULTIPLE STEPS TO ALLOW MORE ITERATIONS FOR THE NON-LINEAR BRUCO ANALYSIS IIIIII JI1 c>·-1I BRUCO STEP-BY-STEP CABLE FORCES PLAN JACKING FORCE (TYP) BRUCO CABLE 1 CABLE 2 CABLE 3 CABLE 4 CABLE 5 CABLE 6 CABLE 7 CABLE 8 CABLE 9 STEP North (LT) South (RT) North (LT) South (RT) North (LT) South (RT)" " North (LT) South (RT) North (LT) South (RT) North (LT) South (RT) North (LT) South (RT) North (LT) South (RT) North (LT) South (RT) 7 5.0 5.0 8 2.6 2.6 4.9 5.0 , 9 5.0 5.0 0.0 0.0 6.2 6.3 10 6.9 6.9 0.0 0.0 2.9 3.0 5.1 51.0 11 5.1 5.0 4.1 4.0 0.0 0.0 3.9 4.0 " 6.5 6.4 12 6.0 5.9 4.9 4.9 0.2 0.1 4.0 -4.2 3.5 3',4 5.1 5.0 13 5.0 5.0 3.1 3.0 5.0 5.0 1.0 0.9 4.7 4.8 4.0 319 5.8 5.6 14 5.3 5.2 3.3 3.2 5.2 5.2 1.3 1.2 5.1 5.3 3.9 3.8 3.1 2.9 5.0 5.0 15 5.0 5.0 2.7 2.5 3.3 3.1 5.7 5.6 1.7 1.6 5.3 5.5 4.1 4.0 3.3 3.0 5.2 5.2 20 67.2 55.8 17.5 13.6 0.0 0.0 0.0 0.0 238.1 194.8 0.0 , "" 0.0 0.0 0.0 18.3 14.5 67.7 56.2 24 84.2 68.7 52.3 41.3 0.0 0.0 0.0 0.0 174.7 143.6 146.2 116.3 0.0 0.0 0.0 0.0 66.7 54.8 28 102.0 82.9 3.3 2.1 0.0 0.0 159.0 125.6 98.6 82.4 158.4 126.6 0.0 0.0 4.0 2.5 102.5 83.1 32 115.0 93.0 26.4 18.9 -0.0 0.0 186.1 146.8 97.6 81.8 79.2 63.1 162.4 127.1 0.0 0.0 -50.8 41.0. 36 69.8 55.5 0.0 0.0 192.6 150.4 98.2 76.4 93.2 78.9 100.8 80.1 188.4 147.0 0.0 0.0 72.9 57.6 39 80.9 64.3 0.0 0.0 204.0 159.3 110.5 86.0 105.8 89.0 96.0 77.0 120.9 93.7 158.9 124.6 0.0 0.0 42 0.0 0.0 171.1 􀀨􀀱􀀳􀀴􀁟􀀷􀁾 117.0 90.6 98.2 77.1 113.0 95.0 102.6 82.2 123.8 95.9 158.3 124.4 0.0 0.0 44 0.0 0.0 168.0 /132.2 115.9 89.7 98.6 77.3 116.6 97.7 108.5 86.9 115.2 89.9 70.8 54.0 142.1 111.9 46 146.1 115.2 78.4 I 60.1 107.0 83.3 104.6 82.1 120.2 100.3 108.8 87.0 114.3 89.0 69.6 53.0 138.9 109.4 47 (FINAL) 149.5 118.5 80.0 I 61.9 108.5 85.1 106.9 84.6 123.4 103.7 111.1 89.5 115.8 90.8 71.1 54.8 142.3 112.9 PLAN 148.4 115.2 93.4 I 72.5 98.8 77.5 106.7 83.5 113.5 88.7 106.8 83.6 99.1 77.7 93.7 72.7 146.6 113.7 /1I J BRUCO STEP-BY-STEP CABLE FORCES (kips) J 􀁾􀁬.J] _J -l1 J]1\I 8/15/2005 \b I 1I1jI BRUCO STEP-BY-STEP ARCH DEFLECTIONS -r:::P -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 c:: 0.7 co 0.8 +:i 0.9 () (1) 1.0 q:: (1) 1.1 o 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 Arch Vertical DisDlacement [ -+-STEP 6 North Vertical Deflection, in ----STEP 6 South Vertical Deflection, in Station, ft. C) 0 0 0 0 0 c c c c ::» 􀁣􀁾 􀁾􀁩 """': """': d """': """': d """': """': d """': 0 0 0 0 0 0 0 II: • H 􀁾 ; 􀁾 a: 􀁾 􀁾 􀁾 􀁾 􀁾 􀁾 ," ... II(} II(} II(} 􀁾 􀁾 􀁾 􀁾 􀁾 􀁾 􀁾 II: •••••••••••••••••••••••••••••••••••• II" •••••••••••• - ---0 Arch Vertical DisDlacement I -+-STEP 15 North Vertical Deflection, in 1_ -STEP 15 South Vertical Deflection, in Q -0.4 c •0.3 a4::t2 -. -. -• -. -• -. . . . . -0.2 I "';' 􀁾 :: "= -0.1 1$ It) It) It) co --0.0 I _ I I I 0.1 -0.2 0.3 0.4 0.5 c 0.6 0.7 § 0.8 15 0.9 Q) 1.0 +-----------------------------------------l 'Q; 1.1 +-----------------------------------------l o 1.2 +-----------------------------------------l 1.3 􀀫􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀁾􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀁬 1.4 +---------------------------------------1 1.5 +---------------------------------------1 1.6 +-------------------------------------------l 1.7 +-----------------------------------------l 1.8 􀀫􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀁾􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭� �􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀁬 1.9 +---------------------------------------1 2.0 +---------------------------------------1 2.1 +---------------------------------------1 2.2 --'----..l Arch Vertical DisDlacement I -+--STEP 20 North Vertical Deflection, In ---STEP 20 South Vertical Deflection, in Station, ft. o o-oe oe eo eo oe eo o o o C5 C5 0 0 0 0 0 0 is is 􀁣􀁾 0 0 0 0 2 9 􀁾 2 􀁾 2 􀀵􀁾 􀁾 co co 0 􀁾 c» 􀁾 -, c» 􀁾 0 􀁾 0 0 􀁾 􀁾 "I" 􀀭􀁾 -----..... .. 􀁾􀀻􀀭 .. 􀁾􀀭 ----,,/'-, ..ff '\\. J''" 􀁾 !'J \ til JT 􀁾􀁜 /1 \" J4r 􀁜􀀮􀁾 J'j \.. ,IT ,'II ",/, \. ____ -I \ '/'-. 􀁾 ....... _0.4 0 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 c 0.6 􀀭􀁾 0.7 § 0.8 :.o;:; 0.9 (1) 1.0 􀁾 1.1 Cl 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 !'J o Arch Vertical Displacement -+-STEP 24 North Vertical Deflection, in -STEP 24 South Vertical Deflection, in Station, ft. -Q -Q -Q -o -o -o -Q -o o-o-o o 0 0 Q 0 0 Q 0 0 0 􀁣􀁾 g 􀁾 􀁾􀁾 􀁾 E g 􀁾 S! 􀁾 E 􀁣􀁾 QJf-__III 􀁾􀁃􀁄􀁾__􀀭􀁊􀁃􀁄􀁾􀁲􀁊􀀢􀀢􀀧􀁬􀁊􀁾􀁾􀁾􀀽􀁾􀀧􀀭􀀧􀁉􀁾􀀽􀀺􀁩􀁾 0 Q Q Q Q.............. --.. !'o iA 􀁾􀀮 􀁾 ....-",--􀁾 􀀮􀁾 -../..... '-.-" .1/""\\ tiIlI 􀁾 IJ ,\ 􀁾 I 􀁜􀁾 til 􀁾􀁟 /1' ,\-􀀢􀁊􀁾 //\\ til 􀁾 􀁾 /r \ \. Ji /\.. .;-􀁾 '\ 􀁾 /\ {I '\.. JI 􀀮􀁾 -0.4 Q -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 c 0.6 0.7 § 0.8 t5 0.9 (I) 1.0 l5 1.1 o 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 N f....J ('J Arch Vertical Displacement -+-STEP 28 North Vertical Deflection, in -STEP 28 South Vertical Deflection, in Station, ft. -0.4 􀁾 g I 􀁾 ; I I I 1 ; I j 􀀺􀁧􀂷􀁾􀁳 􀁾 O. 􀁾􀁾􀁾 0 0 0 0;<: 0 O· 0'1 􀁾 !! 􀁾 􀁾 Q Q Q Q /-::n:.'r" 􀁾 --. ,Jr",T' -"" ----S 􀁾􀀭 0.0 ..... \. .r'" 0.1 􀁾 , 0.2 " oJ 0.3 \\ 􀁾 0.4 ",. .1/0.5 􀁾􀀧􀀮 11 c 0.6 ,\" c 0.7 \ \.. , .Q 0.8 \\ 􀁾􀁉 ts 0.9 \.. \ /I 􀁾 1.0 \ 􀁾 • r Q) 1.1 \ \ //o 1.2 􀁾 􀁾 rJ j 1.3 \ .. J r 1.4 \ \ I I 1.5 􀁾 􀁾 }J • 1.6 \.. ---...""-j 1.7 \ -_. r 1.8 \ , 1.9 , /2.0 " .J' 2.1 􀁾􀁾 2.2 NvJ Arch Vertical DisDlacement I -+-STEP 32 North Vertical Deflection, in 􀁾 ---STEP 32 South Vertical Deflection, in Station, ft. 􀁾􀀴􀁑 Q Q Q Q Q Q Q Q Q Q Q . 0 0 0 Q Q Q Q Q Q 0 () ·0 3 . . Sl Q 􀁾􀀭 􀀭􀁾 2 2 Sl 􀁾 2 """-"" 2 sa 􀁾􀁾 .00.21 m r-m"i&. g g g g g...;: 􀁾 􀁾 ,1'0 . . ,., '\.. -----K --=-... -0.0 ...""\ rI 0.1 II " 0.2 " I 0.3 '" 1t 0.4 􀁾 IT 0.5 􀁾􀁜 '/c 0.6 \'. /; c 0.7 􀁜􀁾 􀁾􀁉 .2 0.8 􀁾􀁜 //t5 0.9 􀁜􀁾􀀮r 􀁾 1.0 \ \ " /Q) 1.1 􀁾 .. /J o 1.2 \ 􀁾 • r 1.3 \ \ /; 1.4 " " ? /1.5 􀁾 '). .. • 1.6 \. .? I 1.7 􀁾 j 1.8 \ /1.9 " J 22..10 " 􀁾......... /2.2 ' Arch Vertical DisDlacement 􀁾 -+-STEP 36 North Vertical Deflection, in L_ --STEP 36 South Vertical Deflection, in Station, ft. o o o o o o o o-o-o-o c 0 0 0 Q Q Q Q Q Q Q 􀁣􀁾 S g 􀁾􀀲 􀁾 S? g 􀁾 􀁧􀁾􀁯 S 􀁣􀁾 􀁾 C» .-"i! g g g g 􀁾 '!:: .. r0-M"" 1Ii ----Z ... ., -\ /..... '-J l-I \\ II \\ 1'1 "\\ I' 􀁜􀁾 _I \..\ /1 \-,j! \'1. .i/􀁾􀁜 FJ. \ . "/, \ /, \ 􀁾 ,. I 􀁾 .. 􀁾 , \ 􀁾 􀁾 /􀁾 .... ..--" \ -/"\.. J' "-. /"'-.. ......../_0.4 0 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 c 0.6 0.7 § 0.8 t5 0.9 Q) 1.0 l5 1.1 o 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 N_.t:. Arch Vertical Displacement -+-STEP 39 North Vertical Deflection, in -STEP 39 South Vertical Deflection, in Station, ft. o--o o-o o o o o o o o coo􀁾 0 0 0 0 0 0 0 0 C) r􀁾 g 􀀭􀁉􀁣􀁟􀁾􀁾􀁾􀁾􀁾􀁉􀀮􀀮� �􀀦􀁃􀀵􀀡􀁬􀁐􀀭__􀀭􀀭􀁣􀀲􀁾__O􀁾 0􀁾 0􀁾 0􀁾 0 0 􀁾􀁾 0 􀁾 • 􀁾 􀁾 􀁾 9 9 9 􀁾 9 􀁾 􀁾􀂭 -. r -. 􀁾 ----...... 􀁾 '7&.. ./... 􀁾 , \\ rII ... If 􀁾􀁜 ,.f }. ,.. \ /J. ,\ !'f \\ JJ 􀁜􀁾 I T '\.\ ,. I 􀁾 ", \ ). .I f \. \ 􀁾 , 􀁜􀁾 ",/, \. "-Jl,/\ -...... /􀁾, J' 􀁾 '" .r" 􀁾 -" 􀁾 _0.4 0 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 c 0.6 0.7 § 0.8 t5 0.9 Q) 1.0 Q) 1.1 o 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 t"-j U\ 􀁴􀂷􀁾􀀭􀁜 0'"'" Arch Vertical DisDlacement I -+-STEP 42 North Vertical Deflection, in L_ -STEP 42 South Vertical Deflection, in Station J ft. o 0 0 0 000 0 0 000 􀁾􀀴 c c c c c c c c c c -0·3coo 0 0 00 0 0 0 0 C􀁾 • C 5! Q 0 0 0 0 0 g 9 􀁾 C[) 􀁾􀀲􀁾 􀁾 􀁾 0 N 􀁾 􀁾 􀁾 a_ 􀁾 0.1 􀁾 􀁾 a:a:a.. 􀁾 􀁾 0 􀁾 􀁾 0 __ 􀁾􀀮 􀁾 ,1" -. 􀁾 -'DJ----.... 0.0 ... \. _ .... 0.1 􀁾 􀁾 0.2 1'. H 0.3 \\ rJ/0.4 􀁜􀁾 riJ 0.5 ,""\ Iii. c 0.6 􀁾􀀮􀀮 !'/c: 0.7 \ \ -'L .Q 0.8 􀁾 '\ i I o 0.9 \ 􀁾 "L 􀁾 1.0 , .. ]I /Q) 1.1 \ .. " , o 1.2 \. .. ." , 1.3 '"\ II-__ I 1.4 􀁾 "II.. .... 􀁾 1.5 .. -_ 11 1.6 ".. JI 1.7 , L 1.8 ..... 􀁾 1.9 .......... 􀁾􀀺􀁾 j I 2.2 Arch Vertical 􀁄􀁩􀁳􀁾􀁡􀁣􀁥􀁭􀁥􀁮􀁴 'L-+-STEP 44 North Vertical Deflection, in -STEP 44 South Vertical Deflection, in StationI ft. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 􀁾 􀁾 􀁾 􀁾 􀁾 0 0 0 0 0 􀁾 IIii!l' ..., ..., ..., ..., 0 0 0 0 0 ; N "¢ co co 0 N gJ 􀁟􀀮􀁾 gJ g g 0 0 0 "I'"" "I'"" II) CD CD CD CD CD CD CD o -0.4 e 0 0 0 0 0 C -0.3 .:E --; -; --:: • • -0.2 g,I 'q' 􀁾 go ':"' 􀁾􀀮 -0.1 II) II) 0.0 ... '-0.1 •􀁾 . .r------0.2 􀁾 􀁾􀁾 0.3 \Ii //0.4 ... .fY 0.5 􀁾􀁜 J' /c 0.6 \" ]I 􀁾 c 0.7 \ .. " ./.oQ 0.8 \ \. " 7 0.9 􀁾 -. ]I JI 􀁾 1.0 \ \. }Ii ,,/Q) 1.1 ... '\. }Ii tf o 1.2 \. 'I .. ,,/11..34 ..., --...... __ ... ,//1.5 􀁾 􀁾 1.6 "'.... /1.7 􀁾 , 1.8 1.9 2.0 2.1 2.2 􀁲􀁾 •..J Arch Vertical Displacement I -+-STEP 46 North Vertical Deflection, in l_ --STEP 46 South Vertical Deflection, in Station, ft. !c'oo -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 £; 0.7 § 0.8 1:5 0.9 Q) 1.0 Q) 1.1 o 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 ----------􀁣􀁾 2 2 2 2 2 2 2 2 2 2 5) 􀁣􀁾 . . = . . = = = . 0 0 0 0 0 0 􀁣􀁾 􀁾􀀻 0') (!; a; 0 (; 0 0 0 􀁾 􀁾 ,10 "I "I "I .., .., .., .., .., .., .., .. I I ---.:a.-......... --􀀮􀁾 􀁾 􀀭􀀭􀁾 fi ,"-Jijl ,"-JlJ' " ,,;rt/􀀬􀀬􀁾 ./1' 􀁜􀀮􀁾 /' '"\-. til "\ "-rI'.I '---,. " "\. .. ....1 '"\. ..... ....-/'"\... , -//􀁾 ...- Arch Vertical Displacement I --+-STEP 47 North Vertical Deflection, in l_ --STEP 47 South Vertical Deflection, in Station, ft. N-J] -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 c 0.6 -_ 0.7 § 0.8 15 0.9 Q) 1.0 Q) 1.1 o 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 r. r."'t --r"'II r."'t -r."'t 1""\ 1""\ --􀁾 --1""\ 1""\ 1""\ It' 􀁾􀁾 0 0 0 0 0 0 0 Q 0 0 0 0 0 􀁾 􀁾 􀁾 􀁾 􀁾􀀩 0 0 0 􀁾 0 0 0 0 0 0 0 0 0 􀁾􀁾 c:i 0 Q . 0 0 . Q . 0 . Q . Q . c:i 0 . c:i 0 . 0 . 0 . 0 . 0 . 􀁾􀀺􀁩 􀁾􀁾 as a; m en 0; C5 Q 0 0 0 Q C5 Q ($ ... ... ... ... ... --------0 ----􀁾 -.􀁾..-; 􀁾 ...... --􀁾,'-.Y 􀁾􀀯 􀁾􀀮 //". ... //"'. .... 􀁾􀀯 '\.."'\. ,,/--""-rI/\.""\.. ./? '\.. (\.50' 􀁦􀁕􀀾􀁾 '\ .. II '"\. "-'-• /-"-"ll. r//"'\. ... .-/'" .'-. ...-/"-..... 􀁾 /' 􀁾 /'-..,.K .... ) .... ( U.\\·· (l..f\.J-J \ '- .1jIII BRUCO STEP-BY-STEP DECK DEFLECTIONS 􀁴􀀯􀁾 -0.6 -0.5 -0.4 . -0.3 c: c: 0􀁾 -0.2 Q) 'a5 0 -0.1o 0.1 0.2 Deck Vertical Displacement --+-STEP 6 North Vertical Deflection, in ---STEP 6 South Vertical Deflection, in () 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 􀁾 "l LO co I"-00 en 0 T"'" C\I ('t) 'V LO co I"-00 en 0 T"'" 􀀵􀁾 en en en en en 0 0 0 0 0 0 0 0 0 0 T"'" T"'" LO LO LO LO LO co co co co co co co co co co co co 􀁾 -----,-----------... -----------Station, ft. 􀁟􀁾􀁟􀁬 _ 1_·_-Deck Vertical Displacement L -+-STEP 15 North Vertical Deflection, in ---STEP 15 South Vertical Deflection, in -0.6 ---.--,----------------------1' -0.5 t-------------'--------------- ------------JI -0.4 +-I vo 01 -0.3 cc0U-0.2 Q) i:i= Q) 0 -0.1 􀁾 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 LO c.o I'-co (J) 0 T"'" C'\I ('t) """" LO (0 I'-co (J) 0 T"'" (J) (J) (J) (J) (J) 0 0 0 0 0 0 0 0 0 0 T"'" T"'" LO LO LO LO LO (0 (0 (0 (0 (0 (0 (0 (0 (0 (0 (0 (0 0 􀁾􀂷 •••• -••• w.z ••••• 􀁾􀀭􀁾 0.1 Station, ft. 0.2 ' I Ij) () -0.6 -0.5 -0.4 . -0.3 cc .Q 1) -0.2 CD 'i= CD CI -0.1o 0.1 0.2 Deck Vertical Displacement --+-STEP 20 North Vertical Deflection, in -STEP 20 South Vertical Deflection, in s 0 0 p 9 0 0 0 0 0 0 0 0 􀁾 .Q.. -Q 0 0 􀁾 LO <0 0) 0 􀁾 C'\I ('t) 􀁾 LO 􀁾 0 􀁾 f .r-􀁾 􀁾 0 0 0 0 0 􀁾 0 LO ID <0 <0 <0 co <0 􀁃􀀵􀁾 􀁾 I I I I • • Station, ft. Deck Vertical DisDlacement I -+-STEP 24 North Vertical Deflection, in l_ ---STEP 24 South Vertical Deflection, in -0.6 T'--------------------------------" -0.5 I I -0.4 􀁴􀀭􀀭􀁾􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭 􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭I􀁊 0.1 I I 0.2 Station, ft. J-' 􀁾 --l, L:/J .1:. Deck Vertical Displacement 􀁾 --+-STEP 28 North Vertical Deflection, in 􀁾 --STEP 28 South Vertical Deflection, in -0.6 I I -0.5 I I -0.4 c -0.3 cB-0.2 C,) Q) 'Q) m o -0.1 0) 0 1.0 (0 I -/0 0.1 I Station, ft. 0.2 􀁾 Deck Vertical DisDlacement [ --+-STEP 32 North Vertical Deflection, in -STEP 32 South Vertical Deflection, in -0.6 I I -0.5 +-------------------------------'-----------------jl -0.4 t----------------------------------JI -0.3 cc0U-0.2 Q) ;;:: Q) 0 -0.1 0 0 0 ri.J 0 M 0 0 0 '" CX) 0) o C\I ('i) c.o '" CX) 0) 0) 0) o 0 0 0 0 0 LO LO LO c.o c.o c.o c.o c.o c.o I • 0 0.1 I I Station, ft. 0.2 --,-'􀀭􀀭􀁾􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀁾􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀁾􀀬 tA 0'..... Deck Vertical DisDlacement 􀁾 --+-STEP 36 North Vertical Deflection, in 􀁾 -STEP 36 South Vertical Deflection, in -0.6 I I -0.5 I I -0.4 I I -0.3 t: C0 :g -0.2 Q) l:i= Q) Cl -0.1 0 0 0 0 􀁾 o yo 0 0 0 0 r---00 C> 0 ('t) -.:::t LO (0 r---00 C> C> C> C> 0 o 0 0 0 0 0 LO LO LO (0 (0 (0 (0 (0 (0 (0 I -0 0.1 I I Station, ft. 0.2 I I lJJ .-4 Deck Vertical DisDlacement 􀁾 -+-STEP 39 North Vertical Deflection, in L_ -STEP 39 South Vertical Deflection, in -0.6 I I -0.5 􀁾 I -0.4 +-I -0.3 cc0 15 -0.2 OJ i:i= OJ 0 -0.1 -N 0 0 0 0 0yo 0 0 """'" co 0) 0 ('t) L.O co 0) 0) 0) 0 o 0 0 0"""'" L.O L.O L.O co co co co co I po 0 0.1 I I Station, ft. 0.2 I I f""iJ Cf) 􀁾􀁾􀁾􀁾􀀱 Deck Vertical DisDlacement 􀁾 --+-STEP 42 North Vertical Deflection, in L__ --STEP 42 South Vertical Deflection, in -0.6 I I -0.5 1I ----------------------------------------11 -0.4 t----------------------------------JI . -0.3 c: c: 0 15 -0.2 Q) 􀁾0 -0.1 --a a a a a a a a a a a a a a co "'" co 0>. 0 􀁾 N ('t) 􀁾 LO co "'" co 0> (J) 0> 0> 0> a a a a a a a a a a LO LO LO LO co co co co co co co co co co I r 0 0.1 +--I Station, ft. 0.2 ! I "";.I Deck Vertical Disolacement --+--STEP 44 North Vertical Deflection, in -STEP 44 South Vertical Deflection, in -0.6 I I -0 4 I ' " • 7 _ 11......-. "-... 10: I -0.5 +----------------------------- ----:_-7.".A.􀁾...􀂷􀁾􀂷..􀁾....􀁾.. 􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀁉 -0.3 cc0 15 -0.2 Q) G= Q) 0 -0.1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 to 􀁾 co (J) 0 -r-C\I ('I) V LO co 􀁾 co (J) 0 (J) (J) (J) (J) 0 0 0 0 0 0 0 0 0 0 -r-LO LO LO LO co co to co to co co co co co co I I 0 0.1 1I------------------------.:--------------=--------11 Station: ft. 0.2 I I .:+;;. 􀁉􀀢􀁾 )l Deck Vertical DisDlacement I --.-STEP 46 North Vertical Deflection, in --STEP 46 South Vertical Deflection, in -0.6 I a:;:::o co::: .-I -0•5+--J l " .. _/r "'\0 I -0.4 I r I 􀁾-.. ' _ 'lII \ I -0.3 cc0U-0.2 Q) Q) 0 -0.1 0 0 0 0 0 0 0 0 0 0 0 0 0 co "-co c» 0 T""" C\I ('t) 􀁾 LO co "-co c» c» c» c» 0 0 0 0 0 0 0 0 0 LO LO LO LO co co co co co co co co co 1 I 0 0.1 T'------------------------------JI Station, ft. 0.2 --,--I􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀮􀀺􀀮􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀀭􀁾􀁉 ..r:. C\I o o M C\I "'C"""" o 000 I I I 􀁾oI LO oI co oI Ii I 􀀰􀀰􀁾􀀹 0609 0909 ...., Ol09 c: .5 .5 0909 (I) E M C co: .0_ (I) .--0909 (.) -Go >0G_> ca &-I-&GI>--􀁾􀁃 01709 .::= C. c -(ij 0 -t-n oca .0_ 0£09 :0ct:l; 􀀻􀁾 C ..... ... G> C/) -􀁾􀀾 ca .c:.c: Ol09 (.) 􀁾􀀺􀀻 --o 0 1:= zen 􀀰􀁾􀀰􀀹 .......... (I) 􀁾􀁾 > 1U1J.1U1J. 0009 􀁾 1-1-en en (.) + + 0669 I (I) i C 0969 U Ol69 0969 I .J . ) '1II jJI STARDYNE DEFLECTIONS 1 LlO ICI y x z utput Set: DL + PT + Cables Defonned(0.126): T2 Translation ontour: T2 Translation Stardyne Model: Vertical Deflection (ft) 0.0552 0.0439 0.0326 0.0213 0.00995 -0.00137 -0.0127 -0.024 -0.0353 -0.0466 -0.0579 -0.0693 -0.0806 -0.0919 -0.103 -0.115 -0.126 Stardyne Model: Vertical Deflection (ft) 1 LIO C1 yz X IOutput Set: DL + PT + Cables Defonned(0.126): T2 Translation Contour: T2 Translation 0.0552 0.0439 0.0326 0.0213 0.00995 -0.00137 -0.0127 -0.024 -0.0353 -0.0466 -0.0579 -0.0693 -0.0806 -0.0919 -0.103 -0.115 -0.126 '\::'" 􀁣􀁲􀁾􀀢 Stardyne Model: Vertical Deflection (ft) y x z Output Set: DL + PT + Cables Defonned(0.126): T2 Translation Contour: T2 Translation 0.0552 0.0439 0.0326 0.0213 0.00995 -0.00137 -0.0127 -0.024 -0.0353 -0.0466 -0.0579 -0.0693 -0.0806 -0.0919 -0.103 -0.115 -0.126 Stardyne Beam Defections 0.500 .,..--------------------. ...---..---04 ",..."",'" -...... . 00 i "..' 􀁾􀁾 ... .... .... --:... --.... " ... .. ,.. I '\ 6084 .... ... ... 6004 6024 6044 6064 .... .... 5984 .. .. , 5964 ..... ... -------..............-----..... .... ....., -,.---••••••.•.••. -""" ..... , '. ---j ., /' . . . """' ' ' ' /' --....._'\--.. 0.3001 ,/.' _ '" ". , , /,/-.... , . /• ,/_., '. '.:-.. I 􀁾􀀬􀀭 '.", . . .r".' \. ,. /" 'I.. , ... -􀀧􀀧􀁾􀀧􀀮 /' -),',,. 􀀧􀁜􀀧􀀮􀁾.. \ 4'",--\.'..' T---H -. , -r-----...---0.1 00 -f--I ------\--1 -c 0.200 # ::. I c0 t5 I I I Cll 􀁾 0.100 -c -0.200 ' , Station (tt) 􀁾􀁾􀀧􀁾􀁾􀀮 􀁂􀁾􀁾􀁾 􀀱􀁁􀀭􀁟􀀭􀂷􀀭􀁂􀁥􀀭􀀬􀀻􀀻􀁾􀀲􀁁􀀭􀀮􀀺􀀺􀀺􀀮􀀮􀀭􀀭􀀭􀀽􀀭􀀭􀁂􀁾􀀳􀁾􀀭􀀭􀀽􀀭􀁳􀀻􀁾􀀴􀁁􀁝 . t'::. J . ! 0.000 -0.10& -0.200 -0.300 -0.400 -0.500 -0.600 -0.700 _ -0.800 c :c::. -0.900 􀁾 -1.000 (,) CD li -1.100 c -1.200 -1.300 -1.400 -1.500 -1.600 -1.700 -1.800 -1.900 -2.000 Stardyne Arch Defections R44 􀀭􀁾􀁾___􀀵􀁾􀀹􀁂􀁌 􀁑􀁏􀁟􀀰􀁾___6_024 6DM 606.4.. 􀀶􀁦􀁲􀁾􀁟􀀶􀁊􀀮􀁯􀁾 􀀢􀁾 /., , /.--/./. _-----􀀭􀁾..􀀬􀁾----.__. /......, //􀁾􀀭 -"----.,-_.._-----,,.-/.: ._.\\\--/;', ---.. //:---, /, , 􀀧􀁾 /. -" 􀁾 , 􀀮􀁟􀀭􀁟􀀮􀁟􀁾􀀮􀀮􀀮 -7 , ------_.'------..-------, , . 􀁟􀀮􀁟􀀬􀀮􀁾...􀀭􀀻􀀻􀀻􀀻􀀭􀀭􀁾 ..._--------.._.. --,.....􀀭􀁾􀀭.. ._----._----._--.. ._--Station (tt) 􀁾􀀮__._--_._.__..􀁟􀀭􀁾 􀁌􀁾􀁟􀁴􀀧􀀡􀀼􀀺􀀾􀁲􀁴􀁨 Arch --South Arch STARDYNE -BRUCO CABLE FO'RCE AND SUPPORT REACTION COMPARISON Arapaho 􀁾 BRuce -5tardyne Cable Force Comparison ' NORTH CABLES Cable BRUCO Stardyne b. b. Force Force Force (kips) (kips) (kips) (%) 1N 149.5 147.1 -2.4 -1.6 2N 80.0 76.4 -3.6 -4.5 3N 108.5 107.6 -0.9 -0.8 4N 106.9 110.1 3.2 3.0 5N 123.4 124.4 1.0 0.8 6N 111.1 113.4 2.3 2.1 7N 115.8 114.3 -1.5 -1.3 8N 71.1 68.2 -2.9 -4.1 9N 142.3 141.2 -1.1 -0.8 SOUTH CABLES Cable BRUCO Stardyne b. b. Force Force Force (kips) (kips) (kips) (%) 1S 118.5 120.6 2.1 1.7 2S 61.9 61.5 -0.4 -0.6 3S 85.1 88.4 3.3 3.9 4S 84.6 88.5 3.9 4.7 5S 103.7 108.2 4.5 4.3 6S 89.5 89.4 -0.1 -0.1 7S 90.8 94.8 4.0 4.4 8S 54.8 56.6 1.8 3.2 9S 112.9 114.4 1.5 1.3 u\ Arapaho Cable Strucuture BRUCO -Stardyne Support Reaction Comparison North Side of Structure -West End BRUCO Stardyne !.l !.l Reactions Reactions Reaction Reaction (kips) (kips) (kips) (%) Rear Thrust Location 1279.3 1291.3 12.0 Middle Location 189.5 176.5 -13.0 Forward Location -75.3 -71.7 3.6 TOTAL 1393.5 1396.1 2.6 0.19 South Side of Structure -West End BRUCO Stardyne !.l !.l Reactions Reactions Reaction Reaction (kips) (kips) (kips) (%) Rear Thrust Location 1090.2 1121.8 31.6 Middle Location 181.6 170.7 -10.9 Forward Location 0.9 -27.4 -28.3 TOTAL 1272.7 1265.1 -7.6 -0.60 North Side of Structure -East End BRUCO Stardyne !.l !.l Reactions Reactions Reaction Reaction (kips) (kips) (kips) (%) Rear Thrust Location 1281.4 1293.7 12.3 Middle Location 190.9 177.9 -13.0 Forward Location -80.9 -76.8 4.1 TOTAL 1391.4 1394.8 3.4 0.24 South Side of Structure -East End BRUCO Stardyne !.l !.l Reactions Reactions Reaction Reaction (kips) (kips) (kips) (%) Rear Thrust Location 1091.8 1123.8 32.0 Middle Location 182.6 171.8 -10.8 Forward Location -3.2 -31.6 -28.4 TOTAL 1271.2 1264.0 -7.2 -0.57 MATERIAL PROPERTIES BRUCO DATA CONCRETE PROPERTIES FOR U54 BEAM 6000 PSI CONCRETE STRENGTH: MODULUS OF ELASTICITY: DENSITY: POISSON'S RATIO: COEFFICIENT OF THERMAL EXPANSION: ALLOWABLE TENSION: 􀁾􀁥 crtens := 3· -. ·psi pSI ALLOWABLE COMPRESSION: crcamp := O.4·fe fe = 6000 psi E := 57000 .J fe·psi w = 150 pef v = 0.20 a = 0.000006 F-1 crtens = 232.379 psi crcamp = 2400 psi BRUCO UNITS rft & kips): fe = 864 ksf E = 635789 ksf w=0.15kef v = 0.20 a = 0.000006 F-1 crtens = 33.463 ksf cr camp = 345.6 ksf **SHRINKAGE STRAIN: c;s1 = 0.00032 c;s1 = 0.00032 **BASIC COEFFICIENT OF CREEP: !J>f1 = 2.0 !J>f1 = 2.0 **DELAYED ELASTIC DEFORMATION (t = 0): 􀁾􀀱 = 0.108 􀁾􀀱 =0.108 **DELAYED ELASTIC DEFORMATION (t = f1 = 2.0 4>f1 = 2.0 **DELAYED ELASTIC DEFORMATION (t -0): /31 =0.108 /31=0.108 **DELAYED ELASTIC DEFORMATION (t = 00): /32 = 0040 /32 = DAD **HALFWAY TIME: t = 30days t=30days CEMENT: Z = 1.0 Z= 1.0 ** SEE FOLLOWING PAGE. BRUCO DATA CONCRETE PROPERTIES FOR DECK 4000 PSI CONCRETE STRENGTH: MODULUS OF ELASTICITY: DENSITY: POISSON'S RATIO: COEFFICIENT OF THERMAL EXPANSION: ALLOWABLE TENSION: 􀁾􀁥 crtens:= 3· -. ·psi PSI ALLOWABLE COMPRESSION: crcamp:= O.4·fc fe = 4000 psi· E := 57000..) fe·psi w = 150 pef v = 0.20 a = 0.000006 F-1 crtens = 189.737 psi crcamp = 1600 psi BRUCO UNITS rft & kips): fe = 576 ksf E = 519120ksf w=0.15kef v = 0.20 a = 0.000006 F-1 crtens = 27.322 ksf cr camp = 230.4 ksf **SHRIt\IKAGE STRAIN: cs1 = 0.00032 <:s1 = 0.00032 **BASIC COEFFICIENT OF CREEP: q,f1 = 2.0 q,f1 = 2.0 **DELAYED ELASTIC DEFORMATION (t -0): [31 = 0.108 [31=0.108 **DELAYED ELASTIC DEFORMATION (t = (0): [32 = 0.40 [32 = 0.40 **HALFWAY TIME: t = 30days t=30days CEMENT: Z = 1.0 Z = 1.0 ** SEE FOLLOWING PAGE. BRUCO DATA CONCRETE PROPERTIES FOR DRILLED SHAFT 3600 PSI CONCRETE BRUCO UNITS rft & kips): STRENGTH: MODULUS OF ELASTICITY: DENSITY: POISSON'S RATIO: COEFFICIENT OF THERMAL EXPANSION: ALLOWABLE TENSION: J!e CYtens := 3· -. ·psi PSI ALLOWABLE COMPRESSION: CYcamp := O.4·fe fe = 3600 psi E := 57000.") fe·psi w = 150 pef v = 0.20 a = 0.000006 F-1 CYtens == 180 psi CYcamp = 1440 psi fe == 518.4 ksf E == 492480 ksf w == 0.15kcf v == 0.20 a = 0.000006 F-1 CYtens = 25.92ksf u camp = 207.36 ksf **SHRINKAGE STRAIN: zs1 = 0.00032 zs1 = 0.00032 **BASIC COEFFICIENT OF CREEP: 􀁾􀁦􀀱 = 2.0 􀁾􀁦􀀱 = 2.0 **DELAYED ELASTIC DEFORMATION (t = 0): 􀁾􀀱􀀽􀀽􀀰􀀮􀀱􀀰􀀸 􀁾􀀱 = 0.108 **DELAYED ELASTIC DEFORMATION (t -(0): 􀁾􀀲 == 0.40 􀁾􀀲 = 0.40 **HALFWAY TIME: t==30days t=30days CEMENT: Z == 1.0 Z = 1.0 ** SEE FOLLOWII\lG PAGE. Pu:= fpu·As BRUCO DATA 0.5" 􀁾 PRE-STRESSING STRAND PROPERTIES YOUNG'S MODULUS: STRAND AREA: ULTIMATE STRAND FORCE: fpu = tensile strength of strand fpu = 270 ksi MAXIMUM JACK FORCE: Pj:= 0.75·Pu MAXIMUM INITIAL TENDON FORCE:' Pi := 0.75·Pu MINIMUM BENDING RADIUS: Eps = 28500 ksi As = 0.153000 in2 Pu = 41.31 kips Pj = 31.0 kips Pi = 31.0 kips r =Oft ( 75% ultimate) ( 75% ultimate) FRICTION COEFFICIENT: WOBBLE COEFFICIENT: K=O BRUCO program multiplies f.1 and K internally K wobble:= -f.1s MINIMUM ANCHOR SET: f.1s = 0 wobble = 0 set = 0.001 in set = 0.0001 ft (Input a small number in Bruco) (Input a small number in Bruco) RELAXATION COEFFICIENT: HALFWAY TIME: MAXIMUM ANCHORAGE FORCE: relax:= 3·(0.035) (Multiply by 3 for infinity) relax = 0.105 Khalfway = 0.20 Pa:= 0.75·Pu Pa = 31.0 kips ( 70% ultimate) t􀁾if () C"i \\ "]-lr) '0 􀁾 ?'-2 -=c --l 􀁾 0-I::l::: 􀁾􀁬 r:: 􀁾 V1 Q::: t:il 􀁾 􀁾l/) \-. W 􀁾 -J 􀁾 􀁾 􀁾 l--0 0 V1 0-J.1j >-cL 1-CL. II N j c::t q 􀁾 (Yj fi:: ;z; '-I'") 􀁾 -E . 0 0 V\ II 􀁾......... 􀁾 􀁾 W l.r\ LLl oC Q;: \) <::C: f--l/) · I SECTION PROPERTIES .£U􀁾 ri ...s >-􀁾 ¥:: 0 􀁾 􀁾 􀁾 􀁾 \) t> 􀁾 c; -. ;a if 1i7 I.:;; 'IF' '17 M 0 C:r-: 􀁾 :J-M M M (11\ -D Q M 􀁾 " 􀁾 ltJ '3 t"N 􀁾 r---r( f'. 􀁶􀁾 :r 􀁾 􀁾 􀁾 􀁾 􀁾􀁉􀁾 ;, x. 0 t-o 􀁾 ('I 􀁾 $ 􀁾􀁾 &1 􀁾 􀁾 C) a 􀁾 0 cr-\.;'\ \i 􀁾 􀁾 .:r= Ii 􀁾 M M :r . 􀁾 <1 I I 􀁉􀁾 I I I -I'V f"'I r \.r, 0 r-!'" c;-.2 =. N 􀁾􀁴􀀺 """ 􀁾 r--􀁾 􀁾 "-􀁾ct:' WCO lr, t;; C'1 rl l-7-Q 􀁲􀁾􀁟􀀭􀀭􀀭􀀭􀀭 􀁾""'-" J-􀁾􀁾$a <..) M-+--0 .J 􀁾 -if'J 􀁾 2 \AJ V') II coL \'0 I \.;. 􀁾 In jQ S? .:::: --:. ..:r--0 0 c:i 0 :r I' 11 II II IM M --. "'" LL 'C--.--. -'"" 􀁾 Cl"'---... 􀁾 ::t-:s-" ¢.:> \..n V> 􀁾 􀁾 :::::i 6 􀁾 l") "---' 􀁾 ...... ,---.., '--' ".----.' -3 0 -0 􀀭􀁾 "'7""' 􀀮􀁾 .....--, 􀁾 "--I"'> <;y-lJ, 􀁾 N I W 0" .::. N fV\ '---' :r-: I -\'1 '--' x _\1" -(I ........... N x ... -1M N rl r-r--􀁾􀁾 +-􀁾 r--.-tr. .?-! 􀁾􀁬 0 0 􀁾􀁉 O! 􀁾􀀮 I 􀁾 j 􀁾 -!n i""--0 0 􀁾 'tp v<> N 0-'" 􀁾 (V\ 0 -􀁾 􀁾 􀁾 􀁾 -J I-e @@® e:t: G:i I-􀁾 V) IL _--------- 5 CROSS-SECTIOJ\J rROP£I{TJES ITf<.CH f< J{S 3'-0" dJ f Ifc 10 15 20 25 30 35 ,j '-0 \\ rf ) " TH1GK (l.'£;-'IOl{-'lio'" I 5 ' l ..l ,I " -I x' 1.0 -0 􀁁􀁾 rr/Jl.r}l.-(I.Lf/(Dl')J = O.703(, fT""L I:: 􀁾 1T[[I,s')"1_( l.ilfoifJ <= 􀁏􀁲􀁾􀀱􀀲􀁾 FT<1 Cr:::Cs= I.s FT p, STRs 􀁾 1.5"" A:: 3.1FT2 r=-11(S.f\)(G.o')'? =-91 􀁆􀁔􀁾 C r ::: CB = .3 ,0 FT 􀁾􀁓􀁔􀁒􀁓􀀽 /.. )'2. A:;. I&.S-FT r=h (5,5'"') (3.0,)3 􀁾 )2. ?7I FT'1 C r:; Cr;, = J.S FT R5TI\5 =}.Sfr 􀁾 32 FT2.. J::: 7-2 (0.0; (-f.333')\ 7s-. 'b 􀁾 FTL; Cr= VB, "" 2,0ro7 Fj RSrR.s ;::"j.S PROJECT: COMPUTED BY: DATE: //JOB NUMBER: CHECKED BY: DATE: //SHEET /;-1.'5, OF I Janssen & Spaans Engineering • 9120 Harrison Park Court • Indianapolis, IN 46216 • Phone (317) 254-9686 • Fax (317) 259-8262 I 5 10 15 20 25 30 35 GROSS 􀁾􀀮􀁳ECTJtJ!IJ PI\OPFRTlE5 2-9/7 Iy lS"' : I y :: +2-(29/7) (f.S') "3 =-O· 'i}.eJ FT'1 􀁾􀀧􀁘 1.5) I y=􀁾 (I-J') cv;')3 :: /./25 Fr'1 Lj' )( (I y :: T2 (I) (J'f ;. 0,333 Fri ;}.:" '-},1 70 FT2.-L= f:z (J.)')(1.117Y=3.103 FJ'1 J:::-C') CIb10: 2-9li b;: l.S' (J/b = 􀁉􀀬􀁾􀁊􀀩􀀭 ==7' C2 =􀁏􀀬􀀱􀁾􀀳 J = 0.22"5 [:2 .qn')U.5rJ == ;) I ICJr 􀁦􀁔􀁾 A􀁾 (;,00 0 􀁆􀁩􀁾 :s I¥= T-2 (Lt) (t-() =: 9),000 􀁦􀁔􀁾 J = C2QP30=:'-1' b= f,.r1 CJ;b = J..GCo7 􀁾CJ.= 0 􀀱􀁾􀀧􀀱 J = 􀁏􀀬􀀲􀁾􀁩 (,.Gao') (1.;')3 =-3, 􀁾􀀲􀁃􀁪 fJ1 A= /.(JO() FT2. I; ·h (! ') C􀁾 f = 􀁾 ]3.) FT􀁾 J= C2 Qb3 􀁱􀁾 􀁾􀀧 J,=J' 0./6 == Lj »G2 :: 0. 2 'i J J::. O,21JJ(1.000')(J.o'f=-/./21 􀁆􀁔􀁾 PROJECT: COMPUTED BY: DATE: //JOB NUMBER: CHECKED BY: DATE: //SHEET A.-It OF I Janssen &Spaans Engineering • 9120 Harrison Park Court • Indianapolis, IN 46216 • Phone (317) 254-9686 • Fax (317) 259-8262 I 164 TORSION Fig. 3.47 The determination of the stresses in noncircular members subjected to a torsional loading is beyond the scope of this text. However, results obtained from the mathematical theory of elasticity for straight bars with a uniform rectangular cross section will be indicated here for convenience. t Denoting by L the length of the bar, by a and b, respectively, the wider and narrower side of its cross section, and by T the magnitude of the torques applied to the bar (Fig. 3.47), we find that the maximum shearing stress occurs along the center line of the wider face of the bar and is equal to (3.43) (3.44) The angle of twist, on the other hand, may be expressed as TL cP =--,----c2ab3C The coefficients Cl and C2 depend only upon the ratio alb and are given in Table 3.1 for a number of values of that ratio. Note that Eqs. (3.43) and (3.44) are valid only within the elastic range. Table 3.1 Coefficients for Rectangular Bars in Torsion alb C1 C2 1.0 0.208 0.1406 1.2 0.219 0.1661 1.5 0.231 0.1958 2.0 0.246 0.228 2..5 0.258 0.249 3.0 0.267 0.263 4.0 0.282 0.281 5.0 0.291 0.291 10.0 0.312 0.312 00 I 0.333 0.333 I We note from Table 3.1 that for alb :2: 5, the coefficients Cl and C2 are equal. It may be shown that for such values of alb, we have Cj = C2 = 􀁾􀀨􀀱 -O.630bla) (for alb :2: 5 only) (3.45) The distribution of shearing stresses in a noncircular member may be visualized more easily by using the membrane analogy. A homogeneous elastic membrane attached to a fixed frame and subjected to a uniform pressure on one of its sides happens to constitute an analog of the bar in torsion, i. e., the determination of the deformation of the membrane depends upon the solution of the same partial difFerential equation as the tSee S. P. Timoshenko and J. N. Goodier, Theon) of Elasticity, 3d ed., McGraw-Hill, New York, 1970, sec. 109. : OVERALl:. LENGTH .oF BRIDGE; AlONG p. : OVERALL 'LENGTH oF. T4(S) IMOOl 8 RAIL ;= 1575.46' "-'-'i'--."-.-􀀮􀁾􀀭􀀭 -: --:-.--;-.---􀀭􀀭􀁾􀀭 --.----!---..--.+-..-.-.---..;--.'--􀁾 -.-oVEF;l'At1.: --t;Et1G:ftl"OP--pe[ 0710' 􀁐􀁒􀁅􀁓􀁔􀁾􀁅􀁓􀁓􀁅􀁄 CONCRETE UlSEAM 􀁕􀁎􀁉􀁾 I -: 􀀱􀀷􀀰􀀮􀀰􀀰􀂷􀁓􀁾􀁅􀁅􀁬 ARCf4 UNIT : . : :110 7.00' -:100.00' J ! . . : ; : : : : . .•.Oao 1' -toO 1"" ; : ,..··..···..·r· "T'" 􀁾 -···c····· " , 􀁾 .. .. "STINGER" .:... : tTYP) 􀁾 ··_·..·t········..·_·t·..·..􀂷􀁟􀁾􀂷􀂷􀂷 ..·:··..._·..···: u'l : : ;; : : . In. _ _ ...􀁾􀁾􀁟􀁑􀀬􀀮􀀺 􀁾 , , i•. V1 1--------------5-9-.0 -0-----------------\-5-0-.0-0---------------:.---6-\....:tO-0 i A??R v, :r-N () 0 :i-N .:f-L.; 􀁾 -1 I '/j -r\ M :rl \J) '1'" \1"'J UJ l-􀁾\) I 􀁾t-I./) 􀁾􀁉 -:t rl.L.J V\ 􀁾W \--r;-::::> "< t-􀁾 􀁾 <41 􀁾 C:::l 􀁾 (JJ l-*-"" ("'" [Z]\ I 􀁾 [g] \ I \I \I 􀁾 􀀺􀀽􀀺􀁾􀀺􀁾􀀺􀁾􀀺􀀽􀀬􀁾􀁽􀁾􀀺􀀽􀀺􀁾􀀺􀁾􀀺􀁾􀀺 1\ 1\ .-_.-x 5 Area Centroid Moment of Inertia RSTRS factor c(x) c(y) I(x) I(y) I(xy) I ( 1 ) I (2) Angle R( 1 ) R(2) 1\ y 11 Concrete only 37.649136 -0.780469 3.318044 76.809969 189.589297 -7.258222 190.054501 76.344765 86.332737 1.241681 1.269752 degr. 4 ARAPAHO BRIDGE TRANASVERSE THRUST BLOCK TIE Janssen & Spaans Engineering, inc. 2825 E 56th street Indianapolis 46220 PROGRAM DSNR (2.50) PLOT 4; DATE 25/07/2005 LOADS A-2\ 5 10 15 20 25 30 35 jLOADSI jftlurJGt! ) JI WIDTH OF U-EEITIVl FLANGE::: 􀁊􀁉􀁾􀀧􀀱 1/\1 /lSSVIIIE IiltuA/utJ T/tlcK1iJe:--S..s =-r 2 WT-=-[cJS:7s') (J.rj/I'1'-1 iyfI] x. (J 􀁉􀁾􀁏 '>'FT2 = UJ02S' I-',:JO! ;"(, 􀁜􀁟􀁾 l:' 􀁾􀀻􀀬 '.,\j.,J:-.r '. I AREA 18.5& Sq.ft. AREA 2&.33 sq.ft. AREA " 18.56 sq.ft. 􀀭􀁾􀀭􀀮􀀬􀀮 '.....,-.. : -_._' -􀀭􀀭􀁾 􀁾􀁾 \' 􀀨􀁾 i C -r \' ! -:; 􀁾􀀮 -r-"' ,..'-.....,..-.....' 􀁾􀀮 ,."\ ',e:-: 􀀧􀁾􀁟􀁪 I' :_--' \5,,00 1? STARMAP Version 4.41 Tue Ju1 26 09:14:46 2005 Model : p:\674-ar-1\star\fu11.mod Report : Element Format : STARDYNE Bar/Beam Element Output Set 4 -TOTAL Dead Load B E A M E L E MEN T LOA D S AXIAL SHEAR SHEAR TORSION BENDING BENDING BEAM P V2 V3 MT M2 M3 9101 JA 0.0 -1.414560E+2 O. o. o. O. O. BEAMG JB 100.0 1.414560E+2 O. O. O. O. O. 9102 JA 0.0 -9.186250E+1 O. O. ·0. O. O. BEAMG JB 100.0 9.186250E+1 O. O. O. O. O. 9103 JA 0.0 -8.845610E+1 O. O. O. O. O. BEAMG JB 100.0 8.845610E+l O. O. O. O. O. 9104 JA 0.0 -9.095080E+1 O. O. O. O. O. BEAMG JB 100.0 9.095080E+l O. O. O. O. O. 9105 JA 0.0 -9.218400E+l O. O. O. O. O. BEAMG JB 100.0 9.218400E+1 O. O. O. O. O. 9106 JA 0.0 -9.094580E+l O. O. O. O. O. BEAMG JB 100.0 9.094580E+1 O. O. O. O. O. 9107 JA 0.0 -8.862550E+1 O. O. O. O. O. BEAMG JB 100.0 8.862550E+1 O. O. O. O. O. 9108 JA 0.0 -9.199920E+l O. O. O. O. O. BEAMG JB 100.0 9.199920E+l O. O. O. O. O. 9109 JA 0.0 -1.410070E+2 O. O. O. O. O. BEAMG JB 100.0 1. 410070E+2 O. O. O. O. O. -' 0'. ._----9201 JA 0.0 -1.114650E+2 O. O. O. O. BEAMG JB 100.0 1. 114650E+2 O. O. O. O. O. 9202 JA 0.0 -7.555400E+1 O. O. O. O. O. BEAMG JB 100.0 7.555400E+1 O. O. O. O. O. 9203 JA 0.0 -7.218080E+1 O. O. '0. O. O. BEAMG JB 100.0 7.218080E+1 O. O. O. O. O. 9204 JA 0.0 -7.377050E+1 O. O. O. O. O. BEAMG JB 100.0 7.377050E+1 O. O. O. O. O. 9205 JA 0.0 -7.456300E+1 O. O. O. O. O. BEAMG JB 100.0 7.456300E+1 O. O. O. O. O. 9206 JA 0.0 -7.376920E+1 O. O. O. O. O. BEAMG JB 100.0 7.376920E+1 O. O. O. O. O. 9207 JA 0.0 -7.214460E+1 O. O. O. O. O. BEAMG JB 100.0 7.214460E+1 O. O. O. O. O. 9208 JA 0.0 -7.543730E+1 O. O. O. O. O. BEAMG JB 100.0 7.543730E+1 O. O. O. O. O. 9209 JA 0.0 -1. 118130E+2 O. O. O. O. O. BEAMG JB 100.0 1.118130E+2 O. O. O. O. 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