ppndix XV rakd Stion Proprti o th Pir ap Bam o th Stl Girdr Bridg ug th omnt urvatur thod and Equation Wt Bound Pir ap Bam Figur XV- Th atual pir ap bam ro tion [Brown, 99] Th ¾ - al i no longr orrt 5 8 Figur XV- Th impliid pir ap bam ro tion Thi igur wa not drawn to al 6
omnt urvatur thod T S + b ' S d + ' ' ' b d d ( ( ( 5 + ( 7( ( 5 ( ( + ( 7( 5 ' ( ( ( 7( 7 889 um th omprion tl will not ild: d d ' d' ' d' d d 6ki 7 E 9,ki 5 ' 7 5 ' ( ki 9 E 57 ki ' E ' b ' d ( ( ( d B pluggg th ollowg valu to th quation abov, 6
( #9bar 6ki ' 889 ( 7#bar E 9,ki 5 ' 7 5 b 5 ' ki 7 9 d 5 thn a third-dgr quation trm o i obtad Th olution o th third-dgr quation ar or 5 or -79-79 i obvioul ruld out, and i ruld out bau th rorg ara at th bottom i l than that at th top, thror i uppod to b l than hal o 5, whih i qual to 55 Thu 5 i th onl poibl olution Now th itial aumption that th omprion tl will not ild mut b hkd: d' 5 5 ' 7 5 < 7 d 5 5 Thu th itial aumption i orrt Now max mut b hkd to i it i l than it i, thn th tr blok will hav a paraboli hap 5 max 7 75 < 9 d 5 5 6
Thu th tr blok will b paraboli Th urvatur at th ild pot i φ max 5 75 655 5 / Now th momnt at ild an b obtad ug Figur V- max max max ( ( 75 9 75 9 max ( ( ( 5 ( 5 ( 5 ( 5 75 9 75 9 79 b ' max ( ( ( 5 ( ki ( 5 ( 5 559k 6k b d max ( 889 ( 9,ki( 7 ( d + ( 5 5 + 79 ( 559k + ( 6k ( 5 5 5,8kip 75 9 + ( d d' 75 9 5 5 5 5 6
E g 5,8kip 9,,kip 5 655 / mm φ 9,,kip 57 ki 6, ( 5 ( 8 5 6, Equation thod ' ki r 75 r r ' 75 pi pi r 7,kip ( ki ( 5 ( 8 Thi rakg momnt mut b ompard with th maximum poitiv and ngativ momnt th pir ap bam ( a, whih ar givn Tabl XV- Tabl XV- Th alulation or th maximum poitiv and ngativ momnt th pir ap bam Eat Bound Lan Wt Bound Lan aximum Poitiv aximum Ngativ aximum Poitiv aximum Ngativ Dign Truk 56-8 77-5 Dign Tandm -9 6 - Two Dign Truk 76-79 65-68 Lan 7-6 - ontrollg Load 76-79 65-68 Liv Load Et -75 8-68 Dad Load Et 59-8 57-88 LL+DL Et 65-78 679-7 Not Load ar kip 6
r 7,kip > 679kip or th maximum poitiv momnt a r 7,kip > 7kip or th maximum ngativ momnt Thror aordg to th Equation mthod, g 5, ( 5 ( 8 a Eat Bound Pir ap Bam Figur XV- Th atual pir ap bam ro tion [Brown, 99] Th /' - al i no longr orrt 65
5 8 Figur XV- Th impliid pir ap bam ro tion Thi igur wa not drawn to al omnt urvatur thod T S + b ' S d + ' ' ' b d d (( 5 ( 5 + ( 7( ( 5 8 ' ( ( (( 5 + ( 7( (( 9 7 66
um th omprion tl will not ild: d d ' d' ' d' d d 6ki 7 E 9,ki 5 ' 7 8 ' ( ki 9 E 57 ki ' E ' b ' d ( ( ( d B pluggg th ollowg valu to th quation abov, ( #9bar 6ki ' ( 9#bar E 9,ki 5 ' 7 8 b 5 ' ki 7 9 d 8 thn a third-dgr quation trm o i obtad Th olution o th third-dgr quation ar or 59 or -9 67
-9 i obvioul ruld out, and i ruld out bau th rorg ara at th bottom i l than that at th top, thror i uppod to b l than hal o 8, whih i qual to 5 Thu 5 i th onl poibl olution Now th itial aumption that th omprion tl will not ild mut b hkd: d' 59 5 ' 7 56 < 7 d 8 59 Thu th itial aumption i orrt Now max mut b hkd to i it i l than it i, thn th tr blok will hav a paraboli hap 59 7 768 < d 8 59 max 9 Thu th tr blok will b paraboli Th urvatur at th ild pot i φ max 5 768 66 59 / Now th momnt at ild an b obtad ug Figur V- max max max ( ( 768 9 768 9 max ( ( ( 59 ( 59 ( 59 ( 59 768 9 768 9 79 68
69 ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 7 8 5 6, 6, 57,,,, / 66 8, 8, 5 8 78 5 758 59 8 ' ( 78 59 8 5 59 7 9, 5 59 9 768 59 9 768 5 ' 5 max max + + + + ki kip kip mm kip E kip k k d d d k ki k ki b d b g φ
Equation thod ' ki r 75 r r ' 75 pi pi r 7,kip ( ki ( 5 ( 8 Thi rakg momnt mut b ompard with th maximum poitiv and ngativ momnt th pir ap bam ( a, whih ar givn Tabl XV- r 7,kip > 6,5kip or th maximum poitiv momnt a r 7,kip >,78kip or th maximum ngativ momnt Thror aordg to th Equation mthod, g 5, ( 5 ( 8 a 7