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E For ve moment, assume 5/8 in diameter bars at 9 in centers at top (approximate solutions are given in design manuals) de 85 15 125 0625/2 544 in; much lower than for bottom section As fy (de a/2) Mu results in a nonlinear equation for As 09 As 60 (544 147/2As) 935 12 29376 As 3969 (As)2 1122 (As)2 74 (As) 283 0, Add and subtract (37)2 (As 37)2 283 (37)2 0 (As 37) 3295; As 040 in2 Top reinforcement 5/8 in diameter @ 9 in centers (041 in2 040 in2) Okay Haunch thickness is neglected Hence conservative Check maximum reinforcement: d 544 in, 085 a T/ fc beam spacing; T As fy 041 60 246 kips
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246/085 4 9 0803; a/ 0803/085 094; 094/544 0174 < 042 Okay (AASHTO 57331)
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Check for exural cracking under service limit state (AASHTO 8168) Check for fs < fsc fsc z / (dc Ac)1/3 < 06 Fy For severe condition, z 130 kip/inch Minimum required dc 1 0625/2 1312 in < 2 in Okay Ac 2 dc Bar spacing 2 1312 in 9 in 2362 in2 fsc 130/(1312 2362)1/3 414 ksi 06 60 36 ksi Use fsc 36 ksi Calculate fs fs n Mu y / It where It is transformed moment of inertia n Es /Ec 29,000/3,640 797 (Use 80) Calculate y and It: It b (k de) 3 n As (de k de)2 Calculate , k: k {(n )2 2n }1/2 n n k k de It y As /bde 041/12 719 00048 (d for ve moment region) 8 00048 00384 {(00384)2 2 00384}1/2 00384 028 00384 0242 0242 719 1735 in 12 (1735) 3/3 8 041(719 1735)2 6322 / 3 9760 11867 in 4/ft width de k de 719 1735 5455 in
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From Section B, total dead moment 056 0158 0718 kip-ft/ft; Max ve M(LL I) 569 kip-ft/ft Mservice 0718 569 6408 kip-ft/ft fs n Mservice y / It 8 6408 5455 12/11867 2828 ksi < fsc 36 ksi (No cracking under service limit state in Hence section rebars are okay ve moment region)
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Similarly, it can be shown that there is no cracking under service limit state in ve moment region Bottom reinforcement 5/8 in diameter @ 10 in centers and top reinforcement 5/8 in diameter @ 9 in centers meet service limit state Overhang Design A Data New Jersey barrier (175 ft base width and 267 ft height) is considered as parapet NJB unit weight 05 kips/ft Effective design cantilever span 333 1/4 of ange width 30 ft from edge of deck Depth of overhang 85 in 15 in 10 in
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Loads Overhang wt 015 10/12 0125 ksf FWS 0025 ksf Total DL 015 ksf Approx LL 10 kip/ft acting at 10 ft from face of barrier B Strength 1 limit state: Total Mu (125 MDC 15 MDW 175 M(LL I) MDC 0125 302 / 2 05 (30 ft 067 ft) 0563 kip-ft/ft, where CG of barrier is 067 ft from edge of deck/barrier MDC 0563 1165 1728 kip-ft/ft MDW 0025 (30 ft 175)2 / 2 002 kip-ft/ft, neglecting the barrier width MLL (1 IMP) WLL (30 ft 175 ft 10 ft) 133 10 025 0333 kip-ft/ft Modi cation Factor D R I; (refer to Sec 622) Ductility Factor D 10 Redundancy Factor R 105 Importance Factor I 10 105 Overhang negative moment Mu (125 1728 15 0020 0333) 105 2911 kip-ft/ft < 935 kip-ft/ft (deck moment) Hence extend 5/8 in diameter top bars to edge of overhang
C Extreme Event II - Collision with parapet Forces are acting in transverse and longitudinal directions Collision moment 22 kip-ft/ft Conservatively assume 5 ft width of deck slab to resist the moment Transverse negative moment 22/5 44 < 935 kip-ft/ft Hence extend 5/8 in diameter bars at 9 in centers at top into overhang slab (For construciton load combinations, refer to Sec 572, Figure 522)
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