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The following steps are provided for ready reference Prior to developing a software or for solving the equations using hand calculations, equations need to be checked against the latest version of applicable AASHTO LRFD Speci cations 1 General load rating equation (LRFD 642) RF [C ( DC) (DC) ( DW) (DW) P (P)] / L (LL Factors for inventory rating: DC 125; DW 125; LI IM) (EQ 6-1) 175
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Factors for operating rating: DC 125; Operating rating Inventory rating (
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125; LI / LO)
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2 Design rating equation Strength I limit state: C ( c) ( s) ( ) Rn RF [( c) ( s) ( ) Rn ( DC) (DC) ( DW) (DW)] / L (LL IM) (LRFD 6541) Condition factor ( c) 10 for no deterioration (LRFD 6423) System factor ( s) 10 for a slab bridge (LRFD 6424) Resistance factor ( ) 09 for exure (LRFD 5542) IM 133
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683 Beamless Reinforced Concrete Slab Bridge
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Some of the older bridges constructed in the earlier part of twentieth century have smaller spans less than 30 feet and were constructed in the pre-prestressed concrete era Nearly all of them were cast in place construction requiring heavy formwork Both single and multiple spans have been used Original design in reinforced concrete was based on AASHO code, which was popular at that time The advantages were that design of beams and bearings was not required Due to live load restrictions they are commonly used for pedestrian bridges or are posted for about 15 tons They are uneconomical since live load de ection requirements lead to a small span/depth ratio Main reinforcement is placed parallel to direction of traf c Distribution reinforcement is required Due to continuity in transverse direction, shear design is not required Although there are lesser local effects of shear distribution due to moving wheels than from vehicles which may be stationary in a traf c jam, the live load impact factor is higher Fatigue stress needs to be considered since reversal of stress from moving vehicles will induce fatigue stress in bending
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684 Solved Example for Design of Single Span Slab Bridge:
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Data: Single span 30 ft with uneven surface of deck overlay Clear distance between curbs 20 ft including 5 ft wide, 5 in thick sidewalk on deck slab Out-to-out bridge width 20 ft 2 175 ft (New Jersey barrier width) 235 ft Slab thickness 18 in with 2 in overlay; fc 030 ksi, fy 30 ksi d 18 15 05 16 in L/D 20 ie 30 12/18 20, hence assumed thickness is okay (AASHTO 824121) Effective span Clear span Depth of slab or distance to center lines of bearings Center-to-center distance Effective width of slab E 4 006 S 4 006 30 ft 58 ft (AASHTO 32432 Case B) Dead load of slab and overlay 015 (18 in/12 2 in/12) 025 ksf Manual of Condition Evaluation of Bridges (3321 to 3323) Dead load of parapet Sidewalk to be distributed over 05 k/ft / (235/2) (015 5)/12 / (235/2) = 0043 0005 0048 ksf; use 005 ksf Total DL 025 005 030 ksf
APPLICATIONS OF BRIDGE DESIGN AND RATING METHODS
Maximum DL negative moment at supports 270 kip-ft Per ft width 270/58 ft 466 kip-ft/ft Maximum positive moment at 04 L=
Figure 66 HS-20 truck wheel loads
Per ft width
Use HS-20 truck with two axles of 32 kips each and one axle of 8 kips Two wheels/axle 16 kips/wheel; imp factor 110 Distance between back axles 14 ft; distance between front axles varies Theorem: Max live load BM occurs when midspan section divides the distance between the resultant and second wheel load equally Procedure: 1 Replace three wheel loads by a single resultant of wheel loads (16 16 4) 36 kip 2 Locate the resultant force from the nearest wheel by taking moments about that wheel M 0 at wheel B (36X) 1614 ft 414 ft 0; X (1214)/36 14/3 4667 ft from wheel B 3 Calculate reactions at supports R1 L 36 (L/2 2333 ft) 0; L 30 ft; R1 1520 kip 4 Maximum moment occurs under the second wheel 4 (14 ft) 1520 (15 ft 2333 ft) 13654 kip-ft at wheel B 5 Consider total vehicle load distributed over an effective width of 58 ft 6 Since every axle has two wheels, maximum BM 2 13654 27308 kip-ft Design as a beam of cross section 58 ft width 15 ft depth