County: Any Design: BRG Date: 9/2007 Hwy: Any Ck Dsn: BRG Date: 9/2007. For prestr. beams, assume 12" top flange, therefore take 4" from CL Gird.

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1 County: Any Design: BRG Date: 9/2007 Hwy: Any Ck Dsn: BRG Date: 9/2007 SLAB DESIGN EXAMPLE Design: Using AASHTO LRFD Bridge Design Specifications - 4 th Ed. and TxDOT LRFD Bridge Design Manual 8" Slab with std. reinf. 9'-0" Beam Spacing, 3'-0" Overhang Deck Design (Traditional) [9.6.1] Use approximate elastic methods in [ ] from [C ], use tabulated LL+IM moments in Appendix A4.1 For prestr. beams, assume 12" top flange, therefore take 4" from CL Gird. as per [ ] -M r ~ Slab Negative Moment Capacity: 1000lb ksi in 2 f y 60ksi b 12in Bars A ~ # 6" Bars B ~ # 6" f c 4 ksi A s.62in 2 β 1.85 SEC c A s f y.85β 1 f c b [ ] c in Page 1

2 d negs slab thickness - top cover - 1/2bar diameter.625in d negs 8in 2in 2 d negs in a c β 1 a in Calc. M n : [ ] and [ ] a ft a M n A s f y d negs 2 M n ft ϕ.9 M r ϕ M n M r ft M negr M r +M r ~ Slab Positive Moment Capacity: A s 0.62 in 2 c in d poss slab thickness - bottom cover - 1/2bar diameter.625in d poss 8in 1.25in 2 d poss in a c β 1 a in Calc. M n : a M n A s f y d poss 2 M n ft M r ϕ M n M r ft M posr M r Page 2

3 Loads & Load Factors: [3.4.1] 2 Limit States apply Strength I1.25DC+1.25DW+1.75(LL+IM) Service IDC+DN+LL+IM No fatigue check required for slabs Use η D η R η I 1.0 DC: (Slab Dead Load) ω DC 8in 12in 0.15 ft 3 ω DC 0.1 ft (TxDOT recommends using γ p for DW1.25, since overlay is typically used in design only to increase the safety factor) [9.5.3] [1.3.2] (Rail DL considered in overhang check) DW: (2" ACP overlay) ω DW 2in 12in 0.14 ft 3 ω DW ft Assume: -M 0.11ω 2 DL +M DL 0.08ω 2 (Equations for Moments: 4 Continuous Spans Uniformly Loaded) Deck Supported by Prestr. Conc. Beams: Beam Type C s 9ft Positive Moment: S M posllim (From Table A4-1) M posllim M posdc M posdc 6.29 k ft 0.08 ω DC s k ft M posdw 0.08 ω DW s 2 M posdw k ft M posu 1.25M posdc M posdw M posllim M posu k ft M posu < M posr < so ok Page 3

4 Negative Moment: CLGirderToDesignSection 4in S (ft) Length to Design Section (in) M negllim (-ft/ft) (Interpolated from Table A4-1) M negllim k ft M negdc 0.11 ω DC s 2 M negdc k ft M negdw 0.11ω DW s 2 M negdw k ft M negu 1.25M negdc M negdw M negllim M negu k ft M negu < M negr < so OK Check Minimum Flexural Reinforcement: [ ] b 12 in h 8in bh 3 I g 12 I g 512 in 4 f r 0.24ksi f r ksi y t 1 2 h y t 4.0 in f c ksi TxDOT policy states when using LRFD to calculate cracking moment, use fr0.24sqrt(fc). I g S y t S in 3 1ft M cr Sf r 12in M cr 5.12 ft Page 4

5 Design for the lesser of 1.2M cr or 1.33Mu when determining minimum area of steel required. Check Negative Moment Reinforcement: Therefore, M cr1 1.2 M cr M cr1 6.1 ft M cr2 M cr2 M f_neg M f_neg 1.33 M negu 15.1 ft min( M cr1, M cr2 ) 6.1 ft M f_neg < M negr 6.1 < 14.6 so OK Check Positive Moment Reinforcement: Therefore, M cr1 1.2 M cr M cr1 6.1 ft M cr2 M cr2 M f_pos M f_pos 1.33 M posu 16.0 ft min( M cr1, M cr2 ) 6.1 ft M f_npos < M posr 6.1 < 16.7 so OK Service I: M negservice1 M negllim + M negdc + M negdw M posservice1 M posllim + M posdc + M posdw M negservice k ft Controls because: M negservice1 M posservice k ft d negs > M posservice1 d poss Page 5

6 Check Crack Control for M6.80kft: [ ] h 8in d c 8in d negs d c in E s E c 29000ksi 3644ksi n E s E c [5.7.1] n A s ρ bd negs ρ k n ρ + ( n ρ) 2 + 2n ρ k j 1 j k f S M negservice1 ja s d negs f S ksi Exposure Condition Factor: γ e 1.00 For class 1 exposure conditions β S 1 + d c 0.7 h d c ( ) β S in γ e S max 2d β S f c S max in S S actual 6in ( ) "OK" if S max S actual, "OK", "No Good" The actual spacing of the bars is taken as the center to center tie spacing, since slab design considers a 1' strip of an infinitely long slab. Page 6

7 Summary: Check Overhang: 8" slab with 6" O.C. T & B Ok for prestr. beams spc. < 10'-6" Ok for steel beams spc.< 10-3" Since TxDOT doesn't use structurally continuous barriers, provisions of [ ] cannot be used. For Strength I & Service I Load Combinations, place 16k wheel load 1' from the toe of the rail [ ]. To make the slab design independent of the type of rail, we will place the wheel load 1' from the nominal face of the rail (1ft from the edge of the slab). No uniform dist. LL need be applied [ ] Rail Type SSTR With 3' overhang x 5in GirderWebThickness 7in Slab ends are critical ~ use [ c] EffectiveStripWidth min ( 45.0in + 10 x), ( 45.0in + 10 x) GirderWebThickness EffectiveStripWidth ft x M LLIM EffectiveStripWidth M rail ( x in) ft 1 M slab ft 0.15 ft 3 ( x + 2ft) 2 1 M DW ft 0.14 ft 3 ( x + 9.5in) 2 * Dist. width or strip width at locations not at slab ends 45+10x [Table ] Page 7

8 M LLIM M rail M slab M DW kft ft kft ft kft ft kft ft ( ) ft M negu 1.25M rail M slab M DW M LLIM M negu k ft ( ) "OK" if M negu M negr, "OK", "No Good" 4.655< so OK Slab strength for rail impacts has been verified through full scale crash testing. Page 8

Appendix K Design Examples

Appendix K Design Examples Example 1 * Two-Span I-Girder Bridge Continuous for Live Loads AASHTO Type IV I girder Zero Skew (a) Bridge Deck The bridge deck reinforcement using A615 rebars is shown below.