SLAB DESIGN EXAMPLE. Deck Design (AASHTO LRFD 9.7.1) TYPICAL SECTION. County: Any Hwy: Any Design: BRG Date: 7/2010
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1 County: Any Hwy: Any Design: BRG Date: 7/2010 SLAB DESIGN EXAMPLE Design example is in accordance with the AASHTO LRFD Bridge Design Specifications, 5th Ed. (2010) as prescribed by TxDOT Bridge Design Manual - LRFD (May 2009). Design: 8" Slab with standard reinforcing Type Tx40 Prestressed Precast Concrete Beams (36" top flange) 9'-0" Beam Spacing, 3'-0" Overhang with a T551 rail "AASHTO LRFD" refers to the AASHTO LRFD Bridge Design Specification, 5th Ed. (2010) "BDM-LRFD" refers to the TxDOT Bridge Design Manual - LRFD (May 2009) "DM" refers to the TxDOT Bridge Detailing Manual (August 2001) "TxSP" refers to TxDOT guidance, recommendations, and standard practice. TYPICAL SECTION (DM, Ch. 5, Sect. 9, Typical Transverse Section Reinforcing) 8 in Slab thickness, 2 in top clear cover, 1.25 in bottom clear cover Bars A ~ # 6" Bars B ~ # 6" Bars T ~ # 9" Bars D ~ # 9" (BDM-LRFD, Ch. 3, Sect. 2, Geometric Constraints) (BDM-LRFD, Ch. 3, Sect. 2, Design Criteria) (DM, Ch. 5, Sect. 9, Typical Reinforcing) Deck Design (AASHTO LRFD 9.7.1) Use the Traditional Method in AASHTO LRFD to design the slab. (BDM-LRFD, Ch.3, Sect. 2, Design Criteria) Use approximate analysis method of AASHTO LRFD (AASHTO LRFD 9.6.1) For interior bays, use the unfactored live load moments in AASHTO LRFD Table A4-1. (AASHTO LRFD C ) For overhangs place one wheel load one foot from the rail. (AASHTO LRFD ) Check the Service Limit State and the Strength Limit State. (AASHTO LRFD & AASHTO LRFD 9.5.4) The Service Limit State is checked by the crack control limits. The live load deflection of the slab is satisfactory by inspection. The Strength Limit State is checked by checking the Ultimate Moment Capacity and the Minimum Steel Requirement (AASHTO LRFD ). Fatigue need not be checked for concrete decks. (AASHTO LRFD 9.5.3) The Extreme Event Limit State (AASHTO LRFD 9.5.5) is satisfied through rail crash testing. (BDM-LRFD, C. 3, Sect. 2, Design Criteria) Check the distribution reinforcement in the secondary direction. (AASHTO LRFD ) LRFD Slab Design Example 1 July 2010
2 Effective Strip Widths: The effective width of the strip is the width over which one axle of the design truck or tandem acts. To get the load per unit width, divide the live load by the effective strip width. (AASHTO LRFD C ) Alternately, the live load moments for the positive and negative regions in interior bays from AASHTO LRFD Table A4-1 can be used for design. (AASHTO LRFD C ) Therefore, we will use the live load moments from AASHTO LRFD Table A4-1 for the positive and negative regions in interior bays, and place one axle on the effective strip for the overhang. Depiction of Transverse Strip Widths Overhang Region: Primary Strip Width: In the equations for strip widths, the values for "X" and "S" are in feet but the strip width resulting from the equations is in inches. PrimaryStrip OH = X (AASHTO LRFD Table ) Edge Strip Width: AASHTO LRFD c defines a transverse edge as a transverse strip along the beam that is located at the edge of the slab as shown above. The Article states, "The effective width of a strip, with or without an edge beam, may be taken as the sum of the distance between the transverse edge of the deck and the centerline of the first line of support for the deck, usually taken as a girder web, plus one-half of the width of strip as specified in Article " The intention of this article is to take an effective strip width as half of the transverse strip width plus the additional slab width past the beam end. When the beams are parallel to traffic, the centerline of the first line of support for the deck is the line that intersects the ends of the beams at the center of the web. The additional slab width is the distance from the beam end to the center of the joint minus half of the joint width. This distance is negligible and therefore neglected in this design example. EdgeStrip OH = 1 2 PrimaryStrip OH LRFD Slab Design Example 2 July 2010
3 Define Variables: f y 60 ksi (BDM-LRFD, Ch. 3, Sect. 2, Materials) E s ksi (AASHTO LRFD ) f c 4 ksi (BDM-LRFD, Ch. 3, Sect. 2, Materials) K (AASHTO LRFD ) w c kcf Unit Weight of Concrete for E c 1.5 E c = K 1 w c f c E c 3644 ksi Modulus of Elasticity of Concrete, (AASHTO LRFD Eq ) β 1 = f c 4 ksi (AASHTO LRFD ) Bounded by: 0.65 β β n E s n 7.96 (AASHTO LRFD 5.7.1) E c b h 8 in S 9 ft OH 3 ft RW 1 ft d RailToe 5in d RailToe ft b tf 36 in Use approximate elastic methods in AASHTO LRFD b tf L = Minimum of: 3 L 15 in X OH RW L X 0.00 ft Width of a 1 ft strip Slab Thickness Beam Spacing Length of Slab Overhang Nominal Width of Rail (T551) Distance from the Edge of the Overhang to the Toe of the Rail (T551) Width of top flange of the Girder (IGD) Distance from CL Girder to Design Section for Negative Moment (AASHTO LRFD ) Distance from load to point of support for Overhangs (AASHTO LRFD ) In the overhang, place a 16 kip wheel load from the toe of the rail. (AASHTO LRFD ) To make the slab design independent of the type of rail, we will place the wheel load from the nominal face of the rail ( from the edge of the slab). LRFD Slab Design Example 3 July 2010
4 +M r ~ Slab Positive Moment Capacity: A s 0.31 in 2 b A 6in s 0.62 in 2 Area of steel in a 1 ft strip (Bars B) c A s f y c in (AASHTO LRFD Eq ) 0.85β 1 f c b a c β 1 a 0.9 (AASHTO LRFD ) d poss = slab thickness - bottom cover - 1/2 bar diameter 0.625in d poss h 1.25in d 2 poss in Calc. M n : (AASHTO LRFD ) a M n A s f y d poss M 2 12in n kipft (AASHTO LRFD Eq ) ϕ 0.9 (AASHTO LRFD ) M r ϕ M n M r kipft (AASHTO LRFD Eq ) M posr M r M posr kipft Positive Factored Flexural Resistance of a 1 ft strip -M r ~ Slab Negative Moment Capacity: A s 0.31 in 2 b A 6in s 0.62 in 2 Area of steel in a 1 ft strip (Bars A) c A s f y c in (AASHTO LRFD Eq ) 0.85β 1 f c b a c β 1 a 0.9 (AASHTO LRFD ) d negs = slab thickness - top cover - 1/2 bar diameter in d negs h 2 in d 2 negs in Calc. M n : (AASHTO LRFD ) a M n A s f y d negs M 2 12in n kipft (AASHTO LRFD Eq ) ϕ 0.9 (AASHTO LRFD ) M r ϕ M n M r kipft (AASHTO LRFD Eq ) M negr M r M negr kipft Negative Factored Flexural Resistance of a 1 ft strip LRFD Slab Design Example 4 July 2010
5 Loads & Load Factors: (AASHTO LRFD 3.4.1) 2 Limit States apply: Strength I = 1.25 DC DW (LL + IM) Service I = DC + DW + LL + IM Use D R I =1.0 (AASHTO LRFD 1.3.2) DC: (Slab Dead Load) ω Slab kcf h 12in b 12in ω Slab klf Rail DL is considered in overhang check. DC Load on a 1 ft strip DW: (2.5" ACP overlay) ω DW kcf 2.5 in ω DW klf b DW Load on a 1 ft strip Design slabs for 2.5" of asphaltic overlay at kcf (TxSP) LL + IM: Use tabulated LL+IM moments in AASHTO LRFD Appendix A4-1 (AASHTO LRFD C ) Check Ultimate Moments at Strength I: Assume: -M DL = M DL = Equations for Moments: Four Continuous Equal Spans Uniformly Loaded Recall: S 9ft Beam Spacing (From Pg. 3) Positive Moment: M posdc ω Slab S 2 Positive DC Moment on a 1 ft strip M posdc 0.63 kipft M posdw ω DW S 2 Positive DW Moment on a 1 ft strip M posdw 0.18 kipft M posllim 6.29 kipft M posu 1.25 M posdc 1.25 M posdw 1.75 M posllim M posu kipft Positive LL + IM Moment on a 1 ft strip (AASHTO LRFD Table A4-1) Positive Factored Moment at Strength I Limit State on a 1 ft strip M posr kipft M posu LRFD Slab Design Example 5 July 2010
6 Check Ultimate Moments at Strength I: (Con't) Recall: S 9ft Beam Spacing (From Pg. 3) L Negative Moment: Distance from CL Girder to Design Section for Negative Moment (From Pg. 3) M negdc ω Slab S 2 Negative DC Moment on a 1 ft strip M negdc 0.87 kipft M negdw ω DW S 2 M negdw 0.25 kipft Negative DW Moment on a 1 ft strip M negllim 3.71 kipft M negu 1.25 M negdc 1.25 M negdw 1.75 M negllim M negu 7.89 kipft Negative LL + IM Moment on a 1 ft strip (AASHTO LRFD Table A4-1 ~ Interpolated between values of L) Negative Factored Moment at Strength I Limit State on a 1 ft strip M negr kipft M negu Check Minimum Flexural Reinforcement: (AASHTO LRFD ) bh 2 S x S 6 x in 3 f r = 0.24 f c f r ksi M cr S x f r M cr 5.12 kipft Section Modulus of a 1 ft section Modulus of Rupture (BDM-LRFD, Ch. 3, Sect. 2, Design Criteria) Cracking Moment of a 1 ft section (AASHTO LRFD Eq ) Check Negative Moment Reinforcement: 1.2 M cr 6.14 kipft M f_neg = Minimum of: Design for the lesser of 1.2M cr or 1.33 M negu kipft 1.33Mu when determining minimum area of steel required. M negr M f_neg 6.14 kipft kipft M f_neg Check Positive Moment Reinforcement: 1.2 M cr 6.14 kipft M f_pos = Minimum of: Design for the lesser of 1.2M cr or 1.33 M posu kipft 1.33Mu when determining minimum area of steel required. M posr M f_pos 6.14 kipft kipft M f_pos LRFD Slab Design Example 6 July 2010
7 Check Crack Control at Service I: Exposure Condition Factor: (AASHTO LRFD ) γ e 0.75 For class 2 exposure conditions. (TxSP) Positive Moment: M poss M posllim M posdc M posdw M poss 7.10 kipft Positive Moment at Service I Limit State on a 1 ft strip d c h d poss d c in ρ A s ρ bd poss Tension Reinforcement Ratio k n ρ ( n ρ) 2 2nρ k j k j Assuming steel does not yield. f ss M poss f ja s d poss ss ksi Service Load Bending Stress in bottom layer of the reinforcing d c β s 1 β 0.7 h d c s (AASHTO LRFD ) s max = minimum of: 700γ e β s f ss 2d c in (AASHTO LRFD Eq ) s max 6in 6in (BDM-LRFD, Ch. 3, Sect. 2, Design Criteria) s actual 6in s max LRFD Slab Design Example 7 July 2010
8 Check Crack Control at Service I: (Con't) Negative Moment: M negs M negllim M negdc M negdw M negs 4.83 kipft Negative Moment at Service I Limit State on a 1 ft strip d c h d negs d c in ρ A s ρ bd negs Tension Reinforcement Ratio k n ρ ( n ρ) 2 2nρ k j k j Assuming steel does not yield. f ss M negs f ja s d negs ss ksi Service Load Bending Stress in top layer of the reinforcing d c β s 1 β 0.7 h d c s (AASHTO LRFD ) s max = minimum of: 700γ e β s f ss 2d c in (AASHTO LRFD Eq ) s max 6in 6in (BDM-LRFD, Ch. 3, Sect. 2, Design Criteria) s actual 6in s max LRFD Slab Design Example 8 July 2010
9 Check Overhang: Slab strength for rail impacts (AASHTO LRFD 9.5.5) has been verified through full scale crash testing. (BDM-LRFD, Ch. 3, Sect. 2, Design Criteria) To make the design independent of the rail type, don't design slabs using structurally continuous barriers. Therefore the provisions of AASHTO LRFD cannot be used. Live Load is composed of the axles of the design truck or tandem only; the lane load is not used to design the deck. (AASHTO LRFD ) Only one lane is loaded on the 3 ft overhang; lane spacing is 12 ft. (AASHTO LRFD ) Only one wheel load can act on the 3 ft overhang; the first wheel is 1 ft from the face of the rail (AASHTO LRFD ), and the wheel spacing is 6 ft. (AASHTO LRFD ) The thickness of the slab in the primary region (8 in) is the same as the thickness of the slab in the edge strip, therefore Slab ends are critical ~ Check the Edge Strip Only m 1.20 IM 33 Multiple Presence Factor (AASHTO LRFD Table ~ For one lane loaded) Impact Load Allowance (AASHTO LRFD Table ) Recall: b Width of a 1 ft strip (From Pg. 3) X 0ft Distance from load to point of support for Overhangs (From Pg. 3) DC: (Slab Dead Load & Rail Dead Load) ω Slab klf P Rail klf b P Rail kip Slab Load on a 1 ft strip (From Pg. 5) Rail Load on a 1 ft strip (T551) DW: (2.5" ACP overlay) ω DW klf DW Load on a 1 ft strip (From Pg. 5) LL + IM: PrimaryStrip OH = X (AASHTO LRFD Table ) PrimaryStrip OH 45 in 1 EdgeStrip OH 2 PrimaryStrip OH EdgeStrip OH 22.5 in In the equations for strip width, the values for "X" is in feet but the strip width resulting from the equation is in inches. (AASHTO LRFD c) See discussion on Pg. 2 for clarification. P LLIM m 16 kip 1 IM 100 b EdgeStrip OH LL + IM Load on a 1 ft strip P LLIM kip LRFD Slab Design Example 9 July 2010
10 Check Overhang: Recall: OH 3 ft (Con't) Length of Slab Overhang (From Pg. 3) RW 1 ft Nominal Width of Rail (From Pg. 3) d RailToe ft Distance from the Edge of the Overhang to the Toe of the Rail (From Pg. 3) L Negative Moment at the Design Section: 1 M slab 2 ω Slab M slab OH L 0.20 kipft M rail P Rail OH 1 2 RW L M rail 0.57 kipft 1 M DW 2 ω DW OH d RailToe L M DW 0.00 kipft M LLIM P LLIM OH RW L M LLIM 0.00 kipft M negu 1.25M rail 1.25M slab 1.25 M DW 1.75 M LLIM M negu 0.97 kipft 2 2 Distance from CL Girder to Design Section for Negative Moment (From Pg. 3) Positive Slab Moment on a 1 ft strip Positive Rail Moment on a 1 ft strip Positive DW Moment on a 1 ft strip Positive LL + IM Moment on a 1 ft strip Negative Factored Moment at Strength I Limit State on a 1 ft strip M negr kipft M negu Check Distribution Reinforcement: A sd 0.31 in 2 b A 9in sd in 2 A s 0.31 in 2 b A 6in s 0.62 in 2 220% A s in 2 A S sd_min = minimum of: A s 67% in 2 Area of distribution reinforcement in a 1 ft strip (Bars D) Area of primary reinforcement in a 1 ft strip (Bars A) (AASHTO LRFD ~ For primary reinforcement perpendicular to traffic) A sd_min in 2 A sd in 2 A sd_min Summary: 8" slab with 6" O.C. Top & Bottom for prestressed beams spcaced 10'-6" for steel beams spcaced 10-3" LRFD Slab Design Example 10 July 2010
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