LRFD Cast-In-Place (CIP) Slab Span Design Example

Transcription

1 LRFD Cast-In-Place (CIP) Slab Span Design Example County: Any Hwy: Any Design: BRG Date: 12/2006 CSJ: Any Project: Any Checked: BRG Date: 12/2006 Design Parameters The basic bridge geometry can be found on the Bridge Layout and 75' Slab Span Details (see the Appendix, Pages 21 and 22). Deck is 46 ft wide with a 15 degree skew Roadway is 44 ft wide Type T501 Rail (0.326k/ft) 14" Thick Slab Span Assume NO 140 pcf (0.023 ksf) Use Class "S" Concrete f' c =4.0 ksi w c =150 pcf (for weight) w c =145 pcf (for Modulus of Elasticity calculation) Grade 60 Reinforcing f y =60 ksi Methodology The following procedure is based on the AASHTO LRFD Bridge Design Specifications, 3rd Ed. 2004, 2005 Interim Revisions, and 2006 Interim Revisions and the TXDOT LRFD Bridge Design Manual (hereafter refered to as TXDOT policy). Calculations Determine the Equivalent Strip Width, E (LRFD ) The equivalent strip width defines the width of the slab that will be impacted by the live load within a design lane. The slab is designed based on the forces developed within this width. L = span length (ft) L 1 = the minimum of L or 60 ft. (ft) W = edge to edge width (ft) W s = the modified edge to edge width taken as a minimum of W or 30 ft (ft) for a single loaded lane W m = the modified edge to edge width taken as a minimum of W or 60 ft (ft) for multiple loaded lanes L = 25 ft L 1 = min( L, 60 ft) L 1 = ft W = W s W m 46 ft = min( W, 30 ft) W s = ft = min( W, 60 ft) W m = ft page 1

2 N = number of lanes, the interger part of W Rdwy /12 ( ) W rdwy = Clear roadway width W rdwy = 44 ft N L 1 W rdwy ft = trunc N 12 L = The trun function truncates the calculated value to a single interger (ie would be 3). E s = equivalent strip width for single loaded lane (in) E s = ( ) in 10.0 in + 5 L 1 W s ft LRFD eq E s = in E s = ft E m = equivalent strip width for multiple loaded lanes (in) E m1 ( ) in = 84.0 in L 1 W m E ft m1 = in LRFD eq in 12.0 W m ft E m2 = E N m2 = in L E m ( ) LRFD eq = min E m1, E m2 E m = in E m = ft Skew For skewed bridges, the longitudinal force effects may be reduced by the factor r, where skew = 15.deg Note: TXDOT policy limits the skew on CIP Slab Spans to 30 degrees. r 1 = tan( skew) r 1 = LRFD eq r shall not be greater than 1 ( ) r = min r 1, 1 r = This factor is applied to the moments developed in the following sections. page 2

3 Determine the Design Loads (Live and Dead) The live load is comprised of the design lane load (0.640 k/ft) and the design wheel loads. The dead load is comprised of the rail and slab weights, as well as any sidewalks or overlay (where applicable). The slab is modelled as a simply supported continuous beam. Dead Load (DL) Rail: Rail Load (RL) is distributed across the slab by the following TxDOT policy. If the slab is width is less than 32 feet, the rail weight is distributed over the entire width of the slab. Otherwise, the rail is distributed over the first 16 feet of slab adjacent to the rail. W r = weight of the rail (kip/ft) DL rail = the distibuted rail load on the slab (kip/ft/ft) W r = kip ft W r 2 W r DL rail = if W < 32 ft,, DL W 16 ft rail = kip ft 2 Slab: W c = weight of concrete (kcf) t = thickness of the slab (inches) DL slab = weight of the slab (kip/ft/ft) W c = kip ft 3 t = 14 in t DL slab = W c 12 in DL slab = kip ft 2 ft Total DL: DL = DL rail + DL slab DL = kip ft 2 Live Load LRFD The slab is designed based on 1-foot strips, therefore the live load most be distributed to these strips. To obtained a live load per foot divide the lane load and truck loads by the effective width. LL lane = distributed lane load = k/ft ( ) LL t8 and LL t32 = design truck load, 8 k and 32 k, respectively ( ) I = impact factor LL lane = kip ft LL t8 = 8 kip LL t32 = I = kip page 3

4 LL s = lane load over E s (single lane loaded) LL t8_s = 8 k load over E s (single lane loaded) LL t32_s = 32 k load over E s (single lane loaded) LL lane LL s = LL E s = kip s ft 2 ILL t8 LL t8_s = LL E t8_s = kip s ft LL t32_s ILL t32 = LL E t32_s = kip s ft LL m = lane load over E m (multiple lanes loaded) LL t8_m = 8 k load over E m (multiple lanes loaded) LL t32_m = 32 k load over E m (multiple lanes loaded) LL lane LL m = LL E m = kip m ft 2 ILL t8 LL t8_m = LL E t8_m = kip m ft LL t32_m ILL t32 = LL E t32_m = kip m ft Determine the Design Moment The design moment is determined using BMCOL51 (Moveable Load Analysis of Beam Columns). Due to the nature of the program the moment is determined by first modelling the dead load only and then the live load only. The maximum moment from each analysis is then combined using Tables and of the AASHTO LRFD. BMCOL51 Model page 4

5 BMCOL51 Input Files for Live Load - Single Lane Loaded BMCOL51 Input Files for Dead Load The input and resultant output files for single lane loaded and multiple lanes loaded are included in the Appendix. Output Results - Table 8A Single Lane Loaded M_DL pos_s and M_DL neg_s = Maximum positive and negative moment due to the Dead Load M_LL pos_s and M_LL neg_s = Maximum positive and negative moment due to the Live Load M_DL pos_s M_LL pos_s = kip ft M_DL neg_s = kip ft = kip ft M_LL neg_s = kip ft Multiple Lanes Loaded M_DL pos_m and M_DL neg_m = Maximum positive and negative moment due to the Dead Load M_LL pos_m and M_LL neg_m = Maximum positive and negative moment due to the Live Load M_DL pos_m M_LL pos_m = kip ft M_DL neg_m = kip ft = kip ft M_LL neg_m = kip ft page 5

6 The maximum moment from each analysis is then combined using Tables and of the AASHTO LRFD using Service I and Strength I LL s and LL st = live load factor for service and strength, respectivelly DC s and DC st = dead load factor for service and strength, respectivelly and reduced for skew using r. LL s = 1.00 LL st = 1.75 DC s = 1.00 DC st = 1.25 M_Serv pos_s, M_Serv neg_s = Positive or negative combined Service Moment for single loaded lane M_Serv pos_m, M_Serv neg_m = Positive or negative combined Service Moment for multiple loaded lanes M_Serv pos, M_Serv neg = Positive or negative combined Service Moment for design, the maximum of the moments for single lane loaded or multiple lanes loaded M_Serv pos_s = rll s M_LL pos_s + DC s M_DL pos_s M_Serv pos_s = kip ft M_Serv pos_m = rll s M_LL pos_m + DC s M_DL pos_m M_Serv pos_m = kip ft M_Serv pos M_Serv neg_s M_Serv neg_m M_Serv neg ( ) = max M_Serv pos_s, M_Serv pos_m M_Serv pos = kip ft = rll s M_LL neg_s + DC s M_DL neg_s M_Serv neg_s = kip ft = rll s M_LL neg_m + DC s M_DL neg_m M_Serv neg_m = kip ft ( ) = max M_Serv neg_s, M_Serv neg_m M_Serv neg = kip ft M_Ult pos_s, M_Ult neg_s = Positive or negative combined Strength Moment for single loaded lane M_Ult pos_m, M_Ult neg_m = Positive or negative combined Strength Moment for multiple loaded lanes M_Ult pos, M_Ult neg = Positive or negative combined Strength Moment for design, the maximum of the moments for single lane loaded or multiple lanes loaded M_Ult pos_s M_Ult pos_m M_Ult pos M_Ult neg_s M_Ult neg_m M_Ult neg = rll st M_LL pos_s + DC st M_DL pos_s M_Ult pos_s = kip ft = rll st M_LL pos_m + DC st M_DL pos_m M_Ult pos_m = kip ft ( ) = max M_Ult pos_s, M_Ult pos_m M_Ult pos = kip ft = rll st M_LL neg_s + DC st M_DL neg_s M_Ult neg_s = kip ft = rll st M_LL neg_m + DC st M_DL neg_m M_Ult neg_m = kip ft ( ) = max M_Ult neg_s, M_Ult neg_m M_Ult neg = kip ft Summary of Results (includes reduction for skew) M s_pos M s_neg M u_pos M u_neg = M_Serv pos M s_pos = kip ft = M_Serv neg M s_neg = kip ft = M_Ult pos M u_pos = kip ft = M_Ult neg M u_neg = kip ft page 6

7 Moment Capacity Design - Negative (Top) - Typ. Bars A LRFD b h = = 12 in Design strip width per TxDOT policy 14 in Compressive Strength of Concrete: f c = 4 ksi Thickness of the slab. Yield Strength of Rebar: f y = 60 ksi cover neg = 2in "cover" is measured to edge of top reinforcement. Try, #8's at 6 inch spacing N bar_neg = 2 Number of bars in 12 in strip. d bar_neg = 1.00in Diameter of main reinforcing bars. A bar_neg 0.79in 2 = Area of one main reinforcing bar. A s_neg = ( N bar_neg ) A bar_neg A s_neg = in 2 Area of steel in tension. 1 d neg = h cover neg 2 d bar_neg d neg = in ( ) 0.05 β 1_neg = min 0.85, max 0.65, 0.85 f 1ksi c 4ksi β 1_neg = LRFD Resistance Factor: φ M = 0.9 LRFD Depth of Cross Section in Compression under Ultimate Load: c neg A s_neg f y = c 0.85 f c β 1_neg b neg = in LRFD Eq Depth of Equivalent Stress Block: a neg = c neg β 1_neg a neg = in LRFD Thus, Nominal Flexural Resistance: a neg 1ft M n_neg = A s_neg f y d neg M 2 12in n_neg = kip ft LRFD Eq Factored Flexural Resistance: M r_neg = φ M M n_neg M r_neg = kip ft M u_neg = kip ft ( ) OK UltimateMom = if M r_neg M u_neg,, NG UltimateMom = "OK!" page 7

8 Check Serviceability- Negative (Top) - Typ. Bars A LRFD To find s max_neg : 1 d c_neg = cover neg + 2 d bar_neg d c_neg = in Es = ksi "cover" is measured to edge of the top reinforcement. 1 Ec = 1820 f c ksi ksi Ec = ksi LRFD Eq. C Modular Ratio: n Es = n = Ec A s_neg Tension Reinforcement Ratio: ρ neg = ρ bd neg = neg For service loads, the stress on the cross-section is located as drawn: k neg = ( 2 ρ neg n) + ( ρ neg n) 2 ( ρ neg n) k neg = k neg j neg = 1 j 3 neg = Service Load Bending Stress: f s_neg M s_neg 12in = f A s_neg j neg d neg 1ft s_neg = ksi Exposure Condition Factor: γ e_top = 0.75 For class 2 exposure conditions. d c_neg β s_neg = 1 + β 0.7 h d s_neg = c_neg ( ) kip 700 in γ e_top s max_neg = 2d β s_neg f c_neg s max_neg = in LRFD Eq s_neg s Actual_neg = 6in ( ) OK ServiceabilityCheck = if s max_neg s Actual_neg,, NG ServiceabilityCheck = "OK!" The negative reinforcement can usually be reduced to #8 bars at 12 inches about 6 feet from the centerline of the bent. However, this shoud be verified by checking the moment capacity of 1 bar versus the moment at 6 feet from the centerline of the cap. For this example problem, 1 bar will provide kip-ft of M r_neg with a M u_neg of kip-ft. In addition, the max. bar spacing is in excess of 12 inches. page 8

9 Moment Capacity Design - Positive (Bottom) - Typ. Bars B LRFD cover pos = 1.25 in "cover" is measured to edge of the bottom reinforcement. Try, #8's at 6 inch spacing N bar_pos = 2 Number of bars in 12 in strip. d bar_pos = 1.00in Diameter of main reinforcing bars. A bar_pos = 0.79in 2 Area of one main reinforcing bar. A s_pos = ( N bar_pos ) A bar_pos A s_pos = in 2 Area of steel in tension. 1 d pos = h cover pos 2 d bar_pos d pos = in ( ) 0.05 β 1pos = min 0.85, max 0.65, 0.85 f 1ksi c 4ksi β 1pos = LRFD Depth of Cross Section in Compression under Ultimate Load: LRFD Eq c pos A s_pos f y = c 0.85 f c β 1pos b pos = in Depth of Equivalent Stress Block: a pos = c pos β 1pos a pos = in Thus, Nominal Flexural Resistance: LRFD Eq M n_pos a pos 1ft = A s_pos f y d pos M 2 12in n_pos = kip ft Factored Flexural Resistance: M r_pos = φ M M n_pos M r_pos = kip ft M u_pos = kip ft ( ) OK UltimateMom pos = if M r_pos M u_pos,, NG UltimateMom pos = "OK!" page 9

10 Check Serviceability- Positive (Bottom) - Typ. Bars B To find s max_pos : "Control of cracking by Distribution of Reinforcement", LRFD d c_pos = cover pos + 2 d bar_pos d c_pos = in "cover" is measured to edge of the bottom reinforcement. Tension Reinforcement Ratio: ρ pos = A s_pos bd pos ρ pos = k pos = ( 2 ρ pos n) + ( ρ pos n) 2 ( ρ pos n) k pos = k pos j pos = 1 j 3 pos = Service Load Bending Stress: f s_pos M s_pos 12in = f A s_pos j pos d pos 1ft s_pos = ksi Exposure Condition Factor: γ e_bot = 1.00 For class 1 exposure conditions. d c_pos β s_pos = 1 + β 0.7 h d s_pos = c_pos ( ) kip 700 in γ e_bot s max_pos = 2d β s_pos f c_pos s max_pos = in s_pos LRFD Eq s Actual_pos = 6in ( ) OK ServiceabilityCheck pos = if s max_pos s Actual_pos,, NG ServiceabilityCheck pos = "OK!" page 10

11 Shrinkage and Temperature Reinforcement- Negative (Top) - Typ. Bars T LRFD Try #4 bars at 12 inch spacing N bar_t_neg = 1 d bar_t_neg = 0.500in A bar_t_neg = 0.20in 2 A s_t_neg = ( N bar_t_neg ) A bar_t_neg A s_t_neg = in 2 As req_t_neg min max 0.11 in 2 ( 1.3 b h) in =, 1 2 ( b + h) f y ksi, 0.60 in 2 As req_t_neg = in 2 ( ) OK TemperatureCheck neg = if A s_t_neg As req_t_neg,, NG TemperatureCheck neg = "OK!" Transverse Distribution Reinforcement- Positive (Bottom) - Typ. Bars D LRFD and TxDOT policy Try #4 bars at 6 inch spacing N bar_d_pos = 2 d bar_d_pos = 0.500in A bar_d_pos = 0.20in 2 A s_d_pos = ( N bar_d_pos ) A bar_d_pos A s_d_pos = in 2 PercentAs d_pos = min 50, 100 L 1 ft PercentAs d_pos = LRFD Eq PercentAs d_pos As req_d_pos = A s_pos As 100 req_d_pos = in 2 ( ) OK Distribution d_pos = if A s_d_pos As req_d_pos,, NG Distribution d_pos = "OK!" Shear Reinforcement From LRFD , "Slabs and slab bridges designed for moment in conformance with Atricle may be considered satisfactory for shear." page 11

12 Design for the Edge Beam The edge for the slab is designed based on LRFD and The design width (W edge ) of the longitudinal edge is the sum of the distance between the edge of the deck and the inside face of the barrier (C) plus 12 inches plus 1/4E, not to exceed 1/2E or 72 inches. C = 17 in Type T501 Rail, bottom width is 17 inches E m = ft ( ) 0.5 E m W edge = min C + 12 in E m,, 72 in W edge = ft Determine the Design Loads (Live and Dead) The live load is comprised of the design lane load (0.640 k/ft) and the design wheel loads. The dead load is comprised of the rail and slab weights, as well as any sidewalks or overlay (if applicable). The slab is modelled as a simply supported continuous beam. Dead Load Same as calculated on page 2. DL rail = kip ft 2 DL slab = kip ft 2 page 12

13 Live Load LRFD The slab is designed based on 1-foot strips, therefore the live load must be distributed to these strips. To obtained a live load per foot divide the lane load and truck loads by the effective width. LL lane = distributed lane load = k/ft ( ) LL t4 and LL t16 = design truck load, 4 k and 16 k, respectively ( ). The truck load is half the load because the edge width only accommodates half the truck. I = impact factor LL lane = ft kip ft 2 LL t4 = 4 kip LL t16 = 16 kip I = LL edge = lane load over W edge LL t4_edge = 4 k load over W edge LL t16_edge = 16 k load over W edge W edge LL lane 12 LL edge = LL W edge = ft kip edge ft 2 ILL t4 LL t4_edge = LL W t4_edge = kip edge ft LL t16_edge ILL t16 = LL W t16_edge = kip edge ft Determine the Design Moment The design moment is determined using BMCOL51 (Moveable Load Analysis of Beam Columns). Due to the nature of the program the moment is determined by first modelling the dead load only and then the live load only. The maximum moment from each analysis is then combined using Tables and of the AASHTO LRFD. The input and resultant output files for single lane loaded and multiple lanes loaded are included in the Appendix. Output Results - Table 8A M_DL edge_pos and M_DL edge_neg = Maximum positive and negative moment due to the Dead Load M_LL edge_pos and M_LL edge_neg = Maximum positive and negative moment due to the Live Load M_DL edge_pos M_LL edge_pos = kip ft M_DL edge_neg = kip ft = kip ft M_LL edge_neg = kip ft page 13

14 The maximum moment from each analysis is then combined using Tables and of the AASHTO LRFD using Service I and Strength I LL s and LL st = live load factor for service and strength, respectivelly DC s and DC st = dead load factor for service and strength, respectivelly and reduced for skew using r. LL s = LL st = DC s = DC st = M_Serv edge_pos, M_Serv edge_pos = Positive or negative combined Service Moment for edge beam M_Serv edge_pos = rll s M_LL edge_pos + DC s M_DL edge_pos M_Serv edge_pos = kip ft M_Serv edge_neg = rll s M_LL edge_neg + DC s M_DL edge_neg M_Serv edge_neg = kip ft M_Ult edge_pos, M_Ult edge_neg = Positive or negative combined Strength Moment for edge beam M_Ult edge_pos = rll st M_LL edge_pos + DC st M_DL edge_pos M_Ult edge_pos = kip ft M_Ult edge_neg = rll st M_LL edge_neg + DC st M_DL edge_neg M_Ult edge_neg = kip ft Summary of Results (includes reduction for skew) M s_edge_pos M s_edge_neg M u_edge_pos M u_edge_neg = M_Serv edge_pos M s_edge_pos = kip ft = M_Serv edge_neg M s_edge_neg = kip ft = M_Ult edge_pos M u_edge_pos = kip ft = M_Ult edge_neg M u_edge_neg = kip ft page 14

15 Moment Capacity Design - Negative (Top) - Typ. Bars A LRFD b = in Design stip width per TxDOT policy h = in Thickness of the slab. cover e_neg = 2in "cover" is measured to edge of the top reinforcement. Try, #8's at 6 inch spacing N bar_e_neg = 2 Number of bars in 12 in strip. d bar_e_neg = 1.00in Diameter of main reinforcing bars. A bar_e_neg 0.79in 2 = Area of one main reinforcing bar. A s_e_neg = ( N bar_e_neg ) A bar_e_neg A s_e_neg = in 2 Area of steel in tension. 1 d edge_neg = h cover e_neg 2 d bar_e_neg d edge_neg = in ( ) 0.05 β 1_e_neg = min 0.85, max 0.65, 0.85 f 1ksi c 4ksi β 1_e_neg = LRFD Resistance Factor: φ M = LRFD Depth of Cross Section in Compression under Ultimate Load: c e_neg A s_e_neg f y = c 0.85 f c β 1_e_neg b e_neg = in LRFD Eq Depth of Equivalent Stress Block: a e_neg = c e_neg β 1_e_neg a e_neg = in Thus, Nominal Flexural Resistance: a e_neg 1ft M n_e_neg = A s_e_neg f y d edge_neg M 2 12in n_e_neg = kip ft LRFD Eq Factored Flexural Resistance: M r_e_neg = φ M M n_e_neg M r_e_neg = kip ft M u_edge_neg = kip ft ( ) OK UltimateMom edge_neg = if M r_e_neg M u_edge_neg,, NG UltimateMom edge_neg = "NO GOOD!" Thought the resistance is less than the ultimate, the presented design is considered acceptable because the difference is less than 3 percent of the ultimate. Though not necessary, the bar spacing is reduced to 4 inches within the outside 1-foot of the slab in order to provide additional reinforcement for rail attachment. page 15

16 Check Serviceability- Negative (Top) - Typ. Bars A To find s max_e_neg : 1 d c_e_neg = cover e_neg + 2 d bar_e_neg d c_e_neg = in Tension Reinforcement Ratio: "Control of cracking by Distribution of Reinforcement", LRFD "cover" is measured to edge of the bottom reinforcement. ρ e_neg = A s_e_neg bd edge_neg ρ e_neg = k e_neg = ( 2 ρ e_neg n) + ( ρ e_neg n) 2 ( ρ e_neg n) k e_neg = k e_neg j e_neg = 1 j 3 e_neg = Service Load Bending Stress: f s_e_neg M s_edge_neg 12in = f A s_e_neg j e_neg d edge_neg 1ft s_e_neg = ksi Exposure Condition Factor: γ e_top = 0.75 For class 2 exposure conditions. d c_e_neg β s_e_neg = 1 + β 0.7 h d s_e_neg = c_e_neg ( ) kip 700 in γ e_top s max_e_neg = 2d β s_e_neg f c_e_neg s max_e_neg = in LRFD Eq s_e_neg s Actual_e_neg = 6in ( ) OK ServiceabilityCheck e_neg = if s max_e_neg s Actual_e_neg,, NG ServiceabilityCheck e_neg = "NO GOOD!" Thought the spacing is greater than the maximum spacing, the presented design is considered acceptable because the difference is less than 1/2 inch. page 16

17 Moment Capacity Design - Positive (Bottom) - Typ. Bars B LRFD b = in Design stip width per TxDOT policy h = in Thickness of the slab. cover e_pos = 1.25 in "cover" is measured to edge of the bottom reinforcement. Try, #8's at 6 inch spacing N bar_e_pos = 2 Number of bars in 12 in strip. d bar_e_pos = 1.00in Diameter of main reinforcing bars. A bar_e_pos 0.79in 2 = Area of one main reinforcing bar. A s_e_pos = ( N bar_e_pos ) A bar_e_pos A s_e_pos = in 2 Area of steel in tension. 1 d edge_pos = h cover e_pos 2 d bar_e_pos d edge_pos = in ( ) 0.05 β 1_e_pos = min 0.85, max 0.65, 0.85 f 1ksi c 4ksi β 1_e_pos = LRFD Resistance Factor: φ M = LRFD Depth of Cross Section in Compression under Ultimate Load: c e_pos A s_e_pos f y = c 0.85 f c β 1_e_pos b e_pos = in LRFD Eq Depth of Equivalent Stress Block: a e_pos = c e_pos β 1_e_pos a e_pos = in Thus, Nominal Flexural Resistance: a e_pos 1ft M n_e_pos = A s_e_pos f y d edge_pos M 2 12in n_e_pos = kip ft LRFD Eq Factored Flexural Resistance: M r_e_pos = φ M M n_e_pos M r_e_pos = kip ft M u_edge_pos = kip ft ( ) OK UltimateMom edge_pos = if M r_e_pos M u_edge_pos,, NG UltimateMom edge_pos = "OK!" Based on past experience, the above reinforcement is considered acceptable. Though not necessary, the bar spacing is reduced to 4 inches within the outside 1-foot of the slab in order to provide additional reinforcement for rail attachment. page 17

18 Check Serviceability- Positive (Bottom) - Typ. Bars B "Control of cracking by Distribution of Reinforcement", LRFD To find s max_e_pos : 1 d c_e_pos = cover e_pos + 2 d bar_e_pos d c_e_pos = in "cover" is measured to edge of the bottom reinforcement. Tension Reinforcement Ratio: ρ e_pos = A s_e_pos bd edge_pos ρ e_pos = k e_pos = ( 2 ρ e_pos n) + ( ρ e_pos n) 2 ( ρ e_pos n) k e_pos = k e_pos j e_pos = 1 j 3 e_pos = Service Load Bending Stress: f s_e_pos M s_edge_pos 12in = f A s_e_pos j e_pos d edge_pos 1ft s_e_pos = ksi Exposure Condition Factor: γ e_bot = 1.00 For class 1 exposure conditions. d c_e_pos β s_e_pos = 1 + β 0.7 h d s_e_pos = c_e_pos ( ) kip 700 in γ e_bot s max_e_pos = 2d β s_e_pos f c_e_pos s max_e_pos = inlrfd Eq s_e_pos s Actual_e_pos = 6in ( ) OK ServiceabilityCheck e_pos = if s max_e_pos s Actual_e_pos,, NG ServiceabilityCheck e_pos = "OK!" page 18

19 Shrinkage and Temperature Reinforcement- Negative (Top) - Typ. Bars T LRFD Try #4 bars at 12 inch spacing N bar_te_neg = 1 d bar_te_neg = 0.500in A bar_te_neg = 0.20in 2 A s_te_neg = ( N bar_te_neg ) A bar_te_neg A s_te_neg = in 2 As req_te_neg min max 0.11 in 2 ( 1.3 b h) in =, 1 2 ( b + h) f y ksi, 0.60 in 2 As req_te_neg = in 2 ( ) OK TemperatureCheck e_neg = if A s_te_neg As req_te_neg,, NG TemperatureCheck e_neg = "OK!" Transverse Distribution Reinforcement- Positive (Bottom) - Typ. Bars D LRFD and TxDOT policy Try #4 bars at 6 inch spacing N bar_de_pos = 2 d bar_de_pos = 0.500in A bar_de_pos = 0.20in 2 A s_de_pos = ( N bar_de_pos ) A bar_de_pos A s_de_pos = in 2 PercentAs de_pos = min 50, 100 L 1 ft LRFD Eq PercentAs de_pos = PercentAs de_pos As req_de_pos = A s_e_pos As 100 req_de_pos = in 2 ( ) OK Distribution de_pos = if A s_de_pos As req_de_pos,, NG Distribution de_pos = "OK!" Shear Reinforcement From LRFD , "Slabs and slab bridges designed for moment in conformance with Atricle may be considered satisfactory for shear." page 19

20 Appendix Bridge Layout... pg 21 Slab Span Details... pg 22 BMCOL51 Input File (Dead Load)... BMCOL51 Output File (Dead Load)... BMCOL51 Input File (Single Loaded - Live Load)... pg 23 pg 24 pg 41 BMCOL51 Output File (Single Lane Loaded - Live Load)... pg 42 BMCOL51 Input File (Multiple Lanes - Live Load)... pg 59 BMCOL51 Output File (Multiple Lanes Loaded - Live Load)... pg 60 BMCOL51 Input File (Edge Beam - Live Load)... BMCOL51 Output File (Edge Beam - Live Load)... pg 77 pg 78 page 20

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23 COUNTY HWY BRG 12/02/2006 SLAB SPAN DESIGN EXAMPLE 1 DEAD LOAD E CEASE 01/30/2007 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 23

24 PSF HIGHWAY PD- CONTROL- CODED NO COUNTY NO IPE SECTION-JOB BY DATE COUNTY HWY BRG 12/02/2006 SLAB SPAN DESIGN EXAMPLE PROB 1 DEAD LOAD TABLE 1 - PROGRAM-CONTROL DATA ENVELOPES TABLE NUMBER OF MAXIMUMS HOLD FROM PRECEDING PROBLEM (1=HOLD) NUM CARDS INPUT THIS PROBLEM DEFL MOM SHR RCT OPTION (IF=1) TO PLOT ENVELOPES OF MAXIMUMS TABLE 2 - CONSTANTS NUM INCREMENTS 150 INCREMENT LENGTH 5.000E-01 NUMBER OF INCREMENTS FOR MOVABLE LOAD 56 INITIAL POSITION OF MOVABLE LOAD STA ZERO -56 FINAL POSITION OF MOVABLE LOAD STA ZERO 150 NUMBER OF INCREMENTS BETWEEN EACH POSITION OF MOVABLE LOAD 2 TABLE 3 - SPECIFIED DEFLECTIONS AND SLOPES STA CASE DEFLECTION SLOPE E+00 NONE E+00 NONE E+00 NONE E+00 NONE TABLE 4 - STIFFNESS AND FIXED-LOAD DATA FROM TO CONTD F QF S T R P E E E E E E+00 TABLE 5 - MOVABLE-LOAD DATA FROM TO CONTD QM NONE TABLE 6 - SPECIFIED STATIONS FOR INFLUENCE DIAGRAMS ( SHEAR IS COMPUTED ONE HALF INCREMENT TO THE LEFT OF THE DESIGNATED STATION) NONE 01/30/2007 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 24

25 PSF HIGHWAY PD- CONTROL- CODED NO COUNTY NO IPE SECTION-JOB BY DATE COUNTY HWY BRG 12/02/2006 SLAB SPAN DESIGN EXAMPLE PROB 1 DEAD LOAD TABLE 7 - FIXED-LOAD RESULTS STA I DIST DEFL SLOPE MOM SHEAR SUP REACT E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+00 01/30/2007 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 25

26 TABLE 7 - FIXED-LOAD RESULTS STA I DIST DEFL SLOPE MOM SHEAR SUP REACT E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+00 01/30/2007 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 26

27 TABLE 7 - FIXED-LOAD RESULTS STA I DIST DEFL SLOPE MOM SHEAR SUP REACT 1.923E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+00 01/30/2007 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 27

28 TABLE 7 - FIXED-LOAD RESULTS STA I DIST DEFL SLOPE MOM SHEAR SUP REACT E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+00 01/30/2007 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 28

29 TABLE 7 - FIXED-LOAD RESULTS STA I DIST DEFL SLOPE MOM SHEAR SUP REACT E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+00 01/30/2007 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 29

30 TABLE 7 - FIXED-LOAD RESULTS STA I DIST DEFL SLOPE MOM SHEAR SUP REACT E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+00 01/30/2007 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 30

31 PROB (CONTD) 1 DEAD LOAD TABLE 8A- ENVELOPES OF MAXIMUMS * = HELD FROM PRIOR PROBLEM STA MAX +DEFL LOC MAX -DEFL LOC MAX +MOM LOC MAX -MOM LOC E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E /30/2007 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 31

32 TABLE 8A- ENVELOPES OF MAXIMUMS * = HELD FROM PRIOR PROBLEM STA MAX +DEFL LOC MAX -DEFL LOC MAX +MOM LOC MAX -MOM LOC E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E /30/2007 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 32

33 TABLE 8A- ENVELOPES OF MAXIMUMS * = HELD FROM PRIOR PROBLEM STA MAX +DEFL LOC MAX -DEFL LOC MAX +MOM LOC MAX -MOM LOC E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E /30/2007 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 33

34 TABLE 8A- ENVELOPES OF MAXIMUMS * = HELD FROM PRIOR PROBLEM STA MAX +DEFL LOC MAX -DEFL LOC MAX +MOM LOC MAX -MOM LOC E E E E /30/2007 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 34

35 TABLE 8B- ENVELOPES OF MAXIMUMS * = HELD FROM PRIOR PROBLEM STA MAX +SHEAR LOC MAX -SHEAR LOC MAX +REACT LOC MAX -REACT LOC E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E /30/2007 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 35

36 TABLE 8B- ENVELOPES OF MAXIMUMS * = HELD FROM PRIOR PROBLEM STA MAX +SHEAR LOC MAX -SHEAR LOC MAX +REACT LOC MAX -REACT LOC E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E /30/2007 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 36

37 TABLE 8B- ENVELOPES OF MAXIMUMS * = HELD FROM PRIOR PROBLEM STA MAX +SHEAR LOC MAX -SHEAR LOC MAX +REACT LOC MAX -REACT LOC 4.583E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E /30/2007 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 37