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

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 Overlay @ 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 4.6.2.3) 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 = 25.000 ft W = W s W m 46 ft = min( W, 30 ft) W s = 30.000 ft = min( W, 60 ft) W m = 46.000 ft page 1

N = number of lanes, the interger part of W Rdwy /12 (3.6.1.1.1) W rdwy = Clear roadway width W rdwy = 44 ft N L 1 W rdwy ft = trunc N 12 L = 3.000 The trun function truncates the calculated value to a single interger (ie 3.987 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. 4.6.2.3-1 E s = 146.931 in E s = 12.244 ft E m = equivalent strip width for multiple loaded lanes (in) E m1 ( ) in = 84.0 in + 1.44 L 1 W m E ft m1 = 132.833 in LRFD eq. 4.6.2.3-2 in 12.0 W m ft E m2 = E N m2 = 184.000 in L E m ( ) LRFD eq. 4.6.2.3-2 = min E m1, E m2 E m = 132.833 in E m = 11.069 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 = 1.05 0.25 tan( skew) r 1 = 0.983 LRFD eq. 4.6.2.3-3 r shall not be greater than 1 ( ) r = min r 1, 1 r = 0.983 This factor is applied to the moments developed in the following sections. page 2

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 = 0.326 kip ft W r 2 W r DL rail = if W < 32 ft,, DL W 16 ft rail = 0.020 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 = 0.150 kip ft 3 t = 14 in t DL slab = W c 12 in DL slab = 0.175 kip ft 2 ft Total DL: DL = DL rail + DL slab DL = 0.195 kip ft 2 Live Load LRFD 3.6.1.3.3 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 = 0.640 k/ft (3.6.1.2.4) LL t8 and LL t32 = design truck load, 8 k and 32 k, respectively (3.6.1.2.2) I = impact factor LL lane = 0.640 kip ft LL t8 = 8 kip LL t32 = I = 1.33 32 kip page 3

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 = 0.052 kip s ft 2 ILL t8 LL t8_s = LL E t8_s = 0.869 kip s ft LL t32_s ILL t32 = LL E t32_s = 3.476 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 = 0.058 kip m ft 2 ILL t8 LL t8_m = LL E t8_m = 0.961 kip m ft LL t32_m ILL t32 = LL E t32_m = 3.845 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 3.4.1-1 and 3.4.1-2 of the AASHTO LRFD. BMCOL51 Model page 4

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 = 19.50 kip ft M_DL neg_s = 24.36 kip ft = 23.92 kip ft M_LL neg_s = 22.01 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 = 19.50 kip ft M_DL neg_m = 24.36 kip ft = 26.44 kip ft M_LL neg_m = 24.34 kip ft page 5

The maximum moment from each analysis is then combined using Tables 3.4.1-1 and 3.4.1-2 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 = 43.014 kip ft M_Serv pos_m = rll s M_LL pos_m + DC s M_DL pos_m M_Serv pos_m = 45.491 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 = 45.491 kip ft = rll s M_LL neg_s + DC s M_DL neg_s M_Serv neg_s = 45.996 kip ft = rll s M_LL neg_m + DC s M_DL neg_m M_Serv neg_m = 48.287 kip ft ( ) = max M_Serv neg_s, M_Serv neg_m M_Serv neg = 48.287 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 = 65.524 kip ft = rll st M_LL pos_m + DC st M_DL pos_m M_Ult pos_m = 69.859 kip ft ( ) = max M_Ult pos_s, M_Ult pos_m M_Ult pos = 69.859 kip ft = rll st M_LL neg_s + DC st M_DL neg_s M_Ult neg_s = 68.313 kip ft = rll st M_LL neg_m + DC st M_DL neg_m M_Ult neg_m = 72.321 kip ft ( ) = max M_Ult neg_s, M_Ult neg_m M_Ult neg = 72.321 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 = 45.491 kip ft = M_Serv neg M s_neg = 48.287 kip ft = M_Ult pos M u_pos = 69.859 kip ft = M_Ult neg M u_neg = 72.321 kip ft page 6

Moment Capacity Design - Negative (Top) - Typ. Bars A LRFD 5.7.3.2 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 = 1.580 in 2 Area of steel in tension. 1 d neg = h cover neg 2 d bar_neg d neg = 11.500 in ( ) 0.05 β 1_neg = min 0.85, max 0.65, 0.85 f 1ksi c 4ksi β 1_neg = 0.850 LRFD 5.7.2.2 Resistance Factor: φ M = 0.9 LRFD 5.5.4.2.1 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 = 2.734 in LRFD Eq. 5.7.3.1.2-4 Depth of Equivalent Stress Block: a neg = c neg β 1_neg a neg = 2.324 in LRFD 5.7.2.2 Thus, Nominal Flexural Resistance: a neg 1ft M n_neg = A s_neg f y d neg M 2 12in n_neg = 81.672 kip ft LRFD Eq. 5.7.3.2.2-1 Factored Flexural Resistance: M r_neg = φ M M n_neg M r_neg = 73.505 kip ft M u_neg = 72.321 kip ft ( ) OK UltimateMom = if M r_neg M u_neg,, NG UltimateMom = "OK!" page 7

Check Serviceability- Negative (Top) - Typ. Bars A LRFD 5.7.3.4 To find s max_neg : 1 d c_neg = cover neg + 2 d bar_neg d c_neg = 2.500 in Es = 29000 ksi "cover" is measured to edge of the top reinforcement. 1 Ec = 1820 f c ksi ksi Ec = 3640.000 ksi LRFD Eq. C5.4.2.4-1 Modular Ratio: n Es = n = 7.967 Ec A s_neg Tension Reinforcement Ratio: ρ neg = ρ bd neg = 0.0114 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 = 0.346 k neg j neg = 1 j 3 neg = 0.885 Service Load Bending Stress: f s_neg M s_neg 12in = f A s_neg j neg d neg 1ft s_neg = 36.041 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 = 1.311 c_neg ( ) kip 700 in γ e_top s max_neg = 2d β s_neg f c_neg s max_neg = 6.115 in LRFD Eq. 5.7.3.4-1 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 40.595 kip-ft of M r_neg with a M u_neg of 19.576 kip-ft. In addition, the max. bar spacing is in excess of 12 inches. page 8

Moment Capacity Design - Positive (Bottom) - Typ. Bars B LRFD 5.7.3.2 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 = 1.580 in 2 Area of steel in tension. 1 d pos = h cover pos 2 d bar_pos d pos = 12.250 in ( ) 0.05 β 1pos = min 0.85, max 0.65, 0.85 f 1ksi c 4ksi β 1pos = 0.850 LRFD 5.7.2.2 Depth of Cross Section in Compression under Ultimate Load: LRFD Eq. 5.7.3.1.2-4 c pos A s_pos f y = c 0.85 f c β 1pos b pos = 2.734 in Depth of Equivalent Stress Block: a pos = c pos β 1pos a pos = 2.324 in Thus, Nominal Flexural Resistance: LRFD Eq. 5.7.3.2.2-1 M n_pos a pos 1ft = A s_pos f y d pos M 2 12in n_pos = 87.597 kip ft Factored Flexural Resistance: M r_pos = φ M M n_pos M r_pos = 78.837 kip ft M u_pos = 69.859 kip ft ( ) OK UltimateMom pos = if M r_pos M u_pos,, NG UltimateMom pos = "OK!" page 9

Check Serviceability- Positive (Bottom) - Typ. Bars B To find s max_pos : "Control of cracking by Distribution of Reinforcement", LRFD 5.7.3.4 1 d c_pos = cover pos + 2 d bar_pos d c_pos = 1.750 in "cover" is measured to edge of the bottom reinforcement. Tension Reinforcement Ratio: ρ pos = A s_pos bd pos ρ pos = 0.0107 k pos = ( 2 ρ pos n) + ( ρ pos n) 2 ( ρ pos n) k pos = 0.337 k pos j pos = 1 j 3 pos = 0.888 Service Load Bending Stress: f s_pos M s_pos 12in = f A s_pos j pos d pos 1ft s_pos = 31.773 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 = 1.204 c_pos ( ) kip 700 in γ e_bot s max_pos = 2d β s_pos f c_pos s max_pos = 14.797 in s_pos LRFD Eq. 5.7.3.4-1 s Actual_pos = 6in ( ) OK ServiceabilityCheck pos = if s max_pos s Actual_pos,, NG ServiceabilityCheck pos = "OK!" page 10

Shrinkage and Temperature Reinforcement- Negative (Top) - Typ. Bars T LRFD 5.10.8 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 = 0.200 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 = 0.110 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 5.14.4.1 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 = 0.400 in 2 PercentAs d_pos = min 50, 100 L 1 ft PercentAs d_pos = 20.000 LRFD Eq. 5.14.4.1-1 PercentAs d_pos As req_d_pos = A s_pos As 100 req_d_pos = 0.316 in 2 ( ) OK Distribution d_pos = if A s_d_pos As req_d_pos,, NG Distribution d_pos = "OK!" Shear Reinforcement From LRFD 5.14.4, "Slabs and slab bridges designed for moment in conformance with Atricle 4.6.2.3 may be considered satisfactory for shear." page 11

Design for the Edge Beam The edge for the slab is designed based on LRFD 9.7.1.4 and 4.6.2.1.4. 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 = 11.069 ft ( ) 0.5 E m W edge = min C + 12 in + 0.25 E m,, 72 in W edge = 5.184 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 = 0.020 kip ft 2 DL slab = 0.175 kip ft 2 page 12

Live Load LRFD 3.6.1.3.3 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 = 0.640 k/ft (3.6.1.2.4) LL t4 and LL t16 = design truck load, 4 k and 16 k, respectively (3.6.1.2.2). The truck load is half the load because the edge width only accommodates half the truck. I = impact factor LL lane = 0.640 ft kip ft 2 LL t4 = 4 kip LL t16 = 16 kip I = 1.330 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 = 0.053 ft kip edge ft 2 ILL t4 LL t4_edge = LL W t4_edge = 1.026 kip edge ft LL t16_edge ILL t16 = LL W t16_edge = 4.105 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 3.4.1-1 and 3.4.1-2 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 = 19.50 kip ft M_DL edge_neg = 24.36 kip ft = 28.46 kip ft M_LL edge_neg = 26.27 kip ft page 13

Moment Capacity Design - Negative (Top) - Typ. Bars A LRFD 5.7.3.2 b = 12.000 in Design stip width per TxDOT policy h = 14.000 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 = 1.580 in 2 Area of steel in tension. 1 d edge_neg = h cover e_neg 2 d bar_e_neg d edge_neg = 11.500 in ( ) 0.05 β 1_e_neg = min 0.85, max 0.65, 0.85 f 1ksi c 4ksi β 1_e_neg = 0.850 LRFD 5.7.2.2 Resistance Factor: φ M = 0.900 LRFD 5.5.4.2.1 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 = 2.734 in LRFD Eq. 5.7.3.1.2-4 Depth of Equivalent Stress Block: a e_neg = c e_neg β 1_e_neg a e_neg = 2.324 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 = 81.672 kip ft LRFD Eq. 5.7.3.2.2-1 Factored Flexural Resistance: M r_e_neg = φ M M n_e_neg M r_e_neg = 73.505 kip ft M u_edge_neg = 75.642 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

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 = 2.500 in Tension Reinforcement Ratio: "Control of cracking by Distribution of Reinforcement", LRFD 5.7.3.4 "cover" is measured to edge of the bottom reinforcement. ρ e_neg = A s_e_neg bd edge_neg ρ e_neg = 0.0114 k e_neg = ( 2 ρ e_neg n) + ( ρ e_neg n) 2 ( ρ e_neg n) k e_neg = 0.346 k e_neg j e_neg = 1 j 3 e_neg = 0.885 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 = 37.457 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 = 1.311 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 = 5.695 in LRFD Eq. 5.7.3.4-1 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

Moment Capacity Design - Positive (Bottom) - Typ. Bars B LRFD 5.7.3.2 b = 12.000 in Design stip width per TxDOT policy h = 14.000 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 = 1.580 in 2 Area of steel in tension. 1 d edge_pos = h cover e_pos 2 d bar_e_pos d edge_pos = 12.250 in ( ) 0.05 β 1_e_pos = min 0.85, max 0.65, 0.85 f 1ksi c 4ksi β 1_e_pos = 0.850 LRFD 5.7.2.2 Resistance Factor: φ M = 0.900 LRFD 5.5.4.2.1 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 = 2.734 in LRFD Eq. 5.7.3.1.2-4 Depth of Equivalent Stress Block: a e_pos = c e_pos β 1_e_pos a e_pos = 2.324 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 = 87.597 kip ft LRFD Eq. 5.7.3.2.2-1 Factored Flexural Resistance: M r_e_pos = φ M M n_e_pos M r_e_pos = 78.837 kip ft M u_edge_pos = 73.334 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

Check Serviceability- Positive (Bottom) - Typ. Bars B "Control of cracking by Distribution of Reinforcement", LRFD 5.7.3.4 To find s max_e_pos : 1 d c_e_pos = cover e_pos + 2 d bar_e_pos d c_e_pos = 1.750 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 = 0.0107 k e_pos = ( 2 ρ e_pos n) + ( ρ e_pos n) 2 ( ρ e_pos n) k e_pos = 0.337 k e_pos j e_pos = 1 j 3 e_pos = 0.888 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 = 33.160 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 = 1.204 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 = 14.032 inlrfd Eq. 5.7.3.4-1 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

Shrinkage and Temperature Reinforcement- Negative (Top) - Typ. Bars T LRFD 5.10.8 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 = 0.200 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 = 0.110 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 5.14.4.1 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 = 0.400 in 2 PercentAs de_pos = min 50, 100 L 1 ft LRFD Eq. 5.14.4.1-1 PercentAs de_pos = 20.000 PercentAs de_pos As req_de_pos = A s_e_pos As 100 req_de_pos = 0.316 in 2 ( ) OK Distribution de_pos = if A s_de_pos As req_de_pos,, NG Distribution de_pos = "OK!" Shear Reinforcement From LRFD 5.14.4, "Slabs and slab bridges designed for moment in conformance with Atricle 4.6.2.3 may be considered satisfactory for shear." page 19

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

COUNTY HWY 0000-00-000 BRG 12/02/2006 SLAB SPAN DESIGN EXAMPLE 1 DEAD LOAD 1 4 1 0 150 0.5 56-56 150 2 0 1 0.0 50 1 0.0 100 1 0.0 150 1 0.0 0 150 4.000E+06-0.195 CEASE 01/30/2007 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 23

PSF HIGHWAY PD- CONTROL- CODED NO COUNTY NO IPE SECTION-JOB BY DATE COUNTY HWY 0000-00-000 BRG 12/02/2006 SLAB SPAN DESIGN EXAMPLE PROB 1 DEAD LOAD TABLE 1 - PROGRAM-CONTROL DATA ENVELOPES TABLE NUMBER OF MAXIMUMS 2 3 4 5 6 HOLD FROM PRECEDING PROBLEM (1=HOLD) 0 0 0 0 0 0 NUM CARDS INPUT THIS PROBLEM 1 4 1 0 0 DEFL MOM SHR RCT OPTION (IF=1) TO PLOT ENVELOPES OF MAXIMUMS 0 0 0 0 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 0 1 0.000E+00 NONE 50 1 0.000E+00 NONE 100 1 0.000E+00 NONE 150 1 0.000E+00 NONE TABLE 4 - STIFFNESS AND FIXED-LOAD DATA FROM TO CONTD F QF S T R P 0 150 0 4.000E+06-1.950E-01 0.000E+00 0.000E+00 0.000E+00 0.000E+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

PSF HIGHWAY PD- CONTROL- CODED NO COUNTY NO IPE SECTION-JOB BY DATE COUNTY HWY 0000-00-000 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 -1-5.000E-01 1.904E-05 0.000E+00 0.000E+00-3.808E-05 0.000E+00 0 0.000E+00 0.000E+00 0.000E+00 3.900E+00-3.808E-05 3.803E+00 1 5.000E-01-1.904E-05 1.901E+00 0.000E+00-3.785E-05 3.608E+00 2 1.000E+00-3.796E-05 3.705E+00 0.000E+00-3.738E-05 3.413E+00 3 1.500E+00-5.666E-05 5.412E+00 0.000E+00-3.671E-05 3.218E+00 4 2.000E+00-7.501E-05 7.021E+00 0.000E+00-3.583E-05 3.023E+00 5 2.500E+00-9.292E-05 8.532E+00 0.000E+00-3.476E-05 2.828E+00 6 3.000E+00-1.103E-04 9.946E+00 0.000E+00-3.352E-05 2.633E+00 7 3.500E+00-1.271E-04 1.126E+01 0.000E+00-3.211E-05 2.438E+00 8 4.000E+00-1.431E-04 1.248E+01 0.000E+00-3.055E-05 2.243E+00 9 4.500E+00-1.584E-04 1.360E+01 0.000E+00-2.885E-05 2.048E+00 10 5.000E+00-1.728E-04 1.463E+01 0.000E+00-2.702E-05 1.853E+00 11 5.500E+00-1.863E-04 1.555E+01 0.000E+00-2.508E-05 1.658E+00 12 6.000E+00-1.989E-04 1.638E+01 0.000E+00-2.303E-05 1.463E+00 13 6.500E+00-2.104E-04 1.711E+01 0.000E+00-2.089E-05 1.268E+00 14 7.000E+00-2.208E-04 1.775E+01 0.000E+00-1.867E-05 1.073E+00 15 7.500E+00-2.302E-04 1.828E+01 0.000E+00-1.639E-05 8.780E-01 16 8.000E+00-2.384E-04 1.872E+01 0.000E+00-1.405E-05 6.830E-01 17 8.500E+00-2.454E-04 1.907E+01 0.000E+00-1.166E-05 4.880E-01 18 9.000E+00-2.512E-04 1.931E+01 0.000E+00-9.248E-06 2.930E-01 19 9.500E+00-2.558E-04 1.946E+01 0.000E+00-6.816E-06 9.797E-02 20 1.000E+01-2.592E-04 1.950E+01 0.000E+00-4.378E-06-9.703E-02 21 1.050E+01-2.614E-04 1.946E+01 0.000E+00 01/30/2007 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 25

TABLE 7 - FIXED-LOAD RESULTS STA I DIST DEFL SLOPE MOM SHEAR SUP REACT -1.946E-06-2.920E-01 22 1.100E+01-2.624E-04 1.931E+01 0.000E+00 4.675E-07-4.870E-01 23 1.150E+01-2.622E-04 1.907E+01 0.000E+00 2.851E-06-6.820E-01 24 1.200E+01-2.607E-04 1.873E+01 0.000E+00 5.192E-06-8.770E-01 25 1.250E+01-2.581E-04 1.829E+01 0.000E+00 7.477E-06-1.072E+00 26 1.300E+01-2.544E-04 1.775E+01 0.000E+00 9.696E-06-1.267E+00 27 1.350E+01-2.496E-04 1.712E+01 0.000E+00 1.184E-05-1.462E+00 28 1.400E+01-2.436E-04 1.639E+01 0.000E+00 1.388E-05-1.657E+00 29 1.450E+01-2.367E-04 1.556E+01 0.000E+00 1.583E-05-1.852E+00 30 1.500E+01-2.288E-04 1.463E+01 0.000E+00 1.766E-05-2.047E+00 31 1.550E+01-2.200E-04 1.361E+01 0.000E+00 1.936E-05-2.242E+00 32 1.600E+01-2.103E-04 1.249E+01 0.000E+00 2.092E-05-2.437E+00 33 1.650E+01-1.998E-04 1.127E+01 0.000E+00 2.233E-05-2.632E+00 34 1.700E+01-1.887E-04 9.953E+00 0.000E+00 2.357E-05-2.827E+00 35 1.750E+01-1.769E-04 8.539E+00 0.000E+00 2.464E-05-3.022E+00 36 1.800E+01-1.645E-04 7.028E+00 0.000E+00 2.552E-05-3.217E+00 37 1.850E+01-1.518E-04 5.420E+00 0.000E+00 2.620E-05-3.412E+00 38 1.900E+01-1.387E-04 3.714E+00 0.000E+00 2.666E-05-3.607E+00 39 1.950E+01-1.254E-04 1.910E+00 0.000E+00 2.690E-05-3.802E+00 40 2.000E+01-1.119E-04 9.359E-03 0.000E+00 2.690E-05-3.997E+00 41 2.050E+01-9.846E-05-1.989E+00 0.000E+00 2.665E-05-4.192E+00 42 2.100E+01-8.513E-05-4.085E+00 0.000E+00 2.614E-05-4.387E+00 43 2.150E+01-7.206E-05-6.279E+00 0.000E+00 2.536E-05-4.582E+00 44 2.200E+01-5.938E-05-8.570E+00 0.000E+00 2.429E-05-4.777E+00 45 2.250E+01-4.724E-05-1.096E+01 0.000E+00 2.292E-05-4.972E+00 46 2.300E+01-3.578E-05-1.344E+01 0.000E+00 2.123E-05-5.167E+00 47 2.350E+01-2.517E-05-1.603E+01 0.000E+00 01/30/2007 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 26

TABLE 7 - FIXED-LOAD RESULTS STA I DIST DEFL SLOPE MOM SHEAR SUP REACT 1.923E-05-5.362E+00 48 2.400E+01-1.555E-05-1.871E+01 0.000E+00 1.689E-05-5.557E+00 49 2.450E+01-7.103E-06-2.149E+01 0.000E+00 1.421E-05-5.752E+00 50 2.500E+01 0.000E+00-2.436E+01 1.072E+01 1.116E-05 4.778E+00 51 2.550E+01 5.581E-06-2.197E+01 0.000E+00 8.415E-06 4.583E+00 52 2.600E+01 9.788E-06-1.968E+01 0.000E+00 5.954E-06 4.388E+00 53 2.650E+01 1.277E-05-1.749E+01 0.000E+00 3.768E-06 4.192E+00 54 2.700E+01 1.465E-05-1.539E+01 0.000E+00 1.844E-06 3.997E+00 55 2.750E+01 1.557E-05-1.339E+01 0.000E+00 1.695E-07 3.802E+00 56 2.800E+01 1.566E-05-1.149E+01 0.000E+00-1.267E-06 3.608E+00 57 2.850E+01 1.502E-05-9.690E+00 0.000E+00-2.478E-06 3.412E+00 58 2.900E+01 1.378E-05-7.983E+00 0.000E+00-3.476E-06 3.217E+00 59 2.950E+01 1.204E-05-6.375E+00 0.000E+00-4.273E-06 3.023E+00 60 3.000E+01 9.908E-06-4.863E+00 0.000E+00-4.881E-06 2.827E+00 61 3.050E+01 7.468E-06-3.450E+00 0.000E+00-5.312E-06 2.633E+00 62 3.100E+01 4.812E-06-2.133E+00 0.000E+00-5.579E-06 2.437E+00 63 3.150E+01 2.022E-06-9.146E-01 0.000E+00-5.693E-06 2.242E+00 64 3.200E+01-8.241E-07 2.067E-01 0.000E+00-5.667E-06 2.047E+00 65 3.250E+01-3.658E-06 1.230E+00 0.000E+00-5.514E-06 1.852E+00 66 3.300E+01-6.415E-06 2.157E+00 0.000E+00-5.244E-06 1.657E+00 67 3.350E+01-9.036E-06 2.985E+00 0.000E+00-4.871E-06 1.463E+00 68 3.400E+01-1.147E-05 3.717E+00 0.000E+00-4.406E-06 1.268E+00 69 3.450E+01-1.367E-05 4.350E+00 0.000E+00-3.862E-06 1.072E+00 70 3.500E+01-1.561E-05 4.887E+00 0.000E+00-3.252E-06 8.775E-01 71 3.550E+01-1.723E-05 5.325E+00 0.000E+00-2.586E-06 6.825E-01 72 3.600E+01-1.852E-05 5.667E+00 0.000E+00-1.877E-06 4.875E-01 73 3.650E+01-1.946E-05 5.910E+00 0.000E+00 01/30/2007 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 27

TABLE 7 - FIXED-LOAD RESULTS STA I DIST DEFL SLOPE MOM SHEAR SUP REACT -1.139E-06 2.925E-01 74 3.700E+01-2.003E-05 6.057E+00 0.000E+00-3.816E-07 9.750E-02 75 3.750E+01-2.022E-05 6.105E+00 0.000E+00 3.816E-07-9.750E-02 76 3.800E+01-2.003E-05 6.057E+00 0.000E+00 1.139E-06-2.925E-01 77 3.850E+01-1.946E-05 5.910E+00 0.000E+00 1.877E-06-4.875E-01 78 3.900E+01-1.852E-05 5.667E+00 0.000E+00 2.586E-06-6.825E-01 79 3.950E+01-1.723E-05 5.325E+00 0.000E+00 3.252E-06-8.775E-01 80 4.000E+01-1.561E-05 4.887E+00 0.000E+00 3.862E-06-1.072E+00 81 4.050E+01-1.367E-05 4.350E+00 0.000E+00 4.406E-06-1.268E+00 82 4.100E+01-1.147E-05 3.717E+00 0.000E+00 4.871E-06-1.463E+00 83 4.150E+01-9.036E-06 2.985E+00 0.000E+00 5.244E-06-1.657E+00 84 4.200E+01-6.415E-06 2.157E+00 0.000E+00 5.514E-06-1.852E+00 85 4.250E+01-3.658E-06 1.230E+00 0.000E+00 5.667E-06-2.047E+00 86 4.300E+01-8.241E-07 2.067E-01 0.000E+00 5.693E-06-2.242E+00 87 4.350E+01 2.022E-06-9.146E-01 0.000E+00 5.579E-06-2.437E+00 88 4.400E+01 4.812E-06-2.133E+00 0.000E+00 5.312E-06-2.633E+00 89 4.450E+01 7.468E-06-3.450E+00 0.000E+00 4.881E-06-2.827E+00 90 4.500E+01 9.908E-06-4.863E+00 0.000E+00 4.273E-06-3.023E+00 91 4.550E+01 1.204E-05-6.375E+00 0.000E+00 3.476E-06-3.217E+00 92 4.600E+01 1.378E-05-7.983E+00 0.000E+00 2.478E-06-3.412E+00 93 4.650E+01 1.502E-05-9.690E+00 0.000E+00 1.267E-06-3.608E+00 94 4.700E+01 1.566E-05-1.149E+01 0.000E+00-1.695E-07-3.802E+00 95 4.750E+01 1.557E-05-1.339E+01 0.000E+00-1.844E-06-3.997E+00 96 4.800E+01 1.465E-05-1.539E+01 0.000E+00-3.768E-06-4.192E+00 97 4.850E+01 1.277E-05-1.749E+01 0.000E+00-5.954E-06-4.388E+00 98 4.900E+01 9.788E-06-1.968E+01 0.000E+00-8.415E-06-4.583E+00 99 4.950E+01 5.581E-06-2.197E+01 0.000E+00 01/30/2007 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 28

TABLE 7 - FIXED-LOAD RESULTS STA I DIST DEFL SLOPE MOM SHEAR SUP REACT -1.116E-05-4.778E+00 100 5.000E+01 0.000E+00-2.436E+01 1.072E+01-1.421E-05 5.752E+00 101 5.050E+01-7.103E-06-2.149E+01 0.000E+00-1.689E-05 5.557E+00 102 5.100E+01-1.555E-05-1.871E+01 0.000E+00-1.923E-05 5.362E+00 103 5.150E+01-2.517E-05-1.603E+01 0.000E+00-2.123E-05 5.167E+00 104 5.200E+01-3.578E-05-1.344E+01 0.000E+00-2.292E-05 4.972E+00 105 5.250E+01-4.724E-05-1.096E+01 0.000E+00-2.429E-05 4.777E+00 106 5.300E+01-5.938E-05-8.570E+00 0.000E+00-2.536E-05 4.582E+00 107 5.350E+01-7.206E-05-6.279E+00 0.000E+00-2.614E-05 4.387E+00 108 5.400E+01-8.513E-05-4.085E+00 0.000E+00-2.665E-05 4.192E+00 109 5.450E+01-9.846E-05-1.989E+00 0.000E+00-2.690E-05 3.997E+00 110 5.500E+01-1.119E-04 9.359E-03 0.000E+00-2.690E-05 3.802E+00 111 5.550E+01-1.254E-04 1.910E+00 0.000E+00-2.666E-05 3.607E+00 112 5.600E+01-1.387E-04 3.714E+00 0.000E+00-2.620E-05 3.412E+00 113 5.650E+01-1.518E-04 5.420E+00 0.000E+00-2.552E-05 3.217E+00 114 5.700E+01-1.645E-04 7.028E+00 0.000E+00-2.464E-05 3.022E+00 115 5.750E+01-1.769E-04 8.539E+00 0.000E+00-2.357E-05 2.827E+00 116 5.800E+01-1.887E-04 9.953E+00 0.000E+00-2.233E-05 2.632E+00 117 5.850E+01-1.998E-04 1.127E+01 0.000E+00-2.092E-05 2.437E+00 118 5.900E+01-2.103E-04 1.249E+01 0.000E+00-1.936E-05 2.242E+00 119 5.950E+01-2.200E-04 1.361E+01 0.000E+00-1.766E-05 2.047E+00 120 6.000E+01-2.288E-04 1.463E+01 0.000E+00-1.583E-05 1.852E+00 121 6.050E+01-2.367E-04 1.556E+01 0.000E+00-1.388E-05 1.657E+00 122 6.100E+01-2.436E-04 1.639E+01 0.000E+00-1.184E-05 1.462E+00 123 6.150E+01-2.496E-04 1.712E+01 0.000E+00-9.696E-06 1.267E+00 124 6.200E+01-2.544E-04 1.775E+01 0.000E+00-7.477E-06 1.072E+00 125 6.250E+01-2.581E-04 1.829E+01 0.000E+00 01/30/2007 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 29

TABLE 7 - FIXED-LOAD RESULTS STA I DIST DEFL SLOPE MOM SHEAR SUP REACT -5.192E-06 8.770E-01 126 6.300E+01-2.607E-04 1.873E+01 0.000E+00-2.851E-06 6.820E-01 127 6.350E+01-2.622E-04 1.907E+01 0.000E+00-4.675E-07 4.870E-01 128 6.400E+01-2.624E-04 1.931E+01 0.000E+00 1.946E-06 2.920E-01 129 6.450E+01-2.614E-04 1.946E+01 0.000E+00 4.378E-06 9.703E-02 130 6.500E+01-2.592E-04 1.950E+01 0.000E+00 6.816E-06-9.797E-02 131 6.550E+01-2.558E-04 1.946E+01 0.000E+00 9.248E-06-2.930E-01 132 6.600E+01-2.512E-04 1.931E+01 0.000E+00 1.166E-05-4.880E-01 133 6.650E+01-2.454E-04 1.907E+01 0.000E+00 1.405E-05-6.830E-01 134 6.700E+01-2.384E-04 1.872E+01 0.000E+00 1.639E-05-8.780E-01 135 6.750E+01-2.302E-04 1.828E+01 0.000E+00 1.867E-05-1.073E+00 136 6.800E+01-2.208E-04 1.775E+01 0.000E+00 2.089E-05-1.268E+00 137 6.850E+01-2.104E-04 1.711E+01 0.000E+00 2.303E-05-1.463E+00 138 6.900E+01-1.989E-04 1.638E+01 0.000E+00 2.508E-05-1.658E+00 139 6.950E+01-1.863E-04 1.555E+01 0.000E+00 2.702E-05-1.853E+00 140 7.000E+01-1.728E-04 1.463E+01 0.000E+00 2.885E-05-2.048E+00 141 7.050E+01-1.584E-04 1.360E+01 0.000E+00 3.055E-05-2.243E+00 142 7.100E+01-1.431E-04 1.248E+01 0.000E+00 3.211E-05-2.438E+00 143 7.150E+01-1.271E-04 1.126E+01 0.000E+00 3.352E-05-2.633E+00 144 7.200E+01-1.103E-04 9.946E+00 0.000E+00 3.476E-05-2.828E+00 145 7.250E+01-9.292E-05 8.532E+00 0.000E+00 3.583E-05-3.023E+00 146 7.300E+01-7.501E-05 7.021E+00 0.000E+00 3.671E-05-3.218E+00 147 7.350E+01-5.666E-05 5.412E+00 0.000E+00 3.738E-05-3.413E+00 148 7.400E+01-3.796E-05 3.705E+00 0.000E+00 3.785E-05-3.608E+00 149 7.450E+01-1.904E-05 1.901E+00 0.000E+00 3.808E-05-3.803E+00 150 7.500E+01 0.000E+00 0.000E+00 3.900E+00 3.808E-05 0.000E+00 151 7.550E+01 1.904E-05 0.000E+00 0.000E+00 01/30/2007 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 30

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 -1 1.904E-05 150 1.904E-05 999 0.000E+00 999 0.000E+00 999 0 0.000E+00 999 0.000E+00 999 0.000E+00 999 0.000E+00 999 1-1.904E-05 999-1.904E-05 150 1.901E+00 999 1.901E+00 999 2-3.796E-05 999-3.796E-05 150 3.705E+00 999 3.705E+00 999 3-5.666E-05 150-5.666E-05 999 5.412E+00 999 5.412E+00 999 4-7.501E-05 150-7.501E-05 999 7.021E+00 999 7.021E+00 999 5-9.292E-05 999-9.292E-05 150 8.532E+00 999 8.532E+00 999 6-1.103E-04 999-1.103E-04 150 9.946E+00 999 9.946E+00 999 7-1.271E-04 999-1.271E-04 150 1.126E+01 999 1.126E+01 999 8-1.431E-04 150-1.431E-04 999 1.248E+01 999 1.248E+01 999 9-1.584E-04 999-1.584E-04 150 1.360E+01 999 1.360E+01 999 10-1.728E-04 150-1.728E-04 999 1.463E+01 999 1.463E+01 999 11-1.863E-04 999-1.863E-04 150 1.555E+01 999 1.555E+01 999 12-1.989E-04 150-1.989E-04 999 1.638E+01 999 1.638E+01 999 13-2.104E-04 150-2.104E-04 999 1.711E+01 999 1.711E+01 999 14-2.208E-04 999-2.208E-04 150 1.775E+01 999 1.775E+01 999 15-2.302E-04 999-2.302E-04 150 1.828E+01 999 1.828E+01 999 16-2.384E-04 999-2.384E-04 150 1.872E+01 999 1.872E+01 999 17-2.454E-04 150-2.454E-04 999 1.907E+01 999 1.907E+01 999 18-2.512E-04 150-2.512E-04 999 1.931E+01 999 1.931E+01 999 19-2.558E-04 999-2.558E-04 150 1.946E+01 999 1.946E+01 999 20-2.592E-04 150-2.592E-04 999 1.950E+01 999 1.950E+01 999 21-2.614E-04 150-2.614E-04 999 1.946E+01 999 1.946E+01 999 22-2.624E-04 999-2.624E-04 150 1.931E+01 999 1.931E+01 999 23-2.622E-04 999-2.622E-04 150 1.907E+01 999 1.907E+01 999 24-2.607E-04 150-2.607E-04 999 1.873E+01 999 1.873E+01 999 25-2.581E-04 999-2.581E-04 150 1.829E+01 999 1.829E+01 999 26-2.544E-04 999-2.544E-04 150 1.775E+01 999 1.775E+01 999 27-2.496E-04 999-2.496E-04 150 1.712E+01 999 1.712E+01 999 28-2.436E-04 999-2.436E-04 150 1.639E+01 999 1.639E+01 999 29-2.367E-04 999-2.367E-04 150 1.556E+01 999 1.556E+01 999 30-2.288E-04 999-2.288E-04 150 1.463E+01 999 1.463E+01 999 31-2.200E-04 150-2.200E-04 999 1.361E+01 999 1.361E+01 999 32-2.103E-04 150-2.103E-04 999 1.249E+01 999 1.249E+01 999 33-1.998E-04 150-1.998E-04 999 1.127E+01 999 1.127E+01 999 34-1.887E-04 999-1.887E-04 150 9.953E+00 999 9.953E+00 999 35-1.769E-04 999-1.769E-04 150 8.539E+00 999 8.539E+00 999 36-1.645E-04 999-1.645E-04 150 7.028E+00 999 7.028E+00 999 37-1.518E-04 150-1.518E-04 999 5.420E+00 999 5.420E+00 999 38-1.387E-04 150-1.387E-04 999 3.714E+00 999 3.714E+00 999 39-1.254E-04 150-1.254E-04 999 1.910E+00 999 1.910E+00 999 40-1.119E-04 999-1.119E-04 150 9.359E-03 999 9.359E-03 999 41-9.846E-05 999-9.846E-05 150-1.989E+00 999-1.989E+00 999 42-8.513E-05 999-8.513E-05 150-4.085E+00 999-4.085E+00 999 43-7.206E-05 999-7.206E-05 150-6.279E+00 999-6.279E+00 999 44-5.938E-05 150-5.938E-05 999-8.570E+00 999-8.570E+00 999 45-4.724E-05 150-4.724E-05 999-1.096E+01 999-1.096E+01 999 46-3.578E-05 999-3.578E-05 150-1.344E+01 999-1.344E+01 999 01/30/2007 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 31

TABLE 8A- ENVELOPES OF MAXIMUMS * = HELD FROM PRIOR PROBLEM STA MAX +DEFL LOC MAX -DEFL LOC MAX +MOM LOC MAX -MOM LOC 47-2.517E-05 999-2.517E-05 150-1.603E+01 999-1.603E+01 999 48-1.555E-05 999-1.555E-05 150-1.871E+01 999-1.871E+01 999 49-7.103E-06 999-7.103E-06 150-2.149E+01 999-2.149E+01 999 50 0.000E+00 999 0.000E+00 999-2.436E+01 999-2.436E+01 999 51 5.581E-06 999 5.581E-06 150-2.197E+01 999-2.197E+01 999 52 9.788E-06 999 9.788E-06 150-1.968E+01 999-1.968E+01 999 53 1.277E-05 150 1.277E-05 999-1.749E+01 999-1.749E+01 999 54 1.465E-05 150 1.465E-05 999-1.539E+01 999-1.539E+01 999 55 1.557E-05 150 1.557E-05 999-1.339E+01 999-1.339E+01 999 56 1.566E-05 150 1.566E-05 999-1.149E+01 999-1.149E+01 999 57 1.502E-05 150 1.502E-05 999-9.690E+00 999-9.690E+00 999 58 1.378E-05 150 1.378E-05 999-7.983E+00 999-7.983E+00 999 59 1.204E-05 999 1.204E-05 150-6.375E+00 999-6.375E+00 999 60 9.908E-06 999 9.908E-06 150-4.863E+00 999-4.863E+00 999 61 7.468E-06 150 7.468E-06 999-3.450E+00 999-3.450E+00 999 62 4.812E-06 150 4.812E-06 999-2.133E+00 999-2.133E+00 999 63 2.022E-06 150 2.022E-06 999-9.146E-01 999-9.146E-01 999 64-8.241E-07 150-8.241E-07 999 2.067E-01 999 2.067E-01 999 65-3.658E-06 150-3.658E-06 999 1.230E+00 999 1.230E+00 999 66-6.415E-06 999-6.415E-06 150 2.157E+00 999 2.157E+00 999 67-9.036E-06 150-9.036E-06 999 2.985E+00 999 2.985E+00 999 68-1.147E-05 999-1.147E-05 150 3.717E+00 999 3.717E+00 999 69-1.367E-05 150-1.367E-05 999 4.350E+00 999 4.350E+00 999 70-1.561E-05 150-1.561E-05 999 4.887E+00 999 4.887E+00 999 71-1.723E-05 999-1.723E-05 150 5.325E+00 999 5.325E+00 999 72-1.852E-05 999-1.852E-05 150 5.667E+00 999 5.667E+00 999 73-1.946E-05 999-1.946E-05 150 5.910E+00 999 5.910E+00 999 74-2.003E-05 999-2.003E-05 150 6.057E+00 999 6.057E+00 999 75-2.022E-05 999-2.022E-05 150 6.105E+00 999 6.105E+00 999 76-2.003E-05 999-2.003E-05 150 6.057E+00 999 6.057E+00 999 77-1.946E-05 999-1.946E-05 150 5.910E+00 999 5.910E+00 999 78-1.852E-05 999-1.852E-05 150 5.667E+00 999 5.667E+00 999 79-1.723E-05 999-1.723E-05 150 5.325E+00 999 5.325E+00 999 80-1.561E-05 150-1.561E-05 999 4.887E+00 999 4.887E+00 999 81-1.367E-05 150-1.367E-05 999 4.350E+00 999 4.350E+00 999 82-1.147E-05 999-1.147E-05 150 3.717E+00 999 3.717E+00 999 83-9.036E-06 150-9.036E-06 999 2.985E+00 999 2.985E+00 999 84-6.415E-06 999-6.415E-06 150 2.157E+00 999 2.157E+00 999 85-3.658E-06 150-3.658E-06 999 1.230E+00 999 1.230E+00 999 86-8.241E-07 150-8.241E-07 999 2.067E-01 999 2.067E-01 999 87 2.022E-06 150 2.022E-06 999-9.146E-01 999-9.146E-01 999 88 4.812E-06 150 4.812E-06 999-2.133E+00 999-2.133E+00 999 89 7.468E-06 150 7.468E-06 999-3.450E+00 999-3.450E+00 999 90 9.908E-06 999 9.908E-06 150-4.863E+00 999-4.863E+00 999 91 1.204E-05 999 1.204E-05 150-6.375E+00 999-6.375E+00 999 92 1.378E-05 150 1.378E-05 999-7.983E+00 999-7.983E+00 999 93 1.502E-05 150 1.502E-05 999-9.690E+00 999-9.690E+00 999 94 1.566E-05 150 1.566E-05 999-1.149E+01 999-1.149E+01 999 95 1.557E-05 150 1.557E-05 999-1.339E+01 999-1.339E+01 999 96 1.465E-05 150 1.465E-05 999-1.539E+01 999-1.539E+01 999 97 1.277E-05 150 1.277E-05 999-1.749E+01 999-1.749E+01 999 98 9.788E-06 999 9.788E-06 150-1.968E+01 999-1.968E+01 999 01/30/2007 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 32

TABLE 8A- ENVELOPES OF MAXIMUMS * = HELD FROM PRIOR PROBLEM STA MAX +DEFL LOC MAX -DEFL LOC MAX +MOM LOC MAX -MOM LOC 99 5.581E-06 999 5.581E-06 150-2.197E+01 999-2.197E+01 999 100 0.000E+00 999 0.000E+00 999-2.436E+01 999-2.436E+01 999 101-7.103E-06 999-7.103E-06 150-2.149E+01 999-2.149E+01 999 102-1.555E-05 999-1.555E-05 150-1.871E+01 999-1.871E+01 999 103-2.517E-05 999-2.517E-05 150-1.603E+01 999-1.603E+01 999 104-3.578E-05 999-3.578E-05 150-1.344E+01 999-1.344E+01 999 105-4.724E-05 150-4.724E-05 999-1.096E+01 999-1.096E+01 999 106-5.938E-05 150-5.938E-05 999-8.570E+00 999-8.570E+00 999 107-7.206E-05 999-7.206E-05 150-6.279E+00 999-6.279E+00 999 108-8.513E-05 999-8.513E-05 150-4.085E+00 999-4.085E+00 999 109-9.846E-05 999-9.846E-05 150-1.989E+00 999-1.989E+00 999 110-1.119E-04 999-1.119E-04 150 9.359E-03 999 9.359E-03 999 111-1.254E-04 150-1.254E-04 999 1.910E+00 999 1.910E+00 999 112-1.387E-04 150-1.387E-04 999 3.714E+00 999 3.714E+00 999 113-1.518E-04 150-1.518E-04 999 5.420E+00 999 5.420E+00 999 114-1.645E-04 999-1.645E-04 150 7.028E+00 999 7.028E+00 999 115-1.769E-04 999-1.769E-04 150 8.539E+00 999 8.539E+00 999 116-1.887E-04 999-1.887E-04 150 9.953E+00 999 9.953E+00 999 117-1.998E-04 150-1.998E-04 999 1.127E+01 999 1.127E+01 999 118-2.103E-04 150-2.103E-04 999 1.249E+01 999 1.249E+01 999 119-2.200E-04 150-2.200E-04 999 1.361E+01 999 1.361E+01 999 120-2.288E-04 999-2.288E-04 150 1.463E+01 999 1.463E+01 999 121-2.367E-04 999-2.367E-04 150 1.556E+01 999 1.556E+01 999 122-2.436E-04 999-2.436E-04 150 1.639E+01 999 1.639E+01 999 123-2.496E-04 999-2.496E-04 150 1.712E+01 999 1.712E+01 999 124-2.544E-04 999-2.544E-04 150 1.775E+01 999 1.775E+01 999 125-2.581E-04 999-2.581E-04 150 1.829E+01 999 1.829E+01 999 126-2.607E-04 150-2.607E-04 999 1.873E+01 999 1.873E+01 999 127-2.622E-04 999-2.622E-04 150 1.907E+01 999 1.907E+01 999 128-2.624E-04 999-2.624E-04 150 1.931E+01 999 1.931E+01 999 129-2.614E-04 150-2.614E-04 999 1.946E+01 999 1.946E+01 999 130-2.592E-04 150-2.592E-04 999 1.950E+01 999 1.950E+01 999 131-2.558E-04 999-2.558E-04 150 1.946E+01 999 1.946E+01 999 132-2.512E-04 150-2.512E-04 999 1.931E+01 999 1.931E+01 999 133-2.454E-04 150-2.454E-04 999 1.907E+01 999 1.907E+01 999 134-2.384E-04 999-2.384E-04 150 1.872E+01 999 1.872E+01 999 135-2.302E-04 999-2.302E-04 150 1.828E+01 999 1.828E+01 999 136-2.208E-04 999-2.208E-04 150 1.775E+01 999 1.775E+01 999 137-2.104E-04 150-2.104E-04 999 1.711E+01 999 1.711E+01 999 138-1.989E-04 150-1.989E-04 999 1.638E+01 999 1.638E+01 999 139-1.863E-04 999-1.863E-04 150 1.555E+01 999 1.555E+01 999 140-1.728E-04 150-1.728E-04 999 1.463E+01 999 1.463E+01 999 141-1.584E-04 999-1.584E-04 150 1.360E+01 999 1.360E+01 999 142-1.431E-04 150-1.431E-04 999 1.248E+01 999 1.248E+01 999 143-1.271E-04 999-1.271E-04 150 1.126E+01 999 1.126E+01 999 144-1.103E-04 999-1.103E-04 150 9.946E+00 999 9.946E+00 999 145-9.292E-05 999-9.292E-05 150 8.532E+00 999 8.532E+00 999 146-7.501E-05 150-7.501E-05 999 7.021E+00 999 7.021E+00 999 147-5.666E-05 150-5.666E-05 999 5.412E+00 999 5.412E+00 999 148-3.796E-05 999-3.796E-05 150 3.705E+00 999 3.705E+00 999 149-1.904E-05 999-1.904E-05 150 1.901E+00 999 1.901E+00 999 150 0.000E+00 999 0.000E+00 999 0.000E+00 999 0.000E+00 999 01/30/2007 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 33

TABLE 8A- ENVELOPES OF MAXIMUMS * = HELD FROM PRIOR PROBLEM STA MAX +DEFL LOC MAX -DEFL LOC MAX +MOM LOC MAX -MOM LOC 151 1.904E-05 150 1.904E-05 999 0.000E+00 999 0.000E+00 999 01/30/2007 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 34

TABLE 8B- ENVELOPES OF MAXIMUMS * = HELD FROM PRIOR PROBLEM STA MAX +SHEAR LOC MAX -SHEAR LOC MAX +REACT LOC MAX -REACT LOC -1 0.000E+00 999 0.000E+00 999 0.000E+00 999 0.000E+00 999 0 3.900E+00 999 3.900E+00 999 3.803E+00 999 3.803E+00 999 1 0.000E+00 999 0.000E+00 999 3.608E+00 999 3.608E+00 999 2 0.000E+00 999 0.000E+00 999 3.413E+00 999 3.413E+00 999 3 0.000E+00 999 0.000E+00 999 3.218E+00 999 3.218E+00 999 4 0.000E+00 999 0.000E+00 999 3.023E+00 999 3.023E+00 999 5 0.000E+00 999 0.000E+00 999 2.828E+00 999 2.828E+00 999 6 0.000E+00 999 0.000E+00 999 2.633E+00 999 2.633E+00 999 7 0.000E+00 999 0.000E+00 999 2.438E+00 999 2.438E+00 999 8 0.000E+00 999 0.000E+00 999 2.243E+00 999 2.243E+00 999 9 0.000E+00 999 0.000E+00 999 2.048E+00 999 2.048E+00 999 10 0.000E+00 999 0.000E+00 999 1.853E+00 999 1.853E+00 999 11 0.000E+00 999 0.000E+00 999 1.658E+00 999 1.658E+00 999 12 0.000E+00 999 0.000E+00 999 1.463E+00 999 1.463E+00 999 13 0.000E+00 999 0.000E+00 999 1.268E+00 999 1.268E+00 999 14 0.000E+00 999 0.000E+00 999 1.073E+00 999 1.073E+00 999 15 0.000E+00 999 0.000E+00 999 8.780E-01 999 8.780E-01 999 16 0.000E+00 999 0.000E+00 999 6.830E-01 999 6.830E-01 999 17 0.000E+00 999 0.000E+00 999 4.880E-01 999 4.880E-01 999 18 0.000E+00 999 0.000E+00 999 2.930E-01 999 2.930E-01 999 19 0.000E+00 999 0.000E+00 999 9.797E-02 999 9.797E-02 999 20 0.000E+00 999 0.000E+00 999-9.703E-02 999-9.703E-02 999 21 0.000E+00 999 0.000E+00 999-2.920E-01 999-2.920E-01 999 22 0.000E+00 999 0.000E+00 999-4.870E-01 999-4.870E-01 999 23 0.000E+00 999 0.000E+00 999-6.820E-01 999-6.820E-01 999 24 0.000E+00 999 0.000E+00 999-8.770E-01 999-8.770E-01 999 25 0.000E+00 999 0.000E+00 999 01/30/2007 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 35

TABLE 8B- ENVELOPES OF MAXIMUMS * = HELD FROM PRIOR PROBLEM STA MAX +SHEAR LOC MAX -SHEAR LOC MAX +REACT LOC MAX -REACT LOC -1.072E+00 999-1.072E+00 999 26 0.000E+00 999 0.000E+00 999-1.267E+00 999-1.267E+00 999 27 0.000E+00 999 0.000E+00 999-1.462E+00 999-1.462E+00 999 28 0.000E+00 999 0.000E+00 999-1.657E+00 999-1.657E+00 999 29 0.000E+00 999 0.000E+00 999-1.852E+00 999-1.852E+00 999 30 0.000E+00 999 0.000E+00 999-2.047E+00 999-2.047E+00 999 31 0.000E+00 999 0.000E+00 999-2.242E+00 999-2.242E+00 999 32 0.000E+00 999 0.000E+00 999-2.437E+00 999-2.437E+00 999 33 0.000E+00 999 0.000E+00 999-2.632E+00 999-2.632E+00 999 34 0.000E+00 999 0.000E+00 999-2.827E+00 999-2.827E+00 999 35 0.000E+00 999 0.000E+00 999-3.022E+00 999-3.022E+00 999 36 0.000E+00 999 0.000E+00 999-3.217E+00 999-3.217E+00 999 37 0.000E+00 999 0.000E+00 999-3.412E+00 999-3.412E+00 999 38 0.000E+00 999 0.000E+00 999-3.607E+00 999-3.607E+00 999 39 0.000E+00 999 0.000E+00 999-3.802E+00 999-3.802E+00 999 40 0.000E+00 999 0.000E+00 999-3.997E+00 999-3.997E+00 999 41 0.000E+00 999 0.000E+00 999-4.192E+00 999-4.192E+00 999 42 0.000E+00 999 0.000E+00 999-4.387E+00 999-4.387E+00 999 43 0.000E+00 999 0.000E+00 999-4.582E+00 999-4.582E+00 999 44 0.000E+00 999 0.000E+00 999-4.777E+00 999-4.777E+00 999 45 0.000E+00 999 0.000E+00 999-4.972E+00 999-4.972E+00 999 46 0.000E+00 999 0.000E+00 999-5.167E+00 999-5.167E+00 999 47 0.000E+00 999 0.000E+00 999-5.362E+00 999-5.362E+00 999 48 0.000E+00 999 0.000E+00 999-5.557E+00 999-5.557E+00 999 49 0.000E+00 999 0.000E+00 999-5.752E+00 999-5.752E+00 999 50 1.072E+01 999 1.072E+01 999 4.778E+00 999 4.778E+00 999 51 0.000E+00 999 0.000E+00 999 01/30/2007 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 36

TABLE 8B- ENVELOPES OF MAXIMUMS * = HELD FROM PRIOR PROBLEM STA MAX +SHEAR LOC MAX -SHEAR LOC MAX +REACT LOC MAX -REACT LOC 4.583E+00 999 4.583E+00 999 52 0.000E+00 999 0.000E+00 999 4.388E+00 999 4.388E+00 999 53 0.000E+00 999 0.000E+00 999 4.192E+00 999 4.192E+00 999 54 0.000E+00 999 0.000E+00 999 3.997E+00 999 3.997E+00 999 55 0.000E+00 999 0.000E+00 999 3.802E+00 999 3.802E+00 999 56 0.000E+00 999 0.000E+00 999 3.608E+00 999 3.608E+00 999 57 0.000E+00 999 0.000E+00 999 3.412E+00 999 3.412E+00 999 58 0.000E+00 999 0.000E+00 999 3.217E+00 999 3.217E+00 999 59 0.000E+00 999 0.000E+00 999 3.023E+00 999 3.023E+00 999 60 0.000E+00 999 0.000E+00 999 2.827E+00 999 2.827E+00 999 61 0.000E+00 999 0.000E+00 999 2.633E+00 999 2.633E+00 999 62 0.000E+00 999 0.000E+00 999 2.437E+00 999 2.437E+00 999 63 0.000E+00 999 0.000E+00 999 2.242E+00 999 2.242E+00 999 64 0.000E+00 999 0.000E+00 999 2.047E+00 999 2.047E+00 999 65 0.000E+00 999 0.000E+00 999 1.852E+00 999 1.852E+00 999 66 0.000E+00 999 0.000E+00 999 1.657E+00 999 1.657E+00 999 67 0.000E+00 999 0.000E+00 999 1.463E+00 999 1.463E+00 999 68 0.000E+00 999 0.000E+00 999 1.268E+00 999 1.268E+00 999 69 0.000E+00 999 0.000E+00 999 1.072E+00 999 1.072E+00 999 70 0.000E+00 999 0.000E+00 999 8.775E-01 999 8.775E-01 999 71 0.000E+00 999 0.000E+00 999 6.825E-01 999 6.825E-01 999 72 0.000E+00 999 0.000E+00 999 4.875E-01 999 4.875E-01 999 73 0.000E+00 999 0.000E+00 999 2.925E-01 999 2.925E-01 999 74 0.000E+00 999 0.000E+00 999 9.750E-02 999 9.750E-02 999 75 0.000E+00 999 0.000E+00 999-9.750E-02 999-9.750E-02 999 76 0.000E+00 999 0.000E+00 999-2.925E-01 999-2.925E-01 999 77 0.000E+00 999 0.000E+00 999 01/30/2007 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 37