Design Slab Spans

LRFD Cast-In-Place (CIP) Slab Span Design ExampleCounty: Any Hwy: Any Design: BRG Date: 9/2009

CSJ: Any Project: Any Checked: BRG Date: 9/2009

Design ParametersThe basic bridge geometry can be found on the Bridge Layout and 75' Slab Span Details (see theAppendix, Pages 21 and 22).

Deck is 46 ft wide with a 15 degree skewRoadway is 44 ft wideType T501 Rail (0.326k/ft)14" Thick Slab SpanAssume NO Overlay Use Class "S" Concrete

f'c=4.0 ksi wc=150 pcf (for weight) wc=145 pcf (for Modulus of Elasticity calculation)Grade 60 Reinforcing

fy=60 ksi

MethodologyThe following procedure is based on the AASHTO LRFD Bridge Design Specifications,4th Ed. 2007 with 2008 Interim Revisions and the TXDOT LRFD Bridge Design Manual,May 2009 (BDM; hereafter referred to as TXDOT policy).

CalculationsDetermine the Equivalent Strip Width, E AASHTO LRFD 4.6.2.3The equivalent strip width defines the width of the slab that will be impacted by the live load within adesign lane. The slab is designed based on the forces developed within this width.

L = span length (ft)L1 = the minimum of L or 60 ft. (ft)W = edge to edge width (ft)Ws = the modified edge to edge width taken as a minimum of W or 30 ft (ft) for a single loaded laneWm = the modified edge to edge width taken as a minimum of W or 60 ft (ft) for multiple loaded lanes

L 25 ft

L1 min L 60 ft( ) L1 25.0 ft

W 46 ft

Ws min W 30 ft( ) Ws 30.0 ft

Wm min W 60 ft( ) Wm 46.0 ft

Page 1

N = number of lanes, the integer part of WRdwy/12Wrdwy = Clear roadway width

AASHTO LRFD 3.6.1.1.1

Wrdwy 44 ft

The "trunc" function truncatesthe calculated value to a singleinteger (i.e. 3.987 would be 3).NL trunc

Wrdwy1ft

12NL 3.000

Es = equivalent strip width for single loaded lane (in)

Es 10.0 in 5 L1 Wsinft

AASHTO LRFD Eq. 4.6.2.3-1

Es 146.931 in Es 12.244 ft

Em = equivalent strip width for multiple loaded lanes (in)

Em1 84.0 in 1.44 L1 Wminft

Em1 132.833 in AASHTO LRFD Eq. 4.6.2.3-2

Em2

12.0 Winft

NLEm2 184.000 in AASHTO LRFD Eq. 4.6.2.3-2

Em min Em1 Em2 Em 132.833 in

Em 11.069 ft

SkewFor skewed bridges, the longitudinal force effects may be reduced by the factor r, where

skew 15.deg Note: TXDOT policy limits the skew of CIP SlabSpans to 30 degrees. (BDM 3.11)

r1 1.05 0.25 tan skew( ) r1 0.983 AASHTO LRFD Eq. 4.6.2.3-3

r shall not be greater than 1

r min r1 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 deadload is comprised of the rail and slab weights, as well as any sidewalks or overlay (where applicable).The slab is modeled 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 width isless than 32 feet, the rail weight is distributed over the entire width of the slab. Otherwise, eachrail is distributed over the first 16 feet of slab adjacent to the rail. (BDM 3.11)

Wr = weight of the rail (kip/ft)DLrail = the distributed rail load on the slab (kip/ft/ft)

Wr 0.326kipft

DLrail if W 32 ftWr 2

W

Wr16 ft

DLrail 0.020kip

ft2

Slab:Wc = weight of concrete (kcf)t = thickness of the slab (inches)DLslab = weight of the slab (kip/ft/ft)

Wc 0.150kip

ft3

t 14 in

DLslab Wct

12inft

DLslab 0.175kip

ft2

Total DL:DL DLrail DLslab DL 0.195

kip

ft2

Live Load AASHTO LRFD 3.6.1.3.3The slab is designed based on 1-foot strips, therefore the live load must be distributed to thesestrips. To obtained a live load per foot, divide the lane load and truck loads by the effective width.

LLlane = distributed lane load = 0.640 k/ft AASHTO LRFD 3.6.1.2.4

LLt8 and LLt32 = design truck load, 8 k and 32 k, respectively AASHTO LRFD 3.6.1.2.2

IM = impact factor AASHTO LRFD Table 3.6.2.1-1

LLlane 0.640kipft

LLt8 8 kip

LLt32 32 kip

IM 1.33

Page 3

LLs = lane load over Es (single lane loaded)LLt8_s = 8 k load over Es (single lane loaded)LLt32_s = 32 k load over Es (single lane loaded)

LLsLLlane

EsLLs 0.052

kip

ft2

LLt8_sIM LLt8

EsLLt8_s 0.869

kipft

LLt32_sIM LLt32

EsLLt32_s 3.476

kipft

LLm = lane load over Em (multiple lanes loaded)LLt8_m = 8 k load over Em (multiple lanes loaded)LLt32_m = 32 k load over Em (multiple lanes loaded)

LLmLLlane

EmLLm 0.058

kip

ft2

LLt8_mIM LLt8

EmLLt8_m 0.961

kipft

LLt32_mIM LLt32

EmLLt32_m 3.845

kipft

Determine the Design MomentThe 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 modeling the dead load onlyand then the live load only. The maximum moment from each analysis is then combined usingTables 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 theAppendix.

Output Results - Table 8A

Single Lane LoadedM_DLpos_s and M_DLneg_s = Maximum positive and negative moment due to the Dead LoadM_LLpos_s and M_LLneg_s = Maximum positive and negative moment due to the Live Load

M_DLpos_s 19.50 kip ft M_DLneg_s 24.36 kip ft

M_LLpos_s 23.92 kip ft M_LLneg_s 22.01 kip ft

Multiple Lanes LoadedM_DLpos_m and M_DLneg_m = Maximum positive and negative moment due to the Dead LoadM_LLpos_m and M_LLneg_m = Maximum positive and negative moment due to the Live Load

M_DLpos_m 19.50 kip ft M_DLneg_m 24.36 kip ft

M_LLpos_m 26.44 kip ft M_LLneg_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 theAASHTO LRFD (Service I and Strength I) and reduced for skew using r.

LLs and LLst = live load factor for service and strength, respectivelyDCs and DCst = dead load factor for service and strength, respectively

LLs 1.00 LLst 1.75

DCs 1.00 DCst 1.25

M_Servpos_s, M_Servneg_s = Positive or negative combined Service Moment for single loaded laneM_Servpos_m, M_Servneg_m = Positive or negative combined Service Moment for multiple loaded lanesM_Servpos, M_Servneg = Positive or negative combined Service Moment for design (maximum

moment for single lane loaded or multiple lanes loaded)

M_Servpos_s r LLs M_LLpos_s DCs M_DLpos_s M_Servpos_s 43.014 kip ft

M_Servpos_m r LLs M_LLpos_m DCs M_DLpos_m M_Servpos_m 45.491 kip ft

M_Servpos max M_Servpos_s M_Servpos_m M_Servpos 45.491 kip ft

M_Servneg_s r LLs M_LLneg_s DCs M_DLneg_s M_Servneg_s 45.996 kip ft

M_Servneg_m r LLs M_LLneg_m DCs M_DLneg_m M_Servneg_m 48.287 kip ft

M_Servneg max M_Servneg_s M_Servneg_m M_Servneg 48.287 kip ft

M_Ultpos_s, M_Ultneg_s = Positive or negative combined Strength Moment for single loaded laneM_Ultpos_m, M_Ultneg_m = Positive or negative combined Strength Moment for multiple loaded lanesM_Ultpos, M_Ultneg = Positive or negative combined Strength Moment for design (maximum

moment for single lane loaded or multiple lanes loaded)

M_Ultpos_s r LLst M_LLpos_s DCst M_DLpos_s M_Ultpos_s 65.524 kip ft

M_Ultpos_m r LLst M_LLpos_m DCst M_DLpos_m M_Ultpos_m 69.859 kip ft

M_Ultpos max M_Ultpos_s M_Ultpos_m M_Ultpos 69.859 kip ft

M_Ultneg_s r LLst M_LLneg_s DCst M_DLneg_s M_Ultneg_s 68.313 kip ft

M_Ultneg_m r LLst M_LLneg_m DCst M_DLneg_m M_Ultneg_m 72.321 kip ft

M_Ultneg max M_Ultneg_s M_Ultneg_m M_Ultneg 72.321 kip ft

Summary of Results (includes reduction for skew)

Ms_pos M_Servpos Ms_pos 45.491 kip ft

Ms_neg M_Servneg Ms_neg 48.287 kip ft

Mu_pos M_Ultpos Mu_pos 69.859 kip ft

Mu_neg M_Ultneg Mu_neg 72.321 kip ftPage 6

Moment Capacity Design - Negative (Top) - Typ. Bars A AASHTO LRFD 5.7.3.2Design strip width perTxDOT policy (BDM 3.11)b 12 in

h 14 in Thickness of the slab.

fc 4 ksiCompressive Strength of Concrete:

fy 60 ksiYield Strength of Rebar:

coverneg 2 in "cover" is measured to edgeof top reinforcement.

Minimum Flexural Reinforcement AASHTO LRFD 5.7.3.3.2

Factored Flexural Resistance, Mr, must be greater than or equal to the lesser of 1.2 Mcr (Cracking Moment)or 1.33 Mu (Ultimate Moment)

Gross Moment of Inertia:

Igb h3

12Ig 2744 in

4

Modulus of Rupture:TxDOT policy states whenusing AASHTO LRFD5.7.3.3.2 to calculatecracking moment, usefr=0.24sqrt(fc). (BDM 3.11)

fr 0.24ksifcksi

fr 0.480 ksi

Distance from Center of Gravity to extreme tension fiber:

yt12

h yt 7.0 in

Section Modulus:

SIgyt

S 392.00 in3

Cracking Moment:

Mcr S fr1ft

12inMcr 15.680 kip ft

Therefore,

Design for the lesser of 1.2Mcror 1.33Mu when determiningminimum area of steelrequired.

Mcr1 1.2 Mcr Mcr1 18.8 kip ft

Mcr2 1.33 Mu_neg Mcr2 96.2 kip ft

Mf_neg min Mcr1 Mcr2

Thus, Mr must be greater than Mf_neg 18.8 kip ft

Page 7

Moment Capacity Design - Negative (Top) - Typ. Bars A AASHTO LRFD 5.7.3.2

Try, #8's at 6 inch spacingNumber of bars in 12 in strip.

Nbar_neg 2Diameter of main reinforcingbars.dbar_neg 1.00in

Area of one main reinforcingbar.Abar_neg 0.79in

2

As_neg Nbar_neg Abar_neg As_neg 1.580 in2

Area of steel in tension.

dneg h coverneg12

dbar_neg dneg 11.500 in

1_neg min 0.85 max 0.65 0.850.051ksi

fc 4ksi 1_neg 0.850 AASHTO LRFD 5.7.2.2

Resistance Factor: M 0.9 AASHTO LRFD 5.5.4.2.1

Depth of Cross Section in Compression under Ultimate Load:

cnegAs_neg fy

0.85 fc 1_neg bcneg 2.734 in AASHTO LRFD Eq.

5.7.3.1.2-4

Depth of Equivalent Stress Block:

aneg cneg 1_neg aneg 2.324 in AASHTO LRFD 5.7.2.2

Thus,

Nominal Flexural Resistance:

Mn_neg As_neg fy dneganeg

21ft

12inMn_neg 81.672 kip ft AASHTO LRFD Eq.

5.7.3.2.2-1

Factored Flexural Resistance:

Mr_neg M Mn_neg Mr_neg 73.505 kip ft

Mu_neg 72.321 kip ft

Mf_neg 18.816 kip ft

Min_reinf_neg if Mr_neg Mf_neg OK NG Min_reinf_neg "OK!"

UltimateMom_neg if Mr_neg Mu_neg OK NG UltimateMom_neg "OK!"

Page 8

Check Serviceability- Negative (Top) - Typ. Bars A AASHTO LRFD 5.7.3.4

To find smax_neg :

"cover" is measured to edgeof the top reinforcement.dc_neg coverneg

12

dbar_neg dc_neg 2.500 in

Es 29000 ksi

Ec 1820 fc1

ksiksi Ec 3640 ksi AASHTO LRFD Eq. C5.4.2.4-1

Modular Ratio:

nEsEc

n 7.967

Tension Reinforcement Ratio: For service loads, the stresson the cross-section islocated as drawn:

negAs_negb dneg

neg 0.0114

kneg 2 neg n neg n2

neg n kneg 0.346

jneg 1kneg

3jneg 0.885

Service Load Bending Stress:

fs_negMs_neg

As_neg jneg dneg

12in1ft

fs_neg 36.041 ksi

Exposure Condition Factor:

e_top 0.75 For class 2 exposureconditions.

s_neg 1dc_neg

0.7 h dc_negs_neg 1.311

smax_neg

700kipine_top

s_neg fs_neg2dc_neg smax_neg 6.115 in AASHTO LRFD Eq. 5.7.3.4-1

sActual_neg 6 in

ServiceabilityCheck if smax_neg sActual_neg OK NG ServiceabilityCheck "OK!"

The negative reinforcement can usually be reduced to #8 bars at 12 inches about 6 feet from thecenterline of the bent. However, this should be verified by checking the moment capacity of 1 barversus the moment at 6 feet from the centerline of the cap. For this example problem, 1 bar willprovide 40.595 kip-ft of Mr_neg with a Mu_neg of 19.576 kip-ft. In addition, the max. bar spacing isin excess of 12 inches.

Page 9

Moment Capacity Design - Positive (Bottom) - Typ. Bars B AASHTO LRFD 5.7.3.2"cover" is measured to edgeof the bottom reinforcement.coverpos 1.25 in




Igb h3

12Ig 2744 in

4


fr 0.24ksifcksi

fr 0.480 ksi


yt12

h yt 7.0 in

Section Modulus:

SIgyt

S 392.00 in3

Cracking Moment:

Mcr S fr1ft


Therefore,



Mcr2 1.33 Mu_pos Mcr2 92.9 kip ft

Mf_pos min Mcr1 Mcr2

Thus, Mr must be greater than Mf_pos 18.8 kip ft

Page 10

Moment Capacity Design - Positive (Bottom) - Typ. Bars B AASHTO LRFD 5.7.3.2

Try, #8's at 6 inch spacing

Nbar_pos 2 Number of bars in 12 in strip.

Diameter of main reinforcingbars.dbar_pos 1.00in

Area of one main reinforcingbar.Abar_pos 0.79in

2

As_pos Nbar_pos Abar_pos As_pos 1.580 in2 Area of steel in tension.

dpos h coverpos12

dbar_pos dpos 12.250 in

1pos min 0.85 max 0.65 0.850.051ksi

fc 4ksi 1pos 0.850 AASHTO LRFD 5.7.2.2


cposAs_pos fy

0.85 fc 1pos bcpos 2.734 in AASHTO LRFD Eq. 5.7.3.1.2-4


apos cpos 1pos apos 2.324 in AASHTO LRFD Eq. 5.7.2.2

Thus,


Mn_pos As_pos fy dposapos

21ft

12inMn_pos 87.597 kip ft AASHTO LRFD Eq.

5.7.3.2.2-1Factored Flexural Resistance:

Mr_pos M Mn_pos Mr_pos 78.837 kip ft

Mu_pos 69.859 kip ft

Mf_pos 18.816 kip ft

Min_reinf_pos if Mr_pos Mf_pos OK NG Min_reinf_pos "OK!"

UltimateMompos if Mr_pos Mu_pos OK NG UltimateMompos "OK!"

Page 11

Check Serviceability- Positive (Bottom) - Typ. Bars B AASHTO LRFD 5.7.3.4

To find smax_pos :

"cover" is measured to edgeof the bottom reinforcement.dc_pos coverpos

12

dbar_pos dc_pos 1.750 in

Tension Reinforcement Ratio:

posAs_posb dpos pos 0.0107

kpos 2 pos n pos n2

pos n kpos 0.337

jpos 1kpos

3jpos 0.888


fs_posMs_pos

As_pos jpos dpos

12in1ft

fs_pos 31.773 ksi

Exposure Condition Factor:

e_bot 1.00 For class 1 exposureconditions.

s_pos 1dc_pos

0.7 h dc_poss_pos 1.204

smax_pos

700kipine_bot

s_pos fs_pos2dc_pos smax_pos 14.797 in AASHTO LRFD Eq.

5.7.3.4-1

sActual_pos 6 in

ServiceabilityCheckpos if smax_pos sActual_pos OK NG ServiceabilityCheckpos "OK!"

Page 12

Shrinkage and Temperature Reinforcement-Negative (Top) - Typ. Bars T

AASHTO LRFD 5.10.8

Try #4 bars at 12 inch spacing

Nbar_t_neg 1

dbar_t_neg 0.500in

Abar_t_neg 0.20in2

As_t_neg Nbar_t_neg Abar_t_neg As_t_neg 0.200 in2

Asreq_t_neg min max 0.11 in2 1.3 b h( ) in

2 b h( ) fy1

ksi

0.60 in2 Asreq_t_neg 0.110 in2

TemperatureCheckneg if As_t_neg Asreq_t_neg OK NG TemperatureCheckneg "OK!"

Transverse Distribution Reinforcement-Positive (Bottom) - Typ. Bars D

AASHTO LRFD 5.14.4.1 andTxDOT policy


Nbar_d_pos 2

dbar_d_pos 0.500in

Abar_d_pos 0.20in2

As_d_pos Nbar_d_pos Abar_d_pos As_d_pos 0.400 in2

PercentAsd_pos min 50100

L1ft

PercentAsd_pos 20.0 AASHTO LRFD Eq.5.14.4.1-1

Asreq_d_pos As_posPercentAsd_pos

100Asreq_d_pos 0.316 in

2

Distributiond_pos if As_d_pos Asreq_d_pos OK NG Distributiond_pos "OK!"

Shear ReinforcementFrom AASHTO LRFD 5.14.4, "Slabs and slab bridges designed for moment in conformance with Article4.6.2.3 may be considered satisfactory for shear."

Page 13

Design for the Edge BeamThe edge for the slab is designed based on AASHTO LRFD 9.7.1.4 and 4.6.2.1.4b. 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 thebarrier, 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

Em 11.069 ft

Wedge min C 12 in 0.25 Em 0.5 Em 72 in AASHTO LRFD 4.6.2.1.4b

Wedge 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 deadload is comprised of the rail and slab weights, as well as any sidewalks or overlay (if applicable). Theslab is modeled as a simply supported continuous beam.

Dead LoadSame as calculated on page 2.

DLrail 0.020kip

ft2DLslab 0.175

kip

ft2

Page 14

Live Load AASHTO LRFD 3.6.1.3.3The slab is designed based on 1-foot strips, therefore the live load must be distributed to these strips. Toobtained a live load per foot divide the lane load and truck loads by the effective width.

LLlane = distributed lane load = 0.640 k/ft (AASHTO LRFD 3.6.1.2.4)LLt4 and LLt16 = 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. (AASHTO LRFD 3.6.1.2.2)I = impact factor (AASHTO LRFD Table 3.6.2.2-1)

LLlane 0.640 ftkip

ft2AASHTO LRFD 3.6.1.2.4

LLt4 4 kip

LLt16 16 kip

IM 1.330

LLedge = lane load over WedgeLLt4_edge = 4 k load over WedgeLLt16_edge = 16 k load over Wedge

LLedge

LLlaneWedge

12Wedge

LLedge 0.053 ftkip

ft2

LLt4_edgeIM LLt4Wedge

LLt4_edge 1.026kipft

LLt16_edgeIM LLt16Wedge

LLt16_edge 4.105kipft

Determine the Design MomentThe 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 modeling the dead load onlyand then the live load only. The maximum moment from each analysis is then combined usingTables 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 theAppendix.

Output Results - Table 8A

M_DLedge_pos and M_DLedge_neg = Maximum positive and negative moment due to the Dead LoadM_LLedge_pos and M_LLedge_neg = Maximum positive and negative moment due to the Live Load

M_DLedge_pos 19.50 kip ft M_DLedge_neg 24.36 kip ft

M_LLedge_pos 28.46 kip ft M_LLedge_neg 26.27 kip ft

Page 15

The maximum moment from each analysis is then combined using Tables 3.4.1-1 and 3.4.1-2 of theAASHTO LRFD (Service I and Strength I) and reduced for skew using r.

LLs and LLst = live load factor for service and strength, respectivelyDCs and DCst = dead load factor for service and strength, respectively

LLs 1.000 LLst 1.750

DCs 1.000 DCst 1.250

M_Servedge_pos, M_Servedge_pos = Positive or negative combined Service Moment for edge beam

M_Servedge_pos r LLs M_LLedge_pos DCs M_DLedge_pos M_Servedge_pos 47.477 kip ft

M_Servedge_neg r LLs M_LLedge_neg DCs M_DLedge_neg M_Servedge_neg 50.184 kip ft

M_Ultedge_pos, M_Ultedge_neg = Positive or negative combined Strength Moment for edge beam

M_Ultedge_pos r LLst M_LLedge_pos DCst M_DLedge_pos M_Ultedge_pos 73.334 kip ft

M_Ultedge_neg r LLst M_LLedge_neg DCst M_DLedge_neg M_Ultedge_neg 75.642 kip ft

Summary of Results (includes reduction for skew)

Ms_edge_pos M_Servedge_pos Ms_edge_pos 47.477 kip ft

Ms_edge_neg M_Servedge_neg Ms_edge_neg 50.184 kip ft

Mu_edge_pos M_Ultedge_pos Mu_edge_pos 73.334 kip ft

Mu_edge_neg M_Ultedge_neg Mu_edge_neg 75.642 kip ft

Page 16

Moment Capacity Design - Negative (Top) - Typ. Bars A AASHTO LRFD 5.7.3.2b 12.000 in Design strip width per

TxDOT policy (BDM 3.11)h 14.000 in Thickness of the slab.

covere_neg 2 in "cover" is measured to edgeof the top reinforcement.




Igb h3

12Ig 2744 in

4


fr 0.24ksifcksi

fr 0.480 ksi


yt12

h yt 7.0 in

Section Modulus:

SIgyt

S 392.00 in3

Cracking Moment:

Mcr S fr1ft


Therefore,



Mcr2 1.33 Mu_edge_neg Mcr2 100.6 kip ft

Mf_edge_neg min Mcr1 Mcr2

Thus, Mr must be greater than Mf_edge_neg 18.8 kip ft

Page 17

Moment Capacity Design - Negative (Top) - Typ. Bars A AASHTO LRFD 5.7.3.2


Nbar_e_neg 2Diameter of main reinforcingbars.dbar_e_neg 1.00in

Area of one main reinforcingbar.Abar_e_neg 0.79in

2

As_e_neg Nbar_e_neg Abar_e_neg As_e_neg 1.580 in2 Area of steel in tension.

dedge_neg h covere_neg12

dbar_e_neg dedge_neg 11.500 in

1_e_neg min 0.85 max 0.65 0.850.051ksi

fc 4ksi 1_e_neg 0.850 AASHTO LRFD 5.7.2.2

Resistance Factor:

M 0.900 AASHTO LRFD 5.5.4.2.1


ce_negAs_e_neg fy

0.85 fc 1_e_neg bce_neg 2.734 in AASHTO LRFD Eq. 5.7.3.1.2-4


ae_neg ce_neg 1_e_neg ae_neg 2.324 in AASHTO LRFD Eq. 5.7.2.2

Thus,


Mn_e_neg As_e_neg fy dedge_negae_neg

21ft

12inAASHTO LRFD Eq. 5.7.3.2.2-1

Mn_e_neg 81.672 kip ft


Mr_e_neg M Mn_e_neg Mr_e_neg 73.505 kip ft

Mu_edge_neg 75.642 kip ft

Mf_edge_neg 18.816 kip ft

Min_reinfedge_neg if Mr_e_neg Mf_edge_neg OK NG Min_reinfedge_neg "OK!"

UltimateMomedge_neg if Mr_e_neg Mu_edge_neg OK NG UltimateMomedge_neg "NO GOOD!"

Though the resistance is less than the ultimate, the presented design is considered acceptablebecause the difference is less than 3 percent of the ultimate. Though not necessary, the bar spacingis reduced to 4 inches within the outside 1-foot of the slab in order to provide additional reinforcementfor rail attachment.

Page 18

Check Serviceability- Negative (Top) - Typ. Bars A AASHTO LRFD 5.7.3.4

To find smax_e_neg :

"cover" is measured to edgeof the bottom reinforcement.dc_e_neg covere_neg

12

dbar_e_neg dc_e_neg 2.500 in


e_negAs_e_neg

b dedge_neg e_neg 0.0114

ke_neg 2 e_neg n e_neg n2

e_neg n ke_neg 0.346

je_neg 1ke_neg

3je_neg 0.885


fs_e_negMs_edge_neg

As_e_neg je_neg dedge_neg

12in1ft

fs_e_neg 37.457 ksi

Exposure Condition Factor: e_top 0.75 For class 2 exposureconditions.

s_e_neg 1dc_e_neg

0.7 h dc_e_negs_e_neg 1.311

smax_e_neg

700kipine_top

s_e_neg fs_e_neg2dc_e_neg smax_e_neg 5.695 in AASHTO LRFD Eq.

5.7.3.4-1

sActual_e_neg 6 in

ServiceabilityChecke_neg if smax_e_neg sActual_e_neg OK NG

ServiceabilityChecke_neg "NO GOOD!"

Though the spacing is greater than the maximum spacing, the presented design is consideredacceptable because the difference is less than 1/2 inch.

Page 19


Design strip width per TxDOTpolicy (BDM 3.11)b 12.000 in

h 14.000 in Thickness of the slab.

covere_pos 1.25 in "cover" is measured to edgeof the bottom reinforcement.




Igb h3

12Ig 2744 in

4


fr 0.24ksifcksi

fr 0.480 ksi


yt12

h yt 7.0 in

Section Modulus:

SIgyt

S 392.00 in3

Cracking Moment:

Mcr S fr1ft


Therefore,



Mcr2 1.33 Mu_edge_pos Mcr2 97.5 kip ft

Mf_edge_pos min Mcr1 Mcr2

Thus, Mr must be greater than Mf_edge_pos 18.8 kip ft

Page 20



Nbar_e_pos 2Diameter of main reinforcingbars.dbar_e_pos 1.00in

Area of one main reinforcingbar.Abar_e_pos 0.79in

2

As_e_pos Nbar_e_pos Abar_e_pos As_e_pos 1.580 in2 Area of steel in tension.

dedge_pos h covere_pos12

dbar_e_pos dedge_pos 12.250 in

1_e_pos min 0.85 max 0.65 0.850.051ksi

fc 4ksi 1_e_pos 0.850 AASHTO LRFD 5.7.2.2

Resistance Factor: M 0.900 AASHTO LRFD 5.5.4.2.1


ce_posAs_e_pos fy

0.85 fc 1_e_pos bce_pos 2.734 in AASHTO LRFD Eq. 5.7.3.1.2-4


ae_pos ce_pos 1_e_pos ae_pos 2.324 in

Thus,


Mn_e_pos As_e_pos fy dedge_posae_pos

21ft

12inAASHTO LRFD Eq. 5.7.3.2.2-1

Mn_e_pos 87.597 kip ft


Mr_e_pos M Mn_e_pos Mr_e_pos 78.837 kip ft

Mu_edge_pos 73.334 kip ft

Mf_edge_pos 18.816 kip ft

Min_reinfedge_pos if Mr_e_pos Mf_edge_pos OK NG Min_reinfedge_pos "OK!"

UltimateMomedge_pos if Mr_e_pos Mu_edge_pos OK NG UltimateMomedge_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 additionalreinforcement for rail attachment.

Page 21

Check Serviceability- Positive (Bottom) - Typ. Bars B AASHTO LRFD 5.7.3.4

To find smax_e_pos :

"cover" is measured to edgeof the bottom reinforcement.dc_e_pos covere_pos

12

dbar_e_pos dc_e_pos 1.750 in


e_posAs_e_pos

b dedge_pos e_pos 0.0107

ke_pos 2 e_pos n e_pos n2

e_pos n ke_pos 0.337

je_pos 1ke_pos

3je_pos 0.888


fs_e_posMs_edge_pos

As_e_pos je_pos dedge_pos

12in1ft

fs_e_pos 33.160 ksi

Exposure Condition Factor: e_bot 1.00 For class 1 exposureconditions.

s_e_pos 1dc_e_pos

0.7 h dc_e_poss_e_pos 1.204

smax_e_pos

700kipine_bot

s_e_pos fs_e_pos2dc_e_pos smax_e_pos 14.032 in AASHTO LRFD Eq.

5.7.3.4-1

sActual_e_pos 6 in

ServiceabilityChecke_pos if smax_e_pos sActual_e_pos OK NG ServiceabilityChecke_pos "OK!"

Page 22

Shrinkage and Temperature Reinforcement-Negative (Top) - Typ. Bars T

AASHTO LRFD 5.10.8


Nbar_te_neg 1

dbar_te_neg 0.500in

Abar_te_neg 0.20in2

As_te_neg Nbar_te_neg Abar_te_neg As_te_neg 0.200 in2

Asreq_te_neg min max 0.11 in2 1.3 b h( ) in

2 b h( ) fy1

ksi

0.60 in2 Asreq_te_neg 0.110 in2

TemperatureChecke_neg if As_te_neg Asreq_te_neg OK NG TemperatureChecke_neg "OK!"

Transverse Distribution Reinforcement-Positive (Bottom) - Typ. Bars D

AASHTO LRFD 5.14.4.1 andTxDOT policy


Nbar_de_pos 2

dbar_de_pos 0.500in

Abar_de_pos 0.20in2

As_de_pos Nbar_de_pos Abar_de_pos As_de_pos 0.400 in2

AASHTO LRFD Eq.5.14.4.1-1PercentAsde_pos min 50

100

L1ft

PercentAsde_pos 20.000

Asreq_de_pos As_e_posPercentAsde_pos

100Asreq_de_pos 0.316 in

2

Distributionde_pos if As_de_pos Asreq_de_pos OK NG Distributionde_pos "OK!"

Shear ReinforcementFrom AASHTO LRFD 5.14.4, "Slabs and slab bridges designed for moment in conformance with Article4.6.2.3 may be considered satisfactory for shear."

Page 23

AppendixBridge Layout Slab Span Details BMCOL51 Input File (Dead Load)BMCOL51 Output File (Dead Load) BMCOL51 Input File (Single Loaded - Live Load)BMCOL51 Output File (Single Lane Loaded - Live Load)BMCOL51 Input File (Multiple Lanes - Live Load)BMCOL51 Output File (Multiple Lanes Loaded - Live Load)BMCOL51 Input File (Edge Beam - Live Load)BMCOL51 Output File (Edge Beam - Live Load)

................................................................................. pg 25pg 26pg 27pg 28pg 45pg 46pg 63pg 64pg 81pg 82

............................................................................................................................

..........................................................................

.......................................

..........................................

.............................

Page 24

COUNTY HWY 0000-00-000 BRG 12/02/2006SLAB 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 -0.195CEASE

Page 27

BMCOL51 MOVABLE LOAD ANALYSIS OF BEAM COLUMNS NT Ver 5.01 Apr 99

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 Page 28


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 29




-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 30




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 31




-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)

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-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)

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-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)

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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)

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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)

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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)

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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)

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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)

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-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)

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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)

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-4.875E-01 999 -4.875E-01 999 78 0.000E+00 999 0.000E+00 999 -6.825E-01 999 -6.825E-01 999 79 0.000E+00 999 0.000E+00 999 -8.775E-01 999 -8.775E-01 999 80 0.000E+00 999 0.000E+00 999 -1.072E+00 999 -1.072E+00 999 81 0.000E+00 999 0.000E+00 999 -1.268E+00 999 -1.268E+00 999 82 0.000E+00 999 0.000E+00 999 -1.463E+00 999 -1.463E+00 999 83 0.000E+00 999 0.000E+00 999 -1.657E+00 999 -1.657E+00 999 84 0.000E+00 999 0.000E+00 999 -1.852E+00 999 -1.852E+00 999 85 0.000E+00 999 0.000E+00 999 -2.047E+00 999 -2.047E+00 999 86 0.000E+00 999 0.000E+00 999 -2.242E+00 999 -2.242E+00 999 87 0.000E+00 999 0.000E+00 999 -2.437E+00 999 -2.437E+00 999 88 0.000E+00 999 0.000E+00 999 -2.633E+00 999 -2.633E+00 999 89 0.000E+00 999 0.000E+00 999 -2.827E+00 999 -2.827E+00 999 90 0.000E+00 999 0.000E+00 999 -3.023E+00 999 -3.023E+00 999 91 0.000E+00 999 0.000E+00 999 -3.217E+00 999 -3.217E+00 999 92 0.000E+00 999 0.000E+00 999 -3.412E+00 999 -3.412E+00 999 93 0.000E+00 999 0.000E+00 999 -3.608E+00 999 -3.608E+00 999 94 0.000E+00 999 0.000E+00 999 -3.802E+00 999 -3.802E+00 999 95 0.000E+00 999 0.000E+00 999 -3.997E+00 999 -3.997E+00 999 96 0.000E+00 999 0.000E+00 999 -4.192E+00 999 -4.192E+00 999 97 0.000E+00 999 0.000E+00 999 -4.388E+00 999 -4.388E+00 999 98 0.000E+00 999 0.000E+00 999 -4.583E+00 999 -4.583E+00 999 99 0.000E+00 999 0.000E+00 999 -4.778E+00 999 -4.778E+00 999 100 1.072E+01 999 1.072E+01 999 5.752E+00 999 5.752E+00 999 101 0.000E+00 999 0.000E+00 999 5.557E+00 999 5.557E+00 999 102 0.000E+00 999 0.000E+00 999 5.362E+00 999 5.362E+00 999 103 0.000E+00 999 0.000E+00 999 01/30/2007 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT)

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5.167E+00 999 5.167E+00 999 104 0.000E+00 999 0.000E+00 999 4.972E+00 999 4.972E+00 999 105 0.000E+00 999 0.000E+00 999 4.777E+00 999 4.777E+00 999 106 0.000E+00 999 0.000E+00 999 4.582E+00 999 4.582E+00 999 107 0.000E+00 999 0.000E+00 999 4.387E+00 999 4.387E+00 999 108 0.000E+00 999 0.000E+00 999 4.192E+00 999 4.192E+00 999 109 0.000E+00 999 0.000E+00 999 3.997E+00 999 3.997E+00 999 110 0.000E+00 999 0.000E+00 999 3.802E+00 999 3.802E+00 999 111 0.000E+00 999 0.000E+00 999 3.607E+00 999 3.607E+00 999 112 0.000E+00 999 0.000E+00 999 3.412E+00 999 3.412E+00 999 113 0.000E+00 999 0.000E+00 999 3.217E+00 999 3.217E+00 999 114 0.000E+00 999 0.000E+00 999 3.022E+00 999 3.022E+00 999 115 0.000E+00 999 0.000E+00 999 2.827E+00 999 2.827E+00 999 116 0.000E+00 999 0.000E+00 999 2.632E+00 999 2.632E+00 999 117 0.000E+00 999 0.000E+00 999 2.437E+00 999 2.437E+00 999 118 0.000E+00 999 0.000E+00 999 2.242E+00 999 2.242E+00 999 119 0.000E+00 999 0.000E+00 999 2.047E+00 999 2.047E+00 999 120 0.000E+00 999 0.000E+00 999 1.852E+00 999 1.852E+00 999 121 0.000E+00 999 0.000E+00 999 1.657E+00 999 1.657E+00 999 122 0.000E+00 999 0.000E+00 999 1.462E+00 999 1.462E+00 999 123 0.000E+00 999 0.000E+00 999 1.267E+00 999 1.267E+00 999 124 0.000E+00 999 0.000E+00 999 1.072E+00 999 1.072E+00 999 125 0.000E+00 999 0.000E+00 999 8.770E-01 999 8.770E-01 999 126 0.000E+00 999 0.000E+00 999 6.820E-01 999 6.820E-01 999 127 0.000E+00 999 0.000E+00 999 4.870E-01 999 4.870E-01 999 128 0.000E+00 999 0.000E+00 999 2.920E-01 999 2.920E-01 999 129 0.000E+00 999 0.000E+00 999 01/30/2007 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT)

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9.703E-02 999 9.703E-02 999 130 0.000E+00 999 0.000E+00 999 -9.797E-02 999 -9.797E-02 999 131 0.000E+00 999 0.000E+00 999 -2.930E-01 999 -2.930E-01 999 132 0.000E+00 999 0.000E+00 999 -4.880E-01 999 -4.880E-01 999 133 0.000E+00 999 0.000E+00 999 -6.830E-01 999 -6.830E-01 999 134 0.000E+00 999 0.000E+00 999 -8.780E-01 999 -8.780E-01 999 135 0.000E+00 999 0.000E+00 999 -1.073E+00 999 -1.073E+00 999 136 0.000E+00 999 0.000E+00 999 -1.268E+00 999 -1.268E+00 999 137 0.000E+00 999 0.000E+00 999 -1.463E+00 999 -1.463E+00 999 138 0.000E+00 999 0.000E+00 999 -1.658E+00 999 -1.658E+00 999 139 0.000E+00 999 0.000E+00 999 -1.853E+00 999 -1.853E+00 999 140 0.000E+00 999 0.000E+00 999 -2.048E+00 999 -2.048E+00 999 141 0.000E+00 999 0.000E+00 999 -2.243E+00 999 -2.243E+00 999 142 0.000E+00 999 0.000E+00 999 -2.438E+00 999 -2.438E+00 999 143 0.000E+00 999 0.000E+00 999 -2.633E+00 999 -2.633E+00 999 144 0.000E+00 999 0.000E+00 999 -2.828E+00 999 -2.828E+00 999 145 0.000E+00 999 0.000E+00 999 -3.023E+00 999 -3.023E+00 999 146 0.000E+00 999 0.000E+00 999 -3.218E+00 999 -3.218E+00 999 147 0.000E+00 999 0.000E+00 999 -3.413E+00 999 -3.413E+00 999 148 0.000E+00 999 0.

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