EXAMPLE 6 - DECK DESIGN, INCLUDING COLLISION …...Design of deck reinforcement, including flexural resistance, limits of reinforcement, and control of cracking is based on AASHTO

EXAMPLE 6 - DECK DESIGN, INCLUDING COLLISION ON A TYPE 7 & TYPE 10M BARRIER 1

CDOT Bridge Design Manual January 2019

Design Example 6APPENDIX A

EXAMPLE 6 - DECK DESIGN, INLCUDING COLLISIONON A TYPE 7 OR TYPE 10 M BARRIER

EXAMPLE 6.1 - DECK DESIGN

GENERAL INFORMATION

1. Approximate Elastic Method, or "Equivalent Strip" Method (AASHTO 4.6.2.1)2. Refined Methods (AASHTO 4.6.3.2)3. Empirical Design Method (AASHTO 9.7.2)

MATERIAL AND SECTION PROPERTIESStructure typeGirder spacing, maximum SGdr = 8.00 ft.

Number of girders NGdr = 3 ea.

Overall deck width WDeck = 24.00 ft.

Deck slab thickness tDeck = 8.00 in.

Overhang thickness (average) tOH = 9.00 in.

Concrete top cover cTop = 2.00 in. AASHTO T.5.10.1-1Concrete bottom cover cBot = 1.00 in. AASHTO T.5.10.1-1Wearing surface tWS = 3.00 in.

Concrete strength f'c = 4.50 ksi (Concrete Class D compressive strength)

Reinforcement strength fy = 60.00 ksi (Minimum yield strength of grade 60 steel)

Concrete density WC = 0.150 kcf

Deck overlay density WWS = 0.147 kcf Section 3.4.2Allowance for future utilities WUtl = 0.005 ksf Section 3.4.3Resistance factors φSTR = 0.90 (strength limit state) AASHTO 5.5.4.2

φEE = 1.00 (extreme event limit state) AASHTO 1.3.2.1Correction factor for source aggregate K1 = 1.00 AASHTO 5.4.2.4Modulus of elasticity of reinforcement Es = 29000 ksi AASHTO 5.4.3.2Modulus of elasticity of concrete Ec = 4435 ksi AASHTO 5.4.2.4

Modular ratio n = ES / EC = 6.54Girder typeGirder web thickness web = 7.00 in.

Girder top flange width flange = 43.00 in.

Barrier typeArea of barrier section AB = 3.24 ft.2

Based on AASHTO LRFD Bridge Design Specifications 9.6.1, there are three permitted methods ofdeck analysis:

This design example uses the Approximate Elastic Method (Equivalent Strip Method), in which thedeck is divided into transverse strips, assumed to be supported on rigid supports at the center of thegirders.

CIP Concrete Deck

Bulb Tee - BT54

Type 7

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UNFACTORED DEAD LOADS

Dead Load calculation for analysis model:DCDeck = WC tDeck * 1 ft. = 0.100 klf

DCOverhang = WC tOH * 1 ft. = 0.113 klf

DCBarrier = 0.486 kip at 6.84 in. from edge of deck (see Example 6.3)DWWS = WWS tWS * 1 ft. = 0.036 klf

DWUtl = WUtl 1 ft. = 0.005 klf

Where: DCDeck - self-weight of deck slabDCOverhang - self-weigh of overhangDCBarrier - weight of barrierDWWS - weight of wearing surfaceDWUtl - weight of utilities

0.150 kcf * 8.0 in. / 12 in./ft. * 1.0 ft. =

0.145 kcf * 3.0 in. / 12 in./ft. * 1.0 ft. =

0.150 kcf * 9.0 in. / 12 in./ft. * 1.0 ft. =

Dead Loads moments are calculated for a 1.00 ft. wide section of the bridge deck using approvedstructural analysis methods. This includes continuous beam equations, moment distribution, simplebeam equations, or finite element analysis. Dead Load bending moments shown below are producedby a continuous beam model in CSiBridge 2017 using a uniform load for deck and wearing surface anda point load for barriers.

0.005 ksf * 1 ft. =

Typical Section



Results of analysis:Abbreviation : M100 - moment at girder 1

M150 - moment between supportsM200 - moment at girder 2

M100 (kip-ft)

M150 (kip-ft)

M200 (kip-ft)

DCDeck 0.000 0.403 -0.795DCOverhang -0.904 -0.230 0.444DCBarrier -1.667 -0.425 0.818DWWS -0.113 0.116 -0.231DWUtl -0.040 0.010 -0.020

UNFACTORED LIVE LOADS

Deck superstructure type - k AASHTO T.4.6.2.2.1-1Design section = min of 1/3 flange width or 15.00 in. = 14.33 in. AASHTO 4.6.2.1.6Maximum Live Loads per unit width:

Positive Moment from LL +MLL = 5.69 kip-ft. AASHTO T. A4-1Negative Moment from LL -MLL = -3.06 kip-ft. (interpolated) AASHTO T. A4-1

Load

In lieu of determining an equivalent strip width for bridges with decks supported on three or moregirders, Live Load moment can be determined using AASHTO LRFD Bridge Design SpecificationsAppendix A4 T.A4-1. This table lists positive and negative Live Load moments calculated using theEquivalent Strip Method. Table values include multiple presence factors and the dynamic loadallowance. Interpolation between given values is allowed. To use this table, distance from centerline ofgirder to design section for negative moment has to be calculated first.

In general, Live Load effects can be calculated by modeling the deck as a beam supported on girders,with one or more axles placed side by side. These loads are moved transversely to maximize themoments. To determine Live Load moment per unit width of the bridge, calculated total Live Loadmoment is divided by an equivalent strip width, calculated per equations from AASHTO LRFD BridgeDesign Specifications T.4.6.2.1.3-1.

General Pattern of Moment Distribution Diagram in Deck



FACTORED DESIGN LOADS

Mu = η [γDCMDC + γDWMDW + m γLL(MLL+ IM)]η = 1.0 load modifierγ - load factors specified in AASHTO T.3.4.1-1, T.3.4.1-2m - multiple presence factor, included in values from AASHTO T. A4-1IM - dynamic load allowance, included in values from AASHTO T. A4-1

γDC_max γDC_min γDW_max γDW_min γLLM100 (kip-ft)

M150 (kip-ft)

M200 (kip-ft)

Strength I 1.25 0.90 1.50 0.65 1.75 -8.80 10.06 -5.59Service I 1.00 1.00 1.00 1.00 1.00 -5.78 5.56 -2.84

Controlling positive factored moment +Mu = 10.06 kip-ft.

Controlling negative factored moment -Mu = -8.80 kip-ft.

DECK SLAB STRENGTH DESIGN

Width of the design section b = 12.00 in.

Resistance factor for tension-controlled section φSTR = 0.90 AASHTO 5.5.4.2

Positive Moment Capacity (bottom reinforcement)Try Bar size # 5

Bar spacing s = 9.00 in.

Bar diameter db = 0.625 in.

Bar area Ab = 0.31 in.2

Load Combination

Note - it is conservative to use minimum load factors for positive values of M100 and M200 and negative values of M150.

Load Factors Design Moments

Concrete decks must be investigated for strength, service and extreme limit states. Fatigue andfracture limit states do not need to be investigated (AASHTO 9.5).

Design of deck reinforcement, including flexural resistance, limits of reinforcement, and control ofcracking is based on AASHTO LRFD Bridge Design Specifications 5.7.3 (typical rectangular beamdesign). The following design method can be used for normal weight concrete with specifiedcompressive strengths up to 15.0 ksi. Refer to Section 9, Deck and Deck Systems, of this BDM forinformation about acceptable deck reinforcement sizes and spacing.



Area of steel per design stripAS = b (Ab / s) = 0.41 in.2/ft.

Effective depth of sectiondS = tDeck - cBot - 1/2 db = 6.69 in.

Depth of equivalent stress block

0.54 in.

Factored flexural resistance

= 0.90 * 0.41 in. * 60.0 ksi * (6.69 in. - 0.54 in. / 2) / 12 in./ft. = 11.84 kip-ft.

> OK

Negative Moment Capacity (top reinforcement)Try Bar size # 5


Bar Diameter db = 0.625 in.

Bar Area Ab = 0.31 in.2

Area of steel per 1.00 ft. design stripAS = B (Ab / s) = 0.41 in.2/ft.

Effective depth of sectiondS = tDeck - cTop - 1/2 db = 5.69 in.


0.54 in.


= 0.90 * 0.41in. * 60.0 ksi * (5.69 in. - 0.54 in. / 2) / 12 in./ft. = 10.00 kip-ft.

> OK

Minimum Reinforcement AASHTO 5.7.3.3.2

• 1.33 times the positive factored ultimate moment• Cracking moment

Cracking moment AASHTO 5.7.3.3.2-1

Unless otherwise specified, the amount of prestressed and non-prestressed tensile reinforcement shallbe adequate to develop a factored flexural resistance, Mr = φMn, at least equal to the lesser of:

12.0 in. * 0.310 in. / 9.0 in. =

8.0 in. - 1.0 in. - 0.625 in. / 2 =

0.41 in. * 60.0 ksi / (0.85 * 4.5 ksi * 12 in.) =

10.06 kip-ft.

0.41 in./ft. * 60.0 ksi / (0.85 * 4.5 ksi * 12 in.) =

8.80 kip-ft.

12 in. * 0.310 in. / 9.00 in. =

8.0 in. - 2.0 in. - 0.625 in. / 2 =

10.00 kip-ft.

11.84 kip-ft.

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Where:

Flexural cracking variability factor γ1 = 1.60 (non-segmental brg.)

Ratio of specified min. yield strength to ultimate tensile strength γ3 = 0.67 (A615 steel)

Concrete density modification factor λ = 1.00 AASHTO 5.4.2.8

Modulus of rupture 0.51 ksi AASHTO 5.4.2.6

Section modulus of design section 128.00 in.3

- Check Positive Moment reinforcement1.33 (+Mu) = 13.38 kip-ft.

Mcr = 5.83 kip-ft.

> OK

- Check Negative Moment reinforcement1.33 (-Mu) = 11.70 kip-ft.

Mcr = 5.83 kip-ft.

> OK

CONTROL OF CRACKING AT SERVICE LIMIT STATE

AASHTO 5.7.3.4-1

In which: γe = 1.00

s -

fss -

dc -

- Check Cracking at the Bottom of Deck (spacing of Positive Moment reinforcement):dc = cBot + 1/2 db = 1.31 in.

1.28

Tension reinforcement ratio 0.0051

When simplified by removing all values applicable to prestressed and noncomposite sections, thisequation becomes the following:

Cracking is controlled by the spacing of mild steel reinforcement in the layer closest to the tension face,which shall satisfy the following (need not be less than 5.00 in.):

calculated tensile stress in mild steel reinforcement at the service limit state (≤ 0.60 fy ksi)

thickness of concrete cover measured from extreme tension fiber to center of the flexural reinforcement located closest thereto. For calculation purposes, dc need not be taken greater than 2 in. plus the bar radius

- exposure factor (1.0 for Class 1 and 0.75 for Class 2) (assume waterproofing membrane is used)

5.83 kip-ft.

0.41 in. / (12 in. * 6.69 in.) =

1.00 in. + 0.625 in. / 2 =

1 + 1.31 in. / [0.7 (8.0 in. - 1.31 in.)] =

ratio of flexural strain at the extreme tension face to the strain at the centroid of thereinforcement layer nearest the tension face

11.84 kip-ft.

12.0in. * (8.0 in.) / 6 =

0.67 * 1.60 * 0.51 ksi * 128.0 in. / 12 in./ft. =10.00 kip-ft. 5.83 kip-ft.

1.33 * 10.06 kip-ft. =0.67 * 1.60 * 0.51 ksi * 128.0 in. / 12 in./ft. =

1.33 * 8.80 kip-ft. =

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0.230.92

26.44 ksi

18.06 in.

Spacing of positive moment reinforcement used in the design = 9.00 in.

< OK

- Check Cracking at Top of Deck (spacing of Negative Moment reinforcement):dc = cTop + 1/2 db = 2.31 in.

1.58

Tension reinforcement ratio 0.0060

Modular ratio n = ES / EC = 6.54

0.240.92

32.32 ksi

9.09 in.

Spacing of negative moment reinforcement used in the design = 9.00 in.

< OK

LONGITUDINAL REINFORCEMENT

AASHTO 5.10.8-1

AASHTO 5.10.8-2As,min = 1.3 * 12.0 in.* 8.0 in. / [2 (12.0 in. + 8.0 in.) 60.0 ksi] = 0.052 in.2/ft.

As,min = 0.11 in.2/ft. - controls

Minimum reinforcement is required in all directions to accommodate shrinkage and temperaturechanges near the surface of the slab. Longitudinal reinforcement on each face shall meet the following:

2.0 in. + 0.625 in. / 2 =

700 * 1.00 / (1.28 * 26.44 ksi) - 2 * 1.31in. =

5.56 kip-ft. * 12in./ft. / (0.41 in. * 0.92 * 6.69 in.) =

29000 ksi / 4435 ksi =

9.00 in. 9.09 in.

9.00 in. 18.06 in.

1+ 2.31 in. / [0.7 * (8.0 in. - 2.31 in.)] =

0.41 in. / (12 in. * 5.69 in.) =

5.78 kip-ft. * 12in./ft. / (0.41 in. * 0.92 * 5.69 in.) =

700 * 1.00 / (1.58 * 32.32 ksi) - 2 * 2.31 in. =

Also, per Section 9.6 of this BDM, the minimum longitudinal reinforcing steel in the top of the concretebridge deck shall be #4 @ 6.00 in. Longitudinal reinforcement in the bottom of the deck slab can bedistributed as a percentage of the primary reinforcement for positive moment.

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Top reinforcement try # 4 @ 6.00" on center: AS = 0.40 in.2/ft.

OK

Effective span length 7.42 ft. AASHTO 9.7.2.3Amount of reinforcement required in secondary direction in the bottom of the slab

81% Use - 67% AASHTO 9.7.3.2

Area of primary reinforcement for positive moment = 0.41 in.2/ft.

Required area of bottom longitudinal steel: AS_Req = 67% * 0.41 in./ft.= 0.27 in.2/ft.

Bottom reinforcement try # 5 @ 12.00" on center: AS = 0.31 in.2/ft.

OKOK

DECK SECTION SUMMARYDeck Depth 8.00 in.

Top Transverse Reinforcement # 5 @ 9.00"Bottom Transverse Reinforcement # 5 @ 9.00"Top Longitudinal Reinforcement # 4 @ 6.00"Bottom Longitudinal Reinforcement # 5 @ 12.00"

8.0 ft. - 7.0in. / 12in./ft. =

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Deck Section Summary

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EXAMPLE 6.2 - OVERHANG DESIGN

GENERAL INFORMATIONBridge deck overhang shall be designed for three separate design cases: AASHTO A13.4.1• Case 1 - Horizontal and longitudinal forces from vehicle collision load (Extreme Event II limit state)• Case 2 - Vertical force from vehicle collision load (Extreme Event II limit state)• Case 3 - Vertical Dead and Live Load at the overhang section (Strength I limit state)

Barrier typeWidth of barrier base WB = 18.00 in.

Barrier weight WBarrier = 0.486 kip/ft. (see Example 6.1, Deck Design)

Deck overlay density WWS = 0.145 kcf Section 3.4.2Concrete density WC = 0.150 kcf

Barrier center of gravity XC.G. = 6.84 in.

Axial load per unit length TAxial = 7.18 kip/ft. (refer to Example 6.3)

Moment capacity of the barrier MC = 16.16 kip-ft./ft. (refer to Example 6.3)

Critical length of yield line LC = 10.74 ft. (refer to Example 6.3)

Overhang width SOH = 4.00 ft.

Edge of deck to edge of flange SGdr_Edge = 2.21 ft.

Overhang minimum depth tOH(min) = 8.00 in.

Overhang maximum depth tOH(max) = 10.00 in. (at exterior edge of flange)

Concrete top cover cTop = 2.00 in. AASHTO T.5.12.3-1Concrete strength f'c = 4.50 ksi

Reinforcement strength fy = 60.00 ksi

DESIGN CASE 1: HORIZONTAL VEHICULAR COLLISION LOAD

The deck overhang region shall be designed to have resistance larger than the resistance of theconcrete barrier. Therefore, resistance of approved barriers must be established first. Refer to Example6.3 for detailed strength calculations for Barrier Type 7 and to Example 6.4 for Barrier Type 10M.

Type 7 (Overhang design with Barrier Type 10M issimilar)

The deck overhang is designed to resist an axial tension force from vehicular collision actingsimultaneously with the Dead Load moment. The design moment critical section shall be taken at one-third of the flange width from the centerline of exterior girder (AASHTO 4.6.2.1.6). Loads can beassumed to be distributed at a 45° angle starting from the face of the barrier.



1. Design Loads - Dead Load and CollisionDistance from edge of deck to design section K = 2.81 ft. AASHTO 4.6.2.1.6Distance from barrier face to design section X = 1.31 ft.

Depth of the section under consideration hDesign = 8.00

Bending moments from dead load of structural components and nonstructural attachments:Barrier MDC-Barrier = WBarrier * (K - XC.G.) = 0.486 kip * (2.81 ft. - 6.84 in. / 12 in./ft.) = 1.09 kip-ft.

Deck MDC-Deck = WC * tOH(min) * K2 / 2 = 0.150 kcf * 8 in. / 12 in./ft. * (2.81 ft.) / 2 = 0.39 kip-ft.

Additional overhang concrete MDC-Add = 0.5 WC * SGdr_Edge (TOH(max) - TOH(min)) * (K - 2/3 SGdr_Edge) == 0.5 * 0.150 kcf * 2.21 ft. * (10.0 in. - 8.0 in.) / 12 in./ft. * (2.81 ft. - 2/3 * 2.21 ft.) = 0.037 kip-ft.

Total DC = MDC-Barrier + MDC-Deck + MDC-Add = 1.517 kip-ft.

Bending moments from wearing surfaces and utilities:Deck overlay

MDW-WS = WC * 3 in. * X2 / 2 = 0.145 kcf * 3in. / 12 in./ft. * (1.31 ft.) / 2 = 0.031 kip-ft.

Bending moment from vehicular collision MCT = MC = 16.16 kip-ft.

1.09 kip-ft.+0.39 kip-ft.+0.037 kip-ft. =

Both design bending moment and design axial tension are calculated based on the properties of thebarrier on the deck. See Example 6.3 for information about Barrier Type 7 and Example 6.4 forinformation about Barrier Type10M. Per AASHTO A.13.4.2, live load collision moment is taken to equalthe flexural capacity of the barrier.

in. (may add min haunch depth if needed, conservative to use constant deck depth)

Overhang Region - Design Case 1

2

2



Design factored moment (Extreme Event II) AASHTO 3.4.1, A13.4.1Mu1 = 1.0MDC + 1.0MDW + 1.0MCT = 1.517 kip-ft. + 0.031 kip-ft. + 16.16 kip-ft. = 17.71 kip-ft.

Design axial tensile load TAxial = 7.18 kip/ft.

2. Resistance of the SectionTop transverse reinforcement: Bar size # 5 (see Example 6.1)


Area of steel per design strip AS = b (Ab / s) = 12 in. * 0.31 in. / 9.0 in. = 0.41 in.2/ft.

Effective depth of section dS = hDesign - cTop - 1/2 db = 8 in. - 2 in. - 0.625 in./ 2 = 5.69 in.

Maximum allowable tension in reinforcement TReinf = ASFy = 0.41 in.* 60.0 ksi = 24.60 kip


24.60 kip / (0.85 * 4.50 ksi * 12 in.) = 0.54 in.


= 1.0 [24.60 kip (5.69 in. - 0.54 in./ 2) - 7.18 kip (8.00 in./ 2 - 0.54 in./ 2)] /12 in./ft. = 8.88 kip-ft./ft.

< FAILS *

With additional overhang bars # 5 @ 4.50" (one additional bar between top deck reinf.)

Area of steel per design strip AS = 12 in. (Ab / db) = 12 in. * 0.310 in. / 4.5 in. = 0.83 in.2/ft.

Effective depth of section dS = hDesign - cTop - 1/2 db = 8 in. - 2 in. - 0.625 in./ 2 = 5.69 in.

Maximum allowable tension in reinforcement TReinf = ASFy = 0.83 in.* 60.0 ksi = 49.80 kip


49.80 kip / (0.85 * 4.50 ksi * 12 in.) = 1.08 in.


= 1.0 [49.80 kip (5.69 in. - 1.08 in./ 2) - 7.18 kip (8.00 in./ 2 - 1.08 in./ 2)] /12 in./ft. = 19.30 kip-ft./ft.

> OK

8.88 kip-ft. 17.71 kip-ft.

17.71 kip-ft.19.30 kip-ft.

* Top deck reinforcement is not sufficient to resist collision moment and tension. Increase sizeof the top deck reinforcement or place additional bars in overhang region.

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DESIGN CASE 2: VERTICAL COLLISION FORCE

DESIGN CASE 3: DEAD AND LIVE LOADS AT STRENGTH LIMIT STATE

Distance from edge of deck to design section K = 2.81 ft.

Distance from barrier face to design section X = 1.31 ft.

Depth of the section under consideration hDesign = 8.00 in.

Distance from LL application to design section z = 0.31 ft.

Live Load multiple presence factor m = 1.20 AASHTO T.3.6.1.1.2-1Dynamic load allowance IM = 33% AASHTO 3.6.2

The overhang is designed to resist gravity forces from the Dead Load of structural components andattachments to the cantilever, as well as a concentrated Live Load positioned 12.00 in. from the face ofthe barrier. This case rarely controls the design, except for decks with widely spaced girders that allowthe use of wider overhangs.

For decks with overhangs not exceeding 6.00 ft. measured from the centerline of the exterior girder tothe face of a structurally continuous concrete railing, the outside row of wheel loads may be replacedwith a uniformly distributed line load of 1.0 klf intensity per AASHTO LRFD Bridge Design Specifications 3.6.1.3.4.

Based on common practice, the case of vertical collision never controls the design of concreteoverhangs; therefore, it does not have to be checked.

Overhang Region - Design Case 3



Bending moment from Dead Loads (equal to the loads calculated for Design Case 1)Barrier MDC-Barrier = 1.09 kip-ft.

Deck MDC-Deck = 0.39 kip-ft.

Add. overhang concrete MDC-Add = 0.037 kip-ft.

Deck overlay MDW-WS = 0.031 kip-ft.

Bending moment from live load MLL = 0.31 kip-ft.

Design factored moment (Strength I) Mu3 = 1.25MDC+1.50MDW+1.75m(MLL+IM) == 1.25 * 1.52 kip-ft. + 1.50 * 0.031 kip-ft. + 1.75 * 1.20 * 1.33 * 0.31 kip-ft. = 2.81 kip-ft.

DETAILS OF REINFORCEMENT

1. Location at Which Additional Overhang Reinforcement is no Longer Required

2.50 ft.

Girder 1 10% 20% 30% 50% 70% 80% 90% Girder 2Mu1 -12.08 -10.27 -8.46 -6.64 -3.02 0.60 2.42 4.23 6.04Mu3 -1.92 -1.63 -1.34 -1.06 -0.48 0.10 0.38 0.67 0.96Mu1 - Bending moment from Collision Load, Design Case 1 (Extreme event condition)Mu3 - Bending moment from Live and Dead Load, Design Case 3 (Strength I condition)

Negative moment capacity of the section φMn = -10.00 kip-ft. (see Deck Design section)

This moment shall be reduced due to the axial tension force:

* Design moment for this case is smaller than the design moment in Case 1; therefore, Design Case 3will not control the design.

The additional bars placed in the top of the deck overhang must extend beyond the centerline of theexterior beam into the first interior bay. The cutoff length will occur when the sum of collision and DeadLoad moments equals the negative moment strength of the typical deck reinforcement.

Assume that 50% of the bending moment experienced at the design section of the exterior girdercarries over to the next girder (conservative estimate, true for restrained rotation at first interior girder).The design moment over the exterior girder is calculated assuming a 45° load distribution angle.

Bending Moment Along the First Interior Bay

1.0 klf * 0.31 ft. =



1.0 (-10.0 kip-ft.)(1 - 7.18 kip / (1.0 * 49.80 kip)) = -7.08 kip-ft.

Length of the first interior bay SGdr = 8.00 ft.

Distance from edge of deck to CL Ext. Girder SOH = 4.00 ft.

Distance from CL Ext. Girder to point of -M capacity = 2.21 ft. (28)%

Location where additional reinforcement is no longer required = 6.21 ft. (from edge of deck)

2. Embedment Length Beyond the Point Where no Longer Required

dS = 5.69 in. AASHTO 5.11.1.2.1Cut-off length = max 15 db = 9.38 in.

1/20 LSpan = 4.80 in.

9.38 in.

Development length, AASHTO 5.11.2.1

2.4 * 0.625 in.* 60.0 ksi / 4.5 ksi = 42.43 in.

λrl = 1.00 λer = 1.00 (conservative)

λcf = 1.20 λ = 1.00λrc = 0.40

20.37 in. (controls)

Theoretical length of additional overhang bar = 7.74 ft.Use - 8.00 ft.

42.43 in.* 1.00 * 1.20 * 0.40 * 1.00 / 1.00 =

6.21 ft. + 20.37 in. - 2 in. clr =

Extend additional overhang reinforcement beyond the point at which it is no longer required to resistflexure for a distance of not less than the cut-off length or the development length, whichever is greater.

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OVERHANG SECTION SUMMARYTop Deck Reinforcement # 5 @ 9.00"Additional Overhang Bars 8.00 ft. # 5 @ 4.50"Bottom Longitudinal Bars in Overhang # 5 @ 6.00"

Overhang Section Summary



EXAMPLE 6.3 - BARRIER TYPE 7 STRENGTH DESIGN

GENERAL INFORMATION

Overall barrier height HB = 35.00 in.

Concrete strength f'c = 4.50 ksi (Concrete Class D compressive strength)

Reinforcement strength fy = 60.00 ksi (Specified minimum yield strength of grade 60 steel)

Concrete cover c = 2.00 in.

Resistance factor φ = 1.00 (Extreme Event) AASHTO 1.3.2.1Test level TL-4 AASHTO T A13.2-1Transverse design force Ft = 54.00 kips

Impact force distribution Lt = 3.50 ft.

Barrier DimensionsSection1 Section2 Section3

Section top width 10.50 13.00 18.00 in.

Section bottom width 13.00 18.00 18.00 in.

Section height 24.00 7.00 4.00 in.

Center of gravity from back face XC.G. = 6.84 in.

The CDOT Bridge Rail Type 7 design follows the AASHTO LRFD Bridge Design Specifications A13.3.1 design procedure for concrete railings, using strength design for reinforced concrete. The Bridge Rail Type 7 shall be designed for Test Level 4 (TL 4) as required by CDOT. See CDOT Worksheet B-606-7A for barrier details. The following calculations show case of impact within barrier segment, assuming that barrier will be extended past the limits of the bridge. For cases concerning impact at end of the barrier, refer to AASHTO Appendix A13.

Barrier Type 7



BARRIER FLEXURAL CAPACITY

# 4 @ 8.00" Bar Diameter = 0.500 in.

Bar Area = 0.20 in.2

AS

(in.2)h(avg)(in.)

dS(in.)

b(in.)

k=.85f'Cb a=ASfy/k(in.)

φMn(kip-ft.)

MC(kip-ft./ft.)

Section 1 0.30 11.75 9.50 12.00 45.90 0.39 13.96 9.57Section 2 0.30 15.50 13.25 12.00 45.90 0.39 19.58 3.92Section 3 0.30 18.00 15.75 12.00 45.90 0.39 23.33 2.67

Barrier MC = 16.16 kip-ft./ft.

AS - area of steel per design striph(avg) - average section width

dS - effective depth of design sectionb - width of design stripa - depth of equivalent stress block

2. Determine M W : flexural resistance of the parapet about its vertical axis.

Size = # 4 Bar Diameter = 0.500 in.

Bar Area = 0.20 in2

Stirrup Dia. = 0.50 in.

No. of Bars

AS

(in.2)h(avg)(in.)

dS(in.)

b(in.)

k=.85f'Cb a=ASfy/k(in.)

φMW(kip-ft.)

Section 1 3.00 0.60 11.75 9.00 24.00 91.80 0.39 26.42Section 2 1.00 0.20 15.50 12.75 7.00 26.78 0.45 12.53Section 3 1.00 0.20 18.00 15.25 4.00 15.30 0.78 14.86

Barrier MW = 53.81 kip-ft.

Front face vertical reinforcement:

Front and back face horizontal reinforcement

1. Determine M C : flexural resistance of cantilevered parapet about an axis parallel to the longitudinalaxis of the bridge. Flexural moment resistance is based on the vertical reinforcement in the barrier.

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3. Rail resistance within a wall segment.

AASHTO A13.3.1-1

AASHTO A13.3.1-2

Additional flexural resistance at top of wall Mb = 0.00 kip-ft.

Critical length of yield line LC = 10.74 ft.

Nominal transverse load resistance RW = 118.97 kips

Capacity Check Check R W > F t : 118.97 > 54.00 OK

BARRIER INTERFACE SHEAR CAPACITY AASHTO 5.8.4

Interface width considered in shear transfer bV= 18.00 in.

Interface length considered in shear transfer LV = 12.00 in.

Shear contact area ACV = bV LV = 216.00 in.2

Shear reinforcement at front face # 4 @ 8.00" Bar Area = 0.20 in.

Area of shear reinforcement AVF = 12.0 in. * 0.20 in. / 8.00 in. = 0.30 in.2/ft.

0.18 OK AASHTO 5.8.4.4-1

Permanent compression force from barrier weight (neglected) Pc = 0.00 kip

For concrete placed against clean concrete surface, free of laitance, but not intentionally roughenedCohesion factor c = 0.075 ksi AASHTO 5.8.4.3Friction factor μ = 0.6Shear factor 1 K1 = 0.2 (Fraction of concrete strength available to resist interface shear)

Shear factor 2 K2 = 0.8 ksi (Limiting interface shear resistance)

194.40 kip AASHTO 5.8.4.1Vn = min 172.80 kip

27.00 kip

Evaluate the shear capacity of the cold joint to transfer nominal resistance RW between the deck andrailing. Neglect effects of barrier Dead Load and assume that the surface of the deck is not roughened.

0.20 * 4.50 ksi * 216.0 in. =0.80 * 216.0 in. =

0.075 ksi*216in.+0.60(0.30 in.* 60 ksi+0kip) =

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Resistance factor φ = 1.00 (Extreme Event) AASHTO 1.3.2.1

Factored Shear Resistance φVn = 27.00 kip

Shear force acting on the barrier per 1.00 ft. strip 11.08 kip/ft.

Capacity Check Check φV n > V u : 27.00 > 11.08 OK

OVERHANG DESIGN DATA

TAxial = RW /(LC + 2HB) AASHTO A13.4.2

Axial Load Per Unit Length of the Deck TAxial = 7.18 kip/ft.

Moment Capacity of the Barrier Mc = 16.16 kip-ft./ft.

Barrier Type 7 satisfies all checks outlined in AASHTO LRFD Bridge Design Specifications Appendix13. Use the following data for Deck overhang design when Barrier Type 7 is used (Test Level 4):



EXAMPLE 6.4 - BARRIER TYPE 10M STRENGTH DESIGN

GENERAL INFORMATION

See CDOT Worksheet B-606-10 for barrier details.

Overall barrier height HB = 35.00 in.

Concrete cover c = 2.00 in.

Resistance factors φEE = 1.00 (Extreme Event) AASHTO 1.3.2.1φS = 0.80 (A325 bolts in shear) AASHTO 6.5.4.2φT = 0.80 (A325 bolts in tension) AASHTO 6.5.4.2

Test level TL-4 AASHTO T.A13.2-1Transverse design force Ft = 54.00 kips

Impact force distribution Lt = 3.50 ft.

CONCRETE PARAPETHeight HW = 13.50 in.

Average width d = 17.75 in.

f'c = 4.50 ksi

fy = 60.00 ksi

RAIL POSTType W8x18Steel gradePost spacing L = 10.00 ft. (max)

Effective height HR = 27.25 in.

Area of post APost = 5.26 in.2

Web depth D = 7.48 in.

Web thickness tW = 0.23 in.

Flange thickness tF = 0.33 in.

Fy (post) = 50.00 ksi

Zx-x (post) = 17.00 in.3

ASTM A-572, Grade 50

CDOT Bridge Rail Type 10M consists of a concrete parapet and a metal rail. The resistance totransverse vehicular impact loads shall be determined as specified in AASHTO LRFD Bridge DesignSpecifications A13.3.3. Two failure modes shall be evaluated: single span (impact at midspan of therail) and two span (impact directly at the center post). The Bridge Rail Type 10M shall be designed forTest Level 4 (TL 4) as required by CDOT.

Barrier Type 10M



RAIL TUBESTypeSteel gradeArea of one tube ATube = 5.26 in.2

Number of tubes nTubes = 2.00 ea.

Fy (tube) = 46.00 ksi

Z (tube) = 9.16 in.3

BASE PLATEWidth of base plate Wb = 8.00 in.

Distance to bolts db = 6.875 in.

Bolt diameter Ø = 1.00 in.

Bolt area Ab = 0.79 in.2

Min tensile strength Fub = 120.00 ksi

Number of bolts nb = 2.00

CONCRETE PARAPET CAPACITY

Size = # 4 Bar Diameter = 0.500 in.

Number of bars = 2.00 Bar Area = 0.20 in2

Stirrup Dia. = 0.50 in.

Design strip, b = 13.50 in.

Area of steel per design strip AS = Bar Area * NO. of bars = 0.40 in.2/ft.

Effective depth of section dS = d - c - 1/2 Bar Dia. - Stirrup Dia. = 15.00 in.


0.40 in. * 60.0 ksi / (0.85 * 4.50 ksi * 13.5 in.) = 0.46 in.

Flexural resistance

1.0 * 0.40 in. * 60.0 ksi * (15.00 in. - 0.46 in. / 2) / 12 in./ft. = 29.54 kip-ft.

TS 5x5x5/16ASTM A-500, Grade B

1. Determine M W : flexural resistance of the parapet about its vertical axis. Positive and negative moment strength must be evaluated but will be equal based on barrier longitudinal reinforcement.

Back face horizontal reinforcement

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Area of reinforcement for last iteration AS = 0.20 in2 * 6 bars / LC = 0.189 in.2/ft.

Depth of equivalent stress block 0.25 in.

Flexural moment resistance 14.80 kip-ft./ft.

Critical length of yield line failure pattern 6.34 ft.

There is no additional resistance at the top of the parapet in addition to MW , Mb = 0 kip-ft.Values of Lt (longitudinal length of distribution of impact force) are found in AASHTO Table A.13.2-1.

3. Determine R W (nominal railing resistance to transverse load) within a wall segment.

166.69 kip AASHTO A13.3.1-1

4. Calculate applied collision moment MCT .

19.34 kip-ft./ft. > MC = 14.80 kip-ft./ft.

5. Calculate tensile force per unit of deck length, T.

0.77

Axial load per unit length 14.94 kip/ft.

When MCT > MC, the concrete curb will fail at 54 kip TL4 transverse force (CT). Axial tensile force may be reduced by (MC / MCT) for overhang deck reinforcing design.

2. Determine M C : flexural resistance of cantilevered parapet about an axis parallel to the longitudinal axis of the bridge. Flexural moment resistance is based on the vertical reinforcement in the barrier within L C (critical length of yield line failure pattern).

This is an iterative process, since MC and LC depend on each other. Start with calculating MC for a 1 foot section of the barrier, then revise the amount of reinforcement based on the calculated value of LC

(AASHTO A13.3.1-2).

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ANCHOR BOLT CAPACITY AND PUNCHING SHEAR CHECK

SUMMARY

Controlling Axial Load Per Unit Length of the Deck TAxial = 14.94 kip/ft.

Deck Overhang Moment Md = 14.80 kip-ft./ft.

Barriers similar to Bridge Rail Type 10M were crash tested and determined to be satisfactory for theTest Level 4 loads. Therefore, it is assumed that anchor bolt shear and concrete punching shear arenot critical failure modes. These checks will be omitted for the purpose of this design example.

Single span failure mode with impact between posts controls the strength design of the rail. Becauseimpact load on the rail will be transferred to the overhang through the post connection, results from thisfailure mode will also control design of the deck overhang. Use the following values for deck overhangdesign when Barrier Type 10M is used (Test Level 4):

Documents

EXAMPLE 6 - DECK DESIGN, INCLUDING COLLISION …...Design of deck reinforcement, including flexural resistance, limits of reinforcement, and control of cracking is based on AASHTO