Reinforced Concrete Slab Design Using the Empirical Method

Reinforced Concrete Slab Design Using the Empirical Method BridgeSight Solutions for the AASHTO LRFD Bridge Design Specifications BridgeSight Software TM Creators of effective and reliable solutions for the world s bridge engineers 2688 Venado Way Rescue, CA 95672 Phone: 530-672-1569 E-mail: rdp@bridgesight.com Internet: www.bridgesight.com

Title Reinforced Concrete Slab Design Using The Empirical Method Publication No. BSS09011999-1 Abstract This design example illustrates the Empirical Design Method for composite concrete bridge decks specified in Article 9.7.2 of the AASHTO LRFD Bridge Design Specification. Notes Author Staff - BridgeSight Software Sponsor BridgeSight Software 2688 Venado Way Rescue, CA 95672 Specification AASHTO LRFD Bridge Design Specification, 2 nd Edition 1998 Original Publication Date 9/1/99 Date of Latest Revision 9/1/99 Version 1.0 Notice of Copyright Copyright 1999 BridgeSight Software, All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means (electronic, mechanical, photocopied, recorded, or otherwise), without prior written permission from BridgeSight Software. i

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Introduction One of the first components of a bridge that you will design is the deck. The AASHTO LRFD Bridge Design Specification suggests three different methods for the analysis of bridge decks for slab-on-beam systems. This installment of the BridgeSight Solutions series will give a brief overview of the different analysis methods and will focus on the Empirical Method of design. The Empirical Method is by far the easiest method provided the bridge configuration, materials, and construction techniques satisfy some minimum criteria. This design example is part of the BridgeSight Solutions series. The BridgeSight Solutions series is comprised of design aids and design examples to assist practicing engineers and engineering students learn and implement the AASHTO LRFD Bridge Design Specification. Visit the BridgeSight Solutions section of our web site at www.bridgesite.com for more information. 1

Analysis Methods for Decks The LRFD Specification suggests three methods of analysis for slab-on-beam bridge decks; approximate elastic methods, specified in Article 4.6.2.1, refined methods, specified in Article 4.6.3.2, or an empirical design method for concrete slabs specified in Article 9.5 The approximate elastic method of analysis simulates the behavior of the bridge deck with transverse strips of deck. The strips are run from edge-to-edge of the bridge deck and are modeled as continuous beams supported at the centerlines of the girders. The refined method of analysis consist of modeling the bridge deck and girder system with finite elements. This is a time consuming process and difficult to validate. Such a method should only be used for special structures. The empirical method is a no analysis method in which a prescribed amount of reinforcement is to be provided in the slab. This BridgeSight Solution will focus on the Empirical Method. Code Reference 9.6.1 Empirical Design Method This example will illustrate the empirical design method. The empirical design applies only to the main part of the slab and is not to applied to overhangs. Design of the overhang is beyond the scope of this BridgeSight Solution. For continuous bridge decks, the contribution of the longitudinal bars may be utilized for resisting negative moments at interior supports. 9.5.1, 9.7.2 Given The cross section and span configuration show below Alignment of bridge is N 90 E Bearing of piers is N 27 E (27 skew angle) Slab concrete has a 28-day strength of 28MPa. The slab is cast-in-place and water cured. Assume a 15 sacrificial wearing surface. Full depth diaphragms are used at lines of supports Slab and girders are made composite Traffic barriers are composite and structurally continuous with the overhang 240 910 1175 Pier 1-5 spaces @ 2 000 = 10 000 Pier 2-5 spaces @ 2 500 = 12 500 Typical Section (All Dimensions Normal To Alignment) 1175 2

Code Reference 28 000 Span Configuration Determine Effective Length Because of the flared girder lines and the skewed piers, we need to use a coordinate geometry (COGO) model to quickly find the effective length. 9.7.2.3 L 1 L 1 /3 C 5 1 7 3 Girder A Girder B 11 12 2 6 L 2 /3 C 10 9 8 2C 4 L 2 Centerline of Bridge Pier 1 Pier 2 Framing Plan/COGO Model (Girders C-F Omitted for Clairity) The Framing Plan/COGO Model is shown above. The coordinates of the various points shown in the model are: Point X () Y () 1 0 6000 2 28000 7500 3 3142 6168 4 31928 7710 5 0 4000 6 28000 5000 7 2075 4074 8 30595 5093 9 30462 7631 10 29127 5040 11 22333 7196 12 21088 4753 Some important distances are: Item Distance () L 1 28827 3

Item Distance () Code Reference L 2 28537 2C 2938 S effective between points 9 and 10 2742 S effective between points 11 and 12 2915 Effective Length 2915 Design Depth of Slab Design depth is the gross depth of the slab, less any depth that is expected to be lost as a result of grinding, grooving, or wear. Design Depth = 240-15 = 225 Effective Length to Design Depth Ratio The effective length to design depth ratio is 2915/225 = 13 Core Depth Core slab depth is shown in the figure below. It can be computed as Core Depth = Gross Slab Depth - Top Cover - Bottom Cover Core Depth Reinforcement Slab Depth Top Cover = 65 (Deck surfaces subject to tire stud or chain wear) Table 5.12.3-1 Bottom Cover = 25 (Bottom of cast-in-place slabs, Up to No. 36 bar) Core Depth = 240-65 - 25 = 150 Check Design Conditions The design conditions listed below must be satisfied to use the empirical design method. If these conditions are met and the reinforcement provisions are satisfied, for other than the deck overhang, the deck may be assumed to satisfy service, fatigue and fracture, and strength limit states requirements. 9.5.1 9.7.2.4 Criteria Cross-frames or diaphragms are used throughout the cross-section at lines of support; For cross-section involving torsionally stiff units, such as individual separated box beams ; Satisfied (/No) N/A The supporting components are mode of steel and/or concrete; Precast Concrete I- Beams The deck is fully cast-in-place and water cured; Check your standard 4

Criteria The deck is of uniform depth, except for haunches at girder flanges and other local thickening; The ratio of effective length to design depth does not exceed 18.0 and is not less than 6.0; Satisfied (/No) specifications! 6 13 18 Core depth of the slab is not less than 100 ; 150 > 100 The effective length, as specified in Article 9.7.2.3, does not exceed 4100; The minimum depth of slab is not less than 175, excluding a sacrificial wearing surface where applicable; There is an overhang beyond the centerline of the outside girder at least 5.0 times the depth of the slab; this condition is satisfied if the overhang is at least 3.0 times the depth of the slab and a structurally continuous concrete barrier is made composite with the overhang; The specified 28-day strength of the deck concrete is not less than 28MPa The deck is made composite with the supporting structural components 2915 < 4100 175 < 225 1175/225 = 5.22 5.22 > 3.0 Code Reference Select Reinforcement The slab configuration satisfies the necessary design conditions. The slab must be reinforced with four layers of isotropic reinforcement. Reinforcement shall be located as close to the outside surfaces as permitted by cover requirements. Reinforcement shall be provided in each face of the slab with the outermost layers placed in the direction of the effective length. The minimum amount of reinforcement shall be 0.570 2 / of steel for each bottom layer and 0.380 2 / of steel for each top layer. Spacing of steel shall not exceed 450. Reinforcing steel shall be Grade 420 or better. Because the skew angle for this structure exceeds 25, the specified reinforcement in both direction shall be doubled in the end zones of the deck. Each end zone shall be taken as a longitudinal distance equal to the effective length of the slab specified in Article 9.7.2.3. 9.7.2.5 Bottom Layer Reinforcement Use two layers of No. 16 bars. The cross-sectional area of a No. 16 bar is 199 2. The maximum 199 2 allowable spacing of No. 16 bars is 2 350 0570.. = Use No. 16 bars at 175 in the end zones and No. 16 bars at 350 elsewhere. Top Layer Reinforcement Use two layers of No. 13 bars. The cross-sectional area of a No. 13 bar is 129 2. The maximum 129 2 allowable spacing of No. 13 bars is 2 340 0. 380. = Use No. 13 bars at 170 in the end zones and No. 13 bars at 340 elsewhere 5

Appendix Conversion Factors Multiply By To Produce in 25.40 ft 0.3048 m in 2 645.2 2 ft 2 0.0929 m 2 in 3 16387 3 ft 3 0.0283 m 3 in 4 416231 4 ft 4 0.00863 m 4 lbf 4.448 N kip 4.448 kn ton 8.896 kn lbf/in 0.175 N/ lbf/ft 0.015 N/ kip/in 175.2 kn/m kip/ft 14.6 kn/m lbf 0.453 kg lbm 0.453 kg slug 14.594 kg ft/sec 2 0.3048 m/sec 2 psi 6894.757 Pa ksi 6.895 MPa psf 47.88 Pa ksf 0.04788 MPa F ( t-32 )/1.8 C Reinforcing Bar Properties Bar Size Nominal Mass Nominal Diameter Nominal Area Bar Size Nominal Weight Nominal Diameter Nominal Area No. kg/m 2 No lb/ft in in 2 10 0.560 9.5 71 3 0.376 0.375 0.11 13 0.994 12.7 129 4 0.668 0.500 0.20 16 1.552 15.9 199 5 1.043 0.625 0.31 19 2.235 19.1 284 6 1.502 0.750 0.44 22 3.042 22.2 387 7 2.044 0.875 0.60 25 3.973 25.4 510 8 2.670 1.000 0.79 29 5.060 28.7 645 9 3.400 1.128 1.00 32 6.404 32.3 819 10 4.303 1.270 1.27 36 7.907 35.8 1006 11 5.313 1.410 1.56 43 11.380 43.0 1452 14 7.650 1.693 2.25 57 20.240 57.3 2581 18 13.600 2.254 4.00 A-1