Contraflexure Points for Continuous Highway Bridges
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1 Contraflexure Points for Continuous Highway Bridges 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 Phone: rdp@bridgesight.com Internet:
2 Title Contraflexure Points For Continuous Highway Bridges Publication No. BSS Abstract This design aid tabulates points of contraflexure due to a uniform load in all spans for two, three, and four span continuous highway bridge structures. This design aid is intended to assist practicing engineers perform routine computations requiring the effective span lengths of a structure. Notes Fixed errors in Table 2.0 US, Table 2.2 SI and Table 2.2 US. Thanks to Mark Doerflinger of George Butler Associates, Inc. for bringing these errors to our attention. Author Staff - BridgeSight Software Sponsor BridgeSight Software 2688 Venado Way Rescue, CA Specification AASHTO LRFD Bridge Design Specification, 2 nd Edition 1998 Original Publication Date 1/1/99 Date of Latest Revision 5/4/99 Version 1.1 Notice of Copyright, 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
3 Introduction BridgeSight Software is proud to share with you this time saving design aid for the AASHTO LRFD Bridge Design Specification. Several of the equations and procedures given by the specification make use of effective span lengths, most notably Article application of the dual truck train element of the HL93 live load, Article live load distribution factors, and Article effective flange width. The effective span lengths are taken to be the distance between points of contraflexure due to either the permanent weight of the structure or a unit uniform load applied over the entire length of the structure, depending upon the provision. This design aid tabulates the points of contraflexure for two, three, and four span prismatic, continuous bridges subjected to a unit uniform load, for a total of 456 unique configurations. All of the three and four span configurations are symmetrical about their centerline. The ratio of the interior span lengths to the exterior span lengths is designated by N. Interior spans are equal to or longer than exterior spans. While the tables present discrete bridge configurations, the intervals between span lengths and span ratios are small enough to permit linear interpolation without significant error. This design aid 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 for more information. 1
4 Span Lengths 2
5 Table 1.0 Two-span Continuous Beam Symmetrical Four-Span Continuous Beam L NL L NL NL L (m) N = 1.0 N = 1.1 N = 1.2 N = 1.3 N = 1.4 N = 1.5 N = 1.6 N = Spans 4 Spans L (m) NL (m) L (m) NL (m) L (m) NL (m) L (m) NL (m) L (m) NL (m) L (m) NL (m) L (m) NL (m) L (m) NL (m) (ft) N = 1.0 N = 1.1 N = 1.2 N = 1.3 N = 1.4 N = 1.5 N = 1.6 N = Spans 4 Spans L (ft) NL (ft) L (ft) NL (ft) L (ft) NL (ft) L (ft) NL (ft) L (ft) NL (ft) L (ft) NL (ft) L (ft) NL (ft) L (ft) NL (ft)
6 Table 1.1 Symmetrical Three-Span Continuous Beam L NL L Total N = 1.0 N = 1.1 N = 1.2 N = 1.3 N = 1.4 N = 1.5 N = 1.6 N = 1.7 Length L (m) NL (m) L (m) NL (m) L (m) NL (m) L (m) NL (m) L (m) NL (m) L (m) NL (m) L (m) NL (m) L (m) NL (m) Total N = 1.0 N = 1.1 N = 1.2 N = 1.3 N = 1.4 N = 1.5 N = 1.6 N = 1.7 Length (ft) L (ft) NL (ft) L (ft) NL (ft) L (ft) NL (ft) L (ft) NL (ft) L (ft) NL (ft) L (ft) NL (ft) L (ft) NL (ft) L (ft) NL (ft)
7 Points of Contraflexure 5
8 Table 2.0 SI Two-span Continuous Beam L1 L2 L3 L NL N = 1.0 N = 1.1 N = 1.2 N = 1.3 N = 1.4 N = 1.5 N = 1.6 N = 1.7 Total L1/L L2/L L3/L L1/L L2/L L3/L L1/L L2/L L3/L L1/L L2/L L3/L L1/L L2/L L3/L L1/L L2/L L3/L L1/L L2/L L3/L L1/L L2/L L3/L Length (m) L1 (m) L2 (m) L3 (m) L1 (m) L2 (m) L3 (m) L1 (m) L2 (m) L3 (m) L1 (m) L2 (m) L3 (m) L1 (m) L2 (m) L3 (m) L1 (m) L2 (m) L3 (m) L1 (m) L2 (m) L3 (m) L1 (m) L2 (m) L3 (m)
9 Table 2.0 US Two-span Continuous Beam L1 L2 L3 L NL N = 1.0 N = 1.1 N = 1.2 N = 1.3 N = 1.4 N = 1.5 N = 1.6 N = 1.7 Total L1/L L2/L L3/L L1/L L2/L L3/L L1/L L2/L L3/L L1/L L2/L L3/L L1/L L2/L L3/L L1/L L2/L L3/L L1/L L2/L L3/L L1/L L2/L L3/L Length (ft) L1 (ft) L2 (ft) L3 (ft) L1 (ft) L2 (ft) L3 (ft) L3 (ft) L3 (ft) L3 (ft) L3 (ft) L3 (ft) L3 (ft) L3 (ft) L3 (ft) L3 (ft) L3 (ft) L3 (ft) L3 (ft) L3 (ft) L3 (ft) L3 (ft) L3 (ft) L3 (ft) L3 (ft)
10 Table 2.1 SI Symmetrical Three-Span Continuous Beam L1 L2 L3 L2 L1 L NL L N = 1.0 N = 1.1 N = 1.2 N = 1.3 N = 1.4 N = 1.5 N = 1.6 N = 1.7 Total L1/L L2/L L3/L L1/L L2/L L3/L L1/L L2/L L3/L L1/L L2/L L3/L L1/L L2/L L3/L L1/L L2/L L3/L L1/L L2/L L3/L L1/L L2/L L3/L Length (m) L1 (m) L2 (m) L3 (m) L1 (m) L2 (m) L3 (m) L1 (m) L2 (m) L3 (m) L1 (m) L2 (m) L3 (m) L1 (m) L2 (m) L3 (m) L1 (m) L2 (m) L3 (m) L1 (m) L2 (m) L3 (m) L1 (m) L2 (m) L3 (m)
11 Table 2.1 US Symmetrical Three-Span Continuous Beam L1 L2 L3 L2 L1 L NL L N = 1.0 N = 1.1 N = 1.2 N = 1.3 N = 1.4 N = 1.5 N = 1.6 N = 1.7 Total L1/L L2/L L3/L L1/L L2/L L3/L L1/L L2/L L3/L L1/L L2/L L3/L L1/L L2/L L3/L L1/L L2/L L3/L L1/L L2/L L3/L L1/L L2/L L3/L Length (ft) L1 (ft) L2 (ft) L3 (ft) L1 (ft) L2 (ft) L3 (ft) L1 (ft) L2 (ft) L3 (ft) L1 (ft) L2 (ft) L3 (ft) L1 (ft) L2 (ft) L3 (ft) L1 (ft) L2 (ft) L3 (ft) L1 (ft) L2 (ft) L3 (ft) L1 (ft) L2 (ft) L3 (ft)
12 Table 2.2 SI Symmetrical Four-Span Continuous Beam L1 L2 L3 L4 L3 L2 L1 L NL NL L N = 1.0 N = 1.1 N = 1.2 N = 1.3 N = 1.4 N = 1.5 N = 1.6 N = 1.7 Total L1/L L2/L L3/L L4/L L1/L L2/L L3/L L4/L L1/L L2/L L3/L L4/L L1/L L2/L L3/L L4/L L1/L L2/L L3/L L4/L L1/L L2/L L3/L L4/L L1/L L2/L L3/L L4/L L1/L L2/L L3/L L4/L Length (m) L1 (m) L2 (m) L3 (m) L4 (m) L1 (m) L2 (m) L3 (m) L4 (m) L1 (m) L2 (m) L3 (m) L4 (m) L1 (m) L2 (m) L3 (m) L4 (m) L1 (m) L2 (m) L3 (m) L4 (m) L1 (m) L2 (m) L3 (m) L4 (m) L1 (m) L2 (m) L3 (m) L4 (m) L1 (m) L2 (m) L3 (m) L4 (m)
13 Table 2.2 US Symmetrical Four-Span Continuous Beam L1 L2 L3 L4 L3 L2 L1 L NL NL L N = 1.0 N = 1.1 N = 1.2 N = 1.3 N = 1.4 N = 1.5 N = 1.6 N = 1.7 Total L1/L L2/L L3/L L4/L L1/L L2/L L3/L L4/L L1/L L2/L L3/L L4/L L1/L L2/L L3/L L4/L L1/L L2/L L3/L L4/L L1/L L2/L L3/L L4/L L1/L L2/L L3/L L4/L L1/L L2/L L3/L L4/L Length (ft) L1 (ft) L2 (ft) L3 (ft) L4 (ft) L1 (ft) L2 (ft) L3 (ft) L4 (ft) L1 (ft) L2 (ft) L3 (ft) L4 (ft) L1 (ft) L2 (ft) L3 (ft) L4 (ft) L1 (ft) L2 (ft) L3 (ft) L4 (ft) L1 (ft) L2 (ft) L3 (ft) L4 (ft) L1 (ft) L2 (ft) L3 (ft) L4 (ft) L1 (ft) L2 (ft) L3 (ft) L4 (ft)
14 Appendix Conversion Factors Multiply By To Produce in mm ft m in mm 2 ft m 2 in mm 3 ft m 3 in mm 4 ft m 4 lbf N kip kn ton kn lbf/in N/mm lbf/ft N/mm kip/in kn/m kip/ft 14.6 kn/m lbf kg lbm kg slug kg ft/sec m/sec 2 psi Pa ksi MPa psf Pa ksf 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 mm mm 2 No lb/ft in in A-1
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