Bridge Problems for the Structural Engineering (SE) Exam: Lateral Loads
David Connor, SE, PE Website: www.davidconnorse.com Email:
[email protected]
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Reference Bridge Code – S!"# $R%D & Edition, ()*+
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BR-D1E PR#B$E0S %#R "!E S"R2C"2R$ E/1-/EER-/1 3SE4 E50: $"ER$ $#DS Current Printing of this edition: st th eference "ridge Code: ##$%T& '() * +dition, -/ Copyright 0 -1 by )avid Connor, $+, P+ #ll rights reserved. 2o part of the publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without t he prior written permission of the author. Contact the author via e3mail at
[email protected] for in4uiries. This publication shall be used for educational purposes only. 5t is not a substitute for professional and sound engineering 6udgment. The author does not guarantee the accuracy or completeness of any information published herein and shall not be responsible for any errors, omissions, or damages aris ing out of use of the information in this publication. 5t is understood that the author is not rendering professional engineering services via this publication. The #merican #ssociation of $tate %ighway and Transportation &fficials 7##$%T&8 and the 2ational Council of +9aminers for +ngineering and $urveying 72C++$8 were not involved in producing this publication. #ny mention of these, or similar organiations, within this publication does not con stitute an endorsement of the publication, nor the information published herein. #ny similarity between the problems appearing in t his publication and problems published by othe rs or that appear on the 2C++$ $tructural +ngineering 7$+8 +9am is purely coincidental. The sub6ect matter of the problems was chosen based on what the author believed what may appear on future $+ +9ams only. Printed by Create$pace, #n #maon.com Company e$tore address: www.Create$pace.com;1<= 5$"2: ?
Table of Contents $ub6ect atter of +ach Problem. #bout the #uthor .
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#cknowledgements. Preface.
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Tips and ecommendations.
$ummary of ##$%T& Changes . 2omenclature. 2otes.
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"ridge Problems for the $tructural +ngineering 7$+8 +9am: 'ateral 'oads / Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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"ridge Problems for the $tructural +ngineering 7$+8 +9am: 'ateral 'oads $olutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . #nswer Bey.
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Problems A through A/.
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#nswer $heet.
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Problems A through A/ $olutions.
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Subject Matter of Each Problem Problem A $uperstructure Dind 'oads in Transverse )irection Problem A- $uperstructure Dind 'oads in 'ongitudinal )irection Problem A< $uperstructure Dind 'oads on (lat $urface Problem A/ $imultaneous $ubstructure Dind and $tre am 'oads Problem A? Esual Firder and $lab "ridge Dind 'oads Problem A1 Dind 'oads on Ge hicles Problem A* $uperstructure Dind 'oads $kewed Pier Problem A> $ubstructure Dind 'oads $kewed Pier Problem A= Pier #nalysis $ub6ect to Dind 'oads Problem A #eroelastic 5nstability Problem A 'ateral $tream Pressure Problem A- $oil "earing Pressures )ue to 'ateral 'oads Problem A< $eismic $ite $pecific %aard #nalysis Problem A/ $eismic esponse $pectrum Problem A? )etermination of +lastic $eismic esponse Coefficient Problem A1 Pier $eismic )esign oments Problem A* Pier (oundation $eismic )esign oments Problem A> Pier (oundation $eismic )esign oments Problem A= 'ongitudinal and 'ateral $e ismic )esign oments Problem A- Pier $eismic $hear (orce Problem A- %old3)own )evice Eplift Problem A-- $eismic #nalysis ethods for "ridges Problem A-< $ingle3ode $pectr al ethod of $eismic #nalysis Problem A-/ Eniform 'oad +lastic ethod of $eismic #nalysis Problem A-? inimum $upport Didth Problem A-1 P∆ Compliance Problem A-* Concrete Column to (ooting Connections $eismic P rovisions Problem A-> Concrete Column 'ongitudinal einforcement )evelopment $eismic Provisions Problem A-= Concrete Column $hear einforcement $eismic Provisions Problem A< Dall3Type Pier einforcement $eismic Provisions Problem A< $teel Cross3(rame )iaphragm Capacity Problem A<- )eck (le9ibility vs. igidity Problem A<< )eck $eismic $hear (orce Problem A $+ Dall $eismic 5nertial (orces Problem A<= +lastomeric "earing Pad 'ateral $hear Problem A/ $ound "arrier Dind 'oads
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Ti#s and $ecommendations •
#fter you have gathered together all of the codes, LtabM them. $olving problems 4uickly is paramount to passing the $+ +9am and the use of tabs will help you to 4uickly find the code information you need. This process will also help you get familiar with the layout of the codes and you may even find information in the codes that is useful in your day3to3 day work e9perience. #gain, donHt underestimate the time it will take to perform this task. 5t took me the better part of - weeks to tab my codes. "e selective with your tabbing. 5f you Lovertab,M you could have the reverse effect of making i t more difficult to find information 4uickly. #lso, leave a gap without tabs in the middle of the page edges to make flipping through the pages easier and so that your thumb does not get caught on the tabbed pages. $ee the photo below.
This photo shows LovertabbingM at the front of the book and correct tabbing with a gap between the tabs at the back of the book.
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This may sound like common sense and trivial, but the best way to study is to work out problems step3by3step, by hand. &bviously, this is how you will need to solve the problems on the e9am as well. The reason 5 mention this is because, many if not all, structural engineers today depend on the use of spreadsheets and structural engineering software to perform the sometimes repetitive structural engineering and analysis tasks. $olving problems by hand will help you to identify the best ways to solve a problem, where in the code to find the information, and where you may get tripped up.
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Summar% of ST Changes Section *.7.'.'.' 5 !istribution %actor 2ethod for 2oment and Shear
/.1.-.-.-a 5nterior "eams with Dood )ecks The lane fraction terminology has been replaced with live load distribution factor, g. /.1.-.-.-b 5nterior "eams with Concrete )ecks The lane fraction terminology has been replaced with live load distribution factor, g. 5n Table /.1.-.-.-b3 the applicable cross3sections for Concrete "eams used in ultibeam )ecks definitions have been slightly modified. /.1.-.-.-c 5nterior "eams with Corrrugated $teel )ecks 3 The lane fraction terminology has been replaced with live load distribution factor, g. /.1.-.-.-d +9terior "eams 3 The lane fraction terminology has been replaced with live load distribution factor, g. )efinitions and application of g interior and the distance d e has been refined. 5n Table /.1.-.-.-d3 the applicable cross3sections for Concrete "eams used in ultibeam )ecks definitions have been slightly modified. /.1.-.-.-e $kewed "ridges 3 5n Table /.1.-.-.-e3 the applicable cross3sections for Concrete )eck on Concrete $pread "eams, Cast3in3Place ulticell "o9 Concrete "o9 "eams and )ouble T3 $ections used in ultibeam )ecks has been changed. )ouble T3$ections used in ultibeam )ecks are no longer specified. The applicable cross sections have been changed. Section *.7.'.'.< 5 !istribution %actor 2ethod for Shear
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Problem *
efer to the bridge elevation, design data, and assumptions below:
)esign )ata and #ssumptions:
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The pier and abutments are not skewe d
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Dind velocity at < ft. above low ground, G< S - mph
The truss profile has the same pro6ect ion in windward and leeward wind directions (or wind pressure calculations the height of struct ure may be taken at mid3height of the element "ase wind velocity G " S mph Epstream $urface Conditions are classified &pen Country &
$kew #ngle of Dind S to 1
&
The ma9imum total design wind pressure 7P )8 that should be applied to the truss m embers for design of the pier, in the bridge transverse direction, is most nearly: 7#8 7"8 7C8 7)8
.*? ksf .>1 ksf .-= ksf ./ ksf
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$ @ + ' " & ! P ' # ! + T # '
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Problem 8):
efer to the illustration of the wall3type bridge pier, design data, and assumptions below:
)esign )ata and #ssumptions:
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$eismic Uone <
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The wall boundary elements are ade4uate to re sist all moments.
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$teel reinforcement properties: f y S 1 ksi
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Pier shear design properties: b S -/M d S
)esign shear Gu'#T S -< kips for +9treme +vent 5 loading and has been reduced by the appropriate response modification factor. Concrete properties: fHc S <.? ksi, 2ormal Deight
The most economical wall reinforcement for t he wall3type bridge pier that meets ##$%T& provisions, per layer of reinforcement, is: 7#8 7"8 7C8 7)8
A? @ M vertical, A? @ M horiontal A? @ M vertical, A1 @ -M horiontal A1 @ -M vertical, A1 @ -M horiontal A* @ -M vertical, A* @ -M horiontal
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Problem ( Correct nswer – 3B4 This problem tests on determining the wind loads to be applied on a bridge truss superstructure in the bridgeHs longitudinal direction. Typically the governing longitudinal wind pressure occurs at the largest skew angle of wind. Pertinent Sections and "ables – $ection <.>. %oriontal Dind Pressure $ection <.>..- Dind Pressures on $tructures: D$ Table <.>..3 Galues of G o and U o for Garious Epstream $urface Conditions
Table <.>..-.-3 "ase Dind Pressures, P ", for Garious #ngles of #ttack and G " S mph
"-P: "ase wind pressures applied to a bridge superstructure in the bridge
longitudinal direction should be determined from Table <.>..-.-3 only. Table <.>..-.3 does not show values longitudinal wind loads at various skew angles of wind.
Sol7tion – Ste# - . /etermine 0 /1 (*ote: This ste# is the same as Problem 3-): G)U is determined by ##$%T& +4. <.>..3:
= 2.5 l!!
(rom the problem statement the following values are determined: Go S >.- 7Table <.>.. 3 &pen Country upstream surface condition8 G< S - mph G" S mph U S /*.? feet 7from illustration8 U S .-< feet 7Table <.>.. 3 &pen Country upstream surface condition8 G)U S -.?Z7>.-8Z7-;8Zln7/*.?;.-<8 S < mph Ste# 2 . /etermine design #ressure P /: P) is determined by ##$%T& +4. <.>..-.3
$ ' " = " # %&&&&
(or wind pressures in the longitudinal direction of the bridge, the ma9imum wind pressure occurs at the o skew angle of wind S 1 . Esing ##$%T& Table <.>..-.- 3 for $uperstructure Trusses, Columns and #rches o the base pressure P " at the skew angle of wind S 1 is .? ksf. -
Thus P ) S .?Z7< ;8 S 3 nswer: ).)<; >sf -ncorrect nswers – 7#8 .? ksf This answer would be determined if the base velocity S mph was used. This value
could also be found in Table <.>..-.-3 7"8 .>1 ksf This is the correct answer. 7C8 .=/ ksf This answer would be determined if the elevation at the top of truss U S 1 ft were used, instead of the mid3height of the truss as shown in the problem statement. 7)8 .-= ksf This answer would be determined if the ma9imum lateral;transverse direction loads were used instead of longitudinal.
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Problem 8* Correct nswer – 3C4 This problem tests on determining the capacity of an end abutment cross3frame diaphragm consisting of steel angle LR3bracing.M The tensile capacity of the angles is determined in order to ultimately arrive at the overall capacity of the diaphragm. Pertinent Sections and "ables – $ection 1.>.- Tensile esistance $ection 1.>.-.- eduction (actor, E Table 1.>.-.-3 $hear 'ag (actors for Connections to Tension embers
"-P: (or cross3frame diaphragms constructed out of steel members, the tensile capacity of the angles typically will govern the design. Enless special conditions e9ist, it is assumed the tension side an gles will develop the lateral shear prior to compression buckling of the compression side angles.
$ection 1.?.? +9treme +vent 'imit $tate esistance (actors Sol7tion –
Ste# - . /etermine the tensile ca#acit% of the cross9frame angles: #s discussed in the Tip above, the cross3frame diaphragm capacity will be governed by the tensile capacity
of the cross3frame angles. #dditionally, the problem statement states that the end connection welds do not govern. Therefore the tensile capacity of the cross3frame angles may be determined per ##$%T& $ection 1.>.- and +4s. 1.>.-.3 and 1.>.-.3-. #dditionally, per $ection 1.?.? φ S . for +9treme +vent 'imit $tate steel design e9cept at bolts as specified. -
Pr S φyPny S φy(y#g S 7.8Z7<1 ksi8Z7.// in 8 S ?.> kips Pr S φuPnu S φu(u#npE where -
#n S .// in 7no holes8, p S . 7no holes8, E S
H ̅
3 S 7M;
E is determined per Table 1.>.-.-3 Case -. Case > in Table 1.>.-.-3 does not apply because welds are used, not bolts. -
Pr S φuPnu S φu(u#npE S 7.8Z7?> ksi8Z7.// in 8Z7.8Z7.1*8 S ?1. kips +4. 1.>.-.3 governs and P r S ?.> kips Ste# 2 . /etermine the cross9frame dia#hragm ca#acit%: eferring to the problem illustration, the tension component in the direction of the force G
u ^$ + K$
cross is:
'anlge S S = ft. Therefore cross3frame capacity per girder bay S 7>;=8Z7?.> kips8 S /1. kips #nd the total cross3frame capacity is 7/ girder bays8Z7/1. kips8 S nswer: *<+ >iAs -ncorrect nswers –
7#8 ?= kips This a nswer would be determined if the resistance factors 7 φ8 per $ection 1.?./.- were used instead of φ S . for +9treme +vent 5 'imit $tate. 7"8 *? kips This a nswer would be determined if the resistance factors 7 φ8 per $ection 1.?./.- were used instead of φ S . and E S .> per Case > in Table 1.>.-.-3. 7C8 >/ kips 3 This is the correct answer. 7)8 - kips This answer would be determined if the value for P r for tensile rupture was used S ?1 kips.
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$ 2 & 5 T E ' & $ ' # ! + T # '
