Bridge Problems for the SE Exam

Bridge Problems for the Structural Engineering (SE) Exam: Vertical Loads

David Connor, SE, PE Website: www.davidconnorse.com Email: [email protected]

Reference Bridge Code – AASHTO LRFD 7th Edition, 2014

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BRIDGE PROBLEMS FOR THE STRUCTURAL ENGINEERING (SE) EXAM: VERTICAL LOADS Current Printing of this edition: 1st th Reference Bridge Code: AASHTO LRFD 7 Edition, 2014 Copyright © 2016 by David Connor, SE, PE All rights reserved. No 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 the prior written permission of the author. Contact the author via e-mail at [email protected] for inquiries. This publication shall be used for educational purposes only. It is not a substitute for professional and sound engineering judgment. 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 arising out of use of the information in this publication. It is understood that the author is not rendering professional engineering services via this publication. The American Association of State Highway and Transportation Officials (AASHTO) and the National Council of Examiners for Engineering and Surveying (NCEES) were not involved in producing this publication. Any mention of these, or similar organizations, within this publication does not constitute an endorsement of the publication, nor the information published herein. Any similarity between the problems appearing in this publication and problems published by others or that appear on the NCEES Structural Engineering (SE) Exam is purely coincidental. The subject matter of the problems was chosen based on what the author believed what may appear on future SE Exams only. Printed by CreateSpace, An Amazon.com Company eStore address: www.CreateSpace.com/6393413 ISBN: 1535055391

Table of Contents Subject Matter of Each Problem. About the Author.

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Acknowledgements. Preface.

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Tips and Recommendations.

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Summary of AASHTO Changes. Nomenclature. Notes.

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Bridge Problems for the Structural Engineering (SE) Exam: Vertical Loads 40 Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Answer Sheet.

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Bridge Problems for the Structural Engineering (SE) Exam: Vertical Loads Solutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Answer Key.

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Problems #1 through #40.

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Problems #1 through #40 Solutions.

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Subject Matter of Each Problem Problem #1 – Design Moment for Bridge Girder Problem #2 – Design Shear for Bridge Girder Problem #3 – Concrete Deck Live Load Moment Problem #4 – Pier Stream Pressure and Vessel Impact Problem #5 – Superstructure Vessel Impact Problem #6 – Lateral Earth Pressure at Abutment Problem #7 – Anchored Wall Tension Problem #8 – Anchored Wall Bonded Length Problem #9 – MSE Wall Reinforcement Problem #10 – Retaining Wall Forces Problem #11 – Expansion Joints Problem #12 – Braking Force and Moment Problem #13 – Long-Term Concrete Deflection Problem #14 – Concrete Column Axial Resistance and Biaxial Flexure Problem #15 – Support Bearing Resistance Problem #16 – Shear Resistance of Prestressed Girder Problem #17 – Interface Shear Resistance Problem #18 – Prestressed Girder Stresses Problem #19 – Prestressed Girder Losses Problem #20 – Development Length Problem #21 – Concrete Deck Reinforcement Cover Problem #22 – Concrete Piles Problem #23 – Pile Caps Problem #24 – Strut and Tie Method Problem #25 – Steel Fatigue Problem #26 – Steel Piles Problem #27 – Fracture-Critical Member Charpy V-Notch (CVN) Testing Problem #28 – Steel Girder Moment Capacity Problem #29 – Plate Girder Dimensions Problem #30 – Plate Girder Web Shear Capacity Problem #31 – Plate Girder End Bearing Capacity Problem #32 – Composite Girder Headed Studs Problem #33 – Use of Slip Critical Connections Problem #34 – Bolted Connection Shear Resistance Problem #35 – Bolted Connection Slip Resistance Problem #36 – Bolted Splice Problem #37 – Wood Decking Problem #38 – Drilled Shafts Problem #39 – Concrete Relieving Slab Problem #40 – Use of Bearing Type

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Tips and Recommendations •

After you have gathered together all of the codes, “tab” them. Solving problems quickly is paramount to passing the SE Exam and the use of tabs will help you to quickly 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 day-today work experience. Again, don’t underestimate the time it will take to perform this task. It took me the better part of 2 weeks to tab my codes. Be selective with your tabbing. If you “overtab,” you could have the reverse effect of making it more difficult to find information quickly. Also, 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. See the photo below.

This photo shows “overtabbing” at the front of the book and correct tabbing with a gap between the tabs at the back of the book.

•

This may sound like common sense and trivial, but the best way to study is to work out problems step-by-step, by hand. Obviously, this is how you will need to solve the problems on the exam as well. The reason I 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. Solving 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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Summary of AASHTO Changes Section 4.6.3.3 - Beam-Slab Bridges 4.6.3.3.1 – General – In the commentary, the bullet points dealing with K-frame and X-frame diaphragms, and live load effects have been removed and are now contained in the new Article 4.3.3.4 – Cross-frames and Diaphragms. 4.6.3.3.2 – This Article has been renamed “Grid and Plate and Eccentric Beam Analyses of Curved and/or Skewed Steel I-Girder Bridges.” This Article describes how to account for steel Igirders that are curved and/or skewed. The warping rigidity of the girders is to be considered in grid and in plate and eccentric beam methods of structural analysis. Equations for IC (connectivity index) and IS (skew index) have been introduced and are to be used to determine if the warping rigidity of the I-girders must be used. 4.6.3.3.3 – This Article is now “Curved Steel Bridges” which was 4.6.3.3.2 in AASHTO 6th edition. 4.6.3.3.4 – This is a new Article named “Cross-frames and Diaphragms”. The Article and commentary describes modeling and analysis techniques for various types of cross-frames and diaphragms. 4.9 – References – Additional references have been added for research that has been performed since the previous AASHTO Edition. Section 5 - Concrete Structures: 5.3 – Notation – Definition for Ecdeck was removed. The definitions for εtl and φcont were added. Section 5.5.3 – Fatigue Limit State 5.5.3.1 – General – The verbiage for fully prestressed components in other than segmentally constructed bridges was modified. The compressive stress for Fatigue I load combination is due to ½ the sum of the unfactored effective prestress and permanent loads. 5.5.3.2 – Reinforcing Bars – Equation 5.5.3.2-1 has been modified and the definition for fy has been added to the section. Fy is not to be taken less than 60 ksi, nor greater than 100 ksi. 5.8.2.5 – Minimum Transverse Reinforcement - The minimum amount of transverse reinforcement for segmental post-tensioned concrete box girder bridges has been modified. Eq. 5.8.2.5-2 has been removed, and the minimum transverse reinforcement is now the equivalent of (2)-#4 bars, grade 60, per foot of length. 5.8.2.7 – Maximum Spacing of Transverse Reinforcement - Additional commentary has been added regarding the maximum spacing of transverse reinforcement in prestressed girders. It explains that a spacing limit of 0.6dv may be appropriate, or reducing the transverse bar reinforcement diameter, and thus reducing the transverse bar spacing.

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Nomenclature A Ab Acv Ag Agirder Aps As Asc Ast Av Avf A1 A2

ADTTSL AEP BR bf bs bt bv C

c Cd CF Cfu Ci CKF CM Cv CV CVN Cλ

fatigue detail category constant 2 cross sectional area of bolt (in ) area of concrete section resisting shear 2 transfer (in ) 2 gross cross sectional area (in ) 2 cross sectional area of girder (in ) cross sectional area of prestressing strands 2 (in ) 2 cross sectional area of steel member (in ) 2 headed stud cross-sectional area (in ) 2 cross sectional area of reinforcement (in ) 2 area of shear reinforcement (in ) area of reinforcement for interface shear 2 between concretes of slab and beam (in ) 2 load area (in ) area of the lower base of the largest frustrum of a pyramid contained wholly within the support and having for its upper base the loaded area (A1) and having side 2 slopes of 1 vertical to 2 horizontal (in ) average daily truck traffic over design life – single lane (trucks/day) apparent earth pressure (psf/ksf) vehicular braking force (kips) flange width (in.) composite effective width of concrete deck (in.) projecting width of bearing stiffener (in.) prestress girder web width (in.) MSE wall reinforcement surface area geometry factor; ratio of shear buckling resistance to the shear specified minimum yield strength cohesion factor (ksi) deck factor size factor flat use factor incising factor format conversion factor = 2.5/φ wet-service factor volume factor vessel collision force (kips) Charpy V-Notch time effect factor

D DC DW DWT Dp

Dt d

db do dv E Ec Eci Ect Ep EH EV F F* Fb Fbo FCM Fp Fu Fub Fy Fyf Fyw Fys f’c f’ci

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plate girder web depth (in.) dead load of superstructure and structural components (kips) dead load of wearing surface (kips) dead weight tonnage of ship (tonnes) distance from top of concrete deck to the neutral axis of the composite section at the plastic moment (in.) total depth of composite section (in.) diameter; depth; distance from extreme compression fiber to centroid of tensile steel (in.) bar diameter (in.) web stiffener spacing (in.) effective shear depth (in.) modulus of elasticity of steel (ksi) modulus of elasticity of concrete (ksi) modulus of elasticity of concrete at transfer (ksi) modulus of elasticity of concrete at transfer or time of load application (ksi) modulus of elasticity of prestressing tendons (ksi) horizontal earth pressure load (psf/ksf) vertical pressure from dead load of earth fill (psf/ksf) strut or tie force pullout friction factor adjusted design flexural strength of wood (ksi) design flexural strength of wood (ksi) fracture-critical member total radial force in concrete deck (kips) steel tensile strength (ksi) tensile strength of bolt (ksi) steel yield strength (ksi) steel yield strength of flange (ksi) steel yield strength of web (ksi) steel yield strength of stiffener (ksi) 28-day compressive strength of concrete (psi/ksi) compressive strength of concrete at strand release (psi/ksi)

BRIDGE PROBLEMS FOR THE STRUCTURAL ENGINEERING (SE) EXAM: VERTICAL LOADS Problem #1 VERTICAL PROBLEMS

Refer to the bridge deck section, design data, and assumptions below:

Design Data and Assumptions: • • • • • • • • • •

Beam span = 50’-0”simple span Total Dead Load of Superstructure (DC) – 3.0 kips/ft Total Dead Load of Wearing Surface (DW) – 0.5 kips/ft HL-93 Design Truck Static Moment – 628 kip-ft HL-93 Design Lane Load – Per AASHTO Ductililty, Redundancy, and Operational Classification factor ηι = 1.0 Bridge Stiffness Factor (Kg/12.0Lts3)0.1 = 1.0 Two design lanes loaded Permanent loads are distributed equally among the girders Loads and moments not shown are negligible or do not govern design

The maximum design moment for an interior girder is most nearly: (A) (B) (C) (D)

1200 kip-ft 1440 kip-ft 1730 kip-ft 2100 kip-ft

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BRIDGE PROBLEMS FOR THE STRUCTURAL ENGINEERING (SE) EXAM: VERTICAL LOADS Problem #30: A bridge plate girder has the following end bearing condition:

Design Data and Assumptions: • Steel Fy = 50 ksi for all plates and stiffeners. • Web stiffeners meet provisions of AASHTO Section 6.10.11.1. • Web stiffeners are milled to bear against the flanges. • All web stiffener welds are adequate. • Ductililty, Redundancy, and Operational Classification factor ηι = 1.0 The design shear capacity for the web end panel is most nearly: (A) (B) (C) (D)

600 kips 670 kips 810 kips 870 kips

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BRIDGE PROBLEMS FOR THE STRUCTURAL ENGINEERING (SE) EXAM: VERTICAL LOADS Problem #2 Correct Answer – (D) This is another fundamental problem necessary for all bridges. Many bridges have shorter end spans and at shorter spans the design tandem live load governs over the design truck live load. This problem also tests the concepts of live load dynamic impact allowance, live load distribution to girders, and application of load combinations. TIP: Tandem live load will govern for the Pertinent Sections and Tables – following: Table 3.4.1-1 - Load Combinations and Load Factors Moment – Simple spans 40 ft or less Table 3.4.1-2 - Load Factors for Permanent Loads Shear – Simple spans 25 ft or less Section 3.6.1.2 – Design Vehicular Live Load Table 3.6.2.1-1 – Load Allowance, IM Table 4.6.2.2.1-1 – Common Deck Superstructures Table 4.6.2.2.3a-1 – Distribution of Live Loads for Shear in Interior Beams Solution – Step 1 – Determination of Shears for each loading: VDC = (3.0 k/ft)*(20 ft) / 2 = 30 k distributed over 5 girders = 6.0 k VDW=(0.5 k/ft)*(20 ft) / 2 = 5 k distributed over 5 girders = 1.0 k VLL(LANE)= Shear due to Design Lane Live Load = .64 kips/ft (Section 3.6.1.2.4) = (.64 k/ft)*(20 ft) / 2 = 6.4 k VLL(HL-93) = The tandem shear governs over the truck shear. Determine by placing (2)-25 kip loads 4 feet apart at the end of the span. VLL(HL-93)= (25k)+(25k)*[(20-4)/20] = 45 k (Note: The shear for the design truck is 41.6 k) VIM = Dynamic Load Allowance (IM) applied to the static HL-93 live load (Section 3.6.2.1) = 0.33*(45 k) = 14.9 k (Note: The IM load for the design truck is 13.7 k) Step 2 – Determination of the Live Load Distribution Factor: Table 4.6.2.2.1-1 - Applicable cross section = (a) Table 4.6.2.2.3a-1 – Given the applicable cross section, range of applicability parameters given in this table, and design for 2 lanes loaded, the live load distribution factor is the following: 2

0.2 + (S/12) - (S/35) 2 The distribution factor = 0.2 + (7/12)-(7/35) = .743 Step 3 – Determination of Design Shear using Table 3.4.1-1 & Table 3.4.1.2: Strength I Load Combination GovernsVDesign = 1.25*(VDC)+1.5*(VDw)+1.75*(LLDIST)*(VLL(LANE)+VLL(HL-93)+VIM) VDesign = 1.25*(6.0)+1.5*(1.0)+1.75*(.743)*(66.3) = 95.2 k - Answer: 96 k Incorrect Answers – (A) 76 kips – This answer does not consider HL-93 tandem impact (B) 84 kips – This answer uses the distribution factor for one design land loaded (C) 89 kips – This answer uses the truck live load versus the tandem live load. (D) 96 kips – This is the correct answer.

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BRIDGE PROBLEMS FOR THE STRUCTURAL ENGINEERING (SE) EXAM: VERTICAL LOADS

This problem tests on determining the axial TIP: Compare the answer to this question to the capacity of end bearing stiffeners at bearing of shear capacity determined in the previous a plate girder. The test taker has to first question. Plate girders tend to be very deep and determine the correct effective column section have relatively thin webs, therefore buckling of the per AASHTO Section 6.10.11.2 and then web in axial compression can occur at end bearing determine the axial capacity per AASHTO locations before the shear capacity of the web end Section 6.9.2.1. panel is reached. Pertinent Sections and Tables – Section 6.10.11.2 – Bearing Stiffeners Section 6.10.11.2.4 – Axial Resistance of Bearing Stiffeners, Parts a and b Section 6.9.2.1 & 6.9.4 – Axial Compression Section 6.5.4.2 – Resistance Factors Solution – Step 1 – Check to see that the projecting width of the bearing stiffener satisfies eq. 6.10.11.2.2-1: The projecting width bt must satisfy the following: }[ ≤ 0.48za N

^

4L(

= 4.33”

Our stiffeners project out just under 4”, thus bt is OK. Step 2 – Determine effective column section and column section properties: The effective column section is defined in AASHTO Section 6.10.11.2.4b. The end bearing stiffeners are 4” from the end of the girder, thus only that portion of the web is considered. 9tw = 5-5/8” is considered on the other side of the stiffeners. The effective column section is illustrated here:

The pertinent section properties for this effective column section about the web axis are as follows: 2 4 I = 16.2 in r = 1.33” Ag = 9.02 in Step 3 – Determine the design axial capacity of the bearing stiffeners/effective column section: Per AASHTO Section 6.10.11.2.4a the axial resistance is determined by taking the effective length of the column section as .75D = .75*(48 in) = 36 in. The nominal axial capacity for non-composite members may be determined per AASHTO Section 6.9.2.1 & 6.9.4. 2 Po = QFyAg = (1.0)(50 ksi)(9.02in ) = 451 kips (Q = 1.0 for bearing stiffeners typical) 2 2 2 Pe = {(π E)/[(36/1.33) ]}*(9.02 in ) = 3520 kips (AASHTO Eq. 6.9.4.1.2-1) (451/3520) Pe/Po = 7.8 thus Pn is per AASHTO Eq. 6.9.4.1.1-1 Pn = [0.658 ]*(451 kips) = 427 kips Design Axial Capacity = Pr = φcPn = (0.9)*(427 kips) = Answer: 385 kips (φc = 0.9 per section 6.5.4.2) Incorrect Answers – (A) 133 kips - This answer would have been determined if the web was not considered as part of the effective column section. (B) 370 kips - This answer would have been determined if KL was taken as 48”. (C) 385 kips - This is the correct answer. (D) 426 kips - This answer would have been determined if the effective column section was considered as 9tw at both sides of the stiffeners, instead of 4” toward the end of the girder.

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VERTICAL SOLUTIONS

Problem #31 Correct Answer – (C)