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Post-Tensioned Concrete Principles and Practice Second Edition K. Dirk Bondy & Bryan Allred

Copyright © 2013 K. Dirk Bondy & Bryan Allred All rights reserved. No part of this book may be reproduced, stored, or transmitted by any means—whether auditory, graphic, mechanical, or electronic—without written permission of both publisher and author, except in the case of brief excerpts used in critical articles and reviews. Unauthorized reproduction of any part of this work is illegal and is punishable by law. ISBN: 978-1-4834-0372-4 (sc) ISBN: 978-1-4834-0371-7 (e) Library of Congress Control Number: 2013916599 Because of the dynamic nature of the Internet, any web addresses or links contained in this book may have changed since publication and may no longer be valid. The views expressed in this work are solely those of the author and do not necessarily reflect the views of the publisher, and the publisher hereby disclaims any responsibility for them. Any people depicted in stock imagery provided by Thinkstock are models, and such images are being used for illustrative purposes only. Certain stock imagery © Thinkstock. Lulu Publishing Services rev. date: 07/17/2014

Table of Contents Preface ....................................................................................................................................................... vi 1)

History of Post-Tensioned Concrete in United States Building Construction ...................................1

2)

Design Philosophy, Equivalent Loads & Concrete Stresses on Determinate Systems ....................23

3)

Review of Moment Distribution .......................................................................................................47

4)

Concrete Stresses in Indeterminate Systems ....................................................................................57

5)

Flexural Design.................................................................................................................................65

6)

Shear Design .....................................................................................................................................87

7)

Two-Span Beam Design Example..................................................................................................131

8)

One-Way Slab Design Example .....................................................................................................153

9)

Two-Way Slab Design Example ....................................................................................................165

10) Two-Way Podium Slab Design Example .......................................................................................185 11) Mat Foundation Design Example ...................................................................................................209 12) Seismic Diaphragm Design Example .............................................................................................223 13) Design & Detailing for Mitigation of Restraint to Shortening Cracking .......................................251 14) Construction Issues and Structural Observations ...........................................................................275 15) Slabs-on-Ground .............................................................................................................................311 16) External Post-Tensioning ...............................................................................................................339 17) About the Authors ..........................................................................................................................355

Preface Writing this book has been a labor of love and it actually began back in the mid-1990s, though I didn’t realize it at the time. Much of the early chapters were written when I was teaching Prestressed Concrete Design at California Polytechnic State University at Pomona. I was a young man at the time, but I was lucky enough to have access to some of the greatest post-tensioned concrete engineers in the world. Over the years Bryan and I have learned the art of designing and detailing post-tensioned concrete from men such as my father, Ross Ellena, Ed Workman, Merrill Walstad, Florian Barth and Chris Deetz. We both owe a tremendous debt of gratitude to all these men for sharing their wisdom. I also want to acknowledge Trailer Martin, C.K. Allen, Bob Englekirk and Jim Cagley who were friends of my father before I even knew I wanted to be a structural engineer and offered opportunities and served as role models for me throughout my developing career. Like most structural engineers in the post-tensioned concrete industry, Bryan and I were waiting for my father to write this book. But when it became clear that he wasn’t going to, we decided to step up and take on the challenge. The book is a combination of history, academic notes intended for use at the university level, design examples straight from actual jobs that Bryan and I have designed and practical applications and detailing intended for the practicing engineer. Chapter 1 describes the history of posttensioned concrete in the United States as only my father can tell it. Chapters 2 through 8 are currently the notes that I use to teach Design of Prestressed Concrete Structures at UCLA. Chapters 9 through 13 are practical design examples in which we attempt to address many of the decisions faced by practicing engineers on typical projects including proper computer analysis and modeling techniques. Chapters 13 and 14 contain the true art of detailing and observing the construction of post-tensioned concrete. This knowledge was obtained over many years of working on our own projects and from listening and learning from the men who were the pioneers of post-tensioned concrete. Chapter 15 is a thorough discussion of the slab on grade industry, which represents more sales of post-tensioning tendons than all other post-tensioning applications combined. And finally, Chapter 16 discusses arguably the most fun and challenging application of post-tensioning – external post-tensioning. I want to acknowledge and thank my 2012 UCLA CEE 143 students for helping me iron out the class notes, and in particular Mr. Ryan Nakamoto and Mr. Christopher Smith for their reviews of the design example chapters. K. Dirk Bondy

This book reflects what Dirk and I do on a daily basis as structural engineers who specialize in posttensioned buildings. When my children ask me what I do for a living, I will give them this book and say “This should explain it.” We tried to cover every detail from the beginning theory of balanced loads to what to look for during the final structural observation. Over the years, we have engineered small residential foundations to large hotels and everything in between. If it’s in a building and post-tensioned, we have designed it, seen it constructed and tried to describe how to do it in the following chapters. As Dirk wrote, we have both been extremely fortunate to be mentored by literally some of the best posttensioning engineers in the world. This book was written by them as much as us and will hopefully help other engineers learn the art of post-tensioning. Bryan Allred

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Post-Tensioned Concrete - Principles and Practice

Example – Flexural Strength with Unbonded Tendons Given: Beam w/ 7 Unbonded Tendons with a Parabolic Profile A ps /Tendon = 0.153in2

Find: The maximum useable moment capacity, IM n at midspan. 40ᇱ (12) = 16 < 35 (this is typical for beams) 30" Ԣୡ = fୱୣ + 10,000 + 100U୮

Span to depth ratio = ? Use f୮ୱ

d f py & f se + 60,000

7(0.153inଶ ) U୮ = = 0.000374 110"(26") (note: b = width of the compression face = 110") f se = 0.70f pu – 15 ksi = 0.7(270 ksi) – 15 ksi = 174 ksi ?f୮ୱ = 174,000psi + 10,000psi +

4,000psi = 290,951psi = 291ksi 100(0.000374)

K. Dirk Bondy & Bryan Allred

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But limited to: f py = 243ksi or f se + 60,000 = 174ksi + 60ksi = 234ksi < 291 ksi ? 234ksi controls Assume the compression steel yields & draw the force diagram.

Using equilibrium, solve for the concrete force C c . C c = T ps + T s – C’ s = 250.6k + 189.6k – 37.2k = 403k Now use the Whitney Stress Block to find “a” & “c”. a=

Cୡ 403k = = 1.08" < t slab =6" (rectangular assumption is correct) ᇱ 0.85f ୡ b 0.85(4ksi)(110")

&

c=

a 1.08" = = 1.27" Eଵ 0.85

This example demonstrates that including compression steel in a tee-beam is of very little value. The neutral axis will typically be in the flange and therefore the compression steel will virtually never be yielding in compression. Therefore for tee-beams we will ignore the compression steel.

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Example

Service Loading: w d = 3.50klf w l = 1.25klf Remember, V u & M u are defined by ACI 318 as 1.2D + 1.6L so even for continuous beams the strength equation (11-9) will not include secondary effects. However, for the demand shear the secondary shears should technically be included. We will demonstrate in the two-span beam design in the next chapter that these shears are relatively small so ignoring them as most designers do is typically inconsequential. Find: Stirrups and spacing required at a distance “h/2” from the face of the support using: a) V cn (Eqn. 11-9) b) Minimum of V ci (Eqn. 11-10) & V cw (Eqn. 11-12) c) V c as a non-prestressed member Solution: a) V cn (11-9) V n = V c + V s IV n = IV c + IV s & IV n V u w u = 1.2(3.50klf) + 1.6(1.25klf) = 6.20klf V u (@ support) = 20’(6.2klf) = 124k Vୡ୬ = ቆ0.6ඥԢୡ + 700

V୳ d୮ ቇ b୵ d M୳

(11 െ 9)


91

“d” is defined as the distance from the compression face to the centroid of all tensile reinforcement, but not less than 0.80h. It’s typical to ignore the non-prestressed steel and take “d” to the prestressing reinforcement only. ? “d” near the support will be controlled by 0.80(30”) = 24” or 2’-0” Somewhat inexplicably, “d p ” does not have the 0.80h stipulation in this equation, though it does in all other equations, as does “d”. ACI 318 Section 11.1.3.2 states that “sections located less than a distance h/2 from face of support shall be permitted to be designed for V u computed at h/2.” In non-prestressed concrete this critical shear location is defined as “d”. However, the commentary explains that because “d” varies in prestressed concrete members, h/2 was arbitrarily chosen as the critical section. The centroid of the prestressing steel at h/2 from the support is: d୮ = 9.32" +

1.ʹͷԢ (16.68") = 10.4" ʹͲԢ

V u @ “h/2” = 124k – (15”/12)(6.2klf) = 116.3k

M u @ “h/2” = the shaded area under the shear diagram since the moment at the support is zero. 124୩ + 116.3୩ = (1.25ƍ ) = 150.2ƍ୩ 2 = 1,802̶୩ 116.3୩ (10.4") ‫ ׵‬Vୡ୬ = ൭0.6ඥ4000psi + 700 ቆ ቇ൱ (16")(24") 1,802̶୩ V୳ d୮ Remember that the term must be < 1.0 M୳ V୳ d୮ 116.3୩ (10.4") =ቆ ቇ = 0.671 < 1.0 ok M୳ 1,802̶୩ Vୡ୬ = (37.9psi + 469.8psi)(16")(24")/1000 = 195.0୩ But V cn has an upper bound of 5ඥf ᇱ ୡ b୵ d = 121.4k m Controls V cn

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A computer software program would now begin iterating to determine the length of rail required by adding studs incrementally, thus increasing Critical Section #2 until the factored shear stress is less than 2IඥԢୡ . According to our software program, 8 studs are required.

Verify Punching Shear Capacity with 8 Studs Per Rail Determine Section Properties of Critical Section #2

L x1 = 20” – 1.25” + 5.6”(tan22.5q) = 21.07” L x2 = 20” + 2[(8)(2.75”) + 2.8”] = 69.6” L y1 = 12” – 1.25”/2 + 5.6”(tan22.5q)/2 = 12.53” L y2 = 12” + [(8)(2.75” + 2.8”)] = 36.8” L = (36.8” – 12.53”) ξ2 = 34.32” The perimeter of Critical Section #2 is: b o2 = 2(34.32”) + 2(12.53”) + 21.07” = 114.8” The area of Critical Section #2 is: A c2 = 114.8”(5.6”) = 642.7 in2 According to the American Concrete Institute document ACI421.1R-08, the polar moments of inertia about each principle axis can be determined by summing the contributions of the individual segments about those axes using the following equations: Polar moment of inertia about the x-axis: Jୡ୶ = d σൣ݈/3൫y୧ଶ + y୧ y୨ + y୨ଶ ൯൧ Polar moment of inertia about the y-axis: Jୡ୷ = d σൣ݈/3൫୧ଶ + ୧ ୨ + ୨ଶ ൯൧


123

Where x i , yi , x j and yj are coordinates of points i and j at the extremities of a segment measured from the centroid of the total critical section, whose length is l.

Polar Moment of Inertia About the X-Axis

x cy2 = [(2)(34.32”)(36.8”-12.53”)/2 + (2)(12.53”)(36.8”-(12.53”/2))/] / 114.8” = 13.92” Segment #1 (occurs once): 21.07" Jଵ = (5.6") ൬ ൰ [(13.92")ଶ + (13.92")(13.92") + (13.92")ଶ ] = 22,863 inସ 3 Segment #2 (occurs twice): 19.69" Jଶ = 2(5.6") ൬ ൰ [(13.92")ଶ + (13.92")(0") + (0")ଶ ] = 14,244 inସ 3 Segment #3 (occurs twice): 14.63" Jଶ = 2(5.6") ൬ ൰ [(0")ଶ + (0")(10.35") + (10.35")ଶ ] = 5,851 inସ 3 Segment #4 (occurs twice): 12.53" Jଶ = 2(5.6") ൬ ൰ [(10.35")ଶ + (10.35")(22.88") + (22.88")ଶ ] = 40,577 inସ 3 Therefore, the total polar moment of inertia about the x-axis is: Jୡ୶ଶ = 22,863 inସ + 14,244 inସ + 5,851 inସ + 40,577 inସ = ૡ૜, ૞૜૞ ܑ‫ܖ‬૝

7 Two-Span Beam Design Example Given:

The following two-span parking structure beam with dimensions, material properties and loads shown below.

Find: 1. Determine the prestressing force & drape in both spans. Balance approximately 70% of the concrete load in each span and provide a minimum of 250psi average compression. 2. Verify that all ACI 318 Code allowable service flexural stresses are satisfied. 3. Design the negative moment non-prestressed reinforcement at the interior support. Show all secondary support reactions. 4. Use Eqn. (11-9) V cn , and determine the required spacing of #3 stirrups (2 legs) at the Span 1 side of the interior support.

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193

Stepped Structural Slab Prior to Placing Concrete

This detail is simple enough for relatively straight step conditions that do not occur over columns, shear caps and beams. The top dashed line in the detail indicates the top of the assumed sloped structural slab. This is similar to the construction of a parking slab at a ramp condition which sometimes slopes as much as 20%. The small portion of concrete above the dashed line is not necessary structurally, and is constructed only to create a flat surface for the wood construction. The weight of this portion of slab must be accounted for in the design of the slab. Averaging this added load over the entire slab is usually acceptable for the design of the columns, foundations and lateral system, but this may not be adequate for the design of the slab itself. The contractor will also often ask to square off the bottom soffit, instead of sloping the forms. This request should be refused. The post-tensioning chairs supplied by the supplier will not account for deeper sections of slab. The chairs will be supplied based upon the slab thickness assuming a flat or sloped (like a parking structure) surface. If the supplied chairs are placed lower than assumed in the design, a large localized balanced load will be generated by the “kink” in the tendon profile.

Incorrect Tendon Profile at Squared of Slab Step

194


A common response from contractors is they will field adjust the tendons to maintain the correct parabolic profile. The iron workers are not qualified and should not be required to “eye ball” the tendons and adjust them at their discretion to match the structural drawings. As described in the previous chapters, the proper profile is critical in post-tensioning to generate the correct balance load and in the intended direction. The consequences of placing the chairs off of localized deepened sections can be very serious. The following photograph demonstrates what can happen when the tendons are installed incorrectly and generate a balance load greatly in excess of the direct tensile strength of the concrete.

Resulting Damage Due to Incorrect Transitioning of Tendons at the Building Line Step

Utilizing a Concrete Over-Pour to Achieve the Building Line Step The practically fool-proof method of achieving a step at the building line is to use a concrete over-pour slab (or topping slab), and this is what will be done in this example. This slab usually only requires a 28day compressive strength of 3,000 psi and is reinforced with only plastic fibers, wire mesh or light rebar. The cost of this slab is substantially less than that of the structural post-tensioned slab supporting it and is comparable to or less expensive than a slab-on-ground. The over-pour slab will require that the structural slab be approximately ½” thicker than it would be without the extra concrete, but the reduction in forming complications as well as the time and effort required to verify that the construction is correct (not to mention the peace of mind you as the engineer of record will have) will often compensate for this added cost. The following is a typical detail depicting the concrete over-pour to achieve the step in a podium slab.

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The concrete spalls because the corrosion byproduct initially expands the on the metal forcing the concrete to dislodge. However, eventually the corrosion will consume and deteriorate the metal leaving only a fossilized looking void.

Severely Corroded Tendon Wires and Complete Voids Where Tendons Originally Existed

The spalling and corrosion evidence is limited to the bottom side only. The corrosion byproduct will also spall the concrete at the top, but since it does not fall it is not always as noticeable.

Corroding Slab Tendon at High Point Over Beam


343

Often a tendon will break in one location, but will loop out of the slab in a different location. The elastic energy will find the point of least resistance to loop, which is usually the location with the least concrete cover.

Broken Tendon Looping Out of Top of Slab

Broken Tendons Looping Out of Bottom of Slab

About the Authors K. Dirk Bondy

Dirk Bondy earned his Bachelor’s degree from California Polytechnic State University at San Luis Obispo in 1988 and his Master’s degree from the University of California at Berkeley in 1989. He is the president of Seneca Structural Engineering, Inc. and The Great American Cable Company II, Inc., both located in Laguna Hills, California. While he has been the engineer of record on millions of square feet of post-tensioned concrete structures he is probably best known for being the son of Ken Bondy. His professional interest and expertise are in the area of post-tensioned and reinforced concrete, seismic design, seismic retrofit and vertical load retrofit. In addition to his structural design experience, Mr. Bondy currently teaches Prestressed Concrete Design at the University of California at Los Angeles in the Spring Quarter, and has been an instructor at the University of California, Irvine and California Polytechnic State University, Pomona where he taught courses on Prestressed Concrete Design, Reinforced Concrete Design, Steel Design, Structural Design and Seismic Design. He has been published in numerous journals and conference proceedings. He is a registered Civil and Structural Engineer in the states of California, Nevada, Hawaii and Arizona as well as a licensed C50 contractor in the state of California. He is a licensed private pilot (single-engine, multi-engine and instrument ratings) with over 400 hours total pilot-in-command time. He resides in Laguna Hills, California with his wife Kristen and their three children; Cameron, Ryan and Elizabeth. Bryan Allred

Bryan Allred has been a practicing engineer since 1993 and is the Vice-President of Seneca Structural Engineering Inc. in Laguna Hills California. He received his Bachelors and Master’s degree in Civil Engineering from the University of California at Irvine and is a licensed civil and structural engineer in the state of California. Bryan specializes in the design of concrete buildings utilizing post-tensioned floor systems, post-tensioned slab on ground foundations and retrofits of existing building using external post-tensioning. He is a member of the Structural Engineers Association of California, American Concrete Institute and is a Fellow of the Post-Tensioning Institute where he is also a member of the Building Design, Slab on Ground and Education Committees. He has written several magazine articles relating to post-tensioned construction and engineering and has also given numerous post-tensioning educational seminars across the country. Bryan and his wife Marisa have three children, two beautiful girls and one ultra cool son.

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