Floor/ceiling assembly weight.
\\n\\n
More than half of the publishers listed alongside IntechOpen (18 out of 30) are Social Science and Humanities publishers. IntechOpen is an exception to this as a leader in not only Open Access content but Open Access content across all scientific disciplines, including Physical Sciences, Engineering and Technology, Health Sciences, Life Science, and Social Sciences and Humanities.
\\n\\nOur breakdown of titles published demonstrates this with 47% PET, 31% HS, 18% LS, and 4% SSH books published.
\\n\\n“Even though ItechOpen has shown the potential of sci-tech books using an OA approach,” other publishers “have shown little interest in OA books.”
\\n\\nAdditionally, each book published by IntechOpen contains original content and research findings.
\\n\\nWe are honored to be among such prestigious publishers and we hope to continue to spearhead that growth in our quest to promote Open Access as a true pioneer in OA book publishing.
\\n\\n\\n\\n
\\n"}]',published:!0,mainMedia:null},components:[{type:"htmlEditorComponent",content:'
Simba Information has released its Open Access Book Publishing 2020 - 2024 report and has again identified IntechOpen as the world’s largest Open Access book publisher by title count.
\n\nSimba Information is a leading provider for market intelligence and forecasts in the media and publishing industry. The report, published every year, provides an overview and financial outlook for the global professional e-book publishing market.
\n\nIntechOpen, De Gruyter, and Frontiers are the largest OA book publishers by title count, with IntechOpen coming in at first place with 5,101 OA books published, a good 1,782 titles ahead of the nearest competitor.
\n\nSince the first Open Access Book Publishing report published in 2016, IntechOpen has held the top stop each year.
\n\n\n\nMore than half of the publishers listed alongside IntechOpen (18 out of 30) are Social Science and Humanities publishers. IntechOpen is an exception to this as a leader in not only Open Access content but Open Access content across all scientific disciplines, including Physical Sciences, Engineering and Technology, Health Sciences, Life Science, and Social Sciences and Humanities.
\n\nOur breakdown of titles published demonstrates this with 47% PET, 31% HS, 18% LS, and 4% SSH books published.
\n\n“Even though ItechOpen has shown the potential of sci-tech books using an OA approach,” other publishers “have shown little interest in OA books.”
\n\nAdditionally, each book published by IntechOpen contains original content and research findings.
\n\nWe are honored to be among such prestigious publishers and we hope to continue to spearhead that growth in our quest to promote Open Access as a true pioneer in OA book publishing.
\n\n\n\n
\n'}],latestNews:[{slug:"stanford-university-identifies-top-2-scientists-over-1-000-are-intechopen-authors-and-editors-20210122",title:"Stanford University Identifies Top 2% Scientists, Over 1,000 are IntechOpen Authors and Editors"},{slug:"intechopen-authors-included-in-the-highly-cited-researchers-list-for-2020-20210121",title:"IntechOpen Authors Included in the Highly Cited Researchers List for 2020"},{slug:"intechopen-maintains-position-as-the-world-s-largest-oa-book-publisher-20201218",title:"IntechOpen Maintains Position as the World’s Largest OA Book Publisher"},{slug:"all-intechopen-books-available-on-perlego-20201215",title:"All IntechOpen Books Available on Perlego"},{slug:"oiv-awards-recognizes-intechopen-s-editors-20201127",title:"OIV Awards Recognizes IntechOpen's Editors"},{slug:"intechopen-joins-crossref-s-initiative-for-open-abstracts-i4oa-to-boost-the-discovery-of-research-20201005",title:"IntechOpen joins Crossref's Initiative for Open Abstracts (I4OA) to Boost the Discovery of Research"},{slug:"intechopen-hits-milestone-5-000-open-access-books-published-20200908",title:"IntechOpen hits milestone: 5,000 Open Access books published!"},{slug:"intechopen-books-hosted-on-the-mathworks-book-program-20200819",title:"IntechOpen Books Hosted on the MathWorks Book Program"}]},book:{item:{type:"book",id:"1937",leadTitle:null,fullTitle:"Advances and Applications in Mobile Computing",title:"Advances and Applications in Mobile Computing",subtitle:null,reviewType:"peer-reviewed",abstract:"Advances and Applications in Mobile Computing offers guidelines on how mobile software services can be used in order to simplify the mobile users' life. 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\r\n\tThalassemia disease has stood the test of time and has persisted for thousands of years in humans. Global Disease Burden with Thalassemia still makes it one of the formidable inherited genetic noncommunicable diseases of concern which propagates in families due to lack of access to adequate genetic counseling facilities.
\r\n\r\n\tNew developments in the form of improvement in stem cell transplantation and medication approval in the developed world have shown promise and need to be updated to every clinician managing thalassemia.
\r\n\tBasic science studies have provided new insights into the pathophysiology of β-thalassemia. Studies of genotypic and phenotypic heterogeneity among patients and a better understanding of the control of erythropoiesis have provided new targets for designing novel agents that can be tailored to individual patient needs. JAK-2 kinase inhibitors and agents targeting the GDF-11/SMAD pathway are in clinical trials.
\r\n\tThis book will attempt to discuss the historical background of the disease and present the most up-to-date material regarding disease management in today's world for the reader to be updated on the best practice management of the disease.
",isbn:"978-1-83969-158-4",printIsbn:"978-1-83969-157-7",pdfIsbn:"978-1-83969-159-1",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!0,hash:"23abb2fecebc48a2df8a954eb8378930",bookSignature:"Dr. Akshat Jain",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/10727.jpg",keywords:"History of Gene Mutation, Genetic Counselling, Anemia, Genotyping, Hemoglobin Electrophoresis, HLA typing, Hemolysis, Aplastic Anemia, Blood Transfusion, Laboratory Testing, Fetal Hemoglobin Modifiers, Gene Therapy",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:null,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"February 4th 2021",dateEndSecondStepPublish:"March 4th 2021",dateEndThirdStepPublish:"May 3rd 2021",dateEndFourthStepPublish:"July 22nd 2021",dateEndFifthStepPublish:"September 20th 2021",remainingDaysToSecondStep:"3 days",secondStepPassed:!1,currentStepOfPublishingProcess:2,editedByType:null,kuFlag:!1,biosketch:"A board-certified pediatrician with a specialization in pediatric hematology-oncology and stem cell transplantation. In collaboration with Harvard Medical School, he studied and reported the outcomes of a global hemophilia collaboration. He is a member of the American Board of Pediatrics, Hematology, and American Board of Pediatrics, also he is a Committee member for the American Society of Pediatric Hematology-Oncology Special Interest Group in Global Pediatric Hematology oncology.",coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"344600",title:"Dr.",name:"Akshat",middleName:null,surname:"Jain",slug:"akshat-jain",fullName:"Akshat Jain",profilePictureURL:"https://mts.intechopen.com/storage/users/344600/images/system/344600.jpg",biography:"Akshat Jain M.D. M.P.H.\n11175 Campus Street \nLoma Linda, California 92354\nPhone: (917) 331-3216\nakshatjainusa@gmail.com \n\nMEDICAL EDUCATION \n●\tS.S.R. Medical College, Belle Rive, Mauritius - MBBS, Bachelor of Medicine Bachelor of Surgery, 2007\n●\tPediatrics Residency Training ,The New York Medical College, Metropolitan Hospital , Dec2008-Dec 2011\n●\tPediatric Hematology Oncology and Stem Cell Transplant Fellowship, Cohen’s Children's Hospital of New York at LIJ-North Shore Health system. July 2012- September 2015\n●\tMaster’s in Public Health ,Hofstra University School of Public Health ,New York , August 2015\n\n\nHONORS/ AWARDS \n●\tThe New York Academy of Medicine Honorary Associate Award , December 2009\n●\tProgram Leadership Award - Committee of Interns and Residents (C.I.R./SIEU), April 2010\n●\tAmerican Academy of Pediatrics Program Delegate Award, New York Medical College, December 2010.\n●\tCitation of Honor from New York County for Excellence in Medicine and Service to Long Island, New York,Nassau county executive chambers , August 15,2015 \n●\tTimes of India N.R.I. ( Non Resident Achiever ) award , August 2015 \n●\tCertificate for academic excellence –Hofstra University School of Health Science & Human Services, New York August 26, 2015\n●\tAmerican Society of Hematology Leadership Institute Award , April 2016\n●\tGlobal Health Speaker Award , convener of Global Health Symposium, Hofstra NorthWell School of Medicine and School of Public health , May 2016\n●\tInternational Pediatric Lymphoma Meeting ,Session Chairperson of Pediatric Lymphoma , Indian Society of Hematology and Oncology , November 2016\n●\tContent Leader Award for Hematology perspective’s in the Global CoronaVirus Pandemic Preparedness Response for Medical Association of physicians of Indian Origin, April 2020.\n●\tConvener and Chairperson International Webinar for COVID 19 Coagulopathy, May 2020. \n●\tFeatured in the Top Doctors magazine 2020, ranked top pediatric Hematologist Oncologist for Southern California.\n\nNATIONAL/INTERNATIONAL POSITIONS \n●\tHofstra University Dean Advisory Board for the School of Health Professions, December 2017\n●\tEditorial Board – American Society of Pediatric Hematology Oncology Communications Committee, International Journal of Hematology Research (ISSN 2409-3548)\n●\tReviewer - JAMA Pediatrics (ISSN: 2168-6203), British Medical Journal (ISSN, 1468-5833), JAMA Oncology (ISSN: 2374-2437), International Journal of Hematology Research (ISSN 2394—806X), Journal of Pediatric Hematology and Oncology (ISSN: 1536-3678), New England Journal of Medicine (Resident 360). \n●\tMember – Core committee: American Cancer Society (A.C.S.) and American Academy of Pediatrics (A.A.P.) - Joint global pediatric Oncology taskforce.\n●\tAdvisor -World Health Organization, South East Asia for maternal and child health initiatives.( 2013-Ongoing) , Ministry of Health and Family Welfare ,Government of India ( 2014- Ongoing ) , American Academy of Pediatrics &American Cancer Society Global Taskforce on Pediatric Cancers.( 2014-Ongoing )\n●\tEditor – AAPI journal (American Association of Physicians of Indian Origin. Circulation -40,000)\n●\tVisiting Professorship in Hematology Oncology and Stem Cell Transplantation, Rajasthan University of Medical Sciences, India. ( 2009-Ongoing )\n●\tIndustry Advisor – Bayer, UniQure, Sanofi-Genzyme, Takeda, CSL Behring\n●\tDirector of International Bone Marrow Failure Consortium- India, part of the Global Hematology Initiative of Cohen Children’s Medical Center, New York, August 2015-2017. \n●\tCommittee member for the American Society of Pediatric Hematology Oncology Special Interest Group in Global Pediatric Hematology oncology. ( 2016- Ongoing)\n\n\n WORK EXPERIENCE \nNov 2017- Current Loma Linda University Children’s Hospital \n Director Division of Pediatric Hematology \n Director, Comprehensive Hemophilia Program\n Director, Comprehensive Sickle Cell Program \n Division of Pediatric Hematology Oncology and Stem Cell Transplantation\n Professor of Public Health, Loma Linda University School of Public Health \n\nMar 2017– Oct 2017 Pediatrics and Pediatric Hematology Oncology Practice \n Adventist Health Ukiah Valley, California \n\nSept 2015 –Aug 2016 Assistant Professor Pediatrics, Hofstra North Shore LIJ School of Medicine \n Section Head –Global Pediatric Hematology Oncology and Stem Cell Transplantation\n North Shore LIJ Health system.\n Associate Adjunct Faculty, Hofstra University School of Public Health.\n\nJuly 2012 – Sep 2015 The Steven and Alexandra Cohen’s Children's’ Hospital of New York at LIJ-North Shore \n Hofstra University - Pediatrics Hematology Oncology and Stem Cell Transplant Fellowship \n Chief - Jeffrey Lipton MD\n\nDec 2011- April 2012 Global Health : SMS Medical College and Group of Hospitals, Government of India \n Project Director for Project A.G.N.I. - Set up a regional Lead Poisoning prevention and \n anemia nodal center \n \n Course Director - Pediatric Subspecialty training module for Pediatricians at J.K. Lone \n Children’s Hospital for Government of India. \n\nDec 08- Dec 2011 The New York Medical College, Residency in Pediatrics \n Metropolitan Hospital, NY\n Maria Fareri Children's Hospital at Westchester.\n The Memorial Sloan Kettering Hospital. NY\n House staff on Stem Cell Transplantation service.\n \nApril – August 2008 Oklahoma State Medical Association (O.S.M.A.) Externship Program\n The Integris Baptist Teaching Hospital and Nazih Zuhdi Transplant Center\n\nRESEARCH EXPERIENCE \nNov 2017 – Ongoing: Current and ongoing – Director, Inherited Bleeding Disorder Experimental Therapeutics Program, Loma Linda University School of Medicine\nJan 2014 –July 2015 - Hofstra University School of Public Health \n Needs Assessment to barriers in cancer care for newly diagnosed patients in a resource \n Limited setting. \n Principal Investigator - Akshat Jain, Co-PI -Corrine Kyriacou \n\nJune 2012- July 2015 - Steven and Alexandra Cohen Children’s Medical Center \n Study – Non Invasive assessment of endothelial dysfunction in children with Sickle cell \n Disease. \n Co-Principal Investigator – Banu Aygun MD\n Study – Multicenter study assessing outcome of Reduced Intensity Conditioning for \n patients undergoing hematopoetic stem cell transplantation for Sickle cell disease . \n Co-Principal Investigator – Indira Sahdev MD\n \nJan 2012- Mar12 A.G.N.I. (Anterograde Growth Normalization Initiative) \n Project Director, Project of Government of India for establishment of Universal Lead \n Independent Pilot project to study effects of Elevated Blood Lead levels in children \n suffering from Developmental disorders- Adapted by W.H.O. 2014 for a National Level \n Lead Screening program, India \n \nJan 2009- Dec11 The New York Medical College, Metropolitan Hospital Center. NY\n Resident Physician – Hypothalamic volumes in patients with Growth Hormone deficiency.\n Maria Fareri Children's hospital / Dr.Richard Noto - Pediatric Endocrinology\n \nApril 2008-Dec 08 Nazih Zuhdi Transplant Institute, Integris Baptist Hospital, Oklahoma City\n Project – Single institution outcome study for Solid organ transplants\n Research Assistant Department of Hepatology\n \nOct 2007 – Dec07 Mount Sinai School of Medicine, New York, NY\n Project- Arterio-venous fistula post liver transplantation.\n Research mentor-Dr. Charissa Chang, Assistant Professor in Department of Liver Diseases. \n\nCERTIFICATION\n\n1.\tCalifornia State Medical License 8/2016- Present , New York State Licensure 8/2013-12/16\n2.\tAmerican Board of Pediatrics - Board certified, 11/14- Present\n3.\tAmerican Board of Pediatric Hematology Oncology – Board Certified , 06/2018- Present\n4.\tNeonatal Advanced Life Support 06/2009-Present \n5.\tPediatric Advanced Life Support 06/2009-Present \n6.\tECFMG Certification 12/2007-Present \n\nORAL PRESENTATIONS \n\n\n1.\tLeukemia and Lymphoma Society of America C.M.E. Symposium presentation – Leukemia and Beyond: Advances in Cancer Care and Blood Disorders in the 21st Century, October 2019\n2.\tLoma Linda University School of Medicine – Grand Rounds, Advances in the Management of Sickle Cell Disease, March 2019.\n3.\tLoma Linda University School of Medicine – Experimental Therapeutics in Sickle Cell Disease – New Horizons at Loma Linda , November 2018 .\n4.\tAdventist Health Ukiah , California - Neurological Defects of Iron Deficiency and Lead Poisoning in Humans , October 2017\n5.\tHofstra NorthWell School of Medicine - National Public Health Symposium on Global Public Health , Convener and Moderator ,April 2016 \n6.\tCleveland Clinic Children’s Medical Center, Ohio – Non BCR-ABL Myeloproliferative syndromes of childhood, January 19, 2016.\n7.\tChildren’s Hospital at SMS Medical College ,India – Pediatric Hematology Oncology Emergencies for the Tropics, November 13, 2015 \n8.\tHarvard Medical School, Boston Children’s Hospital Division of Pediatric Hematology – Advances in Global Hematology, Annual Hemophilia Twining symposium, August 2, 2015.\n9.\tNew York Medical College as Grand Rounds, Division of Pediatrics – Emergencies in Pediatric Hematology and Oncology, April 2015.\n10.\tMaurice A. Deane School of Law, Hofstra University, New York - Healthcare Access to Undocumented immigrants: Immigration reform and its impact, March 2015.\n11.\tPediatric Academic Society/Society of Pediatric Research (PAS/SPR) as platform presentation, Vancouver, BC - Global Child Health in Rich & Poor Countries Lessons Learned from Indigenous Health, May 3 2014.\n12.\tDepartment of Medicine and Medical Oncology, as Guest International faculty , SMS Medical College, India - Advances in Stem Cell Transplantation – January 2014.\n13.\tInternational health conference, Global Association of physicians of Indian Origin , New Jersey – Impact of Lead Intoxication in Low to middle income countries , August 2012.\n14.\t139st APHA Annual Meeting and Exposition 2011, Boston - Use of decision support in a Harlem pediatric emergency department to increase prescription of controller medicines to patients with poorly controlled asthma - Wilson Wang, Carolina Valez, Nicole Falanga, Vikas Bhambhani , Akshat Jain , Farhad Gazi, David Spiller, Paper no-227188 , November 2011 \n15.\tThe New York Academy of Medicine, Resident award night - False negative result in newborn screening for Congenital Adrenal hyperplasia - July 2009.",institutionString:"Loma Linda University Children's Hospital",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"0",totalChapterViews:"0",totalEditedBooks:"0",institution:{name:"Loma Linda University Children's Hospital",institutionURL:null,country:{name:"United States of America"}}}],coeditorOne:null,coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"16",title:"Medicine",slug:"medicine"}],chapters:null,productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"280415",firstName:"Josip",lastName:"Knapic",middleName:null,title:"Mr.",imageUrl:"https://mts.intechopen.com/storage/users/280415/images/8050_n.jpg",email:"josip@intechopen.com",biography:"As an Author Service Manager my responsibilities include monitoring and facilitating all publishing activities for authors and editors. From chapter submission and review, to approval and revision, copy-editing and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review, and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. Whether that be identifying an exceptional author and proposing an editorship collaboration, or contacting researchers who would like the opportunity to work with IntechOpen, I establish and help manage author and editor acquisition and contact."}},relatedBooks:[{type:"book",id:"6550",title:"Cohort Studies in Health Sciences",subtitle:null,isOpenForSubmission:!1,hash:"01df5aba4fff1a84b37a2fdafa809660",slug:"cohort-studies-in-health-sciences",bookSignature:"R. Mauricio Barría",coverURL:"https://cdn.intechopen.com/books/images_new/6550.jpg",editedByType:"Edited by",editors:[{id:"88861",title:"Dr.",name:"R. Mauricio",surname:"Barría",slug:"r.-mauricio-barria",fullName:"R. 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Venkateswarlu",coverURL:"https://cdn.intechopen.com/books/images_new/371.jpg",editedByType:"Edited by",editors:[{id:"58592",title:"Dr.",name:"Arun",surname:"Shanker",slug:"arun-shanker",fullName:"Arun Shanker"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"878",title:"Phytochemicals",subtitle:"A Global Perspective of Their Role in Nutrition and Health",isOpenForSubmission:!1,hash:"ec77671f63975ef2d16192897deb6835",slug:"phytochemicals-a-global-perspective-of-their-role-in-nutrition-and-health",bookSignature:"Venketeshwer Rao",coverURL:"https://cdn.intechopen.com/books/images_new/878.jpg",editedByType:"Edited by",editors:[{id:"82663",title:"Dr.",name:"Venketeshwer",surname:"Rao",slug:"venketeshwer-rao",fullName:"Venketeshwer Rao"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"4816",title:"Face Recognition",subtitle:null,isOpenForSubmission:!1,hash:"146063b5359146b7718ea86bad47c8eb",slug:"face_recognition",bookSignature:"Kresimir Delac and Mislav Grgic",coverURL:"https://cdn.intechopen.com/books/images_new/4816.jpg",editedByType:"Edited by",editors:[{id:"528",title:"Dr.",name:"Kresimir",surname:"Delac",slug:"kresimir-delac",fullName:"Kresimir Delac"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"18559",title:"Modeling & Simulation of Hysteresis Current Controlled Inverters Using MATLAB",doi:"10.5772/21143",slug:"modeling-simulation-of-hysteresis-current-controlled-inverters-using-matlab",body:'Hysteresis inverters are used in many low and medium voltage utility applications when the inverter line current is required to track a sinusoidal reference within a specified error margin. Line harmonic generation from those inverters depends principally on the particular switching pattern applied to the valves. The switching pattern of hysteresis inverters is produced through line current feedback and it is not pre-determined unlike the case, for instance, of Sinusoidal Pulse-Width Modulation (SPWM) where the inverter switching function is independent of the instantaneous line current and the inverter harmonics can be obtained from the switching function harmonics.
This chapter derives closed-form analytical approximations of the harmonic output of single-phase half-bridge inverter employing fixed or variable band hysteresis current control. The chapter is organized as follows: the harmonic output of the fixed-band hysteresis current control is derived in Section 2, followed by similar derivations of the harmonic output of the variable-band hysteresis controller in Section 3. The developed models are validated in Section 4 through performing different simulations studies and comparing results obtained from the models to those computed from MATLAB/Simulink. The chapter is summarized and concluded in section 5.
Fig.1 shows a single-phase neutral-point inverter. For simplicity, we assume that the dc voltage supplied by the DG source is divided into two constant and balanced dc sources, as in the figure, each of value
In Fig.2, the fundamental frequency voltage at the inverter ac terminals when the line current equals the reference current is the reference voltage,
Single-phase half-bridge inverter with fixed-band hysteresis control.
Referring to Fig.2, when valve
Reference voltage calculation and the instantaneous outputs.
The bang-bang action delivered by the hysteresis-controlled inverter, therefore, drives the instantaneous line current to track the reference within the relay band
The approach described in this section closely approximates the error current produced by the fixed-band hysteresis action, by a frequency-modulated triangular signal whose time-varying characteristics are computed from the system and controller parameters. Subsequently, the harmonic spectrum of the error current is derived by calculating the Fourier transform of the complex envelope of frequency modulated signal.
Results in the literature derived the instantaneous frequency of the triangular error current
and therefore:
where the average switching (carrier) frequency
and
Detail ofea(t).
Effect of va* on the error current duty cycle.
Examining (Eq. 2), the instantaneous frequency
Now, with the help of Fig.3, we define the instantaneous duty cycle of the error current
Implicit into (Eq. 3) is the reference voltage
As the Fourier series of the triangular signal converges rapidly, the error current spectrum is approximated using the first term of the series in (Eq. 6). Therefore truncating (Eq. 6) to
where
determines the frequency bandwidth
that contains 98% of the spectral energy of the modulated sinusoid in (Eq. 7). To simplify (Eq. 7) further, we use the following convenient approximation (see Appendix-A for the derivation): Given that,
Therefore (Eq. 7) becomes,
Substituting
Next, the cosine term in (Eq. 12) is simplified by using the infinite product identity and truncating to the first term. That is,
Substituting (Eq. 13) into (Eq. 12) and manipulating, the error current approximation becomes:
where
where
The positive frequency half of the spectrum
where
Using the recurrence relation of the Bessel functions,
the positive half of the error current spectrum takes the final form:
where,
Effect of changing β on the harmonic spectrum.
The calculation of the non-characteristic harmonic currents using (Eq. 20) is easily executed numerically as it only manipulates a single array of Bessel functions. The spectral energy is distributed symmetrically around the carrier frequency
The harmonic model derived in the previous section describes the exact spectral characteristics of the error current by including the duty cycle
where the carrier (average) frequency
AC harmonics transfer to the inverter dc side.
The hysteresis switching action transfers the ac harmonic currents into the inverter dc side through the demodulation process of the inverter. As the switching function is not defined for hysteresis inverters, the harmonic currents transfer can be modeled through balancing the instantaneous input dc and output ac power equations.
With reference to Fig. 1, and assuming a small relay bandwidth (i.e.
The power balance equation over the switching period when
Using the instantaneous output voltage
in (Eq. 24), the dc current
where
The positive half of the dc current spectrum is thus computed from the application of the Fourier transform and convolution properties on (Eq. 27), resulting in
where
Each spectrum band of the ac harmonic current creates two spectrum bands in the dc side due to the convolution process implicitly applied in (Eq. 28). For instance, the magnitude of the ac spectrum band at
The harmonic performance of the hysteresis inverter in Fig. 7 under distorted dc and ac system voltages is analyzed. The presence of background harmonics in the ac and dc voltages will affect the instantaneous frequency of the inverter according to (Eq. 30) as
where the dc distortion
Hysteresis inverter operating with distorted system voltages.
Notice that in (Eq. 31),
where
are the frequency noise terms due to the system background distortions. The amplitude modulation indices of the ac and dc harmonic distortions are given by :
Integrating (Eq. 32), the error current
In (Eq. 35): the carrier frequency
where
Applying the Fourier transform and convolution properties on (Eq. 35), the positive half of the frequency spectrum
Where
are the ac and dc modulating spectra. Generally, for any
The harmonic line generation of the half-bridge inverter of Fig.1 under the variable-band hysteresis current control is derived. The constant switching frequency of the error current in (Eq. 2), i.e.
where the maximum value of the modulating relay bandwidth is
and
Substituting (Eq. 41) in (Eq. 43) and then applying the Fourier transform, the positive half of the frequency spectrum of
The error current spectrum in (Eq. 44) consists of a center band at the switching frequency
The approach developed in 2.2.4 also applies to compute the dc current harmonic spectrum when the variable-band hysteresis control. The positive half of the dc current harmonic spectrum is computed by substituting (Eq. 44) in (Eq. 28).
The presence of background harmonics in the ac and dc voltages, given in (Eq. 31) will affect the instantaneous frequency of the inverter according to (Eq. 30). Subsequently, to achieve the constant switching frequency
where
where
The new terms introduced by the background distortion appear as amplitude modulations in (Eq. 45). The error current
The harmonic spectrum of the error current
where
Examining (Eq. 49), the presence of the harmonic distortions in the system tends to scatter the spectrum over lower frequencies, more specifically, to
The harmonic performance of the half-bridge inverter under the fixed- and variable-band hysteresis control is analyzed. Results computed from the developed models are compared to those obtained from time-domain simulations using MATLAB/Simulink. Multiple simulation studies are conducted to study the harmonic response of the inverter under line and control parameter variations. The grid-connected inverter of Fig.1 is simulated in Simulink using:
The ac outputs of the half-bridge inverter under the fixed-band hysteresis current control are shown in Fig.8. the fundamental component
Inverter ac outputs under fixed-band hysteresis control.
Simulation results obtained from the developed model and Simulink.
The harmonic parameters of the model are computed the system and controller parameters as follows: substituting the reference voltage in (Eq. 4) results in an amplitude modulation index of
The spectrum bands are concentrated around the order of the carrier frequency and are stepped apart by two fundamental frequency orders
To study the effect of line parameter variations on the harmonic performance of the inverter, the DG source voltage is decreased to have the dc voltage
Ea(f)| when Vc is decreased to 350V.
With reference to the results shown in Fig.10, the harmonic spectrum
The total spectral energy of the error current depends on the relay bandwidth
|Ea(f)| when the system inductance is decreased by 25%.
Results from reducing ε by 50%.
Next, the system and control parameters are set to their original values and the inductance is decreased by 25% to
The width of the relay band is reduced by half while maintaining the rest of the parameters at their base values. As (Eq. 4) indicates,
To study the harmonic performance of the inverter under distorted system voltages, the system and control parameters are set to the original values and the 11th order voltage oscillator
Effect of injecting the 11th ac harmonic voltage on the inverter ac outputs.
Comparing Fig. 8 and Fig. 13, the reference voltage is distorted due to the presence of the 11th voltage oscillator in the source. The output voltage of the inverter is still bipolar, i.e.
Instantaneous frequency of ea(t) when vs is distorted.
According to (Eq. 32), the carrier frequency
Error spectrum when vsa contains the 11th oscillator voltage.
Fig. 15 compares the harmonic spectrum
Similar analysis is performed to study the harmonic performance of the inverter when the dc voltage contains the distortion
Effect of injecting the 8th dc harmonic voltage on the inverter ac outputs.
The dc distortions impose additional noise component on the instantaneous frequency, see Fig.17, and subsequently, according to (Eq. 38) the harmonic spectrum is drifting to lower order harmonics as shown in Fig.18.
Frequency of ea(t) when the input dc is distorted.
Error spectrum when the 8th dc background distortion exists.
The harmonic performance of the same half-bridge inverter used in section 2.4.1 is analyzed when the variable-band hysteresis current control is employed. Similar harmonic studies to those in the previous section are performed to compute the spectral characteristics of the inverter harmonic outputs using the developed models in section 2.3 and compare them with results obtained from time-domain simulations using Simulink.
Instantaneous outputs of the variable-band hysteresis control.
The instantaneous line outputs of the single-phase inverter operating under variable hysteresis control are shown in Fig.19. With the maximum relay band
Comparing model results to Simulink.
The dc voltage
The new values are shown in Fig.21. Consequently, the spectrum
Error spectra when Vc=350 V.
Error spectra when relay bandwidth is halved.
when
The value of the inductance is decreased to
Inverter harmonic response to 25% reduction in L.
DC current harmonics under variable-band control.
Lower inductance results in higher switching frequency. The harmonic spectrum
Error current under distorted dc and ac system voltages.
The harmonic performance of the inverter under distorted system voltages is studied by simulating the system with the distorted 8th order dc voltage
The spectral characteristics of the line current under the fixed- and variable-band hysteresis control are compared in this section. For identical system configurations and controller settings, i.e.
The THD of the line current is directly proportional to relay bandwidth. For similar controllers setting
A closed-form numerically efficient approximation for the error current harmonic spectrum of single-phase two-level inverters employing either fixed- or variable-band hysteresis current control is derived. The models are based on the amplitude and frequency modulation theorems.
The instantaneous frequency of the inverter is first derived. Then it is used to closely approximate the error current by a modulated sinusoid. The error current harmonic spectrum is basically the Fourier transform of error current complex envelop. In the case of the fixed-band control, the spectrum reduces to a series of Bessel functions of the first kind whose argument is implicitly expressed in terms of the system and controller parameters, where as in the variable-band mode, the spectrum reduces to a 3-element array.
The spectral characteristics such as the carrier frequency and frequency bandwidth are derived analytically and related to line parameters; it is a development useful in inverter-network harmonic interactions. Unlike time-domain simulators, the developed models provide fast numerical solution of the harmonic spectrum as they only involve numerical computation of single arrays. Simulation results agree closely with the developed frequency-domain models in terms of frequency order, magnitude and angle.
In addition to the single-phase two-level inverter, the proposed approximations apply also to the harmonic output of certain three-phase two-level inverters where independent phase control is applicable, such as the neutral point inverter, and the full-bridge inverter in bipolar operation.
The models detailed in this chapter can be extended in a number of ways, both in terms of improving the proposed models as well as in the application of the models in other PWM applications.
The developed models neglected the dynamics of the Phase-Locked Loop (PLL) and assumed that the inverter line current tracks a pure sinusoidal reference current. Possible extensions of the models include the effect of the harmonic current propagation through the ac network and the deterioration of the terminal voltage at the interface level and its effect on the reference current generation. As the PLL synchronizes the reference current with the terminal voltage, the propagation of harmonic currents might affect the detection of the zeros-crossings of the terminal voltage resulting in generating a distorted reference current. The hysteresis controller consequently will force the line current to track a non-sinusoidal reference which, in turn, modifies the harmonic output of the inverter.
The implementation of an LC filter at the inverter ac terminals could trigger a parallel-resonance which tends to amplify the harmonic voltages and currents in the ac network leading, in some cases, to potential harmonic instabilities. The improvement of the developed models to include the effect the filter capacitance on the harmonic performance of the inverter is an interesting improvement.
Reviews of the developed models show that hysteresis current controlled inverters can have a ‘switching function’ notation similar to those inherit with the Sinusoidal PWM inverters. The switching function is based on the error current characteristics which implicitly depend on the system and controller parameters. Such development will enable the various time- and frequency-domain algorithms developed for the harmonic assessment of linear PWM inverters to be applied to hysteresis controlled inverters.
Harmonic load flow studies of systems incorporating inverters with hysteresis current control can be formulated based on the developed models. The iterative solution of the harmonic load flow shall incorporate the harmonic magnitudes and angles obtained from the developed models for a faster convergence to the steady state solution.
Function
A1. Approximation of f(x)=sin(πx)x(1−x) by f¯(x)=(4−π)⋅sin(πx)+π.
satisfies the same properties in
The prevailing system used for the construction of single-family homes in the USA is platform framing using light wooden dimensional lumber. Structural assemblies such as the roof, floors, and walls are generally constructed with nominal 50.8 mm (2 inch) lumber members ranging in nominal depths from 101.6 to 304.8 mm (4–12 inches) and sheathed with structural wood panels for stability and security, such as oriented strand board (OSB) or plywood.
\nWood structural materials are preferred by US homebuilders largely because (1) the US home building industry is mostly familiar with wood framing method, (2) the units of construction (i.e., studs, joists, panels, etc.) are small and easily transportable, and (3) wood-framed structures can be erected without the need for specialized tools or large equipment.
\nIn this chapter, the complete process of designing a typical US residential dwelling using wood-frame systems will be illustrated. The typical US design methodology and basis will be used to accomplish the designs. The International Residential Code (IRC) [1] is the design basis used by most authorities to regulate the design and construction of single-family residences. The following major aspects are discussed in this chapter:
Provide introductory material such as the description of the home to be designed, applicable design codes, and external loading assessment for residential structures.
Design the home using a wood-framed platform system. The load path will be discussed as well as specific design codes relating to wood-framed structures. The result of specifying and detailing typical structural elements of the home will be specified and details provided.
The scope is limited to the structural design and performance of one single-family residential dwelling. The load-bearing wall systems are the primary components of the building enclosure, and the structural properties of the wall system are only one of many considerations that must be taken into account. While cladding compatibility, thermal performance or the hygrothermal characteristics of a wall system are very important, such aspects are not the focus of this study and will not be discussed.
\nThe home design considered in this study is a two-story regular-shaped home with a basement and attached two-car garage. The floor plan was provided by S&A Homes, which is a midsized homebuilder that builds homes and provides architectural design services to customers in Pennsylvania and West Virginia. The floor plans and drawings for one of their standard home packages are provided in the Appendix. Clients of S&A Homes can select this floor plan from an array of floor plans and make slight variations to it if desired. S&A Homes will then design, detail, and construct the home for the client on the chosen lot, typically one of S&A’s own residential developments.
\nThe home plan/style shown in the Appendix is a popular model in S&A’s territory and is representative of the size and style of homes desired by the average homebuyer of this decade. The home consists of nearly 214 m2 (2300 ft2) of finished floor area with the basement available for finishing if so desired by the prospective homeowner. The floor plan has features typically seen in modern homes. The first floor contains a large kitchen open to the family room with access to both the dining room and the attached two-car garage. The second floor has four bedrooms with the master suite containing its own large bathroom as well as a sitting area and walk-in closet (WIC).
\nThe IRC is the prevailing design code used for the construction of one- or two-family dwellings in the USA. The 2015 IRC [1] is the current adopted code in the State College, PA area, and will be used as the governing design code for this study. In order to construct a single-family dwelling, the homebuilder must first apply to the local code office for a building permit. It is necessary to provide a complete architectural plan set detailing how the builder intends to comply with the requirements of the IRC, along with several other items such as the manual J [2] heat loss-gain calculations for the structure and selection of energy compliance path. The IRC largely provides a prescriptive basis for home design and in many instances is adequate for single-family home design. The envelope and structural components are typically selected by the architect, builder, or homeowner from design tables within the code. If prefabricated engineered components such as I-joists, laminated veneer lumber (LVL) components, or roof trusses are used in design, a structural engineer is required to review their specification and application.
\nThis is typically the extent of a structural engineer’s involvement in residential design other than specialized situations not covered by the IRC and occasionally foundation design. If engineered design is necessary in conjunction with the prescriptive standards, then compliance with the 2015 International Building Code (IBC) [3] requirements for those portions of the design is required. Engineers will conduct their analysis based on requirement set forth in the IRC, IBC if necessary, and ASCE 7-10 minimum design loads for buildings and other structures (ASCE 7) [4] [ASCE stands for American Society of Civil Engineers]. The IRC and IBC also permit designers to refer to the 2015 AWC Wood Frame Construction Manual (WFCM) [5] for an alternative prescriptive or engineered approach [AWC stands for American Wood Council].
\nThis study will focus on the appropriate residential structural building loads for the State College, PA area, for an example design case. The designs will include only the effects of dead loading, floor live loading, roof live loading, snow loading, and wind loading. Residential structures in ordinary situations are designed to resist both gravity loads and lateral loads. External loading for homes is prescribed in either Chapter 3 of the 2015 IRC or in ASCE 7. ASCE 7 is the standard referenced in the 2015 IRC, and therefore this version will be referenced in this study. Both the IRC and the ASCE 7 will be used to develop the external loads for this study. In addition to the external loads, the serviceability criteria must also be considered. For this design, only live load deflection limits will be considered.
\nThe gravity loads are those loads that act in the direction of gravity. The gravity loads of importance for residential structures are dead load (DL), floor live load (LL), roof live load (RL), and snow load (SL).
\nDead load is the load that is permanently and continuously applied to a structure. Typically, dead load refers to the self-weight of the material used in construction or a load that is applied in a permanent nature such as a known location of a piece of heavy equipment or a large island in the kitchen. Unless noted otherwise, the S&A Homes dead load criteria will be used for the wood-framed design of this home. These loads are typical for residential design and were largely derived from ASCE 7 Table C3-1. Dead loads are listed in Tables 1, 2, 3.
\nSub-component | \nWeight N/m2 (lbf/ft2) | \n
---|---|
Carpet/vinyl | \n47.9 (1.0)a | \n
19.1 mm (¾ in) plywood | \n114.9 (2.4) | \n
301.6 mm (11 7/8 in) I-joistsb | \n91.0 (1.9) | \n
Mechanical allowance | \n95.8 (2.0) | \n
12.7 mm (½ in) gypsum ceiling | \n105.3 (2.2) | \n
Total | \n≈454.9 (10) | \n
Floor/ceiling assembly weight.
For floor areas known to have ceramic tile floor covering, increase load to 0.96 kN/m2 (20 lbf/ft2).
Weight is derived from Weyerhaeuser publication #TJ-4000 for 230 or 360 series joists.
Sub-component | \nWeight | \n
---|---|
Exterior wall assemblya | \n526.7 N/m2 (11.0 lbf/ft2) | \n
Interior wall assemblyb | \n383.0 N/m2 (8.0 lbf/ft2) | \n
Plain concrete | \n22.8 kN/m3 (145 lbf/ft3) | \n
Reinforced concrete | \n23.6 kN/m3 (150 lbf/ft3) | \n
Miscellaneous materials.
2 × 6 wood studs at 406.4 mm (16 inch) O.C. with 12.7 mm (½ inch) gypsum wallboard and vinyl siding.
Wood or steel studs with 12.7 mm (½ inch) gypsum wallboard on each side.
Live loading is a gravity loading that is temporary or intermittent in nature. The three live loads considered for the design of this home are floor live (LL), roof live (RL), and snow load (SL). The IRC prescribes the minimum uniformly distributed loads that must be used by designers for residential structures. Such minimum loads listed in Table 4 will be used for this study.
\nLoad description | \nWeight kN/m2 (lbf/ft2) | \n
---|---|
LL (sleeping rooms) | \n1.44 (30.0) | \n
LL (other) | \n1.92 (40.0) | \n
LL (habitable attics) | \n1.44 (30.0) | \n
LL (attics w/limited storage)a,b | \n0.96 (20.0) | \n
LL (Attics w/o limited storage)c | \n0.48 (10.0) | \n
Roof live load | \n0.77 (16.0) | \n
Design roof snow loadd | \n1.44 (30.0) | \n
Minimum uniformly distributed live loads.
Attics defined as the unfinished area between the roof and the ceiling of the floor below.
Limited storage refers to non-habitable attic space greater than or equal to 1.07 m (42 inch).
Add to attic space less than 1.07 m (42 inch).
Based on State College area prescriptive requirements. Applied on the horizontal projection rather than along the slope.
The only lateral load being considered for this study is the wind loading. In the State College area, seismic loading does not typically control the design of structural components. The procedures in ASCE 7 will be used to determine wind loading, e.g., Chapter 28 Envelope Procedure Part 2 can be used for this structure. Chapter 28 requires that the structure meets the definition of a low-rise, enclosed simple diaphragm building that is regular-shaped in accordance with Section 26.2.
\nThe wind loads calculated in Table 6 are based on the parameters listed in Table 5 and in accordance with Figure 1. The simplified design wind pressure magnitudes in Tables 6 and 7 include both windward and leeward pressures. The combined pressure will be applied to only the windward side of the structure. For this design, two load cases must be evaluated because the roof pitch is between 25 and 30 degrees. Additionally, these two cases must be compared to the minimum load case described in ASCE 7 Section 28.6.4. The case that produces the larger load effect will be used for design of structural members.
\nParameter | \nDescription | \n
---|---|
Risk category | \nII | \n
Basic wind speed (V) | \n51 m/s 115 mph | \n
Exposure category | \nB | \n
Topographic factor (Kzt) | \n1.0 | \n
Mean roof height | \n7.0 m (23 ft) | \n
Adjustment factor (λ) | \n1.0 | \n
Roof pitch | \n30 degrees | \n
Wind load parameters.
ASCE 7-10 Chapter 28 wind loading designation (with permission from the ASCE).
Zones | \nCase 1 | \nCase 2 | \nMinimum | \n
---|---|---|---|
A | \n1.13 (23.6) | \n1.13 (23.6) | \n0.77 (16) | \n
B | \n0.77 (16.1) | \n0.77 (16.1) | \n0.38 (8) | \n
C | \n0.90 (18.8) | \n0.90 (18.8) | \n0.77 (16) | \n
D | \n0.62 (12.9) | \n0.62 (12.9) | \n0.38 (8) | \n
E | \n0.09 (1.8) | \n0.44 (9.1) | \n0 | \n
F | \n−0.68 (−14.3) | \n−0.34 (−7.1) | \n0 | \n
G | \n0.03 (0.6) | \n0.38 (7.9) | \n0 | \n
H | \n−0.59 (−12.3) | \n−0.24 (−5.0) | \n0 | \n
EOH | \n−0.40 (−8.3) | \n−0.40 (−8.3) | \n0 | \n
GOH | \n−0.45 (−9.5) | \n−0.45 (−9.5) | \n0 | \n
Simplified design wind pressure (Ps) case A θ = 30.
Values in kN/m2 (lbf/ft2).
Zones | \nCase 1 | \nMinimum | \n
---|---|---|
A | \n1.01 (21.0) | \n0.77 (16) | \n
C | \n0.67 (13.9) | \n0.77 (16) | \n
E | \n−1.21 (−25.2) | \n0 | \n
F | \n−0.68 (−14.3) | \n0 | \n
G | \n−0.68 (−14.3) | \n0 | \n
H | \n−0.53 (−11.1) | \n0 | \n
Simplified design wind pressure (Ps) case B θ = 0.
Values in kN/m2 (lbf/ft2).
The main serviceability criterion considered in the design of residential homes is deflection. The IRC prescribes the maximum allowable deflection of structural members and assemblies. Excessive deflections can cause problems for the occupants and potentially damage to nonstructural components such as cladding or fenestration. Excessive interior floor deflections are generally noticed in the form of floor vibration or “spongy” floors. Excessive deflection of roof members can lead to ponding and ultimately moisture issues or overloading of structural members. A portion of Table R301.7 from the IRC that prescribes residential deflection limits is reproduced below in Table 8.
\nSub-component | \nSpan ratio | \n
---|---|
Interior walls and partitions | \nHeight/180 | \n
Floors and plaster ceilingsa,b | \nLength/360 | \n
All other structural members | \nLength/240 | \n
Exterior walls—brittle finish | \nLength/240 | \n
Live load maximum deflection limits.
Limit floor beam deflection to 12.7 mm (½ inch).
Limit I-joist deflection ratio to length/480.
Both allowable stress design (ASD) and load resistance and factor design (LRFD) load combinations will be utilized for different aspects of the home structural design. For example, the ASD approach will be used for wood design, whereas the LRFD approach will be used for concrete foundation design. Approaches for the designs will be discussed as appropriate. The load combinations that will be used for design are listed below and are reproduced from ASCE 7.
\n\n
D
D + L
D + (Lr or S or R)
D + 0.75L + 0.75(Lr or S or R)
D + (0.6W or 0.7E)
D + 0.75L + 0.75(0.6W) + 0.75(Lr or S or R)
0.6D + 0.6W
\n
1.4D
1.2D + 1.6L + 0.5(Lr or S or R)
1.2D + 1.6(Lr or S or R) + (L or 0.5W)
1.2D + 1.0W + L + 0.5(Lr or S or R)
0.9D + 1.0W
In the above load combination, the notation is defined as follows: D for dead load, L for live load, Lr for roof live load, S for snow load, R for rain load, and W for wind load.
\nWood is the most popular material used in the USA for the construction of single-family dwellings. An example of residential framing can be seen below in Figure 2 [6]. Framing lumber is easily obtained in most locations. The units of construction can be easily transported by contractors or homeowners without the need for specialized equipment. Additionally, the erection of a wood-framed structural system is familiar to most and does not require excessive amounts of specialized knowledge or tools. Lastly, wood-framed construction has been well documented in the USA, and many design aids are available.
\nSection view of typical residential wood-framed home. Note: in this figure, a small rectangle with x inside indicates the cross section of wood member, and DBL stands for double.
As noted before, much of the wood-framed structural design can be accomplished using design aids. The design professional will typically use these design aids to the greatest extent possible and then perform structural analysis and design for any item that is beyond the scope of the design aids. This is the approach that will be used for this study. The design drawings are shown in the Appendix. The associated detailed calculation is not provided due to space limitation; only the necessary results will be mentioned.
\nExternal loads must be transmitted to ground through the structural system of the building. Two main systems are needed to accomplish this transfer properly: gravity system and the main wind force resisting system (MWFRS). The gravity system transmits the vertical loads through a system of trusses, joists, and beams to foundation, which in turn transmits the load to ground, while the MWFRS transfers lateral wind load to foundation through a system of shear walls and flexible diaphragms. It is important to recognize that the ground must be properly prepared and evaluated to ensure good load transfer. Typically, foundations are placed on virgin soil or engineered (compacted) fill. All organic materials should be removed along with excessive amounts of water.
\nThe gravity system in this home starts at the roof and ends in the soil. Vertical loads must have a continuous path to the ground. Generally, the gravity system in this example consists of OSB sheathing, engineered roof trusses, load-bearing stud walls, dimensional lumber headers, engineered I-joist floor system, engineered wood beams, structural steel girders, and a concrete foundation.
\nThe OSB roof sheathing, as illustrated in Figure 3, serves to transfer gravity load (i.e., dead, live, and snow loads) and wind suction to roof framing members. The roof sheathing also transfers the lateral wind loading through diaphragm action to the structure. Attachment requirements of the sheathing to roof trusses are governed by the greater of the wind uplift force or the shear transfer requirement of the connection.
\nRoof sheathing illustration.
According to IRC Table R503.2.1.1(1), 11.1 mm (7/16 inch) roof sheathing (24/16 span rating) is acceptable for this example. The sheathing can be used with or without edge support at 609.6 mm (24 inch) spans with an allowable live load of 1.92 kN/m2 (40 lbf/ft2), and a total allowable load of 2.39 kN/m2 (50 lbf/ft2), which is less than the 1.44 kN/m2 (30 lbf/ft2) snow loading plus 0.57 kN/m2 (12 lbf/ft2) roof dead load. It may be possible to use 9.5 mm (3/8 inch) sheathing, but 11.1 mm (7/16 inch) thickness is more readily available and common in the locale. In this example, the sheathing will be specified with panel edge clip support. According to IRC Table R602.3(1), the sheathing is required to be attached to the truss framing with 63.5 mm (2½ inch) 8D common nails spaced at 152.4 mm (6 inch) on center (O.C.) around the edges of the panel and 304.8 mm (12 inch) O.C. at intermediate supports (field). Note that the gable end sheathing connections must be spaced at 152.4 mm (6 inch) O.C. at both the perimeter and intermediate locations.
\nPrefabricated trusses are intended to be used on this residence and required engineering design by the manufacturer. Wood roof trusses must be designed in accordance with IRC Section R802.10. A designer or architect will typically draw the shape of the roof system, and then the truss designer will design the truss system to fit the concept. Typically, it is the responsibility of the home designer to ensure that the gravity and lateral loads from the trusses are properly transferred to the wall below. This involves specifying the connection to wall system below. When the truss drawings are received by the home designer, the loads to the structure, based on the analysis conducted by the truss designer, are typically listed on the engineered truss plans. The designer would use these loads for design. For the example case presented here, however, a set of detailed truss drawings are not available. The assumed loadings described earlier will be used for design. This is typical of an initial home design. A designer will use their assumptions and then verify such assumptions when the final truss plans are received.
\nThe gravity load-bearing elements of the wall system presented here are the 2 × 6 dimensional lumber studs and the top and bottom plates (or sole plate). See Figure 2 for the location of the top and bottom plates. The 2 × 6 designation refers to a wood framing member with a nominal 50.8 mm (2 inch) width and a 152.4 mm (6 inch) depth. The actual measurements of the member are approximately 38.1 mm (1½ inch) wide and 139.7 mm (5½ inch) deep. The top and bottom plates serve to transfer both gravity and lateral loads between floors. The top plate serves three purposes: (1) a chord for the MWFRS, (2) a strut between shear panels in a wall line, and (3) a means to transfer gravity loads to the stud from the joists and trusses.
\nAccording to IRC Table 602.3(5), 2 × 6 studs can be used at 609.6 mm (24 inch) O.C.; however, it is more typical for the studs to be spaced at 406.4 mm (16 inch) O.C. The advantage of this is that when using a double 2 × 6 top plate, the joists or trusses that bear on the wall do not have to bear directly on the stud. If using a single top plate or studs spaced at 609.6 mm (24 inch) O.C., then the joists or trusses must either be directly above the stud or within 25.4 mm (1 inch) of the stud according to IRC Section R602.3.2. It is possible to use 2 × 4 studs spaced at 406.4 mm (16 inch) O.C., but this is not common because of the popularity of using fiberglass batts to meet the International Energy Conservation Code (IECC) [7] envelope insulation requirements. The connections between the studs and the plates are according to IRC Table 603.2(1). The connections are typically nails, and the nail sizes vary between 8D and 16D based on the detail.
\nStructural header members are used to create openings in a load-bearing wall assembly for fenestration (windows and doors) as shown in Figure 2. Dimensional lumber headers are preferred by designers when loading is low. Often times when point loading is present on a header or spans are large, an engineered lumber header, such as an LVL, may become cost-effective. An example of a typical LVL is shown in Figure 4. LVLs are also often used in wall systems when smaller depth members are required due to space constraints.
\nTypical I-joist and LVL (courtesy Timber Rock Homes).
When specifying headers, the designer may choose to specify larger headers in some locations for consistency sake. By minimizing the amount of different beam sizes on the plan, the designer reduces the risk of misplacement of headers. As in the case of the roof sheathing, it may also turn out that some beam sizes may be more readily available, and therefore larger sections may be more economical. For example, a two-ply 2 × 8 beam, with a demand capacity ratio of 0.944 controlled by bearing, is adequate for BM3, but because the entire back wall on the first floor is composed of two-ply 2 × 10 headers and all the other headers in the building are 2 × 6’s, it makes sense just to specify a two-ply 2 × 10 beam for this location as well. This eliminates the need to have another beam size on site and provides for the opportunity to use trim pieces from a different header cut to make up this short beam.
\nIn this home design, an engineered floor system will be used. As shown in Figure 4, I-joists have become popular and cost-effective in the residential home construction market. I-joists have several advantages over dimensional lumber joists, one of which is a greater span-to-depth ratio. This allows for shallower floor assemblies, longer spans, and higher ceilings. I-joists are generally more stable than dimensional lumber. This almost eliminates the need for bridging in a floor system and ensures consistency of engineering properties.
\nAn I-joist floor system is an engineered product. Typically, a designer will send their floor plan along with preliminary input from the designer to the I-joist manufacturer. The manufacturer will then design the floor system according to the requests of the homeowner and designer. Live load deflections are often limited to L/480 (beam span/480). Because longer spans can be achieved by using an I-joist product, the chances of floor vibration occurring increase, but can be controlled, as designers will often restrict deflection to L/480.
\nIt is common for designers to use span tables to select an initial floor joist size. This will provide a fairly accurate estimate and allow the designer to select a floor assembly depth. The improved stability and increased stiffness of I-joists allow designers to consider larger spacing for the floor joists. It is common to specify I-joists at 487.7 mm (19.2 inch) O.C., whereas it was generally common in the past to specify dimensional lumber joists at 406.4 mm (16 inch). Additionally, lumber joists are only available in certain lengths. This made the need for a splice at an internal bearing wall or beam a very common occurrence. The length of I-joists is generally only limited by transportation and site restrictions. An I-joist package will typically arrive at the site precut and ready to be installed with minimal modification.
\nAs in the case of roof sheathing, floor sheathing serves two purposes. First, it acts in the gravity system to distribute floor loads to the joists. Secondly, it is the primary shear resisting component in the floor diaphragm, which will be discussed subsequently. Typically, the gravity loads govern the thickness choice of subflooring, and the shear requirements dictate connection to joists [8].
\nOnce again IRC Table R503.2.1.1(1) will be used to size the sheathing. In this case, the sheathing will serve as both the underlayment and the subflooring. From the table, either 18.3 mm (23/32 inch) or 19.1 mm (3/4 inch) tongue and groove oriented strand board (OSB) sheathing would be appropriate, whichever is more cost-effective and readily available. It is possible that 15.1 mm (19/32 inch) or 15.9 mm (5/8 inch) sheathing could be used, but spans are restricted to 508 mm (20 inch). Although the joists will be specified at 487.7 mm (19.2 inch), which is less than the limit, it is likely that at least a few joists within the floor system will need to be spaced greater than 508 mm (20 inch). An example is when joist bays are used for heating, ventilating, and air conditioning (HVAC) ductwork, the joists are often spread in those locations to 609.6 mm (24 inch). In this instance, the thinner sheathing would be inadequate. IRC Table 602.3(1) specifies attachment of the sheathing to joists with a 50.8 mm (2 inch) 6D deformed nail or a 63.5 mm (2½ inch) 8D common nails spaced at 152.4 mm (6 inch) O.C. around sheathing edges and 304.8 mm (12 inch) O.C. for intermediate field spacing.
\nJoists for this project are selected from the Trus Joist #TJ4000 specifier’s guide [9]. From the span tables within the guide, TJI110 301.6 mm (11 7/8 inch) joists are adequate for both the first and second floors of this residence. The maximum span in the home is approximately 4.70 m (15 foot–5 inch). The TJI110 301.6 mm (11 7/8 inch) joist can span a maximum of 4.90 m (16 foot–1 inch) considering L/480 deflection limit, 1.92 kN/m2 (40 lbf/ft2) live load, and a 0.96 kN/m2 (20 lbf/ft2) dead load. The TJI 28.6 mm (1 1/8 inch) engineered rim board will be used for the perimeter of the floor system. The rim board serves to transfer compressive and shear loads from the exterior walls above to foundation below. It also acts to enclose the perimeter of the floor system. Typically, joists are toenailed to sill plates at ends and nailing plates at intermediate points. Metal hardware such as that made by USP [10] or Simpson Strong Tie [11] is used to make any flush beam-to-beam or joist-to-beam connections within the floor system. An example would be the stair trimmer detail shown in Figure 5.
\nStair trimmer detail.
A double joist or LVL product can be used to function as stair trimmers in an engineered floor system. When loads are low, double joists are economical, but as loading and span increase, an LVL is sometimes needed. LVLs are sometimes used because the installation is cleaner looking and easier to finish than double joists. Double joists often require padding at connections and sometimes bearing, which is usually OSB, to compensate for the space between the web and flanges. LVLs are conveniently made in the same depths as I-joists, which makes it easy to use within the floor systems.
\nA benefit of using I-joists over dimensional lumber is that it is easier to put holes through the joists for mechanical runs. Most I-joist manufacturers will have predetermined locations or precut holes in the joists where mechanical penetrations are anticipated. Some guidance is typically specified in the manufacturer literature. Holes in dimensional lumber typically require structural analysis and stress evaluation as they become large relative to the depth of the joist or beam.
\nFor this example home design, a central steel girder will be used to collect the floor loads and transfer to pad footings in the center of the basement. It is common for designers to use either steel girders or manufactured lumber girders in homes today. These types of girders are much stronger than dimensional lumber beams and are necessary in many instances because of the longer allowable engineered I-joist spans and homeowner request for open basement floor plans. Both manufactured lumber girders and steel girders must be either specified or the design reviewed by a professional engineer.
\nSteel girders are often chosen over manufactured lumber girders when girder spans are long, head room in the basement is a premium, or steel is readily available. For this particular builder, the head room in the basement is important because they like to advertise their homes with basements that can be finished in the future. A W8x18 girder works well for them because it’s a shallow beam and the flange width is small enough that the beam can fit in a 2 × 6 wall making the girder unnoticeable if the basement is ever finished.
\nA W8x18 steel girder, with a design moment capacity of 86.5 kN-m (63.8 kip-ft), is more than adequate to resist the internal moment of 31.5 kN-m (23.2 kip-ft) for the controlling load case. It is possible that a smaller girder could have been used, but W8x18 is the minimum size the builder will use. Small sizes tend to have stability issues and can be susceptible to local buckling problems caused by larger point loads. In addition, this is a readily available steel section from the builder’s steel supplier.
\nThe design of residential girders involves assumptions regarding the bracing of the beam. The American Institute of Steel Construction (AISC) Steel Construction Manual 14th Ed.(SCM) in Chapter B3.6, F1 (2) [12] and Appendix 6.3 all require that girders are restrained against rotation about their longitudinal axis at the points of support unless it can be shown that the restraint is not required. The amount of restraint provided by the adjustable column, which is typically four bolts through the bottom flange, may need a detailed analysis because of the slenderness of the columns.
\nSteel girders in most residential cases are usually ordered in a single length if possible to avoid splices and therefore are continuous over their intermediate supports. Negative moment occurs at the intermediate supports, which puts the bottom flanges in compression in those regions.
\nIf it is assumed that the columns do not provide adequate bottom flange support, then these negative moment regions would be destabilizing, and since inflection points are not typically recognized as a brace point (SCM Appendix 6.3), the unbraced length would have to be taken as the entire beam length of 11.0 m (36 feet), which would require a very large section. Additionally, if no compression flange bracing is assumed at the supports, then the beam fails the concentrated load check in SCM J10.4 for web sidesway buckling. Section J10.4 requires the supports to be adequately braced under these circumstances.
\nIf it is assumed that the column is braced against rotation at the supports by either assuming the column connection is adequate or providing additional bottom flange support, then the unbraced length reduces to the distance between the columns, which in this case is 9′-0″ and the beam passes both strength and concentrated load checks.
\nAlso restraint against rotation should be provided at the ends of the beams, which are seated in the beam pockets. Typically, beam pockets in the concrete wall are oversized to facilitate easy installation of the beams. This creates the opportunity for twisting. SCM Section J10.7 requires all unframed girder ends to have a pair of transverse stiffeners if unrestrained. In this case, a better idea would be to grout the pocket as shown in Figure 6, or provide some type of shim, after installation to restrain the end against rotation. It should be noted that the required moisture management and thermal envelope components are not shown for clarity in the figure.
\nSteel girder beam pocket detailing.
Another consideration for girder sizing is live load pattern loading. Since the girder is a continuous beam having multiple spans, ASCE 7 Section 4.3.3 requires the consideration of pattern loading. In this case, it turns out that applying live loading to spans 1, 2, and 4 only produced the largest internal moment of 31.5 kN-m (23.3 kip-ft) in the beam. Figure 7 shows the moment diagram for the controlling load combination and the spans that were loaded to produce it.
\nMoment diagram showing maximum internal moment over support 2.
Pattern loads are considered in the structural analysis software package Enercalc that was used for beam design. Enercalc runs all permutations of live load application and reports the worst-case scenario in envelope format. Data for individual permutations is not able to be extracted. For this example, a separate check was made using Computers and Structures, Inc. (CSI) SAP2000 finite element modeling software to verify the results of Enercalc and determine the controlling permutation. Results were within 1% of each other between the two analysis packages.
\nPattern loading was significant in this example. If only the full intensity live load application was to be considered, then the design moment would have been underestimated by approximately 5%, and the support reactions would have been underestimated by approximately 5% at supports 2, 4, and 12% at support 3. If ignored, this could have led to the undersizing of both adjustable column and pad footing.
\nAdjustable columns are generally used in residential construction as intermediate supports for basement girders. Adjustable columns are readily available at almost any hardware stores and can be adjusted in height to match site conditions by the contractor. Figure 8 shows an example of typical adjustable columns. The maximum loading, as reported by the manufacturer, is a factored allowable ASD load capacity (Ra). Reactions determined by ASD load combination can be used to directly size the column from the manufacturers testing data. For this particular home design case, the maximum ASD girder reaction is 80.5 kN (18.1 kip). According to the manufacturers data, an 88.9-mm (3½ inch) and 2.31-mm-thick (11 gauge) column with a height between 2.21 m (7 foot–3 inch) and 2.31 m (7 foot–7 inch) has an allowable load of 95.6 kN (21.5 kip), which is greater than the maximum column axial demand of 80.5 kN (18.1 kip). All three columns will be specified for this maximum loading. This will decrease the chances of misplacing columns.
\nTypical adjustable column.
A combination of components are used to transfer load from the above-grade portion of the home to the ground. In this home, concrete walls supported by concrete strip footings are used to support the exterior walls and resist lateral earth pressure. Interior loads are transferred by the intermediate girder through columns to concrete pad footings. It is common practice in residential design to specify the foundation walls prescriptively but design the footings. This is the approach that is taken for this study. The American Concrete Institute (ACI) 332-08 [13] and ACI 318-14 [14] are used as references for this design. These documents are adopted by the 2015 IRC and often lead to more economical designs when compared to the requirements of the IRC.
\nBased on soil categorization, the ACI provides prescriptive foundation sizing tables in Appendix A of ACI 332, which are usually appropriate for most situations. For most residential designs, geotechnical exploration and lab testing are cost prohibitive, and therefore soil pressures must be assumed. ASCE 7 provides design lateral soil load that can be used in the absence of site-specific geotechnical information.
\nFor this design, the equivalent soil pressure will be estimated at 2.15 kn/m2 per linear meter (45 lbf/ft2 per linear foot). According to ASCE 7 Table 3.2.1, this is representative of a type GC soil (unified soil classification), which is described as a clayey gravel, poorly graded, gravel, and sand mix. Assuming horizontal backfill and a vertical foundation wall, this is roughly equivalent to 19.6 kN/m3 (125 lbf/ft3) soil with an internal friction angle of 28 degrees [15].
\nAccording to ACI 332 Table 9, 21 MPa (3000 psi) is the minimum required compressive strength for foundation walls in the severe weather probability category. Because the concrete will be exposed to weathering, it must be air entrained, having an air content of 6% plus or minus 1.5%.
\nWalls | \nLength required | \nLength provided | \nMethod | \n
---|---|---|---|
First floor | \n|||
N | \n4.24 (167) | \n8.23 (324) | \nCS-WSP | \n
S | \n3.40 (134) | \n3.66 (144) | \nWSP | \n
E | \n3.20 (126) | \n3.66 (144)a | \nWSP | \n
W | \n3.20 (126) | \n3.66 (144) | \nWSP | \n
Second floor | \n|||
N | \n1.83 (72) | \n2.44 (96) | \nWSP | \n
S | \n1.83 (72) | \n2.44 (96) | \nWSP | \n
E | \n1.52 (60) | \n3.66 (144) | \nWSP | \n
W | \n1.52 (60) | \n3.66 (144) | \nWSP | \n
Garageb | \n\n | \n | \n |
N | \n1.27 (50) | \n2.44 (96) | \nWSP | \n
E | \n1.32 (52) | \n1.37 (54) | \nWSP | \n
W | \n1.32 (52) | \n2.44 (96) | \nWSP | \n
Wall bracing. Values in meters (inches).
For WSP methods panel lengths between 0.914 and 1.22 m (36 and 48 inches) are allowed but must be adjusted per IRC Table 602.10.3.
The required bracing for the garage/main house common wall will be added directly to the first floor north wall.
The concrete foundation wall for the main structure in this example has an unsupported height of 2.44 m (8 foot) and will be subjected to approximately 2.13 m (7 foot) of unsupported backfill when in service (Figure 9a). For this situation, considering reinforcing bars with a yield strength of 420 MPa (60,000 psi), ACI 332 Table A.4 allows for the use of a plain concrete (no vertical reinforcing needed) 203.2 mm (8-inch)-thick foundation wall. To minimize shrinkage cracking, however, ACI 332 requires the use of three continuous horizontal bars in the wall. One must be placed within 609.6 mm (24 inch) of the top, one within 609.6 mm (24 inch) of the bottom, and the last one in between the other two. ACI 332 also prescribes 12.7 mm diameter (½ inch) dowel rods at a maximum of 609.6 mm (24 inch) O.C. or a keyway to be provided in this instance since unbalanced backfill height exceeds 1.22 m (4 foot).
\n(a) Typical basement wall and (b) typical garage frost wall.
The garage wall foundation walls are all 0.91 m (3 feet) in height and have no unbalanced backfill. According to ACI 332, 203.2 mm (8 inch) plain concrete walls are adequate. No vertical reinforcing is necessary, but horizontal reinforcing is still required (Figure 9b). The wall height is less than 1.83 m (6 feet), which requires only two 12.7 mm diameter (½ inch) reinforcing bars, one within the top 609.6 mm (24 inch) of the wall height and the other within the bottom 609.6 mm (24 inch) of the wall height. Because the unbalanced backfill is less than 1.22 m (4 feet), Section 6.3.4 allows for the use of a clean construction joint versus dowel rods.
\nContinuous strip footings will be used to support the exterior foundation walls. The wall footings will be designed (as opposed to prescriptive). No soil testing data is available, so the IRC minimum of 71.8 kN/m2 (1500 lbf/ft2) prescribed in Table R401.4.1 will be used for design. The assumption will be made that the footings are not exposed to weathering; therefore, ACI 332 prescribes 17 MPa (2500 psi) minimum compressive strength for the concrete.
\nFor this example, it will be assumed that the load from the exterior wall will act concentrically on the footing. In other words, the footings will be designed for uniform pressure only, and no imbalanced soil pressure due to the presence of a moment will be considered. This is a reasonable assumption because basement walls are typically restrained from translation at the top and bottom by the first floor assembly and the basement slab, respectively. The presence of this restraint allows walls to be designed as a vertical beam with pinned ends (no moment transfer). In addition, the opposing soil exterior lateral loading tends to offset the small amounts of eccentricity created by above-grade wall offsets, so in practice the effects of above-grade wall offsets are generally ignored for wall footing design. Figure 10 shows an illustration of the analytical model for a typical residential basement wall.
\nFree body diagram of a basement wall. Note: the arrows show loads, and small rectangle with x inside indicates the cross section of wood member.
Residential wall footings are typically specified in depths of 152.4 mm (6 inch), 203.2 mm (8 inch), or 254 mm (10 inch), and widths are generally varied in 50.8 mm (2 inch), 76.2 mm (3 inch), or 152.4 mm (6 inch) increments. Both the IRC and ACI 332 allow for the use of 152.4 mm (6-inch)-thick footings (assuming adequate strength), but the developer in this case prefers to use 203.2 mm (8-inch)-thick footings. This allows for some additional safety precaution when plain concrete footings are used. When specifying footing widths, this particular developer prefers to use even dimensions in 50.8 mm (2 inch) increments.
\nIn this example, the wall footing design is split into three segments, the main load-bearing walls of the east and west (perpendicular to joist and truss spans), the gable end walls, and the garage walls. Wall footings were designed as plain concrete strip footings according to the requirements of ACI 318, considering the increased modulus of rupture allowed by ACI 332 Chapter 7. Soil bearing pressure controlled all designs. With a soil bearing pressure of approximately 67 kN/m2 (1400 lbf/ft2), the bearing walls required 203.2 × 457.2 mm (8 inch by 18 inch) footings. The gable end wall footings and garage footing were able to be reduced to 203.2 × 406.4 mm (8 inch by 16 inch). The wall region beneath the supporting columns for the garage door header controlled the design. Considering ASD load combination 4 and a point load distribution angle of 45 degrees within the concrete wall, the soil pressure beneath the column would be approximately 67 kN/m2 (1400 lbf/ft2) as well.
\nThe footings were designed as plain concrete footings. Plain concrete footings are the most economical because of the absence of the steel reinforcing cost. Some developers are comfortable relying on the unreinforced concrete footing to maintain its integrity over the service life of the building, but some prefer to add light reinforcing to help prevent cracking due to unexpected soil discontinuities. ACI 332 Section 6.2.4.1 prescribes the use of two 12.7 mm diameter (½ inch) bars for locations with discontinuities less than 914.4 mm (36 inch) in length.
\nIsolated pad footings are typically used to transfer vertical gravity load from interior columns in the basement. In this case, there are three pad footings required to support the interior central steel girder. Interior pad footings are not subjected to weathering, so 17 MPa (2500 psi) concrete compressive strength is adequate. The default value of 71.8 kN/m2 (1500 lbf/ft2) is used for the soil bearing capacity, as in the strip footing design.
\nReinforced square concrete footings were selected as appropriate for this application. Plain concrete pad footings are sometimes adequate for smaller footings with plan dimension of 609.6 mm (24 inch) or 762 mm (30 inch) square but typically require reinforcement as the plan dimensions of the footing increases. In this case, three 1219.2 mm (4 foot) square footings using four 15.9 mm (5/8 inch) diameter bars in each directions were required. Considering LRFD combination 2, two-way shear (punching shear) with a demand/capacity ratio of 1.30 was the controlling failure mechanism for the concrete footing and required an increase in footing depth from 203.2 mm (8 inch) to 254 mm (10 inch). This reduced the demand/capacity ratio to the acceptable level of 0.698.
\nThe typical residential MWFRS system is composed of a system of flexible diaphragms and shear walls. As shown in Figure 11a, wind load is transferred from exterior walls perpendicular to the wind direction to structural wood panels, typically OSB or plywood, attached to roof or floor framing. The flexible roof or floor diaphragms, as shown in Figure 11b, act similar to a deep beam and distribute the wind load as reactions to the exterior walls parallel to the wind loading (Figure 11c) and distribute to the stiff structural shear panels within those walls by direct diaphragm connection or strutting.
\n(a) Wind pressure distributed through external walls to flexible diaphragm. (b) Flexible diaphragm distributes load to parallel walls. (c) An example of a segmental shear wall load distribution approach. (d) Shear wall segment resolution of overturning forces. Note: in this figure, the following notation is used: V for shear force, T for tension force, C for compression force, l and L for Span length, h and H for height, σ for wind pressure, ω for wind load per unit length, and Vw for shear per unit length.
The structural wall panels, as shown in Figure 11d, provide the necessary shear resistance and transmit the loads vertically (overturning tension and compression loads at the corners of each structural panel) to the foundation though a system of hold-downs and connections.
\nTypically, the panels are specified by design aids such as the IRC or the Wood Frame Construction Manual (WFCM). When using the IRC approach, the prescribed nailed connections are assumed to be adequate to transfer the overturning shear forces shown in Figure 11 to the foundation. If an engineered design or the WFCM prescriptive approach is used to specify shear wall panels, then structural connectors must be specified to transfer these overturning forces. The connection system must have an identifiable load path to the foundation. For this reason, most residential designers use the IRC to specify shear panels and their fastening system. When using a wood truss system as part of the roof diaphragm, such as the one in this home design example, structural connectors are typically specified to transfer the horizontal shear loads and uplift loads resulting from the roof wind loading.
\nThe loads from the shear wall panels and floor diaphragm are transferred to the sole plate by nailed connections and sometimes structural connectors if necessary. The sole plate is attached to the foundation wall with cast-in-place anchors such as J-bolts or post-installed anchorage that must be drilled after the concrete has had time to cure, such as expansion anchors, epoxy anchorage, or screw type. With a prescriptive approach, the prescribed anchor bolts are assumed to adequately transfer both the overturning actions and horizontal actions generated by the wind.
\nIt’s generally good practice to review the whole structure for stability under wind loading and then design the individual components of the lateral force resisting system as required. An overturning and sliding analysis is conducted to determine the required strength of the connections between main assemblies such as the roof-to-wall connections, floor-to-wall connections, and the above-grade building-to-foundation connections.
\nMany times, homes have attached garages where the garage is not integral to the main living space, such as the one in this example. The garage and the main building can be somewhat treated as separate buildings for the purposes of MWFRS design. The garage can sometimes help resist main building wind loading as long as the wall offsets are not too large; otherwise they must be treated completely separately as far as wall bracing goes. In the east-west direction, the common north wall between the garage and the main structure is generally treated as an exterior wall, and bracing will be prescriptively specified as such, which will act to transfer load from both the garage and the main building.
\nASCE 7 Figure 28.6.1 cases A and B were used to determine the magnitude of wind forces applied to the building. The magnitudes of the loads were reported previously in Tables 6 and 7. The load effects created by the external wind forces were used to specify the hold-downs and shear connectors necessary to maintain continuity of MWFRS load path. The garage was not analyzed, but the procedure would be the same. To simplify the analysis, the end zone loads for case A were applied on both ends to simplify the analysis. To maintain a uniform balanced load in case B (wind applied to the gable end), a weighted average of 0.69 kN/m2 (14.4 lbf/ft2) was taken for zones A and C and applied horizontally. An average of zones E and F that was calculated to be −0.95 kN/m2 (−19.8 lbf/ft2) was applied vertically to the windward side of the roof, and an average of zones G and H that was calculated to be 0.61 kN/m2 (12.7 lbf/ft2) was applied vertically on the leeward side of the roof.
\nAnalysis showed that structural connectors were needed for the roof, but not for the floor-to-floor connections and the foundation connection. Connectors for the truss ends must be able to simultaneously transfer uplift and north-south shear loading as well as shear loading alone in the east-west direction. Simpson Strong Tie (SST) H2.5A hurricane connectors were considered for the truss end-to-top plate connection. This connection resists both shear and uplift. The H2.5A has a shear capacity of 0.58 kN (130 lbf) and uplift capacity of 1.62 kN (365 lbf). The truss end loads are, respectively, 0.18 kN (40 lbf) and 0.27 kN (60 lbf). Applying a unity equation, the demand/capacity ratio is 0.18 kN/0.58 kN + 0.27 kN/1.62 kN = 0.477 < 1.0; therefore, the connector is adequate. An example of a typical truss connector is shown in Figure 12. SST A21 angles were considered for the gable end truss-to-top plate connection. This connection is subject to a total shear load of 10.7 kN (2400 lbf) when the wind is applied perpendicular to the gable end. SST A21 has a design capacity of 1.09 kN (245 lbf) per connector; therefore, the required number of connectors will be 10.7 kN/1.09 kN, which gives approximately 10 connectors.
\nTypical truss-to-top plate structural connector.
The structure was checked for overturning at the second floor and at the first floor. The weight of the structure was adequate to resist the overturning moment in both locations. Sliding was only checked on the roof to specify the structural connectors. Sliding on the second floor is resisted by the nailed connection between the bottom plate and the floor assembly. Typically, there are sufficient nails engaged to resist the shear force. As for the building-to-foundation connection, there is no reason to expect an extraordinary loading at this junction, so anchor bolts are specified according to IRC Chapter R403.1.6. The I-joist to soleplate toenail connection was not checked in this analysis but should be checked in an actual design.
\nWall bracing for residential construction typically involves designating sections along the exterior wall length as shear panels. Structural wood panels are used on the exterior side of the wood framing, and gypsum wallboard on the interior provides the shear resistance and load transfer capability. Plywood or OSB is typically used for the wood structural panels. IRC Table 602.3(3) prescribes a 9.5 mm (3/8 inch) minimum structural panel thickness for 406.4 mm (16 inch) O.C. stud spacing; however, the builder prefers a 11.1 mm (7/16-inch)-thick OSB panel, which is required to be fastened to framing using 8D common nails at 152.4 (6 inch) O.C. around the perimeter and 304.8 mm (12 inch) O.C. in the field.
\nIRC Section R602.10 will be used to specify shear panel length and location along the wall line. Section R602.10 has provisions for various wall bracing methods. The bracing in this home will follow the requirements for the intermittent wood structural panel (WSP) method or one of the continuous sheathing methods. Because this home is categorized in seismic design category A, Section 602.10.1 allows for different methods to be used along different wall lines. Different intermittent methods could even be used along the same wall line in this category, but if using any of the continuous sheathing methods, the whole wall line must be continuously sheathed.
\nFor the design of this home, it was more economical to use the WSP method for the majority of the shear panels. Section R602.10 requires 609.6 mm (24 inch) corner returns or braced panels at the end of each wall. At least one of the corners does not meet this criterion. When this occurs and the designer is using the continuously sheathed wood structural panel (CS-WSP) method, Section 602.10.4.4 requires the use of 3.56 kN (800 lbf) hold-down devices in lieu of a 2 foot corner return. This is often costlier than the extra amount of sheathing required for the WSP method. Another issue to consider when specifying wall bracing is the stud spacing. In this home, the studs are spaced at 406.4 mm (16 inch O.C.); therefore, it is prudent to specify shear panels 406.4 mm (16 inch) increments, even though the requirements may be less. The location of the shear panels is specified in the drawing set located in Appendix A.
\nThe floor assembly is treated as a flexible diaphragm when transferring lateral loading. Wind is transferred from a tributary area of the exterior wall to the rim board of the floor assembly and then into the structural sheathing. The floor sheathing then transfers that load to the exterior shear walls (structural panels within the wall system) parallel to the wind direction below the floor assembly. The diaphragm is treated like a deep beam for the purposes of analysis. The reactions are the connections with wall below. The floor assembly deflects, which causes tension and compression forces called chord forces in the walls below, which are perpendicular to the wind loading. The sheathing layout and the attachment of the sheathing to the I-joists have the greatest effect on the strength of the diaphragm. In this case, the floor sheathing and the required nailing were specified from the IRC in the floor assembly section of this report.
\nMost connections in wood-framed homes are made up of nailed connections. The majority of the connections in a typical home can be found in IRC Table R602.3. The items specified from the IRC in this wood-framed section are based on compliance with this table. In this study, only a few of the typical critical connections for the structural system were specified.
\nThis chapter presented a complete design of a typical US single-family home made of conventional wood-frame system. Initially, the applicable building and material codes were introduced and relevant provisions discussed. A typical home plan by a PA builder was discussed and explained for detailed design. The process of load selection and load path and load combination was discussed. Then based on application of the resultant loads on typical structural elements, detailed designs for roof sheathing, roof trusses, exterior walls, main wind force resisting system, floor system, girders, columns, and foundation walls and footings were presented and discussed. Where appropriate, tips and guidelines for typical design were offered so that the procedure presented can be followed by designers as appropriate. While other structural systems are becoming increasingly available, the wood-frame system is still the dominating system as in the USA lumber is readily available at highly competitive process. This makes structural systems other than conventional wood-frame less competitive, unless there are special conditions where cost may not be the main determining factor.
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