ML20205F079
| ML20205F079 | |
| Person / Time | |
|---|---|
| Site: | LaSalle  |
| Issue date: | 08/11/1986 |
| From: | Office of Nuclear Reactor Regulation |
| To: | |
| Shared Package | |
| ML20205F065 | List: |
| References | |
| NUDOCS 8608190083 | |
| Download: ML20205F079 (24) | |
Text
SAFETY EVALUATION BY THE OFFICE OF NUCLEAR PEACTOR REGULATION C0 W.NWEALTH EDISON COMPANY LASALLE COUNTY STATIONS 1 AND 2 DOCKET y S: 50-373 AND 50-374
1.0 BACKGROUND
On February 5, 1985, the staff met with Conmonwealth Edison Company (Ceco) and your consultants, Sargent and Lundy (SAL), to discuss the procedures used at la Salle County Stations 1 and 2 for the design of Heating, Venti-lation, and Air-Conditioning (HVAC) hanger frames constructed of single angle members. Specific rules and criteria for the design of single angle members in bendina are not currently available in the American Institute of Steel Construction (AISC) Specifications (AISCS). Existing design rules (from the AISCS, current engineering literature or other sources) which might be applicable to angle member design are, therefore, open to differing interpretations. Pased on the S&L presentation at this meeting and sub-secuent correspondence on this sub,iect, a number of concerns and disagree-ments on interpretations of the AISCS and other existing rules were identified. The five main issues thus identified vere as follows:
1.
The maximum slenderness ratio for members in compression.
The AISCS states clearly that the slenderness ratio for members in compression shall not exceed a stated maximum value. S&L contended that this value was artificial and not applicable to members in struc-tures such as ceiling-hung HVAC duct supports, which are primarily in tension under dead weight.
7.
Allowable flexural stresses and maximum unbraced length in bending.
S&L proposed to determina the allowable stresses or maximum unbraced lenoth in bending based on procedures which appear in the Australian Steel Code, and on analytical work done by Australian researchers on this sub.iect.
(Although annle sections are the simplest next to rectangular sections, they are analytically complex because of their asymmetry.) The issue arose from the fact that these procedures were not currently used in the United States, were not contained in any American code, and had not been accepted by the NRC or the AISC. The staff proposed alternate rules based on methods similar to those of the AISC, which S&L felt to be too conservative.
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3.
Use of.95 F as the maximum allowable flexural stress for Safe Shutdown
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Earthquake (5SE) loads.
The staff objected to the use of this value since it would have exceeded the flexural buckling stresses for most short and other length members.
However, these stresses were determined by the staff by assuming the maximum bending stress at yield and the AISC nethodology, which S&L did not consider applicable, j
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' 4.
Use of the geometric or principal axes in the bending stress calculations.
Since angle sections are in general not symmetrical sections, the maximum bending stresses must be calculated based on the principal axes of the section. Under certain conditions of restraint at loading or end points it is permissible to use the conventional beam formulas for calculating the maximun bending stresses. The use of such formulas for the general loadino case can underestimate the maximum bending stresses by as much as 50%. S&L proposed to apply the conventional beam formulas for all members regardless of loading condition.
5.
Interpretation and application of the AISCS Interaction Equatinns.
Satisfaction of these ecuations is required for members subjected to simultaneous axial compression and bending. A difference on the interpretation of the various facSrs in these equations arose as a result of the ambiguous definitions in the AISCS.
2.0 EVALUATION Your letter, dated February 13, 1986, contains the responses to these issues provided by S&L. The responses are based on independent reviews of the S&L design methodology performed by nationally known authorities in the field of steel design, such as Professor T. V. Galambos of the University of Minnesota, J. Eddinger of the AISC, and Dr. G. Heaijer. Vice President and Director of Engineering of the AISC. The correspondence between S&L and its consultants is shown in Attachment 1 to this Safety Evaluation.
The staff has reviewed this correspondence and concurs with the opinions stated by these experts. Some of these opinions are also in agreement with positions stated previously by the staff.
Based on these opinions, and on independently performed studies, the staff accepted the S&L positions retarding the use of the Australian methodology and the maximum allowable bencing stress of.95 F for SSE leads.
y Ayreement was also reached on the conditions under which geometric or principal axes are t' be used in the bending stress calculations, and on the interpretation of the AISCS interaction equations. The principal axes are to be used for calculating the bending stresses under general loading conditions except when the member is restrained at the loading points or at the ends.
In this case, bending can occur in a plane paralleled to one of the geometric axes only and it is acceptable to calculate the benaing stresses based on the conventional beam formulas. In the evaluation of the AISCS interaction equations (Equations 1.6.la and 1.6.1c) the stability ecuations are to be based on the maximum compressive bending stresses due to each moment acting alone, where each moment may occur at different cross-sections of the member. The strength interaction equation (Eauation 1.6.lb) is to be evaluated at the critical member support cross-section, and need not be based on the maximum moments along the member length.
, The staff has also accepted the position by S&L that the slenderness ratio' for angle members of ceiling-hung structures may be increased beyond the
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maximum value specified in the AISCS on the basis of the advice by the i
above named experts and the oral presentation made at the February 5,1986, meeting by another consultant to S8L, Mr. W. A. Milek, past Director of Engineering of the AISC.
S&L has incorporated the resolution of these issues in their design methodology for HVAC frame supports, and is required and has committed to incorporate this methodology in the FSAR at the earliest opportunity. The staff has also compiled a set of acceptable single angle member design criteria based on the opinions and studies stated above. These criteria are shown in Attachment 2 to this SER and are in general accordance with the rese,lution of the isstes stated above.
3.0 CONCLUSION
Based on the resolution of the issues stated above, the staff finds the design methodology used by SAL for the design of sinole angle cembers acceptable and considers the issues and concerns satisfactorily resolved.
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' ATTACHMENT 1 d+?RL%
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l slR IIk AMERICAN INSTITUTE OF STEEL CONSTRUCTION. INC.
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The Weigtey Building / 400 Notth Michigan Avenue / Chicago. tilinois GOG114185 / 312
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. December 6, 1984
.Ref. No. 205.1..
i Mr. K. T. Kostal, Ass.stant Manager Sargent G Lundy Engineers
-55 East Monroe Street Chicago, IL 60603
Dear Mr. Kostal:
This is'in response to your letter of November 14, 1984 regarding the application of slenderness ratios.
The K1/r limit of 200 foi compression members contained in the AISC Specification since it was first published in 1923 is in keeping with the basic intent stated in the Preface to the Speci-fication which is "to cover the many.cveryday design criteria in routine design office usage".. ]Ihe' effects of the selfweight.of.
a the member, effect. of residual stresses, initial out of, straight-
"neisTand other fact 6ti#iie5IynDIdoc'unented'for acabMs'whose
- 1. slenderness 73reitI9"sicee's200. The specific liinit included in d
the Specification has historically been based on arbitrary judg-ment. Consequently it would not be unexpected to find different specificatrions contain slightly different limits but reassuring that these different specifications all contain limits of approximately equivalent magnitude.
'Ihe Committee'on Specifications reviewed the current statement
.regarding the maximum slenderness ratio for compression members and approved the following revised wording at its meeting of November 7-8, 1984.
"1hc maximum slenderness ratio K1/r of com-Pression members should not exceed 200".
This is in contrast with the current provision, which uses the word shall.
This new wording will first be used in the proposed Load and Resistance Factor Design (LRFD) Specifid:atien and is also applicabic to A110wabic Stress Design (ASD) if and when a revised edition is considered.
EXIIIB_IT 4
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Mr. K. T. Kostal December 6, 1984 Page 2.
'Ihis revised wording is consistent with the philosophy behind the AISC Specification which "is not intended' to cover the infrequent-ly encountered problems within the full range of structural design practice, because to provide such definitive provisions covering all possible cases and their complexities would diminish the Speci-fication; usefulness for routine design office use".
In all instances, "the design of structures is within the scope of ex-pertisc of a competent licensed architect, structural engineer, or other licensed professional for the application of priticiples to a particular structure".
Sincerely,
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John A. Edinger, Assistant Director of Engineering JAE/cd cc:
W. A. Milek 1
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UNIVERSIT/ OFMINNESOTA Department of Civd and Minera! Engincenng f
b::EJ J-TWIN CITIES 122 Civa and Mincral Engineenng Duilo.r.g 500 Piilstxny Drive S E.
8Anneapohs, Minnesota 55455 0220 (612) 373-2008 January 28, 1985
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Assistant Manager, Structural Department Sargent and Lundy, Engincers 55 East Monroe Street ~
Chscago, Illinois 60603
> po'ar Mr. Kostal, l
This is in reply to your letter of Jan. 21, 1985, in which you pose the question of whether a slenderness limit in a design specification is a primary design conditin, having to do with safety, or whether it is a secondary con-dition which facilitates handling and erection.
In reply, I would first of all like to say that I fully agrec with all of the statebents in Mr. Milek's report. The slenderness Timits 'in Soc.1.8.4 of i the 1978.Specifloations. of the American' Institute -of Stool Construction ~ (AISd) 4.aro'. net related t'o'co1umn" strength'at)1l! They are limits inposed by past
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'.eustom's,. tradition and handling convenience, and it is rather unfortunate that the Specification used the word "shall" instcad of "may" in the w(itir.;; of the requir' ment. As you know, this statter has been rectified by the.euSC Specifi-e cation Advisory Committee at its last sceting in November 1984.
Ror.ardless of the particular value of the slenderness ' ratio, be that 90, 200 or 300, the formular for colcun strength in Sec.1.5.1.3 of the AISC Specifications will give a safe buckling stress. The factor of safety for plender colunns fciling by clastic buckling is 1.92, giving a sufficient margin SI saicty. The theory of buchling underlying the AISC requirements is over 200 years old, and it has been tested ot.t many times.
With regard to safety, then, we have a tested relinble theory for deter-cining the compressive strength of the hanger rods describcd by you, and there is a gencrous factor of safety. The strength provisions of the AISC Specifi-cation Sec. 3.5.1.3, in particuler Eq.1.5-2, apply to these hanger rods. The stabil ty of these rods, which are notically in tension, undcr a rarely occurring transient coupressive force is thus assured by Eq.1.5-2 in the AISC Specifica-tion, assuming that the magnitude of these compressive forces is dotcrmined correctly by rational analysis.
Hotover, I contend that the maximum slenderness limit of 200 'does not apply to your rods. This limit, having nothing to do with compressive strength, is applicabic to building-type structures, and it serves solcly the convenience of handling end crectson.
In building structures, anyuay, such long columns are not economical. Personally, I see no need cycn to distinguish between tension and compression in setting slenderncss liuits, and I would be as comfortabic cita a imit of 300 as I am with the linit of 200. Of course, in a building it would really m ake even less sense to have i:olumns with a slenderness ratio of 300 then with a slenderness ratio of 200, for econoa.lcal reasons.
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that ct the Steel. Joist Institute, I am familiar with onc Specification, where tension webs in a truss must also be designed to support an accidental compressive fo.rce of one-fourth of the tensile force. The mazinum sicuderness ratio of these tension webs is, however, the slenderness requirencnt for tension j
tenbers!
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,I In conc.lusion I strongly reiterate my previous comments that: ;,
1.
'the slenderness limit for compres.lon members from AISC Spccification Sec. 1.8.4 does not apply to the longer rods in your structure
- sud 2.
compliance with Eq.1.5-2 will provide adequate reliability 'for mitimate strength.
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Sincerely yours, ee.
T.V. Galambos Ph.D., P.E.
Mcabor National Academy of Encinecting J.L. Record Professor of Structural Eng.
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AMERICAN INSTITUTE OF STEEL CONSTRUCTION. INC.
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The Wagw Dudding E Oghth noor E 400 North MsChegon Avenue 5 ChsCogo. Dhnoes 606114185 5 Todephone (312) c70 2400 January 30, 1985 Mr. K. T. Kostal, Assistant Manager i
Sargent 6 Lundy Engineers 55 East Monroe Street Chicago, IL 60603
Dear Mr. Kostal:
Ris is in response to your letter of November 14, 1984 regarding the application of slenderness ratios.
De arbitrary K1/r limit of 200 for compression members contained in the AISC Specification since it was first published in 1923 is in keeping with the basic intent stated in the Preface to the
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Specification which is "to cover the many everyday design criteria in routine design office usage". Consequently it is not surprising to find that differcnt specifications contain slightly different limits.
I The Committee on Specifications recently confirmed the arbitrary nature of the maximum slenderness ratio for compression members j
and approved the following. revised wording at its meeting of i
November 7-8, 1984. "The maximum slenderness ratio K1/r of com-Pression members should not exceed 200".
This is in contrast with the current provision, which uses the word shalls. h is new
_ wording will first be used in the proposed Load and. Resistance
~~ Factor Design (LRFD) Specification and is also. applicable 'to l~
Allowable Stress Design (ASD) if and when a revised edition is considered.
I n e allowable stresses given by equations 1.S-1 and 1.5-2 are based on recotanendations originally published by the Column Re-search Council *(now Structural Stability.Research Council) that include the effect of residual stresses. The AISC Coannittee on d
- Bruce G. Johnston, editor, " Guide to Design Criteria for Metal Compression Members" Second Edition John Wiley and Sons.
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Mr. K. T. Kostal January 30, 1985 Page 2.
i Specifications also considered the effect of out-of-straightness by increasing the factor of safety from 1.67 for zero slenderness to 1.92 in the elastic range covered by equation 1.5-2.
- Thus, there is no theoretical limit to the validity of these equations.
We believe there is a fundamental difference between building columns that provide the resistance to gravity loads, and ten-sion members that only have to resist compression caused by wind or earthquake loading. For tension members the maximum slender-ness ratio is 300. The Specification Committee now provides the option for the engineer to use his professional judgement to es-tablish the appropriate limit in specific instances.
As mentioned above, the allowable stresses given by the AISC Specification are valid for all slenderness ratios.
Accordingly, the Engineer's judgement of the appropriate slenderness limit would be in com-Pliance with the Specification.
Sincerely, _
John A. Edinger, Assistant Director of Engineering JAE/cd cc:
W. A. Milek 6
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UNIVEFG!TY OF M!NNESOTA cecemem e' c.c.: a c !.Seev Eng rwm s
122 C'..i and t.5r+'N Erg neerrng Dic.ng s.
. ;., T.ter. Ce?.c 5 603 Piistury Dr..e S E i1 Minneapotis. Minneso:a 55455-0220 i (612) 373 2968 20 February 1905 SARGENT & LUNDY FEB 2 5 BC Nr. Ecnneth T. Ecstal Assistant Manager, Structural Department RyggG Snrgent and Lundy, Engineers 55 East Nonroe St.
Chicsso. IL 60603 Deer I!r. Eostal:
This is a reply to your letter of February 14, 1935, in which you dec1 with The questions relating to tne ficzure of laterally unsupported angle-beams.
design of laterally casupported angle-beams is not covered by the AISC for the reasons nentioned by Mr. Fdinger in his letter to you.
Specificatson, Most er.phatically, Sec.1.5.1.4.1 doe s not apply to angic-beams.
I have been aware of the Australian research since 1970, when I was a The rescarch was visiting engineer at the Melbourne Research Laboratory of BHP.
I witnessed some of the tests, and I reviewed the analytical then in pregress.
derivatsons with the anthors.
I subsequently reviewed this work when I gave a This work is 1ecture for ATSC on this topic in February or Narch of 1984.
I also agree with l
correct and applicable to laterally unsupported angle-beams.
1250-1981. yheWork of treatment of this topic in the Australian Standard
$9m'la's"M,lowable Stressinhould Segonytteji byqEg the pf~ applicable.'F Sincerely yours, MW T. V. Galasios Professor of Civil Engineering TVG:shh e
AMERICAN INSTm1TE OF STED. CONSTRbCTION. INC.
The wgiey Building 40C thrih Muhige Mae Chicogo. Ilknois 606114143 Q12) 670 2400 a
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January 15, 1986 Mr. Thomas G. Ionglais Head, Structural Engineering Dir.
Sargent & Lundy Engineers 55 East Monroe Street Chicago, IL 60603 j
Dear Tom,
Your letter of December 23, 1985 addresses several ques-tions related to the design of single angle supports, which were raised by the Nuclear Regulatory Commission (NRC).
Apparently, our previous comments in correspon-dence with you and Mr. Hans Ashar of NRC did not satis-fy the latter.
Before answering your questions, it is important to point out that the American Institute of Steel Construction, Inc.*is not a regulatory body that prescribes design rules and practices.
The Specifica-tion and Code of Standard Practice are voluntary con-census documents.
Specifically, the Committee on Spe-cifications consists of structural engineers with wide experience and high professional standing, represent-ing a wide geographical distribution throughout the United States..The membership of the committea is made i
up of approw4=mtely equal -number representing design en-gineers in, private practice, engineers involved in re-j search and teaching,,and engineers emp&oyed by steel fabricating c - nieaQand suppliers.
The Specification.
developed by this cc::stittee, as approved by..the AISC ~
Board of Directors,:7 sWidely.used 'by designers and code 1
authorities.~.-.However, FAISC recognizes the authority and responsibility of:the licensed professional for the ly design of structures-within his or her scope of expe2.tise.
l To aid design professionals in exercising their authority and responsibility,~.AISC publishes design aids, manuals-i and the Engineering Journal.
Reference is often made to the worldwide literature on steel design.
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.'/ -f Mr. Thomas G.
Longlais January 15, 1986 Page 2.
1.
The AISC Specification is indeed silent on the design rules for laterally unbraced angles subject to bend-j ing.
AISC, however, has frequently referenced the-Australian research on this topic (1,2) in a nation-al series of seminars entitled " Steel Design Cur-rent Practice" beginning in late 1983.
In addition, the Australian article " Safe Load Tables for Lateral-l ly Unsupported Angles" has been reprinted in the First Quarter, 1984 AISC Engineering Journal with the per-mission of the Australian Institute of Steel Construc-tion.
This design methodology is based on an earlier version of the Australian Standard AS.1250-81(3) in the absence of angle-beam criteria in the present AISC Specification.
The Australian methodology for the design of single angles subject to bending is being used for an example in the 1986 First Edition of the AISC Load and Resistance Factor Design (LRFD)
Manual.
2.
In the proposed LRFD Specification, the flexural de-sign capacity of a d,ouble angle beam is constant at the yield moment value until the onset of elastic buckling.
There appears to be no need for an in-elastic transition done because of the absence of major internal residual stresses in angle sections.
A minimum inelastic rotation capacity of 3 is a com-mon criterion for limiting slenderness ratios in the AISC Specifications (see pg. 34 on new LRFD Specifi-cation).
This is approximately equivalent to the requirement that the computed elastic critical stress.
be at least 3 times as large as the yield stress, to ensure that the plastic moment will be reached.
- Thus, the Australian recommendation that single angle flex-ural yielding will control in the slenderness zone wherein the computed elastic buckling moment is at least 3 times the yield moment is valid.
Furthermore, compact angles have a high shape factor to justify use of a 0.66F allowable bending stress.
y 3.
AISC interaction equations 1.6.la and 1.6.lb are in-tended for the design of beam-columns subject to concurrent axial loads and biaxial moments.
In the design of beam-columns, it is recognized that either yielding or stability may control member behavior.
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Mr. Thomas G.
Longlais January 15, 1956 Page 3.
Equation 1.6.la checks stability with maximum moments along the length of a beam.
Equation 1.6.lb is in-tended to be a stress strength check against yielding.
In this latter situation, stresses should be combined at the critical member support cross-section and should not be based upon the maximum moments along the member length as in equation 1.6.la.
Also, equations 1.6.la and 1.6.lb are intended for the simultaneous application of concurrent static loads.
If a member is subject to time dependent dynamic loads, i.e.,
seismic loads, then a rational method which ac-counts for the nonconcurrence of maximum axial bending moments about the two axes and axial loads may be utilized when employing equations 1.6.la and 1.6.lb.
- 4. We agree that in cases where lateral support of un-symmetric sections is provided at the location of con-centrated loads, simple bending theory will apply, i.e.,
the horizontal and vertical axes (geometric) of the angle.may he used to compute the bending stresses.
Otherwise, the principal axes of the member must be used in the interaction equations.
Sincerely yours, N9t_
Lh Geerhard Haaijer GH/cd cc:
N. Iwankiw
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REFERENCES l
- 1. Leigh J.M. and Lay M.G.,
"The Design of Laterally Unsupported Angles", BHP Technical Bulletin 13(3),
Nov. 1969, pp. 24-29
- 2. Thomas, B.F. and Leigh, J.M.,
"The Behavior of Laterully Unsupported Angles", BHP Melbourne Research Laboratory Report MRL 22/4, Dec., 1970 j
- 3. Australian Standard AS 1250-81, Australian Insti-tute of Steel Construction e
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- 4. N
- UNIVERSITY OF MINNESOTA Depanment of Cvd and Mineral Engineenng hs.4 < Ii TWIN CITIES 122 Cnnt and Mineral Engineenng Buitaing 500 Pillsbury Dnve S.E.
Minneapohs. Menesota 55455 0220 (612) 373-2968 i
January 09,1986 Mr. T.G. Longlais, Head Structural Engineering Division Sargent and Lundy, Engineers 55 East Monroe St.
Chicago, Ill. 60603 J
Dear Mr. Longlais,
This letter is to sum up our discussions and to put down my conclusions on the subject of the Sargent and Lundy design method for single-angle hangers for HVAC ducts in several nuclear power plants. This investigation started with your letter of Nov. g,1985, in which you outlined the basis of your method and with which you enclosed copics of previous correspondence on the subject. This correspondence included an exchange of letters between Dr. Hartzman of the U.S.
Nuclear Regulatory Commision and myself, in which I made some general observations without specifically addressing the complete details of your single angle design method. Subsequent to your initialletter we had a further exchange of letters to provide additional clarification, and we had two meetings in my office at the University of Minnesota between you, Dr. S. Fang, and myself (on Nov. 26,1985 and on Jan. 3,1986). As a consequence of these letters and meetings, and after considerabic study and analysis, I believe that I am quite familiar with both the philosophy and the method used by Sargent and Lundy to design these angles. My comments in this letter are intended to assist Sargent and Lundy in responding to NRC questions and to expand on my previous correspondence with the NRC in June 1985.
Before addressing specific issues I want to state that my comments apply to the particular HVAC angle hangers used by Sargent and Lundy, and they are not meant to be a general design methodology for the design of single-angle beam-columns used in any kind of structural design. There 5 and L angles are primarily intended for the tension hanger support of HVAC ducts in several nuclear power plants. Their end-fsaming is such that the er.ds are constrained about one of the geometric axes of the angle. By dynamic analysis it has been determined that under an extreme seismic event these hangers are subject to end moments about one, or sometimes both, geometric axes, and to small axial compressive forces which are usually (but not always)less than 15 percent of the allowable axial compressive force.
The check for combined bending and' compression is covered in Sec.1.6.i of' the AISC Specification. Two criteria are required to be checked: 1) stability (Eq. I.6.la) and 2) cross section strength (Eq.1.6.lb). If the ratio f /F,is.
less than 0.15, then only one conservative interaction equation needs to be checked (i.e., Eq.1.6.2).
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! l '1 Letter to: T.G. Lonplais; Sargent and Lundy, Engineers Page: 2 Date lanuary 09.1986 My first comments relate to the strenath check. There are two questions to be considered:
- 1) Is it appropriate to compute the ficxural stress on the basis of the geometrir. rather than the principal axes?
- 2) What is the allowable flexural stress F,?
It is my opinion that because the applied force and the restraint at ths.
member ends is directed along one of the angle legs, i.e., along one of the geometric axes, the flexural stress should be comnuted for the neometrie axes.
The applied force will produce forces in both the hanger angle and in the restraining members. The background arguments for this are presented in Sec.
11.4 of the book " Basic Steel Design" by Johnston, Lin and Galambos (3rd ed.,
Prentice-Hall,1985).
AISC Specification., to be used for angles is not specifically defined in the The value of F A value of F = 0.66F is recommended for compact wide-b flange shapes bent about the major axis, an,d F = 0.75F for minor axis ficxure.
h These two values contain allowance for the different pl,astic shape factors for major and minor axis bending, i.e.1.10 and 1.55 respectively. It can be shown that the shape factor for a compact angle is about 1.8 when bending is about s.
geometric rxis, and 1.75 when bending is about the minor principal axis. These values are larger than those for wide-flange shapes, so the use of F = 0.66F is conservative for ansics. The use of F = 0.66F, for compact angIes is thus b
entirely within the intent of the AISC Specification.
l The next comments refer to the questions related to the stability check.
The stability interaction equation in the AISC Specification is in a stress-i format for reasons of convenience and convention. The original formulation of l
the interaction equation is in terms of forces (design and ultimate compression j
i and flexural forces; see, for example, Chap. II, in
- Structural Steel Design *,
editor L. Tall, Ronald Press,1974) which are translated into stresses. If, for example, the allowable ficxural moment for the limit state of lateral-torsional buckling is formulated for flexure about a geometric axis, as was done by Leigh and Lay in their paper, then the actual and the allowable stress may be normalized from moments about the geometric axis also. Thus it is permissible, for reasons of convenience, to use the stresses f, and F in Eq.1.6.la with b
reference to the geometric axes. A similar interpretation is used by the Steel Joist Institute for the design of eccentric single-ansic webs in prefabricated trusses. Several dozen angle columns were tested under three different end conditions about 15 years ago at Washington University to substantiate this method of design (see paper by Usami and Galambos, IABSE Memoirs,1971). This design method has been successfully used for over ten years, and tests on full scale trusses performed by John Leigh for his Master's thesis at Washington University showed it to result in a safe structure.
The next question in connection with the stability check has to do with the value of F, to be used in Eq.1.6-1a. The AISC Specification is silent on this l
t,..a Letter to: T.G. Longlais; Sargent and Lundy, Engineers Page: 3 Date hnuary 09.1986 subject, but a recent AISC lecture series acquainted American engineers with the work of Leigh and Lay on the subject. This work was performed in 1970 at the BHP Steel Company Laboratory in Melbourne, Australia. Both Leigh and Lay are my former students, and I reviewed their work when i visited Australia in 1970. I have the highest regard for their research. I have again reviewed their study and rederived their equation in the past weeks. It is my opinion that F, can be safely determined by the criteria given in the Australian SAA Steel Structures Code AS1250-1981 Sec. 5. For the case of wide-flange beams I have compared the Australian design criteria with the new AISC Load and Resistance Factor Design rules and I found the Australian method to be more.:onservative in all cases I checked. The Australian buckling criteria assume that the cross-section plastifies when the clastic buckling stress equals or exceeds three times the yield stress if a wide-flange beam is bent about the major axis. This is a typical approach used on all types of buckling criteria in the Australian steci design specification, and it is justified in a number of papers by Max Lay and Nick Trahair (see also the figure on p.109 of Vol. II of the book by Atsuta and Wilfred Chen). Modern U.S. Specifications do not explicitly formulate the limits of plastic behavior in quite the same way, but the result is just about the same. For the single-angle beam the assumption of plastification under factored loads when F - 0.66F and the clastic buckling stress is 3F is, of g
course, quite conservative becau,se of the high shape factor of about 1.7 to 1.8.
Thus even the criterion of F, = 0.95F carries with it a factor of safety of about 1.9 against plastification, while#F = 0.66F has a safety factor of about 2.7. These remarks concern the behavio,r of comp,act angles (i.e., b/t < 65/ F ).
for non-compact angles we must use F = 0.6F or if b/t > 76/ F,, F - 0.60DF,.
b b
For the cases the Australian design equation m,,ust be topped out at 0.6F, or 0.6QF,, as appropriate.
It is my opinion that the use of the Australian criteria for determiining F,in Eq.1.6-la by Sargent and Lundy for the single-angle HVAC hangers is appropriate and conservative, resulting in safe designs.
The use of AISC Eq.1.6-Ib assures adequate strength at the ends of the hangers where the moments are maximum, while compliance with Eq.1.6-la checks' the lateral-torsional stability of the merrber as a whole. For most of the practical angles for steel with F[r=ength equation needs to be checked if the 36 ksi, and for the compact ansics for
= 50 ksi only the s steel with F[th to thickness is less than 400.
ratio of len The AISC interaction equations apply when the forces acting on them are acting concurrently. They would result in unduly conservative designs if the maxima of several load sets, which do r:ot act simultaneously, were to be assumed to be applied.
The moment caused by the eccentricity of the axial force which is applied through one les should be considered in design. This moment, however,is shared by the restraining members in proportion of the relative stiffnesses. The Usami experiments on restrained-end single angles, and the Leigh truss tests l
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l'i Letter to: T.G. Longlais; Sargent and Lundy, Engineers
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Page: 4 Date Januarv 09.1986 demonstrated the effectiveness of this assumption. With the relatively low axial forces in the Sargent and Lundy hanger angles and the participation of the restraining members the effect of the eccentricity is expected to be quite small.
In summary, while the AISC Specification does not contain explicit rules for the design of single-angle beam columns, the Sargent and Lundy design method i
is rational, it is conservative, and it meets the intent of the AISC Specification. I believe it to be a safe approach for the design of these hatager angles. In conclusion I would add that the safety of these hangers is further enhanced by the fact that compression occurs only during a transient sei;mic event, and not always as in a gravity-type building column.
I am satisfied that the Sargent and Lundy design method is safe and adequate for the single-angle HVAC hanger.
Sincerely yours, T. V. Galambos Professor of Civil Engineering TVG:sbh i
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ATTACHMENT 2 DESIGN CRITERIA FOR SINGLE ANGLE MEMBERS I.
Normal and upset conditions.
A.
Allowable stress for loading other than bending.
1.
Tension The allowable stress shall be determined from Section 1.5.1 of the AISC Specification (AISCS), Reference 1.
2.
Shear The allowable stress shall be determined from Section 1.5.1.2 Oe of the AISCS.
Shear stresses shall include tors,ional effects due to transverse forces not acting thru the shear center.
3.
Compression (a) The allowable stress shall be determined from Section 1.5.1.3 of the AISCS.
(b) The radius of gyration shall be based on the minimum principal moment of inertia of the member cross-section.
(c) For member with b/t > 76/JFy the stress reduction factor Qs of AISCS, Appendix C, sha'l be applied.
, (d) For compression members in systems primarily under tension (such as ceiling mounted supports of cable tray systems or HVAC systems) KL/r shall be limited to 300 (References 6,7).
(e) For compression members in systems other than those described above, KL/r shall be limited to 200 (References 6,7).
4 B.
Allowable st sses for bending loads.
The allowable bending stress shall be determined from the following equations (References 2,3,4):
Fb = [.55
,.10 b] F for F
i F (la) g y
F F = [.95
.50
]F for Fob > F (Ib) b y
y p
where F = allowable bending stress, ksi b
F
= elastic lateral flexural-torsional buckling stress, ksi ob F = yield stress, ksi F shall be limited as follows (Reference 4):
b For b/t < 65/JF F =.66 F (2a) y b
y 65/JFy < b/t i 76/JF Fb =.60 F (2b) y y
b/t > 76/JF F =.60 Q F (2c) y b
sy D
.. 1.
For equal leg angle members F shall be calculated as follows ob (Reference 5):
- For unbraced members bent about the major principal axis:
DE(t/L) pob,
242.6 (3) where L = unbraced length
- For unbraced members bent by an applied moment parallel to a leg:
n2E
" 10 +
fb2 b2 (4,)
Fob =.30 l
(L/t)
,1.3n2 (Lt4 Lt.
i I
or feb,*
- f{
(4b) o where Equation (4a) is applicable if the maximum bending stress is calculated with respect to the principal axes, and Equation (4b) is applicable if the maximum bending stress is calculated i
using the' conventional beam formula.
For unbraced members bent about the minor principal axis the maximum stress shall be limited by the values of Equations (2).
2.
For unequal leg angle members the values of F should be ob determined by applying the methodology of Reference 8.
C.
Combined Stresses 1.
Axial compression and bending.
Members subjected to both axial compression and bending shall satisfy the requirements of Section 1.6.1 of the AISCS, subject to following conditions (Reference 3):'
. a.
In evaluating AISCS Equation 1.6.la or 1.6.lc, the maximum compressive bending stress due to each moment acting alone must be used.
The maximum individual moments may occur at different cross-sections of a member.
b.
AISCS Equation 1.6.lb is to be evaluated at the critical member support cross-sections and need not be based on the maximum moments along the member length.
2.
Axial Tension and Bending Members subjected to both axial tension and bending stresses shall satisfy the requirements of section 1.6.2 pf the AISCS.
3.
Calculation of Maximum Bending Stresses The maximum bending stresses shall be determined with respect to the principal axes, using the conventional beam equations referred to the principal axes, or the beam transformation equation referred to the geometric axes (References 9,10).
For members laterally restrained or braced at the load points, such that bending occurs parallel to one of the geometric axes only (bending in the transverse geometric plane is zero), the maximum bending stress may be deter-mined by using the conventional beam equations referred to the geometric axes (Reference 11).
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. II.
Emergency and faulted conditions The allowable stresses for normal and upset conditions may be increased by a factor of 1.60 with the following exceptions:
A.
For members with axial loading in compression:
1.
AISC jurisdiction:
F, may be increased by a factor of 1.33.
2.
ASME jurisdiction:
a, faulted (F,
- FS)
F
=
~
where FS is determined from the factors of safety of Section 1.5.1.3 of the AISCS.
B.
Allowable stresses in bending may not exceed.95.F.
y III.
References 1.
American Institute of Steel Construction, Specification for the Design, Fabrication and Erection of Structural Steel for Building, effective November 1, 1978. Manual of Steel Construction, 8th Edition.
2.
Australian Institute of Steel Construction, Australian Standard AS1250-1975.
3.
Letter from G. Haaijer, American Institute of Steel Construction, to T. Longlais, Sargent and Lundy Engineers, dated January 15, 1986.
4.
Letter from T. Galambos, University of Minnesota, to T. Longlais, Sargent and Lun'dy Engineers, dated January 9, 1986.
N-
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. 5.
Leigh J. M. and Lay M. G., "The Design of Laterally Unsupported Angles," in American Institute of Steel Construction Steel Design Current Practice, Section 2, " Bending Members", January 1984.
6.
Letter from J. Edinger, American Institute of Steel construction, to K. Kostal, Sargent and Lundy Engineers, dated January 30, 1985.
7.
Letter from T. Galambos, University of Minnesota, to K. Kostal, Sargent and L, undy Engineers, dated January 28, 1985.
8.
Leigh, J. M. and Lay, M. G., " Laterally unsupported Angles with Equal and Unequal Legs", Report MRL 22/2 July 1978, Melbour.ne Research Laboratories, Clayton.
9.
Seely, F. B. and Smith, J. O., " Advanced Mechanics of Materials",
Second Edition, 1952, J. Wiley and Sons, New York.
Chapter 5
" Unsymmetrical Bending".
10.
Bresler, 1, Lin, T. Y., and Scalzi, J.B., " Design of Steel Structures",
Second Edition,1968, J. Wiley and Sons, New York.
Chapter 8 " Bending and Torsion of Beams", Section 8.3.
- 11. Johnston, B.
G.,
Lin, F.
J., and Galambos, T. V., " Basic Steel Design" Third Edition, 1985, Prentice-Hall, New Jersey.
Section 11.4.
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