Ultimate strength tables for beam columns, 1962, Reprint No. 197 (62-3)

Transcription

1 Lehigh University Lehigh Preserve Fritz Laboratory Reports Civil and Environmental Engineering 1962 Ultimate strength tables for beam columns, 1962, Reprint No. 197 (62-3) J. Prasad T. V. Galambos Follow this and additional works at: Recommended Citation Prasad, J. and Galambos, T. V., "Ultimate strength tables for beam columns, 1962, Reprint No. 197 (62-3)" (1962). Fritz Laboratory Reports. Paper This Technical Report is brought to you for free and open access by the Civil and Environmental Engineering at Lehigh Preserve. t has been accepted for inclusion in Fritz Laboratory Reports by an authorized administrator of Lehigh Preserve. For more information, please contact preserve@lehigh.edu.

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3 287 LEHGH UNVERSTY BETHLEHEM. PENNSYLVANA DEPARTMENT OF CVL ENGNEERNG FRTZ ENGNEERNG LABORATORY MEMBERS OF LEHGH PROJECT SUBCOMMTTEE (WRC) January 25, 1962 Higgins, ToRo Amirikian, A o Beedle, LC)So Crowley, JoM. Dill, F.Ho Epstein, So Fox, Go Grover, Lo Ja.meson, Wl>Ho Johnston, BoG. Kavanagh, T 0 C 0 Ketter, RoLo Marshall, R.W. Newmark, N.M. Pisetzner, E. Stuchell, R.M. Vasta, J. Gentlemen: RE: Fritz Lab Report Noo "Ultimate Strength Tables for Beam-Columns" by T.V. Galambos and Jo Prasad The enclosed report p~esents information on the strength of beam-columns in a tabular form for easy use of the designer. The information has been presented previously in several reports as interaction curves o The extent and scale of these curves has never been large. enough for effective use, and this repor~ is written to fill in the need for more precise valueso We wish to submit this report for publication as a WRC Bulletin, and we: solicit your approv~l an4 your comments on the enclosed postcard before March 1,19620 TVG/gem Enclosures Sincerely yours, T~AY'~~~ Theodore V. Galambos.erCZr~P~ George~C o Driscoll,Jr o /'" cc: Messrs. K. Ho Koopman C. F. Larson

4 j J Welded Continuous Frames and Their Components ULTMATE STRENGTH TABLES FOR BEAM-COLUMNS (49 llsf by T. V. Galambos J. Prasad This work has been carried out as part of an investigation sponsored jointly by the Welding Research Council and the Department of the Navy with funds furnished by the following: American nstitute of Steel Construction American ron and Steel nstitute nstitute of Research, Lehigh University Column Research Council (advisory) Office of Naval Research (Contract Nonr 610(03» Bureau of Ships Bureau of Yards and Docks Reproduction of this report in whole or in part is permitted for any purpose of the United States government. Fritz Engineering Laboratory Lehigh University Bethlehem, Pennsylvania Dec~mber, 1961 Fritz Engineering Laboratory Report No

5 S Y N 0 PS S n this report tables are presented for the ultimate strength of as-rolled wide-flange beam-columns bent by endmoments about their major axis. Failure is assumed to take place by excessive bending in the plane of the applied moments. The tables give the critical combinations of length, endmoments and axial force at which failure occurs. N T ROD U C T ON Beam-columns, that is, members which are subjected to an axial force and to bending moments, always fail by in- 1 e1as t, ~c ~nsta b ~ 1't ~ y. (1) f the ben d«~ng moment s ac t' ~n one of the principal planes of the cross section, failure may occur due to one of the following instability phenomena:, Lateral-torsional buckling 2. Local buckling 3. Excessive bending in the plane of the applied moments. Lateral-torsional buckling and local buckling will

6 not influence the ultimate strength of as-rolled steel wideflange beam-columns bent about their major (or strong) axis if the member is adequately braced and if certain width (2) thickness ratios are not exceeded. For these members failure will thus be due to excessive bending in the plane of the applied moments. Because this type of failure takes place in the inelastic range, the ultimate strength cannot be computed by an 1exact17 mathematical procedure. The solution is obtained by numerical integration of the elastic-plastic moment-curvature re1.. h' (1) (3) at~ons ~p. l' nteract~on curvesf' or var~ous cases f 0 1oa d ~ '1 bi (1)(2)(3) d" f ~ng are ava~ a e an approx~mate equat~ons or (1) (2) (4) three extreme loading cases are published. n applying the available information to a given design problem one is faced with two difficulties: (1) The published interaction curves are drawn at too small a scale and with not enough curves to be of any use in the final design, even though they serve their purpose well in preliminary design. (2) The approximate equations have a limited scope of application and they apply only to extreme cases. The ultimate strength tables of this report are presented in order to permit a more precise analysis than that which is possible with the currently available information.

7 The tables were prepared from cross-curves constructed from enlarged versions of the originals of the curves reproduced in Refs. 1, 2, and 3. The tables give only the strength of beam-columnso Where additional conditions of rotation requirements must be met (2) further checks are required to assure adequate rotation capacity ~rt~ 7.4,Ref.2). THE S COP E o F A P P Le A T ON o F THE TAB L E S The tables presented herein are only a convenient arrangement of already published information. They represent no new work, and the values are subject to the same limitations as h f h ~ h,. 1 (1)(3) h bl t ose set art ~n t e or~g~na reports. T e ta es are thus valid for as-rolled wide-flange ASTM-A7 steel sections having a maximum compressive residual stress at the flange tips of 0.3 times the yield stress and which are subjected to endmoments about the major axis. t is assumed that failure is due to excessive bending in the plane of the applied moments, and that lateral-torsional buckling and local buckling will not influence the ultimate strength. The tables list the maximum end-moment which a beamcolumn of a given size and length can support under a given axial force and for a given ratio of the end-moments. All values are given non~dimensionally and therefore the tables

8 are applicable for all wide-flange shapes. The pertinent non-dimensional ratios are as follows: L/r = Slenderness ratio pip = Axial load ratio y ~ = End-moment ratio MO/M p = Maximum moment ratio where L r P = Length of the beam-column = Major radius of gyration = Axial load to be supported Py~y= Yield load A = Cross-sectional area Gy = Yield stress (33ksi for A7 steel) {3 = Ratio of the smaller to the larger endmoment. ~~en the two moments cause single curvature deformation, the value of ~ is positive; when they cause double curvature deformation, the value of ~ is negative. Because ~ is always a ratio of a smaller to a larger number, ~ f3 ~+l. 00. M.. ~. Larger of the two end-moments. o Mp=Z~= Plastic moment of the section. Z = Plastic modulus about the major axis.

9 The ultimate moment values are given for slenderness ratios from 0 to 120, in increments of 10; for axial load ratios from 0 to Per/P y (where Per is the tangent-modulus load for the corresponding axially loaded column) in increments of 0.05; and for end-moment ratios ~ from to in increments of 0.2. The spacing of the points is sufficiently close such that linear interpolation can be used for intermediate points. The use of the tables can be illustrated by the following typical example: Given: From the simple plastic analysis of a rigid frame it is found that a particular member of length L = 180 in, is subjected to the following forces: M o = 376 in-kips' ' ~o = 126 in-kips therefore ~ = Solution: 1 st trial: 8WF24 P/P y = 0.536; Mo/M p = 0.493; L/r = 52.6

10 From the tables (for ~ = 0.4, pip = 0.55; L/r = 60)* y it is found that (Mo/M p ) = 0.40 < and theremax fore the 8WF24 section is inadequate. 2 nd trial: 8WF28 p/p y = 0.459; Mo/M p = 0.420; L/r = 52.2 From the tables (for ~ = 0.4; P/P y = 0.50; L/r = 60) it is found that (M 1M ) = 0.47 /' and there-.,0 P max fore the 8ttJF2 8 sectiol1 is adequate. A C K NOW LED GEM E N T This study is part of a general investigation "Welded Continuous Frames and Their Components" currently bei11g carried out at the Fritz Engineering Laboratory of the Civil Engineering Department of Lehigh University under the general direction of Lynn S. Beedle. The investigation is sponsored jointly by the Welding Research Council and the Department of the Navy, with funds furnished by the American nstitute of Steel Construction, the American ron and Steel nstitute, Lehigh University nstitute of Research, the Office of Naval Research, the *Since interpolation is not used, the more s~ere values of ~, pip, and L/r are chosen. y

11 Bureau of Ships and the Bureau of Yards and Docks. The Column Research Council acts in an advisory capacity. Data for constructing the curves for ~ = +0.5, -0.5 and -1.0 were supplied by Dr. R. L. Ketter, whose cooperation is greatly appreciated.,

12 ULTMATE STRENGTH TABLES FOR BEAM-COLUMNS Scope of the Tables: As-rolled steel wide-flange sections of ASTM A-7 steel* bent about their strong axis and meeting the bracing rules and width-thickness limitations set forth in Chapter 6 and 7 of Ref. 2. M o i, ~Mo p L ~ {3~ in increments of 0.2 o ~ L/r ~ 120 in increments of 10 o ~ P/Py~ Pcr/P y in increments of 0.2 *For use with other steels (up to the 50 ksi high-strength steels), these tables may be used if the slenderness ratio is adjusted as follows(l): (L) = (L) j6y actual \r adjusted r actual 33

13 ULTMATE Mo/~ VALUES FOR (3 = -loa P/P y L/r=O L/r=lO L/r=20 L/r=30 L/r=40 Ljr=50 Ljr=60 L/r=70 L/r=80 L/r=90 L/r=lOO L/r=110 L/r= $ & o<t o~ o~ o~64 G o oe58 o~ O ' OQ O~ # & o~ OslO O~ '"

14 ULTMATE Mo/~ VALUES FOR ;;::; ,) p/p y Lj'r=O L/r;;lO L/J r =20 L/r=JO Ljr=4o L/r=5a L/r=60 L/r==70 L/r=80 L/r=90 -L/r=lOO L/r=110 Ljr= l~oo &00 lctoo ,, Ot> O~ ~ , ,, O~ O~ ~ Oe63 O~ , OQ od Oet & , O~ Oit O«t30 O~ O~ O~O ~- J--' _. -- 0

15 ULTMATE Mo/~ VALUES FOR (3 ;; P/P y L/r=O -L/r=lO Lj-'r=20 L/'r=30 L/r=40 L/r=50 L/r=60 L/r=70 L/r=80 L/r=90 -L/r=lOO L/'r=110 Lj'r= l e OO O~ olt $90 Oc.90 0,, & ob G o #69 o~ o~ Ot) Ott o~ o~ O~ o(to OeO OitOl Oe o~ O ct : t-l ~

16 ~ - ~ -. ~. P!.P y ULTJYATE MaiM VALUES FOR f3> ;;.; -0.4 p "-. ""...,. ~ L/r=O L/r=lO L/r=20 L/r=30 L/r=40 L/r=50 L/r=60 L/r=70 L/r=80 L/r=90 L/r=lOO L/r=110 L/r=120 " ". " l~oo l~oo boo Oe O~96 0& O~ & OQ O~ <t , , , o~ t--l N

17 ULTMATE Mo~ VALUES FOR (3 :::: -0.2 P/p y L/r=O L/r=lO L/r=20 L/r=30 L/r=40 L/r=50 L/r=60 L/r=70 L/r=80 L/r=90 L/r=lOO L/r=110 L/r= ~ o~o5 o~-99 O<t99 a ~_-99 0,, O~ O-~ ,10 ofit ,97 0~96 O~96 O~_96 O~ O~95 ot O?15 O?95 O'~94 O~94 O~94 O~ ~ OQ86 0& o~35 o~ 75- o~ o~74 o~ ';71 O~70 01c 6 7 0,61 o~.51 O~4o O~40 o~,70 O~69 O~ #67 0 0, O~58 O~51 O~4o O~29 O~,45 O~_64 O!64 O~ O~ O? O~ ,20 o~ 12 O~ o~49 O~ O~O4 O~,60 O?,47 O~47 O~47 00,46 o~45 o()44 OQ O~ O~_41 O~,41 O~,41 o~.40 O~,39 o~37 0~.36 00,31 O~ ,03 O~ O~35 O~3.5 o~.34 O~34 O~31 O~29 o~25 O~ O~O a ~.75 O?,30 O~ O~,27 O~ Oce O~ O~ o~ o~ , &0.5 O~90 0 0,12 O~ ,, O~ ~ W

18 ULTMATE Mc!M p VALUES FOR f3 = 0.00 pip L/r=O L/r=lO L/r=20 L/r=30 L/r=40 L/r=50 L/r=60 L/r=70 L/r=80 L/r=90 L/r=lOO L/r=110 L/r= lego laoo l OO lego ,, O~ S OCt? ~ o~ o~ ,, o~ ~ +'

19 ULTMATE Mo/~ VALUES FOR (3 = pip L/r=O L/r=lO L/r=20 L/r=30 L/r=40 L/r=50 L/r=60 L/r=70 L/r=80 L/r=90 L/r=lOO L/r=110 L/r= l~oo leoo doo l~oo l~oo lego l~oo l~oo O~_O O~ # O~ O~ O~ o.e _ <) o~ O<t ,, OQ o(t l~oo ~ \J1

20 ULTMATE Mo/MP VALUES FOR (3 == P!P y L/~=O L/~=lO L/~=20 L/~=30 L/~=4-0 L/~=50 L/~=60 -L/~=70 L/~=80 L/~=90 L/r~lOO L/r~110 L/r~ leoo 1,, l~oo leoo l~oo 1.00 l~oo letoo O~ Oc OQ Oe " 78. O~ Oi) OfJ # o~ Oc ~ 0'\

21 ~ ~... r ~ p/p y ULTMATE Ma/M VALUES FOR (3, ;; +0.6 p L/r=O L/r=lO L/r=20 L/r=30 L/r=40 L/r=50 L/r=60 L/r=70 L/r=80 L/r=90 L/r=lOO L/r=110 L/r= l~oo liloo O~ O~ O~ Oet ' ~ oe & & o.4~ o~ o. 05~ , : t-..l -...,J

22 ULTMATE MciMp VALUES FOR ~ =: +008 P/p y L/r=O L/r=lO L/r=20 L/r=30 L/r=40L/r=50 L/r=60 L/r=70 L/r=80 L/r=90 L/r=lOO L/r=110 L/r= O~78 0~ Oo9l & OQ Oe OCJ ) o~ /t ,, O~ ~ ex>

23 ULTMATE Mc~ VALUES FOR (3 = +1.0 p/p y L/r=O L/r=lO L/r=20 L/r=30 L/r=40 L/r=50 L/r=60 L/r=70 L/r=80 L/r=90 L/r=lOO L/r=110 L/r= '''' ~. ;~. +.,. " O'l « " O~ O~ ,, ,, o~ O<t #' i \0

24 REF ERE NeE S 1. R. L. Ketter, T. V. Galambos COLUMNS UNDER COMBNED BENDNG AND THRUST, Proceedings of the ASeE, 85 (EM2) (April 1959) 2. WRC - ASCE Committee COMMENTARY ON PLASTC DESGN N STEEL ASeE Manual No. 41, (1961) 3. R. L. Ketter FURTHER STUDES ON THE STRENGTH OF BEAM-COLUMNS Proceedings of the ASeE, 87 (8T6) (August 1961) 4. ASC PLASTC DESGN N STEEL ASC, New York, 1959