1、. r -I * . : .- . NATIONAL, ADVISORY COMMITTEE FOR AERONAUTICS TECHNICAL NOTE No. 1817 PLASTIC BUCKLING OF SIMPLY SUPPORTED COMPRJZSSED PLATES By Richard A. Pride and George J. Heimerl Langley Aeronautical Laboratory Langley Air Force Base, Va. Provided by IHSNot for ResaleNo reproduction or network
2、ing permitted without license from IHS-,-,-I!U!l?IONAT; ADVISORY Cm TECHNTCAL NOTE NO. 1817 By Richard A. Pride end George J. Helmerl An Fnvestigation was made to asaertain the validity of various theories for the plastic buckling of use of-inside dimenBiOn6 is consistent with previous method for di
3、mensioning extrudons (refer- ence 4) and gives best agreement with test results in elas- tic range length of platy thickness of plate plate bu number by which criticel stress computed for elastic case must be multi$lied to give criti- cal stress for plastic case (for stresses In elastic range, tl =
4、1, whereas above elastic renge, Q * DIL2 = 1 - c8(2 - P)(W - 1) D* = T.- c6(2p - 1* 7 (6) Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-8 secanmodtilus method. - An empirical method fordetermlning plastic buckling streseee of plates was suggested b
5、y Gerard (reference 10) and has been found to-work qtite well for plate assemblies of H-, Z-, and C-sec- tlans for a number of aircraft structural materials. (See reference 4.) This method defines q *aa *a =- E (71 The results of the local-Instability tests are summarized for the critical. compressi
6、ve stress Jn table I and figure 6 and for the average stress at maximum load in table I. The correlation of the results with the theories for plastic buckljng and the secant-modulus method is shown Fn figure 9. For direct comparisan.with the applicable stress-strain curves for the materl$l, the expe
7、rimsntal critical compressive stress ucr is plot- ted against the calculated elastic critical compressive atraW Gcr (see equation (2) in figure 6 where the teat points are seem to fall saamwhat below the atrese-strain curves in the plastic region. The generalized correlation with the single represen
8、tative compressive etress-strain curve, the theories for plastic buckling, and the eecant- modulus method is madein figure 9 by adjusting the test-results to allow for variations in the compressive yield stress of the material for the various tubes by the method described in reference ll. In this ge
9、neralized comparison the test results In the plastic region can be seen to fall a little below the stress-strain curve which also gives the results of the secant-modulus method; the test results lie closeat to the calculated plate buckling curve ncr aWnat- 6cr given by Stowelle theory. Tlyuahins and
10、 Bijlsards theories give results which are slightly higher but st3Jl fall below the comreasive stress-strain curve. Thus, good agreement with the test-results is shown for the three deformation-type theories of plastic buckling. There is little correlation, however, between the test- results and the
11、 Handelman-%ager theory, and the difference between this flow-type theory and deformation-type theories is marked. (See fig. 9.) With regard to the accuracy of the teat results for ucrr the nearly ideal load-displacement curves obtained for many of the tests (fig* 4) end the unusual degree of isotro
12、py of the mteriel (fig. 7) lead to the belief that the teat specimens came close to being theoretically ideal specimens, and therefore the test-results provide a good basis for dls- criminating between the various theories on plastic buckling of plates. Provided by IHSNot for ResaleNo reproduction o
13、r networking permitted without license from IHS-,-,-NACA TN NO. 1817 CONCLUSIONS 9 The result8 of the local-instability tests of drawn spume tubes warrant the following concluaione a8 regasde the plastic buckling of a long, flat, eimply supported ccmeeeed plate: 1. The result6 of these test6 show go
14、od agreement with Stowelle theory for the plastic buckling of a simply supported plate which ie based on a deformatirm theory of plastioity. This confirmation, together with that previously shown for a flauge aud column, is considered to constitute a satisfactory experimental verification of the the
15、ory. 2. Good agreement with the teat resulte Is evidenced in general by the deformation-type theories for plastic buckling. Stowells theory is in the closest agreerrmnt with the teat results reported herein, but Ilyushins and Bijlaarde theories give results only slightly higher. 3. Wked disagreement
16、 is shown between the test results and the Handem-Prager theory which is based on a flow theory of plasticity. 4. Buckling stresses calculated by the empirical secant-modulus vsthod, are reasonable, though higher than the test results. This convenient rapid method can therefore be used for au approx
17、imte determination ofthe critical compressive stress. Langley Aeronautical Laboratory Nation Advisory Committee for Aeronautics Langley Air Force.Base, Va., January 18, 1949 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-10 NACA TN No. 1817 1. Stowe
18、ll, Elbridge Z.: A Unified Theory of PlaEltic Buckling of Columns end Plates. NACA TN NO. 1556, 1948. 2. I(bllbrunner, C!. F.: Das Ausbeulen der auf eineeitigen, gleictissig verteilten Druck beanspruchten Platten im elastiechen und plastischen Bereich. Mitt.,Nr. 17; Inst. fir Baustatik an der E.T.H.
19、, Gebr. Leemann b“ 2: 7a 7b 2 9a 9b 10a lob lla A A i B C C C C C C C C C D D E E F F F 26.84 26.84 30.06 30.05 4.74 9.41 9.35 14.10 14.11 18.96 18.94 23.45 23.44 17.83 17.83 15.50 15.50 14.42 14.42 19.16 Width is measured (j) a Adjuster =cr ;I 6.69 6.69 21.2 22.0 6.69 6.69 4.68 22.6 22.5 4.68 4.68
20、4.68 4.68 4.68 4.68 4.68 4.68 3.94 3 -94 3.44 3.44 3.19 3.19 3.19 54.6 48.1 48.2 44.6 45.1 42.8 42.9 I 3.1575 4.0 42.5 0.00205 21.2 .1573 4.0 42.5 .00205 22.0 .1600 4.5 41.8 .00211 22.6 .1600 4.5 41.8 .002u 22.5 .1557 1.6 30 .l a0406 54.6 .1557 2.0 30.1 .00406 48.1 .1555 2.0 30.1 .oo406 48.2 -15533.
21、0 30 .l .oo406 44.6 ml553 3.0 30.1 .00406 45.1 -1555 4.0 30.1 .oo406 42.8 .1557 4.0 30.1 .00406 42.9 l553 5-o 30 J a0406 42.4 -1559 5-o 30.1 .00406 42.8 -1539 4.5 -1539 4.5 z-2 - . 000563 -00563 53-3 53-9 .1526 4.5 z-2.5 .00729 57.0 .1528 4.5 22 *5 -00729 57-8 .1531 4.5 20.8 a00853 61.4 .1530 4.5 20
22、.8 a0853 60.8 .1534 6.0 20.8 .00853 60.8 i I inside face to inside face of tubes (fig. L 42.4 42.8 52.2 52.8 58.1 59.0 59.9 59*3 59.3 %sx hi) 31.6 62.2 31.5 62.2 31.7 31.6 54.6 61.4 48.3 61.4 48.4 61.4 45.2 45 -5 43.8 43 -5 61.4 61.4 61.4 61.4 43.5 61.4 43.2 61.4 53.9 54.7 57.6 57.9 63.2 63.2 60 .o
23、60 .o 61.6 61.0 60.9 66:-i . 63.0 =CY ai) fig. 6 ?Chlckness is the mean thickness calculated from the cross-sectional srea. C klfw or = 12(1 i-yz)I-$ %riticsl compressive stress afijusted for variations of compressive yield etress of material by methods of .reference 11. Provided by IHSNot for Resal
24、eNo reproduction or networking permitted without license from IHS-,-,-12 t i - NACA TN No. 18l7 .- _- l- ,094 R i- ,125 R b . b Figure I, - Cross section of square tube, Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN No. 18l7 13 Figure 2.- M
25、ethod of supporting individual plates of a square tube for compression stress-strain tests. . Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN NO
26、. 1817 . . Figure 3.- Method of detecting buckling of plate elements of a square tube under test. . Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-, . Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
27、NACA TN No. l&7 17 L0qd + Maximum load r Critical load P aximum load Displacement Figure 4.- Load-displacetmeni curves for two adjoining plates of square tube specimen Sb. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-6C 2 5 g figure 5.- Variation
28、of critical compressive stress cr and average stress at maximum load 5max with the length-width ratio L/b for square tubes of 14S-T6 aluminum alloy (tube C). 2 . P e Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-1 . , . . . stress, ksi 60. Limits:
29、* - Ir- h I I/Q1 I A I /I I I 60 - .002 l-4 Strain Figurs 6.- Correlation of test results far the critical campressivs stress for long, simply supported, flat plates with the aampr8sslve stress-straln curves for 14S-T6 abninum allay. (Calculated elastic critical catnpressive strain used for plate te
30、sts.) Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-20 NACA TN NO. 1817 6 o With grain 0 Cross grain Figure 7, -Variation of the compressive yield stress in ksi over the cross section of a drawn 14%T6 aluminum-alloy square tube (tube C), . Provided
31、 by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN NO. 1817 21 .8 ES -# E .6 Et -8 E I .4 .2 0 40 (Handelman- Prager theory) r) (Secant -modulus method) 71 (Ilyushin theory) q (Bijlaard theory) 7 (StowelI theory) 50 60 70 Stress, ksi Figure 8 Es Et Vari
32、ation of E, =-, and nondimensional coefficient 7 with stress for i4S-T6 aluminum alloy. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-22 -. NACA TN No. 1817 . 80 60 Stress, kSi 0 I / /-I Handelman-Prager theory / Stress-strain curve / and secant-mo
33、dulus ,004 Strain .008 -012 Figure 9. - Gorreiation of adjusted test results for the critical compres- sive stress with calculated plats buckilng curves for long simply supported, flat plates of 14s.T6 aiumfnum alloy, (Galculated eiasftc critical compressive strain used for plate tests.) . Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
