1、REPORT No. 734CRITICAL COMPRESWVE STRESS FOR OUTSTANDING FLANGESBy EUCiENnE. LURDQUISTand ELBBIDGZ STOWEU.SUMMA13YA chart h prewtdtd for the-duesof the coeji%ientinth formula for th this medium has the basic property thatrotation at one point within it does not influence therotation at any othh poin
2、t.Fure 7 shows the coordinate system md the platedimensions. The differential wpation for the equilib-rium of a plate ehrmnt iswherej uniformly distributed compressive stresst thicknws of plateu) deflection normal to platez Iongitudmal coordinate in direction of applied stressD flexursl rigidity of
3、plate, per unit lengthy transverse coordinate across width of platerl, r, and s coefficients equal to or 1sss than unityIn equation (A-1) the term jt(Z% whereas the term% )rl+2Ta$ whereas the terminvoIving Tzis concerned principally with the tarsicnalstitlness. The caefliciente 71, 7*, and T* allow
4、for thechange in the magnitude of the various terms as theplate is stressed beyond the elastic range. In theelastic range, rl=z=ra= 1.The loaded edges are simply supported and are notdisplaced in the direction w. Of the several forms-2 xFIGVE67.-OutstandIra tkuge under edgE compmsIori.of the general
5、 solution of equation (A1) the followingform was selected as appropriate for tlis prcblem:_ . _ _=”( c thus(A-6)where m=l, 2, 3, etc.In he elastic range, where rl=r=ra= , the valuesThe solution given by equation (A-2)satisfy the boundary conditions of no(A-7)“(i+-jWa9 selected todektion andsimple su
6、pport (no moment) along the loaded edges.The boundary conditions along the unloaded side edgeshave also to be sati (ac9+ f3c4) (A-14)where4 is the strain energy in the elastic restrainingmedium along one side edge of the plate. The criticalstress is obtained from the condition of neutral stability:Z
7、=T”*+T-2 (B-1)If w is the deflection uormal to the plate at anypoint x, v in the plane of the plate shown in figure7 and are given by the following equations(see reference 6, equations(199)and (201) and reference,equation (73):(B-2)“=?J3K%LF“+)In order to evaluate T, rl, and Iz, it is necessaryto as
8、sume a deflected surface w consistent with theboundary conditions. These boundary conditions atIIlsmo-a. stheside edges ofof the magnitudeof the moment vidl depend upon the stihs of theelastic restrainin g medium. If the elastic mediumoffers no restraint against rotation, this moment will be zero an
9、d the plate wiU swing about the edge y= O, as -a-bout a hinge. h this case the plate will remain essen-tially fht across its width. On the other hand, if theelastic mediti offers infinite restraint against rotation,the plate will not rotate along the edge v=O and theplate wll deflect across its widt
10、h into a shape similarto that for a cantilever beam. For any rwd.raint of theelastic medium between zero and infinity the deflectioncurve acroes the width of the plate is taken as the sumof the straight line and the cantileverdefleotion curve.In the direction of the length the usual sine curveindic%
11、ted by the solution of the dif7erentiaI equation iaused. Thus the deflection surface assumed for theplate is, in the coordinate system of figure 7,where A and B are arbitrary deflection amplitudes andal= 4.963, %=9.852, and ag= 9.778. These valuesof al, az, and a: were selected by taking the. propor
12、tionof two deflection curves that gave the Iowest critioalcompressive stress for a fixed-edge ffge for whichp=O.3. These two deflection curves were for a canti-lever beam with lateral uniform load and for a IateraIload proportional toy.The condition I?=(I represents the case of a simply119Provided b
13、y IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-120 BEPORT No. 734NATIoNk DsoEY cOhfhfITTEE FOR MRONAUTICfJsupported or hinged edge at y=O. The case of A=Orepresents the condition of. a clamped edge at y=O.The ratio .AIB is therefore a measure of edge restrain
14、tand is related to the restraint coefficient e through theboundary condition given in equation 6). Sub-stitution of w as given by equation (B-9) in equation(B-6) giVSSwhere, by detition, “. .=42(B-lo)(B-11)Substitution of the value of B as given in expression(B-1O) in the deflection equation (B-9) g
15、ives(B-12)Equation (B-12) shows how the shape of the deflectionsurface is affected by the restraint coefficient . Thisequation is used in the evaluation of VI, Vfi,and T.Thus.(B-15)where( )Cl=$ ;+%+ =0.23694#+a,+G+aJ=o.79546c.G=(6+%1+4+3as) =0.89395/)+80a,+20%+36a,a, +12a#* =0.56712C7=$(5 +9al+8az+7
16、G+4a?+ 7%ag+ 6a+3aJ+5a,a,+2al) =0,19736C8=W,=2.3168c)=aa%4=4.0982It ispermiasi ble to substitute the values of T, 1-1,and Vi as given by equations (B-14) to (B-16) inequation (B-1) only when the applied stress $ has itscritical valuejc. After this substitution it is found that(B-16)whereEquation (B-
17、17) was used to calculati the vakwof k listed in the columns designated (a) of table I.With these values of k as a guide, a number of correctvalues of k were obtained by satisfying equation (A20)of appendix A. In this manner the er0.6 0.9 Lo 1.3 L76 2.0 l,= 23 LL lW L27QL24L271 L? L373 L747L3W L LW
18、k ;2s L 61*1.?W L!M9 L= L uL424 L ixii-mllj-.-.-2 L6i9 L649 L44S L424%009 k L6% L6!M L L 430201 LQi4 L690 L63S L4l ,L4M. . -. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -2024 LW3 L L669 L4i6 L4492 LQQ2 L714 *LLN ;4S L481ZIM 2fY.S3 L782 L L 4S120i6 2023 L7 L724 L64U 1.6132113 2069 L#ll
19、 L706 L L 357 !i.-i-161LISIL 2211. ,;20sL2#L4- .9s3.W3LOML 076L 149L-EL%SL300-43-1hiw :8ii- .m.932 :s%I:M :piL lIMiI?242L26 ;L292 *L.-. 7L3.726i- .74.,%4.s291:01LL 211:8L4. -.-.tzs1-.Cw.636:49.m. 74s. n6.812.s07i%L239H723 “ - aI.611.336:W3.627:E.732irLILL- “. ia4ea:670.616:7. as:999?_+1, L 211; :-ZW3a 7s1-%cValnes obtabmd from the energy method.* Recommended valna.c VulneYobtatned kom the exact solutbn o! tbe diEerentIal eqoatfcm.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
