Buckling on Stiffened Panel

AIRFRAME STATIC ANALYSIS– BUCKLING ON STIFFENED PANELS Objectives for this session:   Understand critical cases for an aircraft structure Able to perform static analysis in order to check margin of safety of stiffened panels under critical load cases Assumption     Majority of modern aircraft structure is highly indeterminate structure due to its complex configuration Accurate solution requires Finite Element Approach For quick analysis, there are simpler approaches using empirical data to support the theory This empirical approach is very beneficial for analysis or preliminary sizing at design stage; or as a quick check toward the computer result from Finite Element calculation or result from Experimental Test Critical Loads Critical Loads . Type of Stiffened Panels . Compression Panels Efficiency . Buckling . Failure Modes of Stiffened Panels Initial Buckling Inter-Rivet Buckling Flexural Buckling . Failure Modes of Stiffened Panels Flexural and Torsional Instability Torsional Instability Skin Wrinkling . Column Buckling . 62 E   b kE t f cr  12(1   2 ) L2 2 2 or 2 t f cr  KE   b 2 .Plate Buckling t f cr  3. 6 E   L 2 .9 E   L 2 t f cr  3.if. All edges: Simply supported t f cr  0. Buckling Coefficients for Different Support Conditions . Effective Width. E = Young’s Modules (use Et in inelastic range) . be Kc E be  t f st Where: fst = Stringer Compression buckling stress Kc = Skin compression buckling coeff. 32 A narrow panel with heavy skin (e. Kc = 6. This effect produces a fixed edge condition for the panel and the compression buckling constant. wing panels near wing root). Kc For large panel with thin skin. as shown in fig (b) produces buckling forces so great that the stringer will twist locally.g.62 . (e.g wing panel near tip) as shown in fig (a) the torsional stiffness of a stringer is large in Comparison to the force tending to twist it. This panel will act as if it had hinged edges and the buckling constant. Kc = 3.Effective Width: Compression Buckling Constant. Kc Kc = 3.62 for b/t < 40 Kc = 6.32 for b/t >110 Between the above two values.Effective Width: Compression Buckling Constant. Kc is plotted in the left figure: . 58"   0.8  Kc E  6.24" F 25000  st  For: (b/t) = 160  Kc = 6.05  25000  Fst  The total effective width of the no.32 10. Fst = 25000 psi Determine the skin effective width Stringer no.2 stringer is: (be1  be 2 ) 2.5 106   be1  t   2.41" 2 2 .2.58  2.32 (b/t) = 60  Kc = 4.24   2.8 10.5 106   0.Effective Width: an Example Assume the allowable crippling stress of the stringers.05  be1  t   2. The effective width is  Kc E  4. ESDU METHODS . Engineering Science Data Unit (ESDU) for Buckling Checks on Stiffened Panels  Local Buckling  Panels with un-flanged Integral Stiffeners  Ref: ESDU 7003  Panels  Ref:  ESDU 71014 Inter Rivet Buckling  Ref:  with Flanged Stringers ESDU 02.09 Crippling of Stringer  Ref: ESDU 78020 .01. fb fb = h (fb)e Where:  (fb)e = KE (t/b)2 Ref: ESDU 70003 .Local Buckling of Compression Panels with unFlanged Integral Stiffeners   Average elastic compressive stress in panel at which local buckling first occurs. Notation Ref: ESDU 70003 . Example Ref: ESDU 70003 . Ref: ESDU 70003 . fb fb = h (fb)e Where:  (fb)e = KE (t/b)2 Ref: ESDU 71014 .Local Buckling of Compression Panels with Flanged Stringers   Average elastic compressive stress in panel at which local buckling first occurs. Notation Ref: ESDU 71014 . Example Ref: ESDU 71014 . Ref: ESDU 71014 . Ref: ESDU 71014 . Ref: ESDU 71014 . Ref: ESDU 71014 . Ref: ESDU 71014 . . Use the same data as in previous example.Exercise  Find local buckling stress for build-up ‘Z’ stringerskin panel. Inter Rivet Buckling Note that: The effective width is important in the interest of structural efficiency and weight economy. it can not carry the compression load and the calculated effective width will be erroneous and the structure is much less efficient. If the skin buckles between rivets. However. K Universal/Flathead rivets 4 Spotwelds Roundhead/Mushro om or snaphead rivets Countersunk or dimpled rivets 3½ 3 1 or 1½ . KE 2t 2 f ir  12(1   2 ) s 2 Type of attachment Fixity coefficient at rivets. . . Inter Rivet Buckling Normally the skin-stringer construction will be designed so that rivet spacing is derived from the crippling stress of the stringer. the skin exhibit the ability to maintain the inter rivet buckling stress while the stringer continues to take load. . However when the inter rivet buckling stress of the skin is reached before the crippling stress of the stringer. Inter Rivet Buckling . Answer: Using Fig.5 x 0.3. go across horizontally to curve (8) for 7075-T6 material.an Example Question: Obtain the rivet. Fcc = 32 ksi Skin thickness.5 (for universal head rivets.05”.68(1.05 = 1. c = 1. t = 0.0.0). material is 7075-T6 bare (non-clad material). c = 4.68” For countersunk head rivets. Go down vertically to read the rivet spacing ratio s/t = 33.0) = 0.Inter Rivet Buckling: .2 with Fir = Fcc = 32 ksi. The rivet spacing of countersunk head rivet is: s= 1. s = 33.spacing for countersunk head rivets from the following given data: Stringer crippling stress.84” .0/4. 14. Crippling of Stringer  fc = (c2 fb)1/2 Where: = h fbe fbe = KE (th/h)2  fb  Ref: ESDU 78020 . Notation Ref: ESDU 78020 . Example Ref: ESDU 78020 . Ref: ESDU 78020 . Ref: ESDU 78020 . Use the same material and the associated dimensions .Exercise  Calculate the crippling stress for z section. Flexural Buckling The Farrar’s efficiency factor (F) accounts for A pure flexural instability (assume flexural-torsional Coupling is small): F f L NEt Where: f – failure stress of skin stringer panel N – end load per inch width of skin stringer panel Et – tangent modulus L – Length of the panel (rib or frame spacing . Flexural (Euler) Buckling .