notes_29_buckling_sti

# notes_29_buckling_sti - Buckling of Stiffened Panels 1...

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Buckling of Stiffened Panels 1 overall buckling vs plate buckling PCCB Panel Collapse Combined Buckling Various estimates have been developed to determine the minimum size stiffener to insure the plate buckles while the stiffener remains straight. this is equivalent to insuring that plate buckling occurs before overall buckling. Timoshenko does so by calculating k in σ cr k π 2 D b 2 t := and observing the value of γ which results in a critical stress above that which will cause plate buckling alone. where; γ flexural_rigidity_of_combined_section flexural_rigidity_of_plate := γ EI x Db := where; I x is the inertia of the plate with the attached plate associated with individual stiffener. Bleich pg 365, 367, for plates with longitudinal stiffness determines minimum γ to insure the plate buckles before the stiffener (overall buckling). unfortunately Bleich uses different ratios than Hughes. Bleich uses B where Hughes uses b. for the following: α a B := δ A x Bt := γ x DB := α 0.1 0.2 , 10 .. := δ 0.1 := κ 1 α n , () n π α 4 α n 1 + := κ 2 α n , n π α 4 α n 1 := γ o αδ , n , 16 π 2 α n 3 1 κ 1 α n , tanh κ 1 α n , 2 1 κ 2 α n , tan κ 2 α n , 2 16 α n 2 ⋅δ + := γ omax , max γ o , 1 , γ o , 2 , γ o , 3 , := 05 1 0 0 20 40 γ o , 1 , γ o , 2 , γ o , 3 , α 1 0 0 20 40 γ omax , α 1

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12345 0 200 400 600 800 γ bx21 Πδ x , () γ bx22 x , Π 0246 0 100 200 300 γ bx11 x , γ bx12 x , Π Π 1 1.1 , 5 .. := γ bx22 x , 288 610 δ x + 325 δ x 2 + := γ bx12 x , 48.8 112 δ x 1 0.5 δ x + + := γ bx21 x , 43.5 Π 3 36 Π 2 ⋅δ x + := γ bx11 x , 22.8 Π 2.5 16 δ x + Π 2 + 10.8 Π := two stiffeners one stiffener to move to Bleich relationships in Hughes terms (ratios) to match text: where: Π a B := δ x A x bt := γ EI x Db := Fig. 180, Bleich 05 1 0 0 10 20 30 40 γ omax αδ , γ bx , α γ bx , min γ bx1 , γ bx2 , := γ bx2 , 48.8 2 112 δ 1 0.5 2 2 + + := Hughes: 13.1.4 slightly modified in terms γ bx1 , 22.8 2 α 2.5 2 16 δ + α 2 + 10.8 2 α := one stiffener, combining Hughes and Bleich terms, N=1 stiffener curve fit: 2
t 0.5 = b3 0 := L9 6 := d5 := A s A w A f + := A f 0.85 := A w 0.8 := set above breadth between stiffeners b panel length stiffener depth stiffener area

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## This note was uploaded on 02/24/2012 for the course MECHANICAL 2.082 taught by Professor Davidburke during the Spring '03 term at MIT.

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notes_29_buckling_sti - Buckling of Stiffened Panels 1...

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