homework5

# homework5 - xx y at the point of buckling 1 Problem 2 A...

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2.081J/16.230J Plates and Shells Homework #5 Due date: class on Monday March 20 Problem 1 A long rectangular simply supported plate is compressed between two rigid blocks. l xx σ b x y uniform thickness, h = 10 mm The following data for the considered steel are provided: ½ for ε < ε y σ = 0 . 3 for ε ε y where E = 210 GPa ; ν = 0 . 3 K = 2 . 141 GPa σ y ε y = ; σ y = 300 MPa E Note that σ and ε are respectively total stress and total strain. (a) Calculate the e ff ective width of the plate, b eff . (b) Assume the actual width of the plate is b = b eff / 2 . Determine the plastic buckling stress σ cr and the total buckling load P cr . (c) Compare the solution ( σ cr and P cr ) for b = b eff and b = b eff / 2 . (d) Plot the stress distribution in both plates, σ

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Unformatted text preview: xx ( y ) , at the point of buckling. 1 Problem 2 A long cylindrical shell made of mild steel ( E = 210 GP a and ν = 0 . 3 ) is sti f ened in x-direction by a system of eight equally spaced stringers. This shell is subjected to axial compression. 1 mm l = 2 m 0.1 m h = a = (a) Determine the buckling mode of the shell, ( ¯ m, n ) . (b) Calculate the corresponding half-wave length, λ . (c) Determine the theoretical buckling stress, σ cr 2...
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