Sample problems for Third Exam

Sample problems for Third Exam - Sample problems for Third...

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Unformatted text preview: Sample problems for Third Exam 1) A thick cylinder (internal and external radii a,b ) under internal pressure p is made from material with zero Poisson’s ratio. It is desirable to prevent it from expanding in the z direction. Calculate the required temperature drop. Young’s modulus is E, and the coefficient of thermal expansion is α . Solution: For zero Poisson’s ratio, Eq. 11.4 gives / zz zz E T ε σ α = + ∆ . Equation 11.16 gives 2 2 zz 2 pa b a σ = − . So for the strain to be zero we get ( ) 2 2 2 pa T E b a α − ∆ = − 2) Derive the buckling load for a column clamped on one side and constrained to zero slope on the other (clamped-guided in Table 12.1). Solution: The general solution for the column buckling problem is . The boundary conditions at zero y(0)=0 and y’(0)=0 provide B+D=0 and kA+C=0. At x=L we have sin cos y A kx B kx Cx D = + + + 3 3 '( ) cos sin "'( ) cos sin y L kA kL kB kL C y L k A kL k B kL = − + = = − + = These two equations give C=0, and then we have also A=0. So These two equations give C=0, and then we have also A=0....
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Sample problems for Third Exam - Sample problems for Third...

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