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hw-2-solution

# hw-2-solution - Homework 2 problem 1 Solve for the...

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Homework 2, problem 1 Solve for the approximate deflection of a simply-supported prestressed cable with uniform static distributed load using the Galerkin method. Take as the trial function N 1 ( x ) = x 3 ( x - L ) 3 , and set the test function to coincide with the trial function, η 1 = N 1 . (a) Compare the midpoint deflection computed analytically and approximately. (b) Compute and plot the balance residual. (c) Compute the reactions at the pins from the approximate solution. Homework 2, problem 2 Solve for the approximate deflection of a simply-supported prestressed cable with uniform static distributed load using the Galerkin method. Model just one half of the problem using a symmetry plane. Take as the trial function N 1 ( x ) = 2 x/L ( x = 0 is the location of the pin support at the left-hand side end of the cable), and set the test function to coincide with the trial function, η 1 = N 1 . (a) Compare the midpoint deflection computed analytically and approximately. (b) Compute the balance residual. (c) Compute the reactions at the pins from the approximate solution. Homework 2, problem 3 Solve for the approximate deflection of a simply-supported prestressed cable with uniform static distributed load using the Galerkin method. Model just one half of the problem using a symmetry plane. (Refer to problem 2 from this homework set.) Use the finite element model shown. (a) Compare the midpoint deflection computed analytically and approximately. (b) Compute the balance residual. (c) Compute the reactions at the pins from the approximate solution. 1

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Homework 2, problem 4 Solve for the approximate deflection of a simply-supported prestressed cable with uniform static distributed load using the Galerkin method. Model just one half of the problem using a symmetry plane. (Refer to problem 2 from this homework set.) Use the finite element model consisting of two elements of equal length. (a) Compare the midpoint deflection computed analytically and approximately. (b) Compute the balance residual. (c) Compute the reactions at the pins from the approximate solution. 2
Homework 2, problem 1 Solve for the approximate deﬂection of a simply-supported prestressed cable with uniform static distributed load using the Galerkin method. Take as the trial function N 1 ( x ) = x 3 ( x - L ) 3 , and set the test function to coincide with the trial function, η 1 = N 1 . (a) Compare the midpoint deﬂection computed analytically and approximately. (b) Compute and plot the balance residual. (c)

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