Exam #2

ME 4093/6093: Finite Element Analysis

Spring 2010

1. The deflection of a cable under the load of its own weight can be determined by solving thefollowing differential equation

Td2ydx2

W = 0, y(0) = y(H) = 0

which also has the potential energy written as

(y) = H

0

T2

(dydx

)2+Wy dx

Assume a deflection of the form y(x) = A sin(pix/H) + B sin(2pix/H). Determine the de-flection (at x = H/4) using

a) the Ritz method.

b) the Galerkin method.

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2. A length of angle iron modeled using Abaqus. The Abaqus DAT file, ODB file, and CAEfile for this model are available at S:\ENS\Mechanical Engineering\Daily\FEA\Exam2\.Using those files (and your own understanding of mechanics), please answer the followingquestions:

a) What is the angle of inclination if zero is vertical?

b) What kind of element was used?

c) What is the cross-sectional area of the angle iron?

d) What is the cross-sectional moment about the global z axis at the centroid?

e) Where are boundary conditions applied (please provide lengths along the neutral axis)?

f) Where are loads applied, what are their magnitudes, and what are their directions?

g) Is the angle iron in tension or compression?

h) How heavy is the length of angle iron being modeled?

i) What is the maximum bending deflection of the beam? (Hint: Redraw the deformedshape along a straight line and determine the deviation from that line.)

j) If the yield strength is 36000 units, will the beam experience yielding? What is themaximum stress in this beam?

k) BONUS: What are the frequencies of the first two mode shapes of this beam?

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3. (Required for Graduate Students) Determine the exact solution for the differential equationof question 1.

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