CE 335
Old exam questions (with solutions following) for Chapters 511
1]
For the 2D static truss system above:
(a) Assuming that the members are each 3 m long, write a system of linear equations for the unknown
reaction forces and forces on the truss members.
(b) Is the problem overdetermined, underdetermined, or determinate?
2]
Use Gaussian elimination with partial pivoting to solve the system of equations below. Show all
steps.
2y + 3z = 4
6x + 2y + 2z = 8
3x + 6y + 7z = 11
3]
Suppose that the cost of a production process scales with the fractional process efficiency x as
C = x
1
+ λ(1  x)
2
where the first term describes the cost savings from higher efficiency, the second term describes the
increase in cost from the more stringent tolerances needed to achieve higher efficiency, and λ is an
adjustable positive parameter that sets the relative importance of the two terms. (As λ → 0, the
minimum cost is achieved with x → 1; as λ →
, the minimum cost is achieved with x → 0.)
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 Spring '11
 Lybas
 1%, Pivot element, largest absolute value

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