2. Minimum-weight Truss Design: Find the minimum-weight truss for the following condition. The load on the truss is 30,000 lb., directed downward. The allowable yield stress is 8,000 psi. Stress in the truss must also be less than the critical buckling stress divided by a safety factor of 1.2. σε = ΠΕΙ L² A , where E = 30,000,000 psi. The cross-sectional area of each member is circular, A =л² and I =лr/4. L is the length of each member and r is its radius. 60 in. 30,000 lb. (a) Formulate the problem as a nonlinear optimization problem. (b) Solve the problem by calling an optimization solver. Include your computer script and result output. (c) Derive the KKT conditions and check whether the optimal result obtained in question 2(b) satisfies the KKT condition. 1
2. Minimum-weight Truss Design: Find the minimum-weight truss for the following condition. The load on the truss is 30,000 lb., directed downward. The allowable yield stress is 8,000 psi. Stress in the truss must also be less than the critical buckling stress divided by a safety factor of 1.2. σε = ΠΕΙ L² A , where E = 30,000,000 psi. The cross-sectional area of each member is circular, A =л² and I =лr/4. L is the length of each member and r is its radius. 60 in. 30,000 lb. (a) Formulate the problem as a nonlinear optimization problem. (b) Solve the problem by calling an optimization solver. Include your computer script and result output. (c) Derive the KKT conditions and check whether the optimal result obtained in question 2(b) satisfies the KKT condition. 1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:2. Minimum-weight Truss Design:
Find the minimum-weight truss for the following condition. The load on the truss is
30,000 lb., directed downward. The allowable yield stress is 8,000 psi. Stress in the truss
must also be less than the critical buckling stress divided by a safety factor of 1.2.
σε
=
ΠΕΙ
L² A
,
where E = 30,000,000 psi. The cross-sectional area of each member is circular,
A =л² and I =лr/4. L is the length of each member and r is its radius.
60 in.
30,000 lb.
(a) Formulate the problem as a nonlinear optimization problem.
(b) Solve the problem by calling an optimization solver. Include your computer script
and result output.
(c) Derive the KKT conditions and check whether the optimal result obtained in question
2(b) satisfies the KKT condition.
1
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