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. σ cr ΠΕΙ L²A where E = 30,000,000 psi. The cross-sectional area of each member is circular, A = r² and I =лr 4. L is the length of e✓ member and r is its radius. 60 in. 30,000 lb. (a) Formulate the problem as a nonlinear optimization problem. (15 points) (b) Solve the problem by calling an optimization solver. Include your computer script and result output. (10 points) (c) Derive the KKT conditions and check whether the optimal result obtained in question 2(b) satisfies the KKT condition. (15 points) 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. σ cr ΠΕΙ L²A where E = 30,000,000 psi. The cross-sectional area of each member is circular, A = r² and I =лr 4. L is the length of e✓ member and r is its radius. 60 in. 30,000 lb. (a) Formulate the problem as a nonlinear optimization problem. (15 points) (b) Solve the problem by calling an optimization solver. Include your computer script and result output. (10 points) (c) Derive the KKT conditions and check whether the optimal result obtained in question 2(b) satisfies the KKT condition. (15 points) 1
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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.
σ cr
ΠΕΙ
L²A
where E = 30,000,000 psi. The cross-sectional area of each member is circular,
A = r² and I =лr 4. L is the length of e✓ member and r is its radius.
60 in.
30,000 lb.
(a) Formulate the problem as a nonlinear optimization problem. (15 points)
(b) Solve the problem by calling an optimization solver. Include your computer script
and result output. (10 points)
(c) Derive the KKT conditions and check whether the optimal result obtained in question
2(b) satisfies the KKT condition. (15 points)
1
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