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4) A two-tier column shown below is made from a material with modulus of E = 25 GPa. The top column has length L₁ = 2 m, and cross-sectional area A1. The bottom column has length L₂ = 1.5 m, and cross- sectional area A2. The entire column is loaded by two forces, P₁ and P2 as shown. Under the action of these loads, the maximum permissible shortening of the column is 1.0 mm. a) If we require that A2 = 3A1, what is the minimum permissible area A₁? b) If the areas A1 and A2 are such that the compressive stresses in both parts of the column are the same, what is the minimum permissible area A₁? P₁ = 400 kN P₂ = 650 kN L₁ = 2 m L₂ = 1.5 m

4) A two-tier column shown below is made from a material with modulus of E = 25 GPa. The top column has length L₁ = 2 m, and cross-sectional area A1. The bottom column has length L₂ = 1.5 m, and cross- sectional area A2. The entire column is loaded by two forces, P₁ and P2 as shown. Under the action of these loads, the maximum permissible shortening of the column is 1.0 mm. a) If we require that A2 = 3A1, what is the minimum permissible area A₁? b) If the areas A1 and A2 are such that the compressive stresses in both parts of the column are the same, what is the minimum permissible area A₁? P₁ = 400 kN P₂ = 650 kN L₁ = 2 m L₂ = 1.5 m

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter3: Introduction To Optimization Modeling
Section: Chapter Questions
Problem 1C
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4) A two-tier column shown below is made from a material with modulus of E = 25 GPa. The top column has length L₁ = 2 m, and cross-sectional area A1. The bottom column has length L₂ = 1.5 m, and cross- sectional area A2. The entire column is loaded by two forces, P₁ and P2 as shown. Under the action of these loads, the maximum permissible shortening of the column is 1.0 mm. a) If we require that A2 = 3A1, what is the minimum permissible area A₁? b) If the areas A1 and A2 are such that the compressive stresses in both parts of the column are the same, what is the minimum permissible area A₁? P₁ = 400 kN P₂ = 650 kN L₁ = 2 m L₂ = 1.5 m
Transcribed Image Text:4) A two-tier column shown below is made from a material with modulus of E = 25 GPa. The top column has length L₁ = 2 m, and cross-sectional area A1. The bottom column has length L₂ = 1.5 m, and cross- sectional area A2. The entire column is loaded by two forces, P₁ and P2 as shown. Under the action of these loads, the maximum permissible shortening of the column is 1.0 mm. a) If we require that A2 = 3A1, what is the minimum permissible area A₁? b) If the areas A1 and A2 are such that the compressive stresses in both parts of the column are the same, what is the minimum permissible area A₁? P₁ = 400 kN P₂ = 650 kN L₁ = 2 m L₂ = 1.5 m
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