Answered: A steel column member shown in the…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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$A steel column member shown in the figure below is pin-connected at the two ends. It could fail either by buckle or yield. The cross-sectional area $ A = 6000 \, \text{mm}^2 $, the moment of inertia about $ y $ and $ z $ axes are $ I_y = 15 \times 10^6 \, \text{mm}^4 $ and $ I_z = 45 \times 10^6 \, \text{mm}^4 $. The Young's modulus of steel is 200 GPa. If length $ L = 11.7 \, \text{m} $, 1. (Not graded part) About which axis the buckle will occur first? 2. What is the critical load in kN for the buckling to occur? **Diagram Explanation:** The image includes a vertical steel column with a height of 4 meters. The column is shown with a pinned connection at both the top and bottom. To the left of the column, a cross-sectional view displays an H-shaped profile labeled with axes $ x $ and $ y $. This indicates the orientation of the cross-section and the principal axes of inertia relevant for calculating buckling.$

Transcribed Image Text:A steel column member shown in the figure below is pin-connected at the two ends. It could fail either by buckle or yield. The cross-sectional area $ A = 6000 \, \text{mm}^2 $, the moment of inertia about $ y $ and $ z $ axes are $ I_y = 15 \times 10^6 \, \text{mm}^4 $ and $ I_z = 45 \times 10^6 \, \text{mm}^4 $. The Young's modulus of steel is 200 GPa. If length $ L = 11.7 \, \text{m} $, 1. (Not graded part) About which axis the buckle will occur first? 2. What is the critical load in kN for the buckling to occur? **Diagram Explanation:** The image includes a vertical steel column with a height of 4 meters. The column is shown with a pinned connection at both the top and bottom. To the left of the column, a cross-sectional view displays an H-shaped profile labeled with axes $ x $ and $ y $. This indicates the orientation of the cross-section and the principal axes of inertia relevant for calculating buckling.

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For same problem setup in Q1 except for the length, if the yield strength is 145 MPa, calculate the critical length under which the column would fail by yield and over which the column would fail by buckling.

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