(a) Explanation The centricity of the load in the column is e = 12 mm . The horizontal deflection at midpoint of the column at point C is y m = 15 mm . The modulus of elasticity of the column is E = 200 GPa . The length of the column is L = 9 m . Refer to the Appendix C “Properties of Rolled-Steel Shapes” in the textbook. For W 310 × 60 Rolled-steel shape; The cross sectional area is A = 7 , 550 mm 2 . The minimum moment of inertia in the y -axis is I = I y = 18.4 × 10 6 mm 4 . The minimum radius of gyration in the y -axis is r = r y = 49.3 mm . The section modulus of the section is S = S y = 180 × 10 3 mm 3 . The effective length of the column ( L e ) is equal to the length of the column ( L ). L e = L = 9 m Determine the critical load ( P cr ) using the equation. P c r = π 2 E I ( L e ) 2 Here, the modulus of elasticity is E . Substitute 200 GPa for E , 18.4 × 10 6 mm 4 for I , and 9 m for L e . P cr = π 2 × 200 GPa × 10 9 N/m 2 1 GPa × 18 (b) To determine Find the maximum stress in the column.

7th Edition

ISBN: 8220102804487

Author: BEER

Publisher: YUZU

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Buckling of columns

The column is described as a vertical member of the structure that carries an axial compressive load, and buckling is a lateral deformation of the column under the application of load.

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Chapter 10.2, Problem 40P

(a)

To determine

Find the applied axial load P.

(b)

To determine

Find the maximum stress in the column.

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Chapter 10.2, Problem 39P

Chapter 10.2, Problem 41P

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Find the applied axial load P .

Solution Summary: The author explains how the applied axial load P is underset_224kN, the centricity of the load in the column and the modulus of elasticity are E