Explanation The effective length of the column ( L e ) is equal to the length of the column ( L ). L e = L Find the cross sectional area of the square ( A ) section using the equation. A = b 2 Here, the dimension of the square cross section is b . Determine the moment of inertia ( I ) of the square cross section using the equation. I = b 4 12 Determine the critical load ( P cr ) using the equation. P c r = π 2 E I ( L e ) 2 Here, the modulus of elasticity of the material is E . Consider the critical load is equal to the axial load. P c r = P Substitute P for P c r , b 4 12 for I , L for L e . P = π 2 E ( b 4 12 ) L 2 Find the total elongation using the relation. Total elongation = ( δ l ) t h e r m a l − ( δ l ) a x i a l = α L ( Δ T ) − P L A E Here, the elongation due to thermal stress is ( δ l ) t h e r m a l , the elongation due to axial loads is ( δ l ) a x i a l , the coefficient of thermal expansion is α , the change in temperature is Δ T , the axial load in the column is P , the length of the column is L , and the cross sectional area of the column is A

7th Edition

ISBN: 8220100257063

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, Problem 123RP

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Show the change in temperature ΔT in terms of b,L, and α.

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Chapter 10, Problem 122RP

Chapter 10, Problem 124RP

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Column ABC has a uniform rectangular cross section and is braced in the xz plane at its midpoint C. (a) Determine the ratio b/d for which the factor of safety is the same with respect to buckling in the xz and yz planes. (b) Using the ratio found in part a, design the cross section of the column so that the factor of safety will be 3.0 when P= 4.4 kN, L=1 m, and E=200 GPa

! Required information Each of the five struts shown consists of a solid steel rod with E= 200 GPa. Given: Po = 7.2 kN 900 mm Po (1) Po (2) Po (3) (5) Knowing that the strut of Fig. (1) is of a 20-mm diameter, determine the factor of safety with respect to buckling for the loading shown. (Round the final answer to two decimal places. You must provide an answer before moving the the next part.) The factor of safety is

1. Column ABC shown has a uniform rectangular cross section and is braced in the xz plane at its midpoint C. Determine the ratio b/d for which the factor of safety is the same with respect to buckling in the xz and yz planes. Take factor of safety as 2.7 when P = 5.4 kN, L = 600 mm, and E = 70 GPa. L

Chapter 10 Solutions

EBK MECHANICS OF MATERIALS

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