Explanation Given information: A wide-flange W12 × 22 of A36 steel acts as a column. The length of the column is L = 6 ft . The column is fixed at its bottom and free at top. The eccentric load applied on the column, P = 4 kip . Show the AISC equation of Sec 13.6 as follows: σ allow = 12 π 2 E 23 ( K L r ) 2 Here, σ allow is the allowable stress, E is the Young’s modulus, and ( K L r ) is the slenderness ratio. Show the expression for Equation 13-30 as follows: σ max = P A + M c I Here, σ max is the maximum compressive stress, P is the load, A is the area, M is the moment, c is the distance between the centroid of member and outer fibre, and I is the moment of inertia. Calculation: Refer to the Appendix B. Show the geometric properties of W12 × 22 section as follows: The area ( A ) of the W12 × 22 section is 6.48 in . 2 The width of the flange, b f = 4.030 in . The radius of gyration ( r y ) of the W12 × 22 section is 0.847 in . The moment of inertia, ( I y ) = 4.66 in . 4 Show the expression for ( K L r ) c as follows: ( K L r ) c = 2 π 2 E σ Y (1) Here, K is the effective length factor, L is the length of the column, and ( r ) is the radius of gyration, E is the Young’s modulus, and σ Y is the yield stress of the material. The value of effective length factor, K = 2 , since the column is fixed at its bottom and free at top. Consider the Young’s modulus of the steel is E = 29 × 10 3 ksi . Consider the yield stress of the steel is σ Y = 36 ksi . Substitute 29 × 10 3 ksi for E and 36 ksi for σ Y in Equation (1). ( K L r ) c = 2 π 2 × 29 × 10 3 36 = 58 , 000 π 2 36 = 126 Calculate the value of ( K L r y ) as follows: Substitute 2 for K, 6 ft for L, and 0.847 in . for r y . ( K L r y ) = ( 2 × 6 ft × 12 in

10th Edition

ISBN: 9780134319650

Author: Russell C. Hibbeler

Publisher: PEARSON

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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 13.7, Problem 13.116P

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To find: whether the column is safe based on AISC equations of Sec.13.6 and Eq13-30.

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Chapter 13.7, Problem 13.115P

Chapter 13.7, Problem 13.117P

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Chapter 13 Solutions

Mechanics of Materials (10th Edition)

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whether the column is safe based on AISC equations of Sec.13.6 and Eq13-30.

Solution Summary: The author explains that the column is not safe based on the AISC equations of Sec.13.6 and Eq13-30.

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Chapter 13 Solutions