Explanation Given information: A wide-flange W12 × 50 of A36 steel acts as a column. The length of the column is L = 10 ft . The column is fixed at the bottom and pinned at the top. The eccentric load applied on the column, P . Show the AISC equation of Sec 13.6 as follows: σ allow = [ 1 − 1 2 ( K L r ( K L r ) c ) 2 ] σ Y [ 5 3 + 3 8 ( K L r ( K L r ) c ) − 1 8 ( K L r ( K L r ) c ) 3 ] Here, σ allow is the allowable stress, σ Y is the yield 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 the Appendix B. Show the geometric properties of W12 × 50 section as follows: The area ( A ) of the W12 × 50 section is 14.7 in . 2 The least radius of gyration ( r y ) of the W12 × 50 section is 1.96 in . The moment of inertia, ( I y ) = 56.3 in . 4 . The depth of the section, d = 12.19 in . The thickness of the web of the section, b f = 8.08 in . 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. 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: The value of effective length factor, K = 2 , since one end fixed and another end free. Substitute 2 for K, 10 ft for L, and 1.96 in . for r y . ( K L r y ) = ( 2 × 10 ft × 12 in . 1 ft 1.96 in . ) = 122.44 Show the condition for the column to be a long column as follows: ( K L r ) c ≤ ( K L r y ) ≤ 200 (2) Substitute 42.857 for ( K L r y ) and 126 for ( K L r ) c in Equation (2)

10th Edition

ISBN: 9780134321158

Author: 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 13.110P

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To find: the largest eccentric load P that can be applied to the column.

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Chapter 13.7, Problem 13.109P

Chapter 13.7, Problem 13.111P

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Chapter 13 Solutions

Mechanics of Materials

Ch. 13.3 - A 50-in long steel rod has a diameter of 1 in....Ch. 13.3 - A 12-ft wooden rectangular column has the...Ch. 13.3 - The A992 steel column can be considered pinned at...Ch. 13.3 - A steel pipe is fixed supported at its ends. If it...Ch. 13.3 - Determine the maximum force P that can be...Ch. 13.3 - The A992 steel rod BC has a diameter of 50 mm and...Ch. 13.3 - Determine the critical buckling load for the...Ch. 13.3 - The column consists of a rigid member that is...Ch. 13.3 - The aircraft link is made from an A992 steel rod....Ch. 13.3 - Rigid bars AB and BC are pin connected at B. If...

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the largest eccentric load P that can be applied to the column.

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Chapter 13 Solutions