Explanation Given information: The load applied on the wooden column is P = 1.5 kip . The eccentricity ( e ) of loading is 3 in . The column ends are pinned. The width of cross-sectional area of the column is b = 1.5 in . The depth of cross-sectional area of the column is d = 12 in . The length of the column, L = 6 ft . Show the expression ofNFPA Equation of Sec 13.6 as follows: ( σ a ) allow = [ 540 ( K L d ) 2 ] ksi, 26 < K L r < 50 Here, ( σ a ) allow is the allowable stress 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 fiber, and I is the moment of inertia. Calculation: Calculate the cross-sectional area ( A ) of the rectangular column using the relation: A = b d (1) Substitute 1.5 in . for b and 12 in . for d in Equation (1): A = 1.5 × 12 = 18 in . 2 Calculate the moment of inertia using the relation: I = d b 3 12 (2) Substitute 1.5 in . for b and 12 in . for d in Equation (2): I = 1.5 × 12 3 12 = 216 in . 4 Calculate the value of ( K L d ) as follows: The ends of the wood column are pinned, thus the value of K = 1 . Substitute 1 for K , 6 ft for L, and 1.5 in . for d . ( K L d ) = ( 1 × 6 ft × 12 in 1 ft 1.5 in

9th Edition

ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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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 13.123P

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To check: whether the wood column can adequately support eccentric load of 1.5 kip .

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Chapter 13.7, Problem 13.122P

Chapter 13.7, Problem 13.124P

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 - 13-1. 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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