Explanation Given information: The load applied on the wooden column, P = 800 lb . The eccentricity ( e ) of loading is 5 in . The column is fixed at the base and free at the top. The width of cross-sectional area of the column is b = 3 in . The depth of cross-sectional area of the column is d = 6 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 6 in . for b and 3 in . for d in Equation (1): A = 3 × 6 = 18 in . 2 Calculate the moment of inertia using the relation: I = d b 3 12 (2) Substitute 6 in . for b and 3 in . for d in Equation (2): I = 3 × 6 3 12 = 54 in . 4 Calculate the value of ( K L d ) as follows: The bottom end of the wood column is fixed and top end is free, thus the value of K = 2 . Substitute 2 for K , 12 ft for L, and 3 in . for d . ( K L d ) = ( 2 × 6 ft × 12 in 1 ft 3 in . ) = ( 144 in . 3 in . ) = 48 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 13.123P

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To check: whether the wood column can adequately support the eccentric load of 800 lb .

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Chapter 13.7, Problem 13.122P

Chapter 13.7, Problem 13.124P

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Chapter 13 Solutions

Mechanics of Materials (10th Edition)

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To check: whether the wood column can adequately support the eccentric load of 800 lb .

Solution Summary: The author explains that the column is inadequate to support the eccentric load of 800lb.

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To check: whether the wood column can adequately support the eccentric load of 800 lb .

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Chapter 13 Solutions