(a) Explanation Given: The axial force on the square wood column is 100 kN , the modulus of elasticity is 8.5 GPa, and the compressive stress is 8 MPa . Concept Used: Write the expression for the allowable axial load. P a = F c C p A C p = P a F c A (1) The allowable load is P a , the column stability factor is C p , and the area is A . Write the expression for the area. A = b × b = b 2 The area is A , the width is b and the height is h . Substitute b 2 for A in equation (1). C p = P a F c × b 2 (2) Write the expression for the column stability factor. C p = 1 + ϕ 2 c − ( 1 + ϕ 2 c ) 2 − ( ϕ c ) ....... (3) The sawn number is c and the Euler’s buckling coefficient ratio is ϕ . Write the expression for the Euler’s buckling coefficient ratio. ϕ = K E F c ( L b ) 2 (4) The Buckling coefficient is K and the length is L . Calculation: As per the given problem P a = 100 kN , b = 120 mm , F c = 8 MPa and E = 8.5 GPa Refer to property table for the wood block of rectangular cross-section to obtain the sawn number as, c = 0.8 K = 0.3 Substitute the values in equation (2). C p = ( 100 kN ) ( 1000 N 1 kN ) 8 × ( 120 ) 2 = 0.8681 Substitute 0.8681 for C p in equation (3). 0 (b) To determine The minimum required dimension b of the square column.

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ISBN: 9781337093354

Author: Barry J. Goodno, James M. Gere

Publisher: Cengage Learning

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Axial Load

When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial …

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Chapter 11, Problem 11.9.36P

(a)

To determine

The maximum allowable length of the bar.

(b)

To determine

The minimum required dimension b of the square column.

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Chapter 11, Problem 11.9.35P

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The maximum allowable length of the bar.

Solution Summary: The author analyzes the axial force, modulus of elasticity, and compressive stress of the square wood column.

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The maximum allowable length of the bar.

The minimum required dimension b of the square column.

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