(a) Explanation Given: The axial force on the round bar is 175 kN and the diameter is 40 mm . Concept Used: Write the expression for the allowable stress. σ a = P a A (1) The allowable axial load is P a , the allowable stress is σ a , and the area of cross-section is A . Write the expression for the area of cross-section. A = π 4 d 2 Substitute π 4 d 2 for A in equation (1). σ a = P a π 4 d 2 (2) The equation for the aluminum alloy (2014-T6) column allowable stress as follows: σ a = 30.7 − 0.23 ( k L r ) ksi k L r ≤ 55 (3) σ a = 54000 ( k L r ) 2 ksi k L r ≥ 55 (4) The radius of gyration is r and the constant is k . Since the column has both end as pinned supports so, k = 1 Write the expression for the radius of gyration. r = I A (5) The area moment of inertia is I . Write the equation of area moment of inertia as follows: I = π 64 d 4 Substitute π 64 d 4 for I and π 4 d 2 for A in equation (5). r = π 64 d 4 π 4 d 2 r = 1 16 d 2 r = d 4 (6) Calculation: As per the given problem P a = 175 kN , d = 40 mm . Convert the diameter into inch . d = ( 40 mm ) ( 1 in 25.4 mm ) = 1 (b) To determine The minimum required diameter of the bar.

Bundle: Mechanics Of Materials, Loose-leaf Version, 9th + Mindtap Engineering, 2 Terms (12 Months) Printed Access Card

9th Edition

ISBN: 9781337594301

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 11.9.26P

(a)

To determine

The maximum allowable length of the bar.

(b)

To determine

The minimum required diameter of the bar.

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Chapter 11, Problem 11.9.25P

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Chapter 11 Solutions

Bundle: Mechanics Of Materials, Loose-leaf Version, 9th + Mindtap Engineering, 2 Terms (12 Months) Printed Access Card

Ch. 11 - A rigid bar of length L is supported by a linear...Ch. 11 - The figure shows an idealized structure consisting...Ch. 11 - -2-3. Two rigid bars are connected with a...Ch. 11 - Repeat Problem 11.2-3 assuming that R= 10 kN ·...Ch. 11 - The figure shows an idealized structure consisting...Ch. 11 - An idealized column consists of rigid bar ABCD...Ch. 11 - An idealized column is made up of rigid segments...Ch. 11 - The figure shows an idealized structure consisting...Ch. 11 - The figure shows an idealized structure consisting...Ch. 11 - The figure shows an idealized structure consisting...

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The maximum allowable length of the bar.

Solution Summary: The author analyzes the axial force on the round bar, the allowable stress, and the area of cross-section for the aluminum alloy (2014-T6) column.

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The maximum allowable length of the bar.

The minimum required diameter of the bar.

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