Explanation Given information: A rectangular bar made up of aluminum alloy 2014-T6. The width of cross-sectional area of the bar, b = 4 in . The depth of cross-sectional area of the bar, d = 6 in . The bottom end of the bar is fixed and top end is pinned. The length of the bar, L = 10 ft . Consider the maximum allowable load acting on the bar as P. Show the expression of aluminum bar (2014-T6 alloy) of Sec 13.6 as follows: σ allow = [ 54 , 000 ( K L r ) 2 ] ksi, K L r > 55 Here, σ 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 cross-section 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 bar using the relation: A = b d (1) Substitute 4 in . for b and 6 in . for d in Equation (1): A = 4 × 6 = 24 in . 2 Calculate the moment of inertia about x- axis using the relation: I x = b d 3 12 (2) Substitute 4 in . for b and 6 in . for d in Equation (2): I x = 4 × 6 3 12 = 72 in . 4 Calculate the moment of inertia about y- axis using the relation: I y = d b 3 12 (3) Substitute 4 in . for b and 6 in . for d in Equation (3): I y = 6 × 4 3 12 = 32 in . 4 Calculate the least radius of gyration ( r y ) using relation: r y = I y A (4) Substitute 32 in . 4 for I y and 24 in . 2 for A in Equation (4): r y = 32 24 = 1.155 in . Calculate the slenderness ratio of bar about y-y axis using the relation: Slenderness ratio = ( K L r ) y (5) The bar is fixed at one end and pinned at another end. Thus, the value of effective length factor, K = 0.7 . Substitute 0.7 for K , 10 ft for L and 1.155 in . for r in Equation (5). Slenderness ratio = 0

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ISBN: 9789810694364

Author: Russell C Hibbeler

Publisher: Pearson Education

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Chapter 13.7, Problem 13.121P

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To find: the maximum allowable eccentric load P that can be applied to the bar.

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Chapter 13.7, Problem 13.120P

Chapter 13.7, Problem 13.122P

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the maximum allowable eccentric load P that can be applied to the bar.

Solution Summary: The author explains the maximum allowable eccentric load P that can be applied to a rectangular bar made of aluminum alloy 2014-T6.

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