Explanation Given information: The width ( b ) of the cross section is as follows: b = 50 mm ( 1 m 1 , 000 mm ) = 0.05 m The depth of the cross section ( d ) is as follows: d = 75 mm ( 1 m 1 , 000 mm ) = 0.075 m Calculation: Sketch the free body diagram of upper segment of the curved beam section through a - a as shown in Figure 1. Refer to Figure 1: Take moment about O : ∑ M 0 = 0 ( 250 sin 60 ° ) ( 0.15 ) + 250 cos 60 ° ( 0.075 ) − M = 0 41.851 − M = 0 M = 41.851 N ⋅ m Show the section properties as follows: Refer to Figure 1: Consider the inner radius of the bar r i is as follows: r i = 162.5 mm ( 1 m 1 , 000 mm ) = 0.1625 m Consider the outer radius of the bar is as follows: r o = 237.5 mm ( 1 m 1 , 000 mm ) = 0.2375 m Find the distance measured from the center of curvature to the centroid of the cross section ( r ¯ ) as shown below: r ¯ = r o + r i 2 (1) Substitute 0.1625 m for r i and 0.2375 m for r o in Equation (1). r ¯ = 0.1625 + 0.2375 2 = 0.2 m Find the area ( A ) of curved bar as shown in below: A = b d (2) Substitute 0.05 m for b and 0.075 m for d in Equation (2). A = 0.05 × 0.075 = 3.75 × 10 − 3 m 2 Find the value of ∫ A d A r as shown in below: ∫ A d A r = b ln r 2 r 1 (3) Substitute 0.05 m for b , 0.2375 m for r 2 , 0.1625 for r 1 in Equation (3). ∫ A d A r = 0.05 ln ( 0.2375 0.1625 ) = 0.018974481 m Find the location of the neutral surface from the center of curvature of the member ( R ) as shown in below: R = A ∫ A d A r (4) Substitute 3.75 × 10 − 3 m 2 for A and 0.018974481 m for ∫ A d A r in Equation (4). R = 3

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ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Processing of Polymer Matrix Composites

The polymer matrix composite is described as a composite material that contains some polymer in the form of either fibers or powder. Polymer matrix composites are also known in short as PMC's.

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Chapter 6.9, Problem 6.145P

To determine

the maximum tensile and compressive stress acting at section a-a.

To sketch: The stress distribution on the section in three dimensions.

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Chapter 6.9, Problem 6.144P

Chapter 6.9, Problem 6.146P

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Mechanics of Materials

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