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The fence board weaves between the three smooth fixed posts. If the posts remain along the same line, determine the maximum bending stress in the board. The board has a width of 6 in. and a thickness of 0.5 in. E 1.60(10') ksi. Assume the displacement of each end of the board relative to its center is 3 in.

The fence board weaves between the three smooth fixed posts. If the posts remain along the same line, determine the maximum bending stress in the board. The board has a width of 6 in. and a thickness of 0.5 in. E 1.60(10') ksi. Assume the displacement of each end of the board relative to its center is 3 in.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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The fence board weaves between the three smooth fixed posts. If the posts remain along the same line, determine the maximum bending stress in the board. The board has a width of 6 in. and a thickness of 0.5 in. E 1.60(10) ksi. Assume the displacement of each end of the board relative to its center is 3 in. 3 in. Support Reactions and Elastic Curve: As shown on FBD(a). Moment Function: As shown on FBD(b). Slope and Elastic Curve: d'v dx El = M(x) d'u EI dx2 dv -x + C, [1) EI dx 4 MCn) El v =5+ Cx + C2 %3D 12 [2) 390625 Boundary Conditions: Due to symmetry, dv = 0 at x = Also, v = 0 at x 0. PL? C, = 16 From Eq. [1]0 = + C From Eq. [2] 0 0 +0+ C2 C = 0 The Elastic Curve: Substitute the values of C, and C, into Eq. [2]. Px ;(4x² - 3L) [1) 48EI Require at x 48 in., v = -3 in. From Eq.[1]. P(48) 14(48) – 3(967)] -3 = 48(1.60)(109)(1) (6)(0.5') * P = 16.28 lb Maximum Bending Stress: From the moment diagram, the maximum moment is Ma = 390.625 lb in. Applying the flexure formula, Mc 390.625(0.25) = 1562.5 psi = 1.56 ksi Ans. max A (6)(0.5)
Transcribed Image Text:The fence board weaves between the three smooth fixed posts. If the posts remain along the same line, determine the maximum bending stress in the board. The board has a width of 6 in. and a thickness of 0.5 in. E 1.60(10) ksi. Assume the displacement of each end of the board relative to its center is 3 in. 3 in. Support Reactions and Elastic Curve: As shown on FBD(a). Moment Function: As shown on FBD(b). Slope and Elastic Curve: d'v dx El = M(x) d'u EI dx2 dv -x + C, [1) EI dx 4 MCn) El v =5+ Cx + C2 %3D 12 [2) 390625 Boundary Conditions: Due to symmetry, dv = 0 at x = Also, v = 0 at x 0. PL? C, = 16 From Eq. [1]0 = + C From Eq. [2] 0 0 +0+ C2 C = 0 The Elastic Curve: Substitute the values of C, and C, into Eq. [2]. Px ;(4x² - 3L) [1) 48EI Require at x 48 in., v = -3 in. From Eq.[1]. P(48) 14(48) – 3(967)] -3 = 48(1.60)(109)(1) (6)(0.5') * P = 16.28 lb Maximum Bending Stress: From the moment diagram, the maximum moment is Ma = 390.625 lb in. Applying the flexure formula, Mc 390.625(0.25) = 1562.5 psi = 1.56 ksi Ans. max A (6)(0.5)
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