Quiz 2 solution

Quiz 2 solution - 025 . 4 m A A π = = = The...

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Quiz 2 - Solution A solid brass axial member, with Young’s modulus E = 100 GPa, is loaded and supported as shown in the figure. Segments (1) and (2) each have a diameter of 25 mm, and segment (3) has a diameter of 10 mm. Determine: (a) Draw the free-body diagrams to find the axial force in each segment, F 1 , F 2 , and F 3 . (b) Find the stretch, δ , in each segment. (c) Locate the maximum axial stress among the three segments. Note: AE FL = Solution (a) Draw a FBD that cuts through segment (2) and includes the free end of the axial member. From this FBD, the sum of forces in the vertical direction reveals the internal force in the segment: = = 0 25 14 2 F F y kN F 39 2 = The internal forces in segments (1) and (3) must be determined at the outset. From a FBD that cuts through segment (1) and includes the free end of the axial member: = = 0 25 14 40 1 F F y kN F 79 1 = Similarly, consider a FBD that cuts through segment (3) and includes the free end of the axial member: = = 0 25 3 F F y kN F 25 3 = The cross-sectional area of the 25-mm-diameter segments is ( ) 2 2 2 1 6400
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Unformatted text preview: 025 . 4 m A A π = = = The cross-sectional area of the 10-mm-diameter segment is ( ) 2 2 3 40000 010 . 4 m A = = (b) The deformation in segment (2) is thus ( )( ) ( )( ) 9 2 2 2 2 2 10 * 100 6400 / 2 . 1 39000 = = E A L F mm 9534 . 2 = The deformation in segment (1) can be computed as ( )( ) ( )( ) 9 1 1 1 1 1 10 * 100 6400 / 8 . 1 79000 π δ = = E A L F mm 8969 . 2 1 = The deformation in segment (3) can be computed as ( )( ) ( )( ) 9 3 3 3 3 3 10 * 100 40000 / 6 . 1 25000 = = E A L F mm 0930 . 5 3 = (c) Since segments (1) and (2) have the same cross-sectional area, the maximum normal stress in these two segments occurs where the axial force is greater; that is, in segment (1): 6400 / 79000 1 1 1 σ = = A F MPa 94 . 160 1 = The normal stress in segment (3) is 40000 / 25000 3 3 3 = = A F MPa 31 . 318 3 = Therefore, the maximum normal stress in the axial member occurs in segment (3): MPa 31 . 318 3 max = =...
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This note was uploaded on 02/08/2011 for the course ME 650:291 taught by Professor Weng during the Fall '11 term at Rutgers.

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Quiz 2 solution - 025 . 4 m A A π = = = The...

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