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problem solution_ch4

problem solution_ch4 - Chapter 4 Problem 3 At room...

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Chapter 4, Problem 3 At room temperature (20 ° C), a gap exits between the wall and the right end of the bars shown in Figure P4.3. Determine ( a ) The compressive axial force in the bars after temperature reaches 140 ° C. ( b ) The corresponding change in length of the aluminum bar. Chapter 4, Solution 3 Increase in length due to T (unrestrained): δ α t o o T L mm = = × + × = ( ) ( )( )( ) ( )( )( ) . 12 10 120 250 23 10 120 300 1188 6 6 ( a ) Compressive axial force P δ δ P t mm = = = 1 1188 1 0188 . . (a) But δ P PL AE P P = = + × ( . ) (10 )( ) ( . ) (10 )( ) 0 25 500 210 10 0 3 1000 70 10 6 9 6 × 9 9 N (b) Equating Eqs.(a) and (b): 0 188 10 2381 10 4 286 10 3 9 . ( ) . ( ) . ( ) = + P P or P k = 28 2 . ( b ) Change in length of aluminum bar δ δ δ α a t a P a a a T L P = = ( ) ( ) ( ) . ( ) 4 286 10 9 = × × = ( )( )( . ) . ( )( . ) . 23 10 120 03 4 28 10 28 2 10 0 707 6 9 3 o mm
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