# solution_hw5 - 6.3 A simple truss in which all members have...

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6.3 A simple truss in which all members have the same axial rigidity AE is loaded as shown in Figure P6.5. Calculate the diameter d necessary for ( a ) The bar AB. ( b ) The bar BC. Given: E = 210 GPa , S y = 250 MPa . Assumption: Buckling occurs in the plane of the truss. The Euler formula applies. ( a ) Applying the method of joints at A: Fk N AB C = 40 ( ) and ) ( 220 C kN F BC = . 5 . 2 m L AB = mm d d A F cr AB 3 . 14 , ) 10 ( 250 ; 4 ) 10 ( 40 6 2 3 = = = π σ W e h a v e rI and Euler s formula: A d == 4 cr E Lr d dm = × 2 2 29 2 250 10 109 8 6 210 10 25025 () (. . ) ;( ) , . m m m Use, a commercial size of : d = 110 diameter ( b ) m L BC 875 . 1 = mm d d A F BC cr 5 . 33 , ) 10 ( 250 ; 4 ) 10 ( 220 6 2 3 = = = Euler formula: cr E d = × 2 2 2 250 10 82 4 6 210 10 1875 025 . ) ) , . m U s e 83 mm diameter

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6.5 A steel pipe of outer diameter D and inner diameter d is employed as a 2-m column
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solution_hw5 - 6.3 A simple truss in which all members have...

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