Assignment2_Solution

Assignment2_Solution - 184 Solutions Manual Solutions to...

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184 Solutions Manual Solutions to Chapter 16 Problems S.16.1 From Section 16.2.2 the components of the bending moment about the x and y axes are, respectively M x = 3000 × 10 3 cos 30 = 2 . 6 × 10 6 Nmm M y = 3000 × 10 3 sin 30 = 1 . 5 × 10 6 The direct stress distribution is given by Eq. (16.18) so that, initially, the position of the centroid of area, C, must be found. Referring to Fig. S.16.1 and taking moments of area about the edge BC (100 × 10 + 115 × 10) ¯ x = 100 × 10 × 50 + 115 × 10 × 5 i.e. ¯ x = 25 . 9mm C E B D C A F x y 100 mm 125 mm 30 ° 10 mm 10 mm Fig. S.16.1 Now taking moments of area about AB (100 × 10 + 115 × 10) ¯ y = 100 × 10 × 5 + 115 × 10 × 67 . 5 from which ¯ y = 38 . 4mm
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Solutions to Chapter 16 Problems 185 The second moments of area are then I xx = 100 × 10 3 12 + 100 × 10 × 33 . 4 2 + 10 × 115 3 12 + 10 × 115 × 29 . 1 2 = 3 . 37 × 10 6 mm 4 I yy = 10 × 100 3 12 + 10 × 100 × 24 . 1 2 + 115 × 10 3 12 + 115 × 10 × 20 . 9 2 = 1 . 93 × 10 6 mm 4 I xy = 100 × 10 × 33 . 4 × 24 . 1 + 115 × 10( 20 . 9)( 29 . 1) = 1 . 50 × 10 6 mm 4 Substituting for M x , M y , I xx , I yy and I xy in Eq. (16.18) gives σ z = 0 . 27 x + 0 . 65 y (i)
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Assignment2_Solution - 184 Solutions Manual Solutions to...

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