hw16_sol - ENGINEERING MECHANICS STATICS 2nd Ed W F RILEY...

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Unformatted text preview: ENGINEERING MECHANICS - STATICS, 2nd. Ed. W. F. RILEY AND L. D. STURGES 10-1* Determine the second moment of area for the isosceles triangle shown in Fig. P10-1 with respect to (a) The base of the triangle (the x-axis). (b) An axis through the centroid parallel to the base. SOLUTION From similar triangles: ENGINEERING MECHANICS - STATiCS, 2nd. Ed. W. F. RILEY AND L. D. STURGES 10-4 Determine the second moment of area for the ha1f~oirole shown in Fig. PIG-4 with respect to {a} The x-axis. {b} An axis through the centroid parallel to the x-axis. SOLUTION Y2 dA R I 92 sin2 e p d9 do 0 R . 1T 4 R 4 =I [am—#31226] mgr] -— 0 O 0 —_—_——-—-— ‘i¢.l ENGINEERING MECHANICS - STATICS. 2nd. Ed. W. F. RILEY AND L. D. STURGES 10-5* Determine the second moment of area for the shaded region shown in Fig. P10—5 with respect to (a) The x—axis. (b) The y—axis. Fig. P10-5 . SOLUTION ,, (a) From the curve: (b) From the results of Example Problem 10-1: bh3 = ix 3 l 3 = I dI A v 4 7 4 4 4 I ‘ . 3’— = 780.2 in. z 780 in. 21 0 ENGINEERING MECHANICS - STATICS, 2nd. Ed. W. F. RILEY AND L. D. STURGES Determine the second moment of area for the shaded region shown in Fig. PIG-7 with respect to (a) The x-axis. (b) The y-axis. SOLUTION (a) From the results of Example Problem 10-1: 1 3 _ 3 bh — L de 4.267 in? a 4.27 in? (b) From the curve: 2 9a ENGINEERING MECHANICS - STATICS, 2nd. Ed. W. F. RILEY AND L. D. STURGES 10-18* Determine the radii of gyration for the triangular area shown in Fig. PIG-18 with respect to (a) The x- and y-axes shown on the figure. (b) Horizontal and vertical centroidal axes. SOLUTION 'Ib 1[% (b - fl]u II::::§ O 1 h 3[b3 y{:x (b3 - 3b2 x + 3bx2 x 3) dx l[: bzx 2 3bx3 x33 3 31”2 + 3 ’ "- b _h 2-3 _ b Io (bx x ) dx = 200 mm and h = 125 mm: %bh = %(200)(125) 12,500 mmz %§(200)(125)3 = 32.55(1o6) mm“ 3 = ——(125)(200)3 = 83.33(106) mm‘1 32. 55(106 ) 12, 500 / 6 = §§L§§ng—l = 81.64 mm 3 81.6 mm Ans. 12,500 - 51.03 mm a 51.0 mm (b) From Eqs. 10-11 with dy = 200/3 = 66.67 mm and dx = 125/3 = 41.67 mm: ‘ 9 k . =/(51. 03)2 - (41.67)“ 29.4 mm Ans. r——--—-—-—————w - =/(81. 64)3 - (66.67)2 47.1 mm Ans. ...
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