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Unformatted text preview: ENGINEERING MECHANICS  STATICS, 2nd. Ed. W. F. RILEY AND L. D. STURGES 101* Determine the second moment of
area for the isosceles triangle
shown in Fig. P101 with respect
to (a) The base of the triangle
(the xaxis). (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 104 Determine the second moment of
area for the ha1f~oirole shown
in Fig. PIG4 with respect to
{a} The xaxis. {b} An axis through the centroid
parallel to the xaxis. 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 105* 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. P105 . SOLUTION ,, (a) From the curve: (b) From the results of
Example Problem 101: 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. PIG7 with
respect to (a) The xaxis. (b) The yaxis. SOLUTION (a) From the results of
Example Problem 101: 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 1018* Determine the radii of gyration
for the triangular area shown
in Fig. PIG18 with respect to
(a) The x and yaxes 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 23
_ 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. 1011 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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 Spring '08
 McVay

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