hw16_sol

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

This preview shows pages 1–5. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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. ...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern