888_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

888_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

Info iconThis preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: 11Ch11.qxd 9/27/08 882 3:39 PM Page 882 CHAPTER 11 Columns Solution 11.6-4 Steel pipe column Pinned ends. DATA 2.1 m E d1 60 mm 0.06 m P 10 kN 10,000 N r 210 * 109 N/m2 210 GPa d2 68 mm e 30 mm 0.068 m p2 (d 2 4 p4 (d 64 2 22.671 * 10 ec 0.03 m 1.9845 r2 6 L P 2r A EA 3 m m2 d2 2 c 0.034 m 0.35638 Substitute into Eq. (1): TUBULAR CROSS SECTION I 513.99 * 10 Units: Newtons and meters L A I A r2 d 2) 1 804.25 * 10 6 4 d1 ) 413.38 * 10 9 38.8 * 106 N/m2 smax m2 m4 38.8 MPa ; (b) MAXIMUM PERMISSIBLE LENGTH sallow 50 MPa P(ec/r 2) EI arccos c d AP smaxA P Solve Eq. (1) for the length L: (a) MAXIMUM COMPRESSIVE STRESS ec P P L c 1 + 2 sec a bd A 2r A EA r L Secant formula (Eq. 11-59): smax P A 6 (1) (2) 2 Substitute numerical values: L max 5.03 m ; 2 12.434 * 10 N/m Problem 11.6-5 A pinned-end strut of length L 5.2 ft is constructed of steel pipe (E 30 * 103 ksi) having inside diameter d1 2.0 in. and outside diameter d2 2.2 in. (see figure). A compressive load P 2.0 k is applied with eccentricity e 1.0 in. (a) What is the maximum compressive stress smax in the strut? (b) What is the allowable load Pallow if a factor of safety n 2 with respect to yielding is required? (Assume that the yield stress sY of the steel is 42 ksi.) Solution 11.6-5 Pinned-end strut Steel pipe. DATA L d1 P (a) MAXIMUM COMPRESSIVE STRESS 5.2 ft 62.4 in. E 2.0 in. d2 e 30 * 103 ksi 2.2 in. 1.0 in. 2.0 k I p2 (d 42 p4 (d 64 2 smax P A r2 TUBULAR CROSS SECTION A P ec L P c 1 + 2 sec a bd A 2r A EA r d2 3.0315 ksi c 1.1 in. 2 Secant formula (Eq. 11-59): Units: kips and inches d 2) 1 0.65973 in.2 4 d 1) 4 0.36450 in. r I A L P 2r A EA 0.55250 in.2 0.74330 in. ec r2 1.9910 0.42195 (1) ...
View Full Document

Ask a homework question - tutors are online