154_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

154_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: Sec_2.4.qxd 9/25/08 148 11:38 AM Page 148 CHAPTER 2 Axially Loaded Members Problem 2.4-16 A rigid bar ABCD is pinned at point B and sup- a = 250 mm ported by springs at A and D (see figure). The springs at A and D have stiffnesses k1 10 kN/m and k2 25 kN/m, respectively, and the dimensions a, b, and c are 250 mm, 500 mm, and 200 mm, respectively. A load P acts at point C. If the angle of rotation of the bar due to the action of the load P is limited to 3°, what is the maximum permissible load Pmax? A b = 500 mm B C D P c = 200 mm k 2 = 25 kN/m k1 = 10 kN/m Solution 2.4-16 Rigid bar supported by springs EQUATION OF EQUILIBRIUM MB 0 FA(a) P(c) FD(b) a 250 mm EQUATION OF COMPATIBILITY dA dD a b FORCE-DISPLACEMENT RELATIONS FA FD dD dA k1 k2 b 500 mm 200 mm k1 10 kN/m k2 25 kN/m Substitute (3) and (4) into Eq. (2): FA FD ak1 bk2 (Eq. 1) SOLUTION OF EQUATIONS c 0 NUMERICAL DATA umax 3° p rad 60 FREE-BODY DIAGRAM AND DISPLACEMENT DIAGRAM (Eq. 2) (Eqs. 3, 4) (Eq. 5) SOLVE SIMULTANEOUSLY EQS. (1) AND (5): ack1P bck2P FA FD 2 2 2 a k1 + b k2 a k1 + b2k2 ANGLE OF ROTATION FD dD bcP cP dD u k2 b a2k1 + b2k2 a2k1 + b2k2 MAXIMUM LOAD u2 (a k1 + b2k2) P c Pmax umax 2 (a k1 + b2k2) c ; SUBSTITUTE NUMERICAL VALUES: Pmax p/60 rad [(250 mm)2(10 kN/m) 200 mm + (500 mm)2(25 kN/m)] 1800 N ; ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online