ENGI 1313 Mechanics I Lecture 33 Frames and

ENGI 1313 Mechanics I Lecture 33: Frames and Machines Shawn Kenny, Ph. D. , P. Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland spkenny@engr. mun. ca

Chapter 33 Objectives n 2 to illustrate the analysis of frames and machines by example © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 33

Example 33 -01 n 3 The compound beam is pin supported at B and supported by rockers at A and C. There is a hinge (pin) at D. Determine the reactions at the supports. © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 33

Example 33 -01 (cont. ) n What FBD to Analyze? Ø Member DC 7 k. N Dx Dy 16 k. N Ay 4 © 2007 S. Kenny, Ph. D. , P. Eng. Bx Cy 6 k. N By ENGI 1313 Statics I – Lecture 33 Dy Dx

Example 33 -01 (cont. ) n Member DC 7 k. N Dx Dy 16 k. N Ay 5 © 2007 S. Kenny, Ph. D. , P. Eng. Bx Cy 6 k. N By ENGI 1313 Statics I – Lecture 33 Dy Dx

Example 33 -01 (cont. ) n Member ABD Ø What equilibrium equation? 7 k. N Dx Dy 16 k. N Ay 6 © 2007 S. Kenny, Ph. D. , P. Eng. Bx Cy 6 k. N By ENGI 1313 Statics I – Lecture 33 Dy Dx

Example 33 -01 (cont. ) n Member ABD 7 k. N Dx Dy 16 k. N Ay 7 © 2007 S. Kenny, Ph. D. , P. Eng. Bx Cy 6 k. N By ENGI 1313 Statics I – Lecture 33 Dy Dx

Example 33 -02 n 8 Determine the horizontal and vertical components of force at each pin. The suspended cylinder has a weight of 80 lb. © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 33

Example 33 -02 (cont. ) n Where to Start? Ø Structural characteristics W • Pulley • Two-force member DC • Two-force member EB ¨ 9 W No. Why? © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 33

Example 33 -02 (cont. ) Draw FBD n What FBD to Analyze? n Ø Member ABC Ex Ey W By Bx W Ax Bx By 10 © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 33 FCD W

Example 33 -02 (cont. ) n What Equilibrium Equation? W Ax Bx By 11 © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 33 FCD W

Example 33 -02 (cont. ) n Find Bx to Help Solve for Unknowns Ex Ey W By 12 © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 33 Bx

Example 33 -02 (cont. ) n Find Ax W Ax Bx By 13 © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 33 FCD W

Example 33 -03 n 14 The link is used to hold the rod in place. Determine the required axial force on the screw at E if the largest force to be exerted on the rod at B, C, or D is to be 100 N. Also, find the magnitude of the force reaction at pin A. Assume all surfaces of contact are smooth. © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 33

Example 33 -03 (cont. ) n Any Structural Characteristic? Ø 15 Concurrent forces © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 33

Example 33 -03 (cont. ) n FBD Ø Assume 1 N unit load at Ex Ay Ax Ex 45 16 © 2007 S. Kenny, Ph. D. , P. Eng. NB ENGI 1313 Statics I – Lecture 33

Example 33 -03 (cont. ) n Equilibrium Analysis Ay Ax Ex 45 17 © 2007 S. Kenny, Ph. D. , P. Eng. NB ENGI 1313 Statics I – Lecture 33

Example 33 -03 (cont. ) n Equilibrium Analysis Ay Ax Ex 45 18 © 2007 S. Kenny, Ph. D. , P. Eng. NB ENGI 1313 Statics I – Lecture 33

Example 33 -03 (cont. ) n Equilibrium Analysis of Cylinder A Ay x Ex 45 19 © 2007 S. Kenny, Ph. D. , P. Eng. NB ENGI 1313 Statics I – Lecture 33

Example 33 -03 (cont. ) n Equilibrium Analysis of Cylinder A Ay x Ex 45 20 © 2007 S. Kenny, Ph. D. , P. Eng. NB ENGI 1313 Statics I – Lecture 33

References Hibbeler (2007) n http: //wps. prenhall. com/esm_hibbeler_eng mech_1 n 21 © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 33