ENGI 1313 Mechanics I Lecture 39 Analysis of

ENGI 1313 Mechanics I Lecture 39: Analysis of Friction with Wedges Shawn Kenny, Ph. D. , P. Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland spkenny@engr. mun. ca

Lecture 39 Objective n 2 to illustrate by example equilibrium analysis of wedges with dry friction forces © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 39

Wedge n Simple Machine Inclined plane Ø Small applied force to generate larger (orthogonal) forces for stability, lifting or moving objects Ø 3 © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 39

Wedge (cont. ) n Analysis of Force P FBD of wedge first then object Ø Analyze FBD with least # of unknowns Ø 4 © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 39

Wedge (cont. ) n Block Lowered onto Wedge If P > 0 (+) then wedge is stable Ø If P = 0 then wedge is self-locking Ø If P < 0 (-) then wedge is unstable Ø • Small s • Large 5 © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 39

Example 39 -01 n 6 The wedge is used to level the floor of a building. For the floor loading shown, determine the horizontal force P that must be applied to move the wedge forward. The coefficient of static friction between the wedge and the two surfaces of contact is μs = 0. 25. Neglect the size and weight of the wedge and the thickness of the beam. © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 39

Example 39 -01 (cont. ) n FBD 4 k. N 2 k. N Ax F 1 N 1 Ay N 1 F 1 P N 2 7 © 2007 S. Kenny, Ph. D. , P. Eng. F 2 ENGI 1313 Statics I – Lecture 39

Example 39 -01 (cont. ) n Beam Normal Reaction Force 4 k. N 2 k. N Ax F 1 N 1 8 © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 39 Ay

Example 39 -01 (cont. ) n Wedge Force P Ø Impending motion N 1 F 1 N 2 9 © 2007 S. Kenny, Ph. D. , P. Eng. F 2 ENGI 1313 Statics I – Lecture 39 P = 15

Example 39 -01 (cont. ) n Wedge Force P Ø Impending motion N 1 F 1 N 2 10 © 2007 S. Kenny, Ph. D. , P. Eng. F 2 ENGI 1313 Statics I – Lecture 39 P = 15

Example 39 -02 n 11 The wedge blocks are used to hold the specimen in a tension testing machine. Determine the design angle θ of the wedges so that the specimen will not slip regardless of the applied load. The coefficients of static friction are μA = 0. 1 at A and μB = 0. 6 at B. Neglect the weight of the blocks. © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 39

Example 39 -02 (cont. ) n FBD Test coupon Ø Wedge grip Ø FB FB NB NB P FB FA NA 12 © 2007 S. Kenny, Ph. D. , P. Eng. NB ENGI 1313 Statics I – Lecture 39

Example 39 -02 (cont. ) n Analysis of Test Coupon FB FB NB NB P 13 © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 39

Example 39 -02 (cont. ) n Analysis of Wedge Grip FB FA NA 14 © 2007 S. Kenny, Ph. D. , P. Eng. NB ENGI 1313 Statics I – Lecture 39

Example 39 -02 (cont. ) n Analysis of Wedge Grip FB FA NA 15 © 2007 S. Kenny, Ph. D. , P. Eng. NB ENGI 1313 Statics I – Lecture 39

Example 39 -02 (cont. ) n Analysis of Wedge Grip FA NA 16 © 2007 S. Kenny, Ph. D. , P. Eng. FB NB ENGI 1313 Statics I – Lecture 39

Chapter 8 Problems n No Problem Set Ø Problem 8 -1 through 8 -70 applicable • Omit 8 -45 and 8 -61 Ø 17 Answers on page 647 -648 © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 39

References Hibbeler (2007) n http: //wps. prenhall. com/esm_hibbeler_eng mech_1 n 18 © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 39