ENGI 1313 Mechanics I Lecture 29 Zero Force

ENGI 1313 Mechanics I Lecture 29: Zero Force Members and Method of Sections Shawn Kenny, Ph. D. , P. Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland spkenny@engr. mun. ca

Lecture 29 Objective to examine zero force members in truss structures n to understand the method of sections for establishing forces in truss members n 2 © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 29

Comprehension Quiz 29 -01 n In the method of joints, ______ equations of equilibrium are typically applied at each joint. Ø Ø n 3 A) two B) three C) four D) six Answer: A © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 29

Example 29 -01 n 4 Identify the zero force members in the following truss structure. © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 29

Example 29 -01 (cont. ) n What Tools are Available? Method of joints by inspection Ø Equilibrium equations Ø 5 © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 29

Example 29 -01 (cont. ) n What are the Known Forces? Fy Fx By 6 © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 29

Example 29 -01 (cont. ) n What are the Zero Force Members? Ø # Equilibrium Equations < # Unknowns Fy ? Fx ? ? ? By 7 © 2007 S. Kenny, Ph. D. , P. Eng. ? ENGI 1313 Statics I – Lecture 29 ? ?

Example 29 -01 (cont. ) n What are the Zero Force Members? Fy Fx By 8 © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 29

Example 29 -01 (cont. ) Truss Members Supporting the Load n Why Have Zero Force Members? n Increase truss frame rigidity Ø Support other applied load conditions Ø 9 © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 29

Comprehension Quiz 29 -02 n Determine the number of zero-force members. Ø Ø Ø n 10 A) 0 B) 1 C) 2 D) 3 E) 4 F 1 F 3 Answer: D © 2007 S. Kenny, Ph. D. , P. Eng. F 2 ENGI 1313 Statics I – Lecture 29

Analysis of Long or Complex Trusses n How to Determine Truss Member Forces of Internal Chords? Ø ? Method of joints? ? ? 11 © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 29

Method of Sections n Cut Truss Member Ø 12 Newtown’s 3 rd Law © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 29

Method of Sections (cont. ) n Why Cut? Ø Ø n Where to Cut? Ø Ø n Force calculation Total # unknowns < 3 What Equations? Ø 13 Limit # joint calculations Directly calculate force for interior members Minimize # reactions to calculate © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 29

Method of Sections (cont. ) n What Section to Use? Minimize unknowns Ø Minimize calculations Ø Section Left 14 © 2007 S. Kenny, Ph. D. , P. Eng. Section Right ENGI 1313 Statics I – Lecture 29

Method of Sections (cont. ) 1. Determine Truss Support Reactions Ø 2. 3. 4. 5. 15 If necessary Select Cut-Line on Truss Select Truss Section to Analyse Draw FBD of Cut Truss Section Apply Equilibrium Equations © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 29

Comprehension Quiz 29 -03 n A cut is made through GH, BG and BC to determine the forces. Which section will you choose for analysis? Ø Ø n 16 A) Right, fewer calculations B) Left, fewer calculations C) Either right or left, same amount of work D) None as there are too many unknowns Answer: A © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 29

Comprehension Quiz 29 -04 n Can you determine the force in member ED by making the cut at section a-a? A) No, 4 unknowns Ø B) Yes, MD = 0 Ø C) Yes, ME = 0 Ø D) Yes, MB = 0 Ø n 17 a a Answer: D © 2007 S. Kenny, Ph. D. , P. Eng. ENGI 1313 Statics I – Lecture 29

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 29