Lecture 29: Zero Force Members and Method of Sections ENGI 1313 Mechanics I Lecture 29: Zero Force Members and Method of Sections

Lecture 29 Objective to examine zero force members in truss structures to understand the method of sections for establishing forces in truss members

Comprehension Quiz 29-01 In the method of joints, ______ equations of equilibrium are typically applied at each joint. A) two B) three C) four D) six Answer: A

Example 29-01 Identify the zero force members in the following truss structure.

Example 29-01 (cont.) What Tools are Available? Method of joints by inspection Equilibrium equations

Example 29-01 (cont.) What are the Known Forces? Fy Fx By

Example 29-01 (cont.) What are the Zero Force Members? # Equilibrium Equations < # Unknowns Fy ? Fx ? ? By

Example 29-01 (cont.) What are the Zero Force Members? Fy Fx By

Example 29-01 (cont.) Truss Members Supporting the Load Why Have Zero Force Members? Increase truss frame rigidity Support other applied load conditions

Comprehension Quiz 29-02 Determine the number of zero-force members. A) 0 B) 1 C) 2 D) 3 E) 4 Answer: D F1 F2 F3

Analysis of Long or Complex Trusses How to Determine Truss Member Forces of Internal Chords? Method of joints? ? ? ?

Method of Sections Cut Truss Member Newtown’s 3rd Law

Method of Sections (cont.) Why Cut? Limit # joint calculations Directly calculate force for interior members Where to Cut? Force calculation Total # unknowns < 3 What Equations? Minimize # reactions to calculate

Method of Sections (cont.) What Section to Use? Minimize unknowns Minimize calculations Section Left Section Right

Method of Sections (cont.) Determine Truss Support Reactions If necessary Select Cut-Line on Truss Select Truss Section to Analyse Draw FBD of Cut Truss Section Apply Equilibrium Equations

Comprehension Quiz 29-03 A cut is made through GH, BG and BC to determine the forces. Which section will you choose for analysis? 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

Comprehension Quiz 29-04 Can you determine the force in member ED by making the cut at section a-a? A) No, 4 unknowns B) Yes, MD = 0 C) Yes, ME = 0 D) Yes, MB = 0 Answer: D a a

References Hibbeler (2007) http://wps.prenhall.com/esm_hibbeler_engmech_1