MEC 0011 Statics Lecture 8 Prof. Sanghee Kim Fall_ 2012

Chapter Objectives -Determine the forces in the members of a truss using the method of joints and the method of sections -Analyze forces acting on the members of frames and machines composed of pin- connected members 1.Simple Trusses 2.The Method of Joints 3.Zero-Force Members 4.The Method of Sections Chapter Outline

6.3 Zero-Force Members ( 무력부재 ) -Members which support no loading - Function: a. Increase stability of truss during construction b. provide added support if the loading is changed -By inspection of each of joint, the zero-force members can be found -Drawing FBD is required

Method of joints is simplified using zero-force members When two of the members are collinear, 3 rd member is Zero-force member In general, when 3 members form a truss joint, the 3 rd member is a zero-force member provided no external force or support reaction is applied to the joint

Truss which supporting load P

Example 6.4 Using the method of joints, determine all the zero-force members of the Fink roof truss. Assume all joints are pin connected. Tip: Find joints which has 3 members with two collinear

Solution For Joint G, GC is a zero-force member. For Joint D,

For Joint F, For Joint B,

F HC satisfy ∑F y = 0 and therefore HC is not a zero-force member. Zero-force member  F GC, F DF, F FC Non Zero-force member  F BH, F HC

6.4 The Method of Sections ( 단면법 ) -If truss is in equilibrium, then any segment of truss is also in equilibrium -Cut truss with imaginary line  expose the “internal” and “external” forces -Member in Tension subjected “pull” whereas Compression is subjected “push”

-Not more than three members in which the forces are unknown -( 부재의 미지의 힘의 수가 세개 보다 많지 않도록 ) -Consider the truss and section a-a as shown -Member forces are equal and opposite to those acting on the other part – Newton’s Law In order to get force acting on member GC

a. 최소 하나의 힘을 알고 있으므로 삼각형 법을 이용하여 Tension/compression 을 assume Tension  BC, GC Compression  GF b. Assume that the unknown members forces at cut section are always tensile force (if negative scalar, it is compression)

-Procedure for Analysis A. Free-Body Diagram Decide the section of the truss Determine the truss’s external reactions Use equilibrium equations to solve member forces at the cut session Draw FBD of the sectioned truss which has the least number of forces acting on it Find the sense of an unknown member force B. Equations of Equilibrium Summed moments about a point Find the 3 rd unknown force from moment equation

Example 6.5 Determine the force in members GE, GC, and BC of the truss. Indicate whether the members are in tension or compression.

Solution Choose section a-a since it cuts through the three members Draw FBD of the entire truss

Draw FBD for the section portion

Example 6.7 Determine the force in members EB of the roof truss shown in Fig a. Indicate whether the members are in tension or compression.

Line a-a Line b-b