#### Read Microsoft PowerPoint - notes_03b trusses - method of joints.ppt [Compatibility Mode] text version

`CIVL 3121Trusses - Method of Joints1/5Method of Joints If a truss is in equilibrium, then each of its joints must be in equilibrium.  The method of joints consists of satisfying the th equilibrium equations for forces acting on ilib i ti f f ti each joint.Method of Joints Recall, that the line of action of a force acting on a joint is determined by the geometry of the truss member.  The line of action is formed by c nnectin the f acti n f rmed connecting two ends of each member with a straight line.  Since direction of the force is known, the remaining unknown is the magnitude of the force. Fx0 Fy0Method of JointsJoint A Joint BMethod of JointsVerticals Upper chord membersTension ForceJoint AJoint BDiagonalsLower chord membersCompression ForceMethod of JointsMethod of JointsUpper chord in compressiongusset plateweldIdealized joint ­ members connected by a frictionless pinLower chord in tensionCIVL 3121Trusses - Method of Joints2/5Method of JointsUpper chord in compressionMethod of Joints Procedure for analysis - the following is a procedure for analyzing a truss using the method of joints:1. 1 If possible determine the support reactions possible,Lower chord in tension2. Draw the free body diagram for each joint. In general, assume all the force member reactions are tension (this is not a rule, however, it is helpful in keeping track of tension and compression members).Method of Joints Procedure for analysis - the following is a procedure for analyzing a truss using the method of joints:3. Write the equations of equilibrium for each joint,Method of Joints Procedure for analysis - the following is a procedure for analyzing a truss using the method of joints:4. If possible, begin solving the equilibrium equations at a joint where only two unknown reactions exist. Work your way from joint to joint, selecting the new joint using the criterion of two unknown reactions. 5. Solve the joint equations of equilibrium simultaneously, typically using a computer or an advanced calculator. Fx0 Fy0Method of Joints Example - Consider the following trussFirst, determine the support reactions for the truss 500 lb 500 lbMethod of Joints Example - Consider the following trussFirst, determine the support reactions for the truss(10 lb  MA  0  500 lb500 ft )  C y (10ft )Cy = 500 lb500 lb10 ft Ax FyAy Cy 0  Ay  C y  0  Ax  500 lb10 ftAy = -500 lb10 ftAx10 ft FxAx = -500 lbAyCyCIVL 3121Trusses - Method of Joints3/5Method of JointsThe equations of equilibrium for Joint AFAB 500 lb FACMethod of JointsThe equations of equilibrium for Joint B500 lb Fx 0  FBC cos 45  500 lb Fx  Fy 0  FAC  500 lb  0  FAB  500 lbFAC = 500 lb FAB = 500 lbFABFBCFBC = -707.2 lb 707.2The forces in the truss can be summarized as: FAB = 500 lb (T) FAC = 500 lb (T) FBC = 707.2 lb (C)500 lbMethod of Joints Problem ­ Determine the force in each member of the truss shown below Method of JointsProblem ­ Determine the force in each member of the truss shown belowB 4 ft CA604 ftE60D4 ft 800 lbIn the notes on page 10Method of Joints Problem ­ Determine the force in each member of the truss shown below Zero Force MembersTruss analysis may be simplified by determining members with no loading or zero­force. These members may provide stability or be useful if the l di th loading changes. h Zero­force members may be determined by inspection of the jointsCIVL 3121Trusses - Method of Joints4/5Zero Force MembersyZero Force Members Case 2: If three members are connected at a joint and there is no external force applied to the joint and two of the members are colineary F1Case 1: If two members are connected at a joint and there is no external force applied to the jointF1 Fy  Fx 0  F1 sin   0  F1 cos   F2F1 = 0 F2 = 0F3 0  F1 sin F2 xF2 x FyF1 = 0Zero Force Members Determine the force in each member of the truss shown below:800 lb CZero Force Members Determine the force in each member of the truss shown below:800 lb CIn the notes on page 11Using Case 1 FAG and FCG g G G are zero-force membersD E BUsing Case 2 FBG and FDF g are zero-force membersBUsing Case 1 FEF and FCF are zero-force members zero forceD E G FA G FA8 ft8 ft8 ft8 ftZero Force Members Determine the force in each member of the truss shown below:800 lb C FBC B D E G F3Method of JointsThe equations of equilibrium for Joint C800 lb4 4 3The remaining non-zero forces can be found using the th method of joints th d f j i t FxFCD 0   FBC  FCD3 5 3 54 54 5FBC = FCD Fy 0   FBC  FCD  800 lbFBC = -666.7 lb FBC = 666.7 lb (C)A8 ft8 ftCIVL 3121Trusses - Method of Joints5/5End of Trusses - Part 2Any questions?`

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