method of joint

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3-3 The Method of Joints : 

1 3-3 The Method of Joints Satisfying the equilibrium eqns for the forces exerted on the pin at each joint of the truss When using this method, it is necessary to draw each joint’s free body diagram before applying the eqns Consider joint B of the truss in Fig 3.19(a) From the free-body diagram in Fig 3.19(b), the unknowns are the magnitude of forces in members BA & BC Applications of eqns yields 2 algebraic eqns that can be solved for the 2 unknowns

3-3 The Method of Joints : 

2 3-3 The Method of Joints Fig 3.19

3-3 The Method of Joints : 

3 3-3 The Method of Joints Always assume the unknown member forces acting on the joint’s free body diagram to be in tension Numerical solution of the equilibrium eqns will yield positive scalars for members in tension & negative for those in compression The correct sense of direction of an unknown member force can in many cases be determined by inspection

3-3 The Method of Joints : 

4 3-3 The Method of Joints A +ve answer indicates that the sense is correct, whereas a –ve answer indicates that the sense shown on the free-body diagram must be reversed

Example 3.2 : 

5 Example 3.2 Determine the force in each member of the roof truss shown in Fig 3.20(a) State whether the members are in tension or compression The reactions at the supports are given Fig 3.20(a)

Example 3.2 - solution : 

6 Example 3.2 - solution Only the forces in half the members have to be determined as the truss is symmetric wrt both loading & geometry

Example 3.2 - solution : 

7 Example 3.2 - solution

Example 3.2 - solution : 

8 Example 3.2 - solution

3-4 Zero-Force Members : 

9 3-4 Zero-Force Members Truss analysis using method of joints is greatly simplified if one is able to first determine those members that support no loading These zero-force members may be necessary for the stability of the truss during construction & to provide support if the applied loading is changed The zero-force members of a truss can generally be determined by inspection of the joints & they occur in 2 cases.

3-4 Zero-Force Members : 

10 3-4 Zero-Force Members Case 1 Consider the truss in Fig 3.22(a) The 2 members at joint C are connected together at a right angle & there is no external load on the joint The free-body diagram of joint C indicates that the force in each member must be zero in order to maintain equilibrium

3-4 Zero-Force Members : 

11 3-4 Zero-Force Members Case 2 Zero-force members also occur at joints having a geometry as joint D in Fig 3.23(a)

3-4 Zero-Force Members : 

12 3-4 Zero-Force Members Case 2 No external load acts on the joint, so a force summation in the y-direction which is perpendicular to the 2 collinear members requires that FDF = 0 Using this result, FC is also a zero-force member, as indicated by the force analysis of joint F, Fig 3.23(c)

Example 3.4 : 

13 Example 3.4 Using the method of joints, indicate all the members of the truss shown in Fig 3.24(a) that have zero force Fig 3.24(a)

Example 3.4 - solution : 

14 Example 3.4 - solution Looking for joints similar to those discussed in Fig 3.22 and 3.23, we have:

Example 3.4 - solution : 

15 Example 3.4 - solution