Truss Assumptions There are four main assumptions made in the analysis of truss 1 Truss members are connected together at their ends only 2 Truss are connected together by frictionless pins 3 The truss structure is loaded only at the joints 4 The weights of the members may be neglected Simple Truss The basic building block of a truss is a triangle Large truss are constructed by attaching several triangles together A new triangle can be added truss by adding two members and a joint A truss constructed in this fashion is known as a simple truss Method of Joints Truss The truss is made up of single bars which are either in compression tension or no load The means of solving force inside of the truss use equilibrium equations at a joint This method is known as the method of joints Method of Joints Truss The method of joints uses the summation of forces at a joint to solve the force in the members It does not use the moment equilibrium equation to solve the problem In a two dimensional set of equations F x 0 F y In three dimensions F z 0 0 Truss Example Problem Determine the loads in each of the members by using the method of joints Truss Example Problem Draw the free body diagram The summation of forces and moment about B result in F F M x 0 RAx RB y 0 RAy 10 kips 10 kips RAy 20 kips A 0 RB 5 ft 10 kips 10 ft 10 kips 20 ft RB 60 kips RAx 60 kips Truss Example Problem Look at Joint B F F x 0 TBC RB TBC 60 kips TBC 60 kips y 0 TBA TBA 0 kips Truss Example Problem Look at Joint D and find the angle 5 ft o 14 04 20 ft Fx 0 TDC TDA cos tan 1 F y 0 TDA sin 10 kips TDA 41 231 kips TDC 40 kips Truss Example Problem Look at Joint C and find the angle 5 ft o 26 565 10 ft Fy 0 TCA sin 10 kips TCA 22 361 kips tan 1 F x 0 TCD TCA cos TCB 40 kips 22 361 kips cos 26 565o 60 kips 0 Example Problem Determine the forces in members FH DH EG and BE in the truss using the method of sections Truss Example Problem Draw the free body diagram The summation of forces and moment about H result in F x F M 0 RHx 3 kips 3 kips 3 kips 3 kips RHx 12 kips y 0 RHy RI H 0 RI 15 ft 3 kips 10 ft 3 kips 20 ft 3 kips 30 ft 3 kips 40 ft RI 20 kips RHy 20 kips Truss Example Problem Do a cut between BD and CE Truss Example Problem Take moment about A 10 ft 0 53 13 7 5 ft tan 1 0 M 0 T cos 53 13 20 ft 3 kips 10 ft A CE TCE 2 5 kips Truss Example Problem Do a cut between HD and GE Truss Example Problem Take the moment about I M I 0 20 kips 15 ft THD 15 ft 3 kips 10 ft THD 18 kips Take the moment about D M D 0 12 kips 20 ft 20 kips 15 ft 3 kips 10 ft TGE 15 ft TGE 6 kips Truss Example Problem Do a cut between HD and HI Truss Example Problem Take the sum of forces in y direction 10 ft 0 tan 53 13 7 5 ft 1 0 F T 0 sin 53 13 THD 20 kips y HF THF 20 kips 18 kips 2 5 kips 0 sin 53 13
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