Trusses - Method of Joints

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Trusses - Method of Joints ME 22 Truss - efinition

1 Trusses - Method of Joints ME 22 Truss - efinition truss is a framework of members joined at ends with frictionless pins to form a stable structure. (Onl two-force members.) asic shape is a triangle. truss is designed to support weight. 2 Truss ridges SX SX Norfolk Southern Knoville Railroad ridges SX Highwa ridge NS 3 4

Method of joints (MOJ) Method of sections (MOS) Show forces acting on pins (not forces acting on members).

2 Joints Tpes of Truss Named after inventor: Pinned Joint Riveted Joint Howe Pratt Named after railroad compan: Frictionless pin is good first approimation. 5 altimore 6 Methods of Truss nalsis MOJ - oncepts raw F s of pins. Method of joints (MOJ) Method of sections (MOS) Show forces acting on pins (not forces acting on members). oncurrent, coplanar sstems. Two independent equations (force summations) at each pin. No more than two unknowns at a pin. 7 8

3 MOJ - Steps 1. Solve for structure s overall support reactions. Follow process for non-concurrent, coplanar sstem. 2. Start at a joint with 1 or 2 unknowns. Follow process for concurrent, coplanar sstem. No-No fter Step 1, the method of joints does not emplo moment summations. 3. Repeat step 2 as necessar. 9 1 MOJ - Eample Given: E 6 ft 1 ft Required: Force in each member using method of joints Solve for support reactions of whole structure. ΣF 1 2 E ΣM E 2( 16) 1( 1) ( 8) F E E = 5,25 lb 12 E E E = 3, lb = 5,25 lb

4 2. raw F of Joint. F F Σ F F comp. comp. F F F F F.6F.8F lb E 525 lb 6 ft 1 ft 3 lb ΣF.8F 2 F = 25 lb ΣF F.6F F =15 lb 2. raw F of Joint. F F F F comp. comp. F F F F F F F F F 1 F Σ 525 lb E 525 lb 6 ft 1 ft 3 lb ΣF F F F = 15 lb ΣF 1 F F = raw F of Joint E. F E 3 lb F F comp. F E F E F E F E F E F E E F E 525 lb comp Σ 525 lb E 525 lb 6 ft 1 ft 3 lb ΣF F E 525 F E = 525 lb ΣF F E 3 F E = 3 lb 2. raw F of Joint. F F F F E F F comp. comp. F F.6F.8F F F F 5 F F 41 F F E F E F E Σ 4 41 F 525 lb E 525 lb 6 ft 1 ft 3 lb ΣF.8F F 4 41 F F = = 48 lb 15 16

FE F F FE comp. comp. 5 4 F F 41 41 F FE 525 Σ 1 ft 3 lb Insert previous results to verif that is in equilibrium. This serves to check previous work.

5 FE F F FE comp. comp. 5 4 F F F FE 525 Σ 1 ft 3 lb Insert previous results to verif that is in equilibrium. This serves to check previous work. 17 Zero-Force Members 15 lb T lb F 6 ft 525 lb 25 F F FE E F F 525 lb 525 lb 15 lb T T lb 525 lb E ft 1 ft 18 onus Which members of this structure carr no force? Some structures are staticall indeterminate. (See Online Homework ) 19 2 F 3 lb 2. raw F of Joint.

6 Trusses - Method of Joints (MOJ) 2 Structures are composed of man pieces which we call members. When we treat a structure as a truss, we neglect the weights of the members. We also assume that each member is connected to other members at onl two points, which are called joints and are assumed to be held together b frictionless pins. Finall, we assume that the structure s overall reactions and all applied loads act onl at joints of the structure. Then ever member of the truss is a two-force member. For a real structure, truss analsis is onl a first approimation. Further analsis that includes loads applied between the joints, such as the members weights, must be done before the design is complete. ut including such loads greatl complicates the analsis and is beond the scope of this course. 3 Notice all of the triangles in these structures. s we will see in the net slide, the two railroad bridges cross the Tennessee River near UTK 4 You have probabl seen these bridges man times. 5 The assumption of frictionless pins is a good first approimation even for riveted joints. Page 1 of 4

7 6 Man truss forms are so common that the have names. 7 The two basic methods of truss analsis are the method of joints and the method of sections. This set of slides eplains the method of joints. The net set will cover the method of sections. 8 There can be an number of joints in a truss, and we might need to draw Fs for all of them. For each such F, we will use the concepts listed here. 9 We need to do the first step onl once, and it is the onl step in which we have a non-concurrent force sstem. We must repeat the second step for one joint after another until we have found all required forces. 1 Once we begin step 2, we deal eclusivel with concurrent, coplanar force sstems. For such sstems, moment summation is meaningless. 11 In the following slides, we will use the MOJ to find the forces in all members of this structure. Page 2 of 4

8 12 ecause of the roller at, there can be no vertical reaction there. 13 The table is used here and on subsequent slides to illustrate one wa of constructing specific equations for a F with concurrent, coplanar forces. dding the cells in the column of components and components and setting the totals equal to zero produces the desired equations. Once we know all of the forces acting on a joint, it is said that we have solved the joint. 14 ecause we found the force in member on the previous slide, the F of joint has onl two remaining unknowns. t an joint with two unknowns, both unknowns can be found from two force summations. gain, the joint is solved b building the equations in a table. 15 ecause we have alread found the structure s overall reactions, joint E has onl two unknowns and can be solved. 16 fter solving joints, and E, we have onl one unknown left at joint. Page 3 of 4

9 17 t this point, we have solved for the forces in all truss members without using a F of joint. ut we can use that F to check our results. 18 This is a common wa of presenting the results of truss analsis. With all the forces known, it is said that we have solved the truss. T indicates tension and indicates compression. 19 considering vertical forces on a F of joint, we find that member carries no force. The same approach shows that member E carries no force. On a F of joint I, b considering forces perpendicular to line FIH, we find that member GI carries no force. Knowing that member GI carries no force, we can analze joint G to find that member FG carries no force. 2 If we can find all loads on a structure using onl the equations of statics, the structure is said to be staticall determinate. This simpl means that we can write at least as man independent equations from statics as there are unknown loads. If the equations of statics cannot produce enough independent equations to find all of the unknown loads, the structure is said to be staticall indeterminate. Page 4 of 4

Trusses - Method of Sections

Trusses - Method of Sections ME 202 Methods of Truss Analsis Method of joints (previous notes) Method of sections (these notes) 2 MOS - Concepts Separate the structure into two parts (sections) b cutting