ME 201 Engineering Mechanics: Statics
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1 ME 201 Engineering Mechanics: Statics Unit 7.1 Simple Trusses Method of Joints Zero Force Members
2 Simple Truss structure composed of slender members joined together at their end points Planar Truss
3 Simple Truss To Design members and connections of a truss, necessary to determine forces developed in each member ssumptions: ll loadings are applied at the joints Members are joined together by smooth pins ssumptions satisfactory for bolted or welded joints
4 Simple Truss Each truss member acts as a 2-force member Force directed along axis of member Tension pull, elongation ompression push, shorten Several analytical approaches to solving
5 Free ody Diagrams Which of the following is NOT a simple truss? D 5. More than 1 D
6 Method of Joints If truss is in equilibrium, each joint must also be in equilibrium pproach: Sketch Free ody Diagram of Entire Truss Solve for Reactions Sketch Free ody Diagrams of Each Joint 2 unknown limit per FD F x =0 F y =0 M o =0
7 4 m 4 m Given: F1 = 400 N F2 = Find: Force in each member Solution: 1-FD 2-Support Reactions Example Problem Solution x Fy M y y 0 y 3 m 400 N F 0 x x 600 or y y 200 or 200 N 3 m y D x 400 N F 1 3 m 3 m D 200 N 4 m 3 m 3 m D F 2
8 Solution: 1-FD 2-Support Reactions 3-Joint FDs 400 N 200 N 4 m 3 m 3 m D Example Problem Solution Joint 4 3 D Fy N Fx 0 3 D D 450 N T D D 450 N Fy Joint D 4 3 D Fx D 5 D 250 N T D 0 5 D N 0
9 Example Problem Solution Solution: 1-FD 2-Support Reactions 3-Joint FDs Joint 200 N Force Diagram N 200 N 4 m D 200 N x F T 200 D 3 m 3 m D
10 Zero Force Members Zero Force Members support NO loading Used for: Stability hanging pplied Loads
11 Zero Force Members If only 2 members form a truss joint ND no external load or support reaction is applied to the joint, then the members must be Zero Force Members X X X X
12 Zero Force Members If 3 members form a truss joint for which 2 members are collinear, the 3 rd member is a Zero Force Member, provided no external force or support reaction is applied to the joint. X X X
13
14 Simple Truss structure composed of slender members joined together at their end points Planar Truss
15 Simple Truss To Design members and connections of a truss, necessary to determine forces developed in each member ssumptions: ll loadings are applied at the joints Members are joined together by smooth pins ssumptions satisfactory for bolted or welded joints
16 Simple Truss Each truss member acts as a 2-force member Force directed along axis of member Tension pull, elongation ompression push, shorten Several analytical approaches to solving
17 Free ody Diagrams Which of the following is NOT a simple truss? D 5. More than 1 D
18 Method of Joints If truss is in equilibrium, each joint must also be in equilibrium pproach: Sketch Free ody Diagram of Entire Truss Solve for Reactions Sketch Free ody Diagrams of Each Joint 2 unknown limit per FD F x =0 F y =0 M o =0
19 4 m Example Problem Given: F 1 = 400 N F 1 F 2 = Find: Force in each member 3 m 3 m D F 2
20 4 m Given: F1 = 400 N F2 = Find: Force in each member Example Problem Solution F 1 3 m 3 m D F 2
21 4 m 4 m Given: F1 = 400 N F2 = Find: Force in each member Solution: 1-FD 2-Support Reactions Example Problem Solution x Fy M y y 0 y 3 m 400 N F 0 x x 600 or y y 200 or 200 N 3 m y D x 400 N F 1 3 m 3 m D 200 N 4 m 3 m 3 m D F 2
22 Solution: 1-FD 2-Support Reactions 3-Joint FDs 400 N 200 N 4 m 3 m 3 m D Example Problem Solution Joint 4 3 D Fy N Fx 0 3 D D 450 N T D D 450 N Fy Joint D 4 3 D Fx D 5 D 250 N T D 0 5 D 200 N 0
23 Example Problem Solution Solution: 1-FD 2-Support Reactions 3-Joint FDs Joint 200 N Force Diagram N 200 N 4 m D 200 N x F T 200 D 3 m 3 m D
24 Zero Force Members Zero Force Members support NO loading Used for: Stability hanging pplied Loads
25 Zero Force Members If only 2 members form a truss joint ND no external load or support reaction is applied to the joint, then the members must be Zero Force Members X X X X
26 Zero Force Members If 3 members form a truss joint for which 2 members are collinear, the 3 rd member is a Zero Force Member, provided no external force or support reaction is applied to the joint. X X
27 2 m In lass Exercise Given: F = 3 kn θ = 30º Find: Force in each member 2 m D F 2 m θ 4.10 T D
28 2 m 2 m Given: F = 3 kn θ = 30º Find: Force in each member Solution: 1-FD 2-Support Reactions x y x Solution 2 m 3 kn D 30º 2 m F 0 x 3 0 x 3 or 3 kn y 2 m D F θ 2 m M 0 y y 1. 5 kn 0 y F y 0 y 1.5 or 1. 5 kn
29 2 m Solution: 1-FD 2-Support Reactions 3-Joint FDs x y Joint 3 kn 1.5 kn F 0 cos 45 Dcos30 3 F 0 sin 45 Dsin kn D 4.10 kn T 45º 30º D Solving simultaneous eqn: Solution 3 kn 3 kn D 30º 2 m 2 m 1.5 kn 1.5 kn Joint y 3 kn 45º.777 kn D Fx sin 45 sin kn F cos cos45 D 0 D kn T
30 2 m Solution: 1-FD 2-Support Reactions 3-Joint FDs Joint D D 4.10 kn Solution 3 kn 3 kn D 30º 2 m 2 m 1.5 kn 1.5 kn D 4.10 kn 30º D Fx 0 D cos cos30 D kn T 0 D 4.10 T Force Diagram
31 In lass Exercise
32 Solution
33 In lass Exercise
34 Solution
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