me 201 engineering mechanics: statics chapter 6 – part a 6.1 simple trusses 6.2 method of joints...
TRANSCRIPT
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ME 201Engineering Mechanics: Statics
Chapter 6 – Part A6.1 Simple Trusses
6.2 Method of Joints
6.3 Zero Force Members
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Simple Truss
A structure composed of slender members joined together at their end points
“Planar Truss”
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Simple Truss
To Design members and connections of a truss, necessary to determine forces developed in each member
Assumptions: All loadings are applied at the joints Members are joined together by smooth pins
Assumptions satisfactory for bolted or welded joints
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Simple Truss
Each truss member acts as a 2-force member Force directed along axis of member
Tension – pull, elongation
Compression – push, shorten
Several analytical approaches to solving
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Method of Joints
If truss is in equilibrium, each joint must also be in equilibrium
Approach: Sketch Free Body Diagram of Entire Truss Solve for Reactions Sketch Free Body Diagrams of Each Joint
2 unknown limit per FBD∑ Fx =0 ∑ Fy =0 ∑ Mo =0
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Example Problem
Given:
F = 500 N
θ = 45º
Find:
Force in each member
θ
2 m
B
CA2 m
F
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Example Problem Solution
Given:F = 500 Nθ = 45º
Find:Force in each member
Solution:1-FBD2-Support Reactions
45º
2 m
B
Ax
2 m
500 N
AyCy
0 yF
0 AM
0 xF
θ
2 m
B
CA2 m
F
0500 xA NorAx 500500
025002 yC NCy 500
0500 yA NorAy 500500
45º
2 m
B
500 N
2 m
500 N
500 N 500 N
A C
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Example Problem Solution
Given:F = 500 Nθ = 45º
Find:Force in each member
Solution:1-FBD2-Support Reactions3-Joint FBDs
500 N
500 N
AC
AB
45º
2 m
B
500 N
2 m
500 N
500 N 500 N
A C
Joint A Joint B
500 N
BCAB
45º
Joint C
500 N
BC
AC45º
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Example Problem Solution
Given:F = 500 Nθ = 45º
Find:Force in each member
Solution:1-FBD2-Support Reactions3-Joint FBDs
0 yF
0 xF
500 N
500 N
AC
AB
Joint A500 N
BCAB
500 N
Joint B
45º
0 xF
B
A C
500 T
500 T
707 C
Results shown in a force diagram
0500 ACTNAC 500
0500 ABTNAB 500
045sin500 BCCNBC 707
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Zero Force Members
Zero Force Members support NO loading Used for:
Stability Changing Applied Loads
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Zero Force Members
If only 2 members form a truss joint AND no external load or support reaction is applied to the joint, then the members must be Zero Force Members
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Zero Force Members
If 3 members form a truss joint for which 2 members are collinear, the 3rd member is a Zero Force Member, provided no external force or support reaction is applied to the joint.
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