Transcript EGR280_Mechanics_4

EGR 280
Mechanics
4 – Analysis of Structures
Trusses
ANALYSIS OF STRUCTURES
• No new theory!
• Only new names and techniques.
TRUSS
Graphics and problem statements © 2004 R.C. Hibbeler.
Published by Pearson Education, Inc., Upper Saddle River, NJ.
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Major engineering structure class
Composed entirely of straight, two-force members pinned at their endpoints
Loading takes place only at the joints, never between
Simple trusses are composed of basic triangular shapes
Analysis of trusses by the Method of Joints, used to find the force in each and
every member of the truss.
Example: Determine the force in each member of the truss shown below:
Graphics and problem statements © 2004
R.C. Hibbeler. Published by Pearson Education, Inc.,
Upper Saddle River, NJ.
Procedure:
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Draw a FBD of the entire truss and determine the support reactions
Draw a FBD of each joint and write equations for the unknown member forces.
Solve the joint equations, report if each member is in tension or compression
Step 1: Determine the reaction forces on the entire truss:
400 N
B
∑Fx = Cx + 600 N = 0
∑Fy = Ay + Cy – 400 N = 0
∑MC = (400 N)(3 m) – Ay (6 m)
+ (600 N)(4 m) = 0
Cx = 600 N ←
Cy = 200 N ↓
Ay = 600 N ↑
A
Cy
C
Cx
D
Ay
600 N
Step 2: Draw a FBD of each joint, assume all members in tension, write and
solve the joint equilibrium equations
FAB
∑Fx = FAD + (3/5)FAB = 0
∑Fy = 600 N + (4/5)FAB = 0
A
FAD
600 N
400 N
B
FBC
FAB
∑Fx = FBC + (3/5)FBD - (3/5)FAB = 0
∑Fy = -400 N - (4/5)FAB - (4/5)FBD = 0
FBD
200 N
FBC
C
∑Fx = -FBC – 600 N = 0
∑Fy = -200 N - FCD = 0
600 N
FCD
FBD
FAD
FCD
D
600 N
∑Fx = -FAD - (3/5)FBD + 600 N = 0
∑Fy = FCD + (4/5)FBD = 0
Solution:
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FAB = 750 N (C)
FAD = 450 N (T)
FBC = 600 N (C)
FBD = 250 N (T)
FCD = 200 N (C)
Graphics and problem statements © 2004
R.C. Hibbeler. Published by Pearson Education, Inc.,
Upper Saddle River, NJ.
Analysis of trusses by the Method of Sections, used to find the force in only a
few members of the truss.
Example: Determine the forces in members GE, GC and BC of the truss
shown
Graphics and problem statements © 2004
R.C. Hibbeler. Published by Pearson Education, Inc.,
Upper Saddle River, NJ.
Procedure:
• After finding the overall reactions, “cut”, or section, the truss through the
members where the forces are to be found
• Draw the FBD of that part of the truss which has the fewest unknowns
• Write equilibrium equations to solve for the unknown forces
EXERCISE: Find the reactions Ax and Ay
G
FGE
FCG
A
FBC
400 N
B
300 N
∑Fx = FGE + (4/5)FCG + FBC – 400 N = 0
∑Fy = 300 N – (3/5)FCG = 0
∑MG = FBC(3 m) – (400 N)(3 m) – (300 N)(4 m) = 0
FGE = 800 N (C)
FGC = 500 N (T)
FBC = 800 N (T)