ME 221 Statics
Lecture #16
Sections 6.6 – 6.7
Final Exam Review
ME221
Lecture #16
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Homework #6
• Chapter 7 problems:
– 6, 19 & 26
• Chapter 6 problems
– 3&6
– Due Today
• MatLab Group Problems
– 7.19, 7.26 & 6.15
– Due Today
ME221
Lecture #16
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Trusses
Composed of slender straight pieces connected
together by frictionless pins where all the loads (no
moments) are applied.
Each member will act as a two-force member
(either in tension or compression).
All the forces acting on a truss member are axial.
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Lecture #16
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Analysis of Trusses Using the Method of Joints
PBy
PBx
B
We need to solve
for:
(1) - Internal forces
FAB, FAC, and FCA
(2) - Reactions
Ax, Ay and Cy
PAx
Ax
PAY
a
A
Ay
ME221
Lecture #16
PCy
b
PCx
C
C
y
4
Using Matrix Notation
1
0
1
 FAB   cos a
 F   sin a
0
0
0
AC

 
cos b 0
 FBC   cos a 0

 =   sin a 0  sin b 0
A
 x  
 1  cos b 0
 Ay   0

  0
0
sin
b
0
C

 y 
Using manual calculations
Look for joints with 2 unknowns
ME221
Lecture #16
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0 0

1 0
0 0

0 0
0 0

0 1
 PAx 
 P 
 Ay 
  PBx 



P
 By 
  PCx 


 PCy 
5
Example
6 kN
A
B
3 kN
0.9 m
C
D
E
1.2 m
ME221
1.2 m
Lecture #16
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6 kN
A
4
B
4
9 5
15
3 kN
C
16
15
16
9
5
4
4
E
D
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Lecture #16
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Method of Sectioning
If the question is to find internal forces in selected
members of the truss, then one can alternatively
use the method of sectioning.
Example: Determine the force in members FG and FH
12 kN
A
C
12 kN
E
G
I
1.8 m
B
D
F
H
J
4 @ 2.4 m=9.6 m
ME221
Lecture #16
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12 kN
A
C
12 kN
E
G
I
FGE
1.8 m
FGF
B
D
FHF F
12 kN
A
C
H
J
12 kN
E
G
FEG
I
FFG
B
D
F
x
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0
F
y
1.8 m
F
FEH
0
M
Lecture #16
H
Anypt
J
0
9
Trusses: 3-D (Space Trusses)
• Consider all the members as two force members
– Joints are ball & socket
• Generally, use the method of joints
• Determinate structures
– Equation for determining 3j = m + r
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Lecture #16
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3-D Truss Methodology
•
•
•
•
•
Determine unit vectors based on structure geometry
Solve for reaction forces with entire structure
Draw FBD of joint
Sum forces at joint to determine member forces
Solve joint-by-joint or write out as a system of
equations
– the latter method may also include reaction forces
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Lecture #16
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Example
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Final Exam
Wednesday, June 30, 10:20am
25% of course grade
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Lecture #16
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Final Exam Topics
Chapter 2: Vectors and Force Systems
–
–
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–
–
–
–
ME221
Scalars & vectors
Laws of sine & cosine
Resolution of a vector into components
3D coordinates & unit base vectors
Directional cosines
Scalar products of two vectors
2D & 3D equilibrium problems
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Final Exam Topics
Chapter 3: Rigid Bodies
–
–
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Calculating moments
Cross products
Moment of force about an axis
Moment of a couple
Equivalent force systems
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Final Exam Topics
Chapter 4: Distributed Forces
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Center of mass
Centroids of areas & volumes
Centroids of composite bodies
Distributed loads on beams
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Final Exam Topics
Chapter 9: Moments of Inertia
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ME221
Second Moment of Area; Ixx & Iyy
Polar Moments; J0z
Parallel Axis Theorem
Composite Areas
Principal Second Moments; Ixy
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Final Exam Topics
Chapter 5: Equilibrium of Rigid Bodies
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Equilibrium Equations
Supports
Free Body Diagrams
Two-Force Members
3D Equilibrium
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Final Exam Topics
Chapter 7: Internal Forces in Structures
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Internal Forces
Shear Forces
Bending Moments
Shear & Bending in Beams
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Final Exam Topics
Chapter 6: Analysis of Structures
– Planar trusses
– Method of joints
– Method of sections
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Final Exam Format
4 to 5 Problems
At least one each:
Internal Forces – Chapter 7
Structures – Chapter 6
Others from previous material
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Other Topics
Check Angel to make sure all scores have
been properly entered
Pick up all old homework & quizzes
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Lecture #16
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