ME221 Lecture #16 1
ME 221 Statics
Lecture #16
Sections 6.6 – 6.7Final Exam Review
ME221 Lecture #16 2
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 3
TrussesComposed 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.
ME221 Lecture #16 4
Analysis of Trusses Using the Method of Joints
Ay
Ax
PAx
PAY
PBy
PBx
PCy
PCx
Cy
A
B
C
We need to solve for:
(1) - Internal forces
FAB, FAC, and FCA
(2) - Reactions
Ax, Ay and Cy
ME221 Lecture #16 5
Using Matrix Notation
100sin00
000cos10
000sin0sin
000cos0cos
01000sin
00101cos
Cy
Cx
By
Bx
Ay
Ax
P
P
P
P
P
P
y
y
x
BC
AC
AB
C
A
A
F
F
F
=
-1
Using manual calculations
Look for joints with 2 unknowns
ME221 Lecture #16 6
Example
1.2 m 1.2 m
6 kN
3 kN
E
BA
C D0.9
m
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6 kN
3 kN
E
BA
C
D441616
4 4
9
915
15
5
5
ME221 Lecture #16 8
1.8 m
12 kN 12 kN
4 @ 2.4 m=9.6 m
B D F H J
A C E G I
Method of SectioningIf 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
ME221 Lecture #16 9
1.8 m
12 kN 12 kN
B D F H J
A C E G IFGE
FGF
FHF
1.8 m
12 kN 12 kN
B D F H J
A C E G IFEG
FFG
FEH
000 Anyptyx MFF
ME221 Lecture #16 10
Trusses: 3-D (Space Trusses)• Consider all the members as two force members
• Generally, use the method of joints
• Determinate structures– Equation for determining 3j = m + r
– Joints are ball & socket
ME221 Lecture #16 11
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
ME221 Lecture #16 12
Example
ME221 Lecture #16 13
Final Exam
Wednesday, June 30, 10:20am
25% of course grade
ME221 Lecture #16 14
Final Exam Topics
Chapter 2: Vectors and Force Systems– 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– 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– 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– 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– Equilibrium Equations– Supports– Free Body Diagrams– Two-Force Members– 3D Equilibrium
ME221 Lecture #16 19
Final Exam Topics
Chapter 7: Internal Forces in Structures– Internal Forces– Shear Forces– Bending Moments– Shear & Bending in Beams
ME221 Lecture #16 20
Final Exam Topics
Chapter 6: Analysis of Structures– Planar trusses– Method of joints– Method of sections
ME221 Lecture #16 21
Final Exam Format
4 to 5 Problems
At least one each:
Internal Forces – Chapter 7
Structures – Chapter 6
Others from previous material
ME221 Lecture #16 22
Other Topics
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