CC601: STRUCTURAL ANALYSIS 2
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CHAPTER 1
ANALYSIS OF STATICALLY DETERMINATE STRUCTURAL FRAMEWORK-2D
(USING METHOD OF JOINTS & METHOD OF SECTIONS)
1. Objective:
a. To calculate internal force for every members of trusses
b. To state of symbols and magnitude for every members.
2. Definition Framework:
 If two or more members are added to the truss to form another triangle with one more
joints has been added. The truss will remain perfects or stable if this relationship is
satisfied.
 All trusses are determinate with respect to the external reaction components.
 Example of trusses/framework:
3. Types of analysis structural framework:
i.
Method of Joint
ii.
Method of section
iii.
Graph Method (Maxwell’s Diagram)
4. Basics formula to determine types of structures:
No. of redundancy = Degree of Indeterminate or Degree of Freedom
D= DOF = DOI = m + r -2j
Where:
m = no. of member
r = no. of reactions
j = no. of joint
CC601: STRUCTURAL ANALYSIS 2
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i.
DOI = 0
stable
m+r=2j(statically determinate)
ii.
DOI ≠ 0
Stable
m+r>2 (indeterminate)
Unstable
m+r<2j
iii.
if DOI > 0 or DOI≠0
DOI = m + r -2j
External, E = r-3
Internal, I = DOI- (r-3)
5. Types of forces:
1. Tension (tegangan)
2. Compression ( Mampatan)
Symbols Magnitude
(+)
T
(-)
C@M
6. Zero bar case
i.
Case 1
: 2 members parallel, 1 is perpendicular AND
WITHOUT External
Forces, (Perpendicular members = 0)
0
ii.
Case 2
: 2 members connected, WITHOUT external forces, both members=0
0
0
7. Steps to solve problems
i.
Draw free body diagram (FBD)
ii.
Find m, r, and j to determine DOI
iii.
State the determinancy criteria – statically determinate or indeterminate
framework
iv.
Determine the reactions.
v.
Solve one by one of the members.
CC601: STRUCTURAL ANALYSIS 2
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8. Example 1: Determine the Redundancy of Structure and find the reaction.
Example 1(A)
20kN
A
B
C
4m
D
E
40kN
5m
F
G
70kN
4m
3m
Example 1 (B)
A
B
60N
5m
C
D
30N
E
4m
6m
CC601: STRUCTURAL ANALYSIS 2
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Example 2: Determine the Degree of Indeterminate framework and find the reaction of this
truss.
Example 2A
20kN
10kN
3m
A
3m
B
C
2m
D
E
1.5m
3m
1.5m
Example 2B
2.5kN
1.5kN
2.5kN
B
C
A
3m
D
4m
E
4m
F
1.5kN
Example 2C
20kN
40kN
A
B
1.25m
C
D
3m
3m
CC601: STRUCTURAL ANALYSIS 2
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METHOD OF JOINTS
Example 3:
From example 1, 2, and 3 as shown in figure below, analysis and determine ALL the
INTERNAL FORCES for the trusses/ framework:
Example 1
20kN
A
B
C
4m
D
E
40kN
F
70kN
5m
Example 2
2.5kN
4m
3m
1.5kN
2.5kN
B
C
A
G
3m
D
4m
E
4m
F
1.5kN
Example 3
20kN
20
A
B
40kN
C
D
4m
3m
2m
CC601: STRUCTURAL ANALYSIS 2
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METHOD OF SECTIONS
1
Method of section is effective method if to determine a certain forces in members.
2
Simple guidelines to solve the problem using this method:
i.
Pass a section through a maximum of three members of the truss [Select cutting
edge based on question]
ii.
Divide the truss into two completely separate parts(section 1 or section 2)
iii.
Takes ONLY one part of the trusses and using equation of equilibrium to solve the
member forces
Example 1:
Using method of section, Determine Internal Forces for members BC, EC, and EF.
20kN
A
B
C
4m
D
E
40kN
5m
F
G
70kN
4m
Solution
i.
Draw FBD and Find Reaction
ii.
Select Cutting edge
Section 1
20kN
A
B
3m
Section 2
C
4m
D
E
40kN
5m
F
G
70kN
4m
3m
CC601: STRUCTURAL ANALYSIS 2
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iii.
Choose ONLY one Section to Solve the problem [section 1]
20kN
A
B
FBC
C
FEC
4m
FEF
D
E
40kN
5m
iv.
F
G
70kN
4m
3m
using equation of equilibrium,
1) + ∑M=0=----------------------------------------****Select at the joint that have a many cutting members
2) +
∑Fv=0=-----------------------------------------
3) +
∑Fx=0=-----------------------------------------
Homework: Section 2
A
B
FCB
FCB
C
4m
FCE
FEF
D
E
40kN
5m
F
G
70kN
4m
3m
CC601: STRUCTURAL ANALYSIS 2
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Example 2
Using method of section, Determine Internal Forces for members BA, BE, and EF.
2.5kN
A
1.5kN
B
2.5kN
C
3m
D
4m
E
4m
1.5kN
Assignment 1
)
F