ENGR 34
Chapter 6, Day 2
Method of Sections
a) Joints recap – 30x30
b) Method of sections
c) Special sections
Method of Joints Recap
• 2J=M+R
• 2x15 = 27 + 3
• Assume tension
Truss Example Problem 6-17
30X30 solution
Matrix setup and solution
ENGR 34 Statics
V. Bertsch
index
P Factor
B41 =
AB
BC
CD
DE
AF
BF
BH
CH
DH
DJ
EJ
FG
GH
HI
IJ
FK
GK
GL
GM
IM
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
1
0
0
0
-0.707
0.707
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-0.707 -0.707
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
1
0
0
0
0
-0.707
0.707
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-0.707 -0.707
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.707
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0.707
0
0
0
0
0
0
0
0
0
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
1
0
0
0
-0.707
0
0.707
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-0.707
-1
-0.707
0
0
0
0
0
0
0
-0.707
0
0.707
0
0
0
-1
1
0
0
0
0
0
0
0
0
0
0
0
0.707
1
0.707
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
1
0
0
0
0
-0.707
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-0.707
0
0
0
0
0
0
0
0
0
-0.707
0
0
0
0
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.707
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.707
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0.707
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-0.707
0.707
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.707
0.707
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
AB
1
-1
BC
2
-0.5
CD
3
-0.5
DE
4
0
AF
5
0
EJ
11
0
FG
12
-0.25
GH
13
0.25
HI
14
-0.25
IJ
15
0.25
BF
BH
6
7
0.354 -0.35
CH
8
0
DH
DJ
9
10
0.354 -0.35
INDEX(MMULT(MINVERSE($B$8:$AE$37),($AF$8:$AF$37)), B40, 1)
FK
GK
16
17
0.25 0.354
GL
18
0
0
0
GM
IM
19
20
-0.35 0.354
Method of Sections
•
•
•
•
Cut through 3 members for 2D RB FBD
Assume tension
3 equa – 3 unkn
Moment equations to isolate variables
Special Sections
• Cutting > 3 members is statically indeterminant
• Tricky cuts > 3 may yield partial information
• Look for force concurrency possibilities
Method of Sections
Key Concepts
• Cut only 3 members
• Assume tension
• Moment equations to isolate unknowns