Kosky, Balmer, Keat and Wise: Exploring Engineering, Fourth Edition
= 360,000 lb
8-2. For the given structure, do your best to identify all of its members as beams,
compression members, or tension members.
10. kN
A
C
B
D
E
F
G
HJ
5.0 kN5.0 kN
cable cable
Need: Identify member types
Know: Topology of the structure; the locations of the forces; cables are present
Kosky, Balmer, Keat and Wise: Exploring Engineering, Fourth Edition
For each of the trusses shown in Exercises 3–7, determine the forces on all members
by the method of joints. Use a spreadsheet to solve the equations.
8-3.
7.00 ft
5.00 ft
A C
7.00 ft
1000. lbf
B
Need: Forces on all members of the truss
7
Kosky, Balmer, Keat and Wise: Exploring Engineering, Fourth Edition
Counts unknowns and equations:
6 unknowns and 6 equations (2 per FBD); therefore statically determinate
Write the equilibrium equations:
0
x
F
F
0
y
Pin B:
0
x
F
0)5.35cos()5.35cos( BCAB FF
0
y
F
01000)5.35sin()5.35sin( BCAB FF
Pin C:
0
x
F
0)5.35cos( BCAC FF
0
y
F
0)5.35sin( YBC CF
Tabulate coefficients and right-hand side constants:
EQ
FAB
FAC
FBC
AX
AY
CY
RHs
1
0.814
1
0
1
0
0
0
2
0.581
0
0
0
1
0
0
3
-0.814
0
0.814
0
0
0
0
4
-0.581
0
-0.581
0
0
0
1000
5
0
-1
-0.814
0
0
0
0
6
0
0
0.581
0
0
1
0
Solve the equations using a spreadsheet:
Kosky, Balmer, Keat and Wise: Exploring Engineering, Fourth Edition
Write the equilibrium equations:
0
y
0
y
0
y
0
y
Tabulate coefficients and right-hand side constants:
EQ
FAB
FBC
FCD
FDE
FAE
FCE
FBE
AX
AY
DY
RHS
1
.448
0
0
0
1
0
0
1
0
0
0
2
.894
0
0
0
0
0
0
0
1
0
0
3
-.448
1
0
0
0
0
.448
0
0
0
0
4
-.894
0
0
0
0
0
-.894
0
0
0
0
5
0
-1
.448
0
0
-.448
0
0
0
0
0
6
0
0
-.894
0
0
-.894
0
0
0
0
0
7
0
0
-.448
-1
0
0
0
0
0
0
0
8
0
0
.894
0
0
0
0
0
0
1
0
9
0
0
0
1
-1
.448
-.448
0
0
0
0
10
0
0
0
0
0
.894
.894
0
0
0
5.00
Solve the equations using a spreadsheet:
Kosky, Balmer, Keat and Wise: Exploring Engineering, Fourth Edition
Write the equilibrium equations:
0
y
0
y
0
y
0
y
0
y
Tabulate coefficients and right-hand side constants:
EQ
FAB
FBC
FCD
FDE
FEF
FAF
FBF
FCF
FDF
AX
AY
EY
RHS
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
.707
0
0
0
0
0
0
4
-1
0
0
0
0
0
-.707
0
0
0
0
0
0
5
0
-1
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
-1
0
0
0
0
0
7
0
0
-1
0
0
0
0
0
-.707
0
0
0
0
8
0
0
0
-1
0
0
0
0
-.707
0
0
0
0
9
0
0
0
0
-1
0
0
0
0
0
0
0
0
10
0
0
0
1
0
0
0
0
0
0
0
1
0
11
0
0
0
0
1
-1
-.707
0
.707
0
0
0
0
12
0
0
0
0
0
0
.707
1
.707
0
0
0
8.00
Kosky, Balmer, Keat and Wise: Exploring Engineering, Fourth Edition
Solve the equations using a spreadsheet:
Solution of the Equations for Exercise 8.6
0 0 0 0 0 1 0 0 0 1 0 0 0
1 0 0 0 0 0 0 0 0 0 1 0 0
0 1 0 0 0 0 0.707 0 0 0 0 0 0
-1 0 0 0 0 0 -0.707 0 0 0 0 0 0
0-1 1 0 0 0 0 0 0 0 0 0 0
[A] = 0 0 0 0 0 0 0 1 0 0 0 0 {b} = 0
0 0 -1 0 0 0 0 0 -0.707 0 0 0 0
0 0 0 -1 0 0 0 0 -0.707 0 0 0 0
0 0 0 0 -1 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 1 0
0 0 0 0 1 -1 -0.707 0 0.707 0 0 0 0
0 0 0 0 0 0 0.707 1 0.707 0 0 0 8
0 0 -0.5 -1 -0.5 0.5 -0.5 0 0 0 0 -0.5 -4
= FAB
0 0 0.5 0 -0.5 0.5 -0.5 0 0 0 0 -0.5 -4
= FBC
0 0 0.5 0 0.5 0.5 -0.5 0 0 0 0 -0.5 -4
= FCD
0 0 0.5 0 0.5 0.5 0.5 -1 0 0 0 -0.5 -4
= FDE
0 0 0 0 0 0 0 0 -1 0 0 0 0
= FEF
inv[A] = 0 0 -1 0-1 0-1 0-1 0-1 0 {x} = 0
= FAF
0 0 0.7072 0 0.7072 -0.707 0.7072 0 0 0 0 0.7072 5.66
= FBF
0 0 0 0 0 1 0 0 0 0 0 0 0
= FCF
0 0 -0.707 0 -0.707 -0.707 -0.7072 0 0 0 0 0.7072 5.66
= FDF
1 0 1 0 1 0 1 0 1 0 1 0 0
= AX
0 1 0.5 1 0.5 -0.5 0.5 0 0 0 0 0.5 4
= AY
0 0 -0.5 0 -0.5 -0.5 -0.5 1 0 1 0 0.5 4
= EY
Kosky, Balmer, Keat and Wise: Exploring Engineering, Fourth Edition
16 unknowns and 16 equations (2 per FBD); therefore statically
determinate
Write the equilibrium equations:
0
y
0
y
0
y
0
y
0
y
0
y
0
y
Tabulate coefficients and right-hand side constants:
Kosky, Balmer, Keat and Wise: Exploring Engineering, Fourth Edition
EQ
FAB
FBC
FCD
FDE
FEF
FGF
FGH
FAH
FBH
FBG
FCG
FDG
FDF
AX
AY
EY
RHS
1
.707
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
.707
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
–
.707
.707
0
0
0
0
0
0
0
.707
0
0
0
0
0
0
0
4
–
.707
.707
0
0
0
0
0
0
-1
–
.707
0
0
0
0
0
0
0
5
0
–
.707
.707
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
–
.707
–
.707
0
0
0
0
0
0
0
-1
0
0
0
0
0
0
7
0
0
–
.707
.707
0
0
0
0
0
0
0
–
.707
0
0
0
0
0
8
0
0
.707
–
.707
0
0
0
0
0
0
0
–
.707
-1
0
0
0
0
9
0
0
0
–
.707
-1
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
.707
0
0
0
0
0
0
0
0
0
0
0
1
0
11
0
0
0
0
1
-1
0
0
0
0
0
0
0
0
0
0
0
12
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
800
13
0
0
0
0
0
1
-1
0
0
–
.707
0
.707
0
0
0
0
0
14
0
0
0
0
0
0
0
0
0
.707
1
.707
0
0
0
0
1600
15
0
0
0
0
0
0
1
-1
0
0
0
0
0
0
0
0
0
16
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
800
Solve the equations using a spreadsheet:
