TKWNT+5
=v
#1
:n

:s
b
:c
Bedford-Fowler, Ex 3.5
#2
:n
W
:v
981
:s
o
:u
N
:d
N
:c
Weight magnitude
#3
:n
m
:v
100
:s
i
:u
kg
:d
kg
:c
Hanging mass
#4
:n
g
:v
9.810000000000001
:s
i
:u
m/s^2
:d
m/s^2
:c
Gravitational constant
#5
:n
Wy
:v
-981
:s
o
:u
N
:d
N
:c
Component value
#6
:n
T_AD
:v
168.2401120248012
:s
o
:u
N
:d
N
:c
Cable force AD (tension)
#7
:n
M_BC
:v
0
:s
o
:u
N-m
:d
N-m
:c
Equilibrium
#9
:n
x_A
:v
0
:s
i
:u
m
:d
m
:c
Point coordinate data
#10
:n
y_A
:v
-4
:s
i
:u
m
:d
m
:c
Point coordinate data
#11
:n
z_A
:v
0
:s
i
:u
m
:d
m
:c
Point coordinate data
#12
:n
x_B
:v
4
:s
i
:u
m
:d
m
:c
Point coordinate data
#13
:n
y_B
:v
0
:s
i
:u
m
:d
m
:c
Point coordinate data
#14
:n
z_B
:v
2
:s
i
:u
m
:d
m
:c
Point coordinate data
#15
:n
x_C
:v
-2
:s
i
:u
m
:d
m
:c
Point coordinate data
#16
:n
y_C
:v
0
:s
i
:u
m
:d
m
:c
Point coordinate data
#17
:n
z_C
:v
-2
:s
i
:u
m
:d
m
:c
Point coordinate data
#18
:n
x_D
:v
-3
:s
i
:u
m
:d
m
:c
Point coordinate data
#19
:n
y_D
:v
0
:s
i
:u
m
:d
m
:c
Point coordinate data
#20
:n
z_D
:v
3
:s
i
:u
m
:d
m
:c
Point coordinate data
#22
:n

:s
b
:c
Moment arm
#23
:n
r_BAx
:v
-4
:s
o
:u
m
:d
m
:c
length increment
#24
:n
r_BAy
:v
-4
:s
o
:u
m
:d
m
:c
length increment
#25
:n
r_BAz
:v
-2
:s
o
:u
m
:d
m
:c
length increment
#27
:n

:s
b
:c
Line unit vectors
#28
:n
e_ADx
:v
-.5144957554275265
:s
o
:c
direction cosine w.r.t. x
#29
:n
e_ADy
:v
.6859943405700353
:s
o
:c
direction cosine w.r.t. y
#30
:n
e_ADz
:v
.5144957554275265
:s
o
:c
direction cosine w.r.t. z
#32
:n
e_BCx
:v
-.8320502943378437
:s
o
:c
direction cosine w.r.t. x
#33
:n
e_BCy
:v
0
:s
o
:c
direction cosine w.r.t. y
#34
:n
e_BCz
:v
-.5547001962252292
:s
o
:c
direction cosine w.r.t. z
#36
:n
temp_x
:v
-2077.411764705882
:s
o
:u
N-m
:d
N-m
:c
temporary component
#37
:n
temp_y
:v
519.3529411764706
:s
o
:u
N-m
:d
N-m
:c
temporary component
#38
:n
temp_z
:v
3116.117647058823
:s
o
:u
N-m
:d
N-m
:c
temporary component
#40
:n
r_ADx
:v
-3
:s
o
:u
m
:d
m
:c
length increment
#41
:n
r_ADy
:v
4
:s
o
:u
m
:d
m
:c
length increment
#42
:n
r_ADz
:v
3
:s
o
:u
m
:d
m
:c
length increment
#43
:n

:s
b
#44
:n
r_BCx
:v
-6
:s
o
:u
m
:d
m
:c
length increment
#45
:n
r_BCy
:v
0
:s
o
:u
m
:d
m
:c
length increment
#46
:n
r_BCz
:v
-4
:s
o
:u
m
:d
m
:c
length increment
#48
:n
L_AD
:v
5.830951894845301
:s
o
:u
m
:d
m
:c
Length of cable AD
#49
:n
L_BA
:v
6
:s
o
:u
m
:d
m
:c
Length of cable BA
#50
:n
L_BC
:v
7.211102550927978
:s
o
:u
m
:d
m
:c
Length of cable BC
=u
#1
:c
Unit Master Sheet by R.L. Norton,
#2
:c
 appended by J.E. Akin
#4
:c
length
#5
:f
cm
:m
10
:t
mm
#6
:f
m
:m
100
:t
cm
#7
:f
mm
:m
1000
:t
um
#8
:f
in
:m
2.5399999999999
:t
cm
#9
:f
ft
:m
12
:t
in
#10
:f
mile
:m
5280
:t
ft
#11
:f
in
:m
1000000
:t
uin
#12
:f
1/mm
:m
25.4
:t
1/in
#13
:f
1/cm
:m
2.54
:t
1/in
#14
:f
1/m
:m
.254
:t
1/in
#15
:c
area
#16
:f
in^2
:m
645.1626
:t
mm^2
#17
:f
m^2
:m
1000000
:t
mm^2
#18
:f
cm^2
:m
100
:t
mm^2
#19
:f
ft^2
:m
144
:t
in^2
#20
:c
volume
#21
:f
in^3
:m
16387.1623
:t
mm^3
#22
:f
ft^3
:m
1728
:t
in^3
#23
:f
m^3
:m
1E9
:t
mm^3
#24
:f
cm^3
:m
1000
:t
mm^3
#25
:f
cm^3
:t
cc
#26
:c
force
#27
:f
lb
:m
4.44822
:t
N
#28
:f
N
:m
100000
:t
dyne
#29
:f
ton
:m
2000
:t
lb
#30
:f
kips
:m
1000
:t
lb
#31
:f
lb
:t
lbf
#32
:f
lb
:t
lbm
#33
:c
moments and energy
#34
:f
in-lb
:m
.1138
:t
N-m
#35
:f
ft-lb
:m
12
:t
in-lb
#36
:f
N-m
:m
100
:t
N-cm
#37
:f
N-m
:m
1000
:t
N-mm
#38
:f
N-m
:m
8.850744000000001
:t
in-lb
#39
:f
N-m
:m
.7375620000000001
:t
ft-lb
#40
:f
lb-in
:t
in-lb
#41
:f
N-m
:t
m-N
#42
:f
N-cm
:t
cm-N
#43
:f
N-m
:t
joule
#44
:f
joules
:t
joule
#45
:f
joule
:t
J
#46
:c
pressure and stress
#47
:f
psi
:m
6894.757
:t
Pa
#48
:f
MPa
:m
1000000
:t
Pa
#49
:f
MPa
:t
Mpa
#50
:f
GPa
:m
1000
:t
MPa
#51
:f
GPa
:t
Gpa
#52
:f
Pa
:t
pa
#53
:f
N/m^2
:t
Pa
#54
:f
N/mm^2
:t
MPa
#55
:f
N/mm^2
:m
1000000
:t
N/m^2
#56
:f
N/cm^2
:m
10000
:t
N/m^2
#57
:f
kpsi
:m
1000
:t
psi
#58
:f
psi
:m
144
:t
psf
#59
:f
kpsi
:t
ksi
#60
:f
psig
:t
psi
:a
14.7
#61
:c
acceleration
#62
:f
in/sec^2
:m
2.5399999999999
:t
cm/sec^2
#63
:f
m/sec^2
:m
100
:t
cm/sec^2
#64
:f
m/sec^2
:m
1000
:t
mm/sec^2
#65
:f
ft/sec^2
:m
12
:t
in/sec^2
#66
:f
ft/s^2
:t
ft/sec^2
#67
:f
G
:m
32.17
:t
ft/sec^2
#68
:c
velocity
#69
:f
in/sec
:m
2.5399999999999
:t
cm/sec
#70
:f
m/sec
:m
100
:t
cm/sec
#71
:f
m/sec
:m
1000
:t
mm/sec
#72
:f
m/s^2
:t
m/sec^2
#73
:f
ft/sec
:m
12
:t
in/sec
#74
:f
rad/sec
:m
9.549296584
:t
rpm
#75
:f
mph
:m
1.466666666666667
:t
ft/sec
#76
:c
mass
#77
:f
blob
:m
386
:t
lb
#78
:f
slug
:m
32.17
:t
lb
#79
:f
kg
:m
2.204623
:t
lb
#80
:f
kg
:m
1000
:t
g
#81
:f
kg
:m
9.806649999999999
:t
N
#82
:c
mass mom of inertia
#83
:f
lb-in-sec^2
:m
.1138
:t
N-m-sec^2
#84
:f
N-m-sec^2
:t
kg-m^2
#85
:f
lb-in-sec^2
:t
lb-in-s^2
#86
:f
blob-in^2
:t
lb-in-s^2
#87
:f
N-m-sec^2
:t
N-m-s^2
#88
:c
area moment of inertia
#89
:f
in^4
:m
416231.4256
:t
mm^4
#90
:f
m^4
:m
1E12
:t
mm^4
#91
:f
m^4
:m
1E8
:t
cm^4
#92
:f
ft^4
:m
20736
:t
in^4
#93
:f
in^4
:m
.0000004162314256
:t
m^4
#94
:c
density
#95
:f
lb/in^3
:m
27.6805
:t
g/cc
#96
:f
g/cc
:m
.001
:t
g/mm^3
#97
:f
lb/ft^3
:m
1728
:t
lb/in^3
#98
:f
kg/m^3
:m
.000001
:t
g/mm^3
#99
:f
lb/in^3
:m
.002590673575129534
:t
blob/in^3
#100
:f
blob/in^3
:m
.08333333333333333
:t
slug/in^3
#101
:f
slug/ft^3
:m
1728
:t
slug/in^3
#102
:f
kg/mm^3
:m
1000
:t
g/mm^3
#103
:f
SG
:t
g/cc
#104
:c
spring rate
#105
:f
lb/in
:m
175.126
:t
N/m
#106
:f
N/mm
:m
1000
:t
N/m
#107
:f
lb/ft
:m
.08333333333333333
:t
lb/in
#108
:c
angles
#109
:f
radians
:m
57.29577951308232
:t
degrees
:c
 
#110
:f
rad
:m
57.2957795129
:t
deg
#111
:f
rev
:m
360
:t
deg
#112
:f
rad
:t
radian
#113
:c
temperature
#114
:f
C
:m
1.8
:t
F
:a
32
#115
:f
F
:t
R
:a
459.69
#116
:f
C
:t
K
:a
273.16
#117
:c
power
#118
:f
HP
:m
550
:t
ft-lb/sec
#119
:f
ft-lb/sec
:m
60
:t
ft-lb/min
#120
:f
ft-lb/sec
:m
12
:t
in-lb/sec
#121
:f
HP
:m
745.699
:t
watts
#122
:f
kw
:m
1000
:t
watts
#123
:f
HP
:t
hp
#124
:f
N-m/sec
:m
8.850756136188998
:t
in-lb/sec
#125
:f
N-m/sec
:t
watts
#126
:f
watt
:t
watts
#127
:c
flow
#128
:f
cfm
:m
1728
:t
cim
#129
:c
percent
#130
:f
dec%
:m
100
:t
%
#132
:c
fracture mechanics
#133
:f
MPa-m^.5
:m
.909
:t
ksi-in^.5
:c
stress intensity
#134
:f
MPa-m^.5
:m
1000000
:t
Pa-m^.5
:c
stress intensity
#135
:f
ksi-in^.5
:m
1000
:t
psi-in^.5
:c
stress intensity
#136
:f
kpsi-in^.5
:m
1000
:t
psi-in^.5
:c
stress intensity
#138
:c
frequency
#139
:f
1/sec
:m
60
:t
1/min
#140
:f
Hz
:t
1/sec
#141
:f
Hz
:t
hz
#142
:c
time
#143
:f
min
:m
60
:t
sec
#144
:f
hr
:m
60
:t
min
#145
:f
day
:m
24
:t
hr
#146
:f
week
:m
7
:t
day
#147
:f
year
:m
52
:t
week
#148
:f
year
:m
12
:t
month
#149
:c
viscosity
#150
:f
reyn
:t
lb-sec/in^2
:c
     absolute
#151
:f
reyn
:m
6894.696003767111
:t
Pa-s
#152
:f
reyn
:m
1000000
:t
ureyn
#153
:f
Pa-s
:m
1000
:t
mPa-s
#154
:f
cP
:t
mPa-s
#155
:c
   kinematic
#156
:f
m^2/sec
:m
10000
:t
cm^2/sec
#157
:f
cm^2/sec
:t
stoke
#158
:f
stoke
:m
100
:t
cS
#159
:f
m^2/sec
:m
1549.996853506387
:t
in^2/sec
#160
:c
stress intensity
#161
:f
psi-in^.5
:m
1098.843447385385
:t
Pa-m^.5
#162
:f
ksi-in^.5
:m
1000
:t
psi-in^.5
#163
:f
MPa-m^.5
:m
1000000
:t
Pa-m^.5
=l
=f
=r
#1
:r
; Ex 3.3 Equilibrium  Revisited
:s
C
#2
:r
; Assume all cables are in tension.  
:s
C
#4
:r
; Position vector from B to A
:s
C
#5
:r
r_BAx = x_A - x_B
#6
:r
r_BAy = y_A - y_B
#7
:r
r_BAz = z_A - z_B
#8
:r
L_BA = sqrt ( r_BAx^2 + r_BAy^2 + r_BAz^2)
#10
:r
; Position vector from B to C
:s
C
#11
:r
r_BCx = x_C - x_B
#12
:r
r_BCy = y_C - y_B
#13
:r
r_BCz = z_C - z_B
#14
:r
L_BC = sqrt ( r_BCx^2 + r_BCy^2 + r_BCz^2)
#16
:r
; Position vector from A to D
:s
C
#17
:r
r_ADx = x_D - x_A
#18
:r
r_ADy = y_D - y_A
#19
:r
r_ADz = z_D - z_A
#20
:r
L_AD = sqrt ( r_ADx^2 + r_ADy^2 + r_ADz^2)
#22
:r
; Unit vectors (Direction cosines)
:s
C
#23
:r
e_BCx = r_BCx / L_BC   ; Line BC
#24
:r
e_BCy = r_BCy / L_BC
#25
:r
e_BCz = r_BCz / L_BC
#27
:r
e_ADx = r_ADx / L_AD    ; Tension T_AD
#28
:r
e_ADy = r_ADy / L_AD
#29
:r
e_ADz = r_ADz / L_AD
#31
:r
; Moments of forces not hitting line BC, taken at point B 
:s
C
#32
:r
temp_x = r_BAy * (T_AD * e_ADz +   0) - r_BAz * (T_AD * e_ADy +Wy) 
#33
:r
temp_y = r_BAz * (T_AD * e_ADx +   0) - r_BAx * (T_AD * e_ADz +    0) 
#34
:r
temp_z = r_BAx * (T_AD * e_ADy +Wy) - r_BAy * (T_AD * e_ADx +   0)  
#36
:r
; Now projected onto line BC (dot product)
:s
C
#37
:r
M_BC = temp_x * e_BCx + temp_y * e_BCy + temp_z * e_BCz
#39
:r
; Equilibrium
:s
C
#40
:r
M_BC = 0
#41
:r
Wy = -W
#42
:r
W = m * g
=p
=t
=n
=c
=g
#1
:c
.000001
:i
100
:t
1
:y
Yes
=d
:c
E
:f
0


:v
E
:g
0.000001
:i
1000
:t
100
:p
0.000001
:r
5.00
:e
0
:d
1
:s
0
:n
0
:a
0
=s
:r
0
:v
%Tv,f,43,5,0,1,0
%Or,f,43,1,0,1,0
%Xl,f,0,0,0,2,0,88,88,634,478,320,815,-1,-1,0,0,4,-1,0,0,2,-13,700,18,0,0,0,0,Times New Roman,4,10,21,31,98
%Xp,f,0,0,0,2,0,110,110,656,500,480,815,-1,-1,0,0,5,-1,0,0,2,-13,700,18,0,0,0,0,Times New Roman,3,13,25,99
%Xt,f,0,0,0,2,0,132,132,678,522,640,815,-1,-1,0,0,6,-1,0,0,2,-13,700,18,0,0,0,0,Times New Roman,2,15,100
%Xn,f,0,0,0,2,0,154,154,700,544,800,815,-1,-1,0,0,7,-1,0,0,2,-13,700,18,0,0,0,0,Times New Roman,2,15,100
%Xc,f,0,0,0,2,0,176,176,722,566,0,791,-1,-1,0,0,8,-1,0,0,2,-13,700,18,0,0,0,0,Times New Roman,3,15,22,99
%Xf,f,0,0,0,2,0,0,0,993,664,0,815,0,0,0,0,2,-1,0,0,2,-13,700,18,0,0,0,0,Times New Roman,4,16,26,38,98
%Xm,f,0,0,0,0,0,154,203,1147,867,160,791,0,0,0,0,9,-1,0,0,2,0,0,0,0,0,0,0,,0
%Xr,f,43,1,0,2,0,0,0,1213,461,-1,-1,0,0,0,0,1,-1,0,0,1,-13,700,18,0,0,0,0,Times New Roman,2,11,105
%Xv,f,43,5,0,2,0,0,461,1213,922,160,815,-4,-23,0,0,0,-1,0,0,2,-13,700,18,0,0,0,0,Times New Roman,6,6,13,20,28,35,86
%Xu,f,31,3,0,2,0,22,29,1015,693,160,815,-4,-23,2,0,3,-1,0,0,3,-13,700,18,0,0,0,0,Times New Roman,5,10,20,34,48,96
\G,0,960,1344,1,-1,-1
\G,0,1920,1344,1,-1,-1
\C,0,1920,0,0,3