TKWNT+5
=v
#1
:n

:s
b
:c
Bedford-Fowler 3rd Ed., Example 10.9
#2
:n

:s
b
:c
Data from P10.70, but all h unknown
#4
:n
T1
:v
1448.957236735067
:s
o
:u
N
:d
N
:c
left reaction force
#5
:n
T1_h
:v
1261.707835801449
:s
o
:u
N
:d
N
:c
left reaction force horizontal component (to left)
#6
:n
T1_v
:v
712.4397595334943
:s
o
:u
N
:d
N
:c
left reaction force vertical component (upwards)
#7
:n
b1
:v
500
:s
i
:u
mm
:d
mm
:c
horizontal distance from left to first weight
#8
:n
h1
:v
282.3315110351776
:s
o
:u
mm
:d
mm
#9
:n
W1
:v
588.6
:s
i
:u
N
:d
N
:c
first weight
#10
:n
b2
:v
700
:s
i
:u
mm
:d
mm
:c
horizontal distance from first to second weight
#11
:n
h2
:v
351.0382505937706
:s
o
:u
mm
:d
mm
#12
:n
W2
:v
294.3
:s
i
:u
N
:d
N
:c
second weight
#13
:n
bn
:v
300
:s
i
:u
mm
:d
mm
:c
horizontal distance from second to weight n
#14
:n
hn
:v
310.507415570884
:s
o
:u
mm
:d
mm
#15
:n
Wn
:v
294.3
:s
i
:u
N
:d
N
:c
third weight
#16
:n
br
:v
300
:s
i
:u
mm
:d
mm
:c
horizontal distance from weight n to right support
#17
:n
hr
:v
200
:s
i
:u
mm
:d
mm
#18
:n
span
:v
1800
:s
o
:u
mm
:d
mm
:c
horizontal span of total cable
#19
:n
Weight
:v
1177.2
:s
o
:u
N
:d
N
:c
total weight supported by the cable
#20
:n
Tr
:v
1344.584970926441
:s
o
:u
N
:d
N
:c
right reaction force
#21
:n
Tr_h
:v
1261.707835801449
:s
o
:u
N
:d
N
:c
right reaction force horizontal component (to right)
#22
:n
Tr_v
:v
464.7602404665058
:s
o
:u
N
:d
N
:c
right reaction force vertical component (upwards)
#24
:n
L
:v
1900
:s
i
:u
mm
:d
mm
:c
total cable length
#25
:n
L1
:v
574.204738854885
:s
o
:u
mm
:d
mm
:c
length of cable 1
#26
:n
L2
:v
703.3637864297336
:s
o
:u
mm
:d
mm
:c
length of cable 2
#27
:n
Ln
:v
302.725533425333
:s
o
:u
mm
:d
mm
:c
length of cable n 
#28
:n
Lr
:v
319.7059412900483
:s
o
:u
mm
:d
mm
:c
length of last cable 
#29
:n
Äh
:v
110.507415570884
:s
o
:u
mm
:d
mm
:c
change in height of last cable
#31
:n
Äh2
:v
68.70673955859292
:s
o
:u
mm
:d
mm
:c
change in height from first weight
#32
:n
T2
:v
1267.770858224817
:s
o
:u
N
:d
N
:c
second cable force
#33
:n
T2_h
:v
1261.707835801449
:s
o
:u
N
:d
N
:c
second cable force horizontal component (to right)
#34
:n
T2_v
:v
-123.8397595334943
:s
o
:u
N
:d
N
:c
second cable force vertical component (upward)
#36
:n
Äh3
:v
-40.53083502288655
:s
o
:u
mm
:d
mm
:c
change in height from second weight
#37
:n
Tn
:v
1273.170592066387
:s
o
:u
N
:d
N
:c
third (n) cable force
#38
:n
Tn_h
:v
1261.707835801449
:s
o
:u
N
:d
N
:c
third cable force horizontal component (to right)
#39
:n
Tn_v
:v
170.4602404665057
:s
o
:u
N
:d
N
:c
third cable force vertical component (upward)
=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
km
:m
1000
:t
m
#8
:f
mm
:m
1000
:t
um
#9
:f
in
:m
2.5399999999999
:t
cm
#10
:f
ft
:m
12
:t
in
#11
:f
mile
:m
5280
:t
ft
#12
:f
in
:m
1000000
:t
uin
#13
:f
1/mm
:m
25.4
:t
1/in
#14
:f
1/cm
:m
2.54
:t
1/in
#15
:f
1/m
:m
.254
:t
1/in
#16
:c
area
#17
:f
in^2
:m
645.1626
:t
mm^2
#18
:f
m^2
:m
1000000
:t
mm^2
#19
:f
cm^2
:m
100
:t
mm^2
#20
:f
ft^2
:m
144
:t
in^2
#21
:c
volume
#22
:f
in^3
:m
16387.1623
:t
mm^3
#23
:f
ft^3
:m
1728
:t
in^3
#24
:f
m^3
:m
1E9
:t
mm^3
#25
:f
cm^3
:m
1000
:t
mm^3
#26
:f
cm^3
:t
cc
#27
:c
force
#28
:f
lb
:m
4.44822
:t
N
#29
:f
N
:m
100000
:t
dyne
#30
:f
ton
:m
2000
:t
lb
#31
:f
kips
:m
1000
:t
lb
#32
:f
lb
:t
lbf
#33
:f
lb
:t
lbm
#34
:c
moments, work and energy
#35
:f
in-lb
:m
.1138
:t
N-m
#36
:f
ft-lb
:m
12
:t
in-lb
#37
:f
N-m
:m
100
:t
N-cm
#38
:f
N-m
:m
1000
:t
N-mm
#39
:f
N-m
:m
8.850744000000001
:t
in-lb
#40
:f
N-m
:m
.7375620000000001
:t
ft-lb
#41
:f
lb-in
:t
in-lb
#42
:f
N-m
:t
m-N
#43
:f
N-cm
:t
cm-N
#44
:f
N-m
:t
joule
#45
:f
joules
:t
joule
#46
:f
joule
:t
J
#47
:f
N-m
:t
kg m^2/sec^2
#49
:c
pressure and stress
#50
:f
bar
:m
100000
:t
Pa
#51
:f
psi
:m
6894.757
:t
Pa
#52
:f
MPa
:m
1000000
:t
Pa
#53
:f
MPa
:t
Mpa
#54
:f
GPa
:m
1000
:t
MPa
#55
:f
GPa
:t
Gpa
#56
:f
Pa
:t
pa
#57
:f
N/m^2
:t
Pa
#58
:f
N/mm^2
:t
MPa
#59
:f
N/mm^2
:m
1000000
:t
N/m^2
#60
:f
N/cm^2
:m
10000
:t
N/m^2
#61
:f
kpsi
:m
1000
:t
psi
#62
:f
psi
:m
144
:t
psf
#63
:f
kpsi
:t
ksi
#64
:f
psig
:t
psi
:a
14.7
#65
:c
acceleration
#66
:f
in/sec^2
:m
2.5399999999999
:t
cm/sec^2
#67
:f
m/sec^2
:m
100
:t
cm/sec^2
#68
:f
m/sec^2
:m
1000
:t
mm/sec^2
#69
:f
m/s^2
:t
m/sec^2
#70
:f
ft/sec^2
:m
12
:t
in/sec^2
#71
:f
ft/s^2
:t
ft/sec^2
#72
:f
G
:m
32.17
:t
ft/sec^2
#73
:c
velocity
#74
:f
in/sec
:m
2.5399999999999
:t
cm/sec
#75
:f
m/sec
:m
100
:t
cm/sec
#76
:f
m/sec
:m
1000
:t
mm/sec
#77
:f
m/s
:t
m/sec
#78
:f
ft/sec
:m
12
:t
in/sec
#79
:f
ft/s
:t
ft/sec
#80
:f
in/s
:t
in/sec
#81
:f
rad/sec
:m
9.549296584
:t
rpm
#82
:f
mph
:m
1.466666666666667
:t
ft/sec
#83
:c
mass
#84
:f
blob
:m
386
:t
lb
#85
:f
slug
:m
32.17
:t
lb
#86
:f
kg
:m
2.204623
:t
lb
#87
:f
kg
:m
1000
:t
g
#88
:f
kg
:m
9.806649999999999
:t
N
#89
:c
mass mom of inertia
#90
:f
lb-in-sec^2
:m
.1138
:t
N-m-sec^2
#91
:f
N-m-sec^2
:t
kg-m^2
#92
:f
lb-in-sec^2
:t
lb-in-s^2
#93
:f
blob-in^2
:t
lb-in-s^2
#94
:f
N-m-sec^2
:t
N-m-s^2
#95
:c
area moment of inertia
#96
:f
in^4
:m
416231.4256
:t
mm^4
#97
:f
m^4
:m
1E12
:t
mm^4
#98
:f
m^4
:m
1E8
:t
cm^4
#99
:f
ft^4
:m
20736
:t
in^4
#100
:f
in^4
:m
.0000004162314256
:t
m^4
#101
:c
density
#102
:f
lb/in^3
:m
27.6805
:t
g/cc
#103
:f
g/cc
:m
.001
:t
g/mm^3
#104
:f
lb/ft^3
:m
1728
:t
lb/in^3
#105
:f
kg/m^3
:m
.000001
:t
g/mm^3
#106
:f
lb/in^3
:m
.002590673575129534
:t
blob/in^3
#107
:f
blob/in^3
:m
.08333333333333333
:t
slug/in^3
#108
:f
slug/ft^3
:m
1728
:t
slug/in^3
#109
:f
kg/mm^3
:m
1000
:t
g/mm^3
#110
:f
SG
:t
g/cc
#111
:c
spring rate
#112
:f
lb/in
:m
175.126
:t
N/m
#113
:f
N/mm
:m
1000
:t
N/m
#114
:f
lb/ft
:m
.08333333333333333
:t
lb/in
#115
:c
angles
#116
:f
radians
:m
57.29577951308232
:t
degrees
:c
 
#117
:f
rad
:m
57.2957795129
:t
deg
#118
:f
rev
:m
360
:t
deg
#119
:f
rad
:t
radian
#120
:c
temperature
#121
:f
C
:m
1.8
:t
F
:a
32
#122
:f
F
:t
R
:a
459.69
#123
:f
C
:t
K
:a
273.16
#124
:c
power
#125
:f
HP
:m
550
:t
ft-lb/sec
#126
:f
ft-lb/sec
:m
60
:t
ft-lb/min
#127
:f
ft-lb/sec
:m
12
:t
in-lb/sec
#128
:f
HP
:m
745.699
:t
watts
#129
:f
kw
:m
1000
:t
watts
#130
:f
HP
:t
hp
#131
:f
N-m/sec
:m
8.850756136188998
:t
in-lb/sec
#132
:f
N-m/sec
:t
watts
#133
:f
watt
:t
watts
#134
:c
flow
#135
:f
cfm
:m
1728
:t
cim
#136
:c
percent
#137
:f
dec%
:m
100
:t
%
#139
:c
fracture mechanics
#140
:f
MPa-m^.5
:m
.909
:t
ksi-in^.5
:c
stress intensity
#141
:f
MPa-m^.5
:m
1000000
:t
Pa-m^.5
:c
stress intensity
#142
:f
ksi-in^.5
:m
1000
:t
psi-in^.5
:c
stress intensity
#143
:f
kpsi-in^.5
:m
1000
:t
psi-in^.5
:c
stress intensity
#145
:c
frequency
#146
:f
1/sec
:m
60
:t
1/min
#147
:f
Hz
:t
1/sec
#148
:f
Hz
:t
hz
#149
:c
time
#150
:f
min
:m
60
:t
sec
#151
:f
hr
:m
60
:t
min
#152
:f
day
:m
24
:t
hr
#153
:f
week
:m
7
:t
day
#154
:f
year
:m
52
:t
week
#155
:f
year
:m
12
:t
month
#156
:c
viscosity
#157
:f
reyn
:t
lb-sec/in^2
:c
     absolute
#158
:f
reyn
:m
6894.696003767111
:t
Pa-s
#159
:f
reyn
:m
1000000
:t
ureyn
#160
:f
Pa-s
:m
1000
:t
mPa-s
#161
:f
cP
:t
mPa-s
#162
:c
   kinematic
#163
:f
m^2/sec
:m
10000
:t
cm^2/sec
#164
:f
cm^2/sec
:t
stoke
#165
:f
stoke
:m
100
:t
cS
#166
:f
m^2/sec
:m
1549.996853506387
:t
in^2/sec
#167
:c
stress intensity
#168
:f
psi-in^.5
:m
1098.843447385385
:t
Pa-m^.5
#169
:f
ksi-in^.5
:m
1000
:t
psi-in^.5
#170
:f
MPa-m^.5
:m
1000000
:t
Pa-m^.5
#171
:c
specific heat
#172
:f
J/kgC
:t
Wsec/kgC
#173
:f
Wsec/kgC
:m
3600
:t
Whr/kgC
=l
=f
=r
#1
:r
; Chap 10, Discrete Loaded Cable, with n=3 loads, r = n + 1
:s
C
#2
:r
; T1_h       b1                  b2              bn               br,         Ó b = span
:s
C
#3
:r
;  <-- *  ............................................................................
:s
C
#4
:r
;       ^                  : h1                 : h2       : hn                : hr
:s
C
#5
:r
;        |   T1_v       :                      :            :                      * --> Tr_h     
:s
C
#6
:r
;                            |  W1              | W2      | Wn               ^ Tr_v
:s
C
#7
:r
;                            v                    v           v                      |
:s
C
#9
:r
; geometry
:s
C
#10
:r
span = b1 + b2 + bn + br
#11
:r
L1^2 = b1^2 + h1^2
#12
:r
L2^2 = b2^2 + (h2 - h1)^2 
#13
:r
Ln^2 = bn^2 + (hn - h2)^2
#14
:r
Lr^2 =  br^2 + Äh^2     
#15
:r
L     = L1 + L2 + Ln + Lr
#16
:r
Äh = hn - hr
#18
:r
Weight = W1 + W2 + Wn
#20
:r
; external force equilibrium
:s
C
#21
:r
T1_v + Tr_v = Weight             ; external reaction
#22
:r
-T1_h + Tr_h = 0                    ; external reaction 
#23
:r
T1^2 = T1_h^2 + T1_v^2         ; left resultant reaction
#24
:r
Tr^2 = Tr_h^2 + Tr_v^2           ; right resultant reaction
#26
:r
; external moment equilibrium
:s
C
#27
:r
Tr_h * hr + Tr_v * span - W1 * b1 - W2 * (b1 + b2) - Wn * (b1 + b2 + bn) = 0 ; ÓM_0
#28
:r
T1_h * hr - T1_v * span + W1 * (b2 + bn + br) + W2 * (bn + br) + Wn * br = 0; ÓM_r
#30
:r
; internal section moment equilibrium
:s
C
#31
:r
T1_h * h1 - T1_v * b1 = 0                                                               ; Ó M_1 = 0
#32
:r
T1_h * h2 - T1_v *( b1 + b2) + W1 * b2 = 0                                    ; Ó M_2 = 0
#33
:r
T1_h * hn - T1_v *( b1 + b2+ bn) + W1 * (b2 + bn) + W2 * bn = 0  ; Ó M_3 = 0
#35
:r
; similar triangles
:s
C
#36
:r
T1_h = T1 * b1 / L1
#37
:r
T1_v = T1 * h1 / L1
#38
:r
Tr_v = Tr * Äh / Lr
#39
:r
Tr_h = Tr * br / Lr
#41
:r
; additional tension segments (FBD of each weight)
:s
C
#42
:r
T1_v - W1 + T2_v = 0    ; W1 FBD
#43
:r
-T1_h + T2_h = 0
#44
:r
Äh2 = h2 - h1
#45
:r
T2_h = T2 * b2 / L2
#46
:r
T2_v = -T2 * Äh2 / L2
#48
:r
-T2_v - W2 + Tn_v = 0    ; W2 FBD, reverse T2
#49
:r
-T2_h + Tn_h = 0
#50
:r
Äh3 = hn - h2
#51
:r
Tn_h = Tn * bn / Ln
#52
:r
Tn_v = -Tn * Äh3 / Ln
=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,41,0,0,1,0
%Or,f,55,1,0,1,0
%Xl,f,0,0,0,2,0,88,88,653,494,320,806,-1,-1,0,0,4,-1,0,0,2,-11,700,34,0,0,0,161,Arial Unicode MS,4,10,21,31,98
%Xp,f,0,0,0,2,0,110,110,675,516,480,806,-1,-1,0,0,5,-1,0,0,2,-11,700,34,0,0,0,161,Arial Unicode MS,3,13,25,99
%Xt,f,0,0,0,2,0,132,132,697,538,640,806,-1,-1,0,0,6,-1,0,0,2,-11,700,34,0,0,0,161,Arial Unicode MS,2,15,100
%Xn,f,0,0,0,2,0,154,154,719,560,0,782,-1,-1,0,0,7,-1,0,0,2,-11,700,34,0,0,0,161,Arial Unicode MS,2,15,100
%Xc,f,0,0,0,2,0,176,176,741,582,160,782,-1,-1,0,0,8,-1,0,0,2,-11,700,34,0,0,0,161,Arial Unicode MS,3,15,22,99
%Xf,f,0,0,0,2,0,0,0,993,664,0,806,0,0,0,0,2,-1,0,0,2,-12,700,34,0,0,0,161,Arial Unicode MS,4,16,26,38,98
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%Xu,f,7,3,0,2,0,0,8,972,672,160,806,0,0,0,0,3,-1,0,0,2,-12,700,34,0,0,0,161,Arial Unicode MS,5,10,22,36,50,98
%Xr,f,55,1,0,2,0,545,0,1090,849,-1,-1,0,0,0,0,1,-1,0,0,1,-12,700,34,0,0,0,161,Arial Unicode MS,2,9,103
%Xv,f,41,0,0,2,0,0,0,545,849,-1,-1,-4,-23,2,0,0,-1,0,0,3,-12,700,34,0,0,0,161,Arial Unicode MS,6,6,14,22,30,40,91
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