Unsymetrical Bending Paul
32
Angle Section Load (g) Load (N) Left Dial Right Dial U (mm) V (mm) 0 0 0 0 0 0 100 0.981 0.48 1.22 1.20 -0.52 200 1.962 0.94 2.53 2.45 -1.12 300 2.943 1.39 4.07 3.86 -1.90 400 3.924 1.99 5.65 5.40 -2.59 500 4.905 2.62 7.43 7.11 -3.40 dU/dP = 1.4428 dV/dP = -0.6981 mm/N Load (g) Load (N) Left Dial Right Dial U V 0 0 0 0 0 0 100 0.981 0.19 0.77 0.68 -0.41 200 1.962 0.51 1.62 1.51 -0.78 300 2.943 0.78 2.52 2.33 -1.23 400 3.924 1.16 3.40 3.22 -1.58 500 4.905 1.49 4.28 4.08 -1.97 dU/dP = 0.8407 dV/dP = -0.4028 mm/N Load (g) Load (N) Left Dial Right Dial U V 0 0 0 0 0 0 100 0.981 0.36 0.42 0.55 -0.04 200 1.962 0.88 0.79 1.18 0.06 300 2.943 1.33 1.20 1.79 0.09 400 3.924 1.80 1.61 2.41 0.13 500 4.905 2.24 2.01 3.01 0.16 dU/dP = 0.6178 dV/dP = 0.0400 mm/N Head Angle 0° Head Angle 22.5° Head Angle 45° 6 8 10 12 f(x) = 0.0138888628311969 x f(x) = 0.0186534768877011 x f(x) = 0.0205960920629245 x f(x) = 0.0191304525528288 x f(x) = 0.0125697872721107 x f(x) = 0.0136060201187222 x ment U (mm)
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Transcript of Unsymetrical Bending Paul
Angle Section
Load (g) Load (N) Left Dial Right Dial U (mm) V (mm) Load (g)0 0 0 0 0 0 0
100 0.981 0.48 1.22 1.20 -0.52 100200 1.962 0.94 2.53 2.45 -1.12 200300 2.943 1.39 4.07 3.86 -1.90 300400 3.924 1.99 5.65 5.40 -2.59 400500 4.905 2.62 7.43 7.11 -3.40 500
dU/dP = 1.4428 dV/dP = -0.6981 mm/N dU/dP =
Load (g) Load (N) Left Dial Right Dial U V Load (g)0 0 0 0 0 0 0
100 0.981 0.19 0.77 0.68 -0.41 100200 1.962 0.51 1.62 1.51 -0.78 200300 2.943 0.78 2.52 2.33 -1.23 300400 3.924 1.16 3.40 3.22 -1.58 400500 4.905 1.49 4.28 4.08 -1.97 500
dU/dP = 0.8407 dV/dP = -0.4028 mm/N dU/dP =
Load (g) Load (N) Left Dial Right Dial U V Load (g)0 0 0 0 0 0 0
100 0.981 0.36 0.42 0.55 -0.04 100200 1.962 0.88 0.79 1.18 0.06 200300 2.943 1.33 1.20 1.79 0.09 300400 3.924 1.80 1.61 2.41 0.13 400500 4.905 2.24 2.01 3.01 0.16 500
dU/dP = 0.6178 dV/dP = 0.0400 mm/N dU/dP =
Head Angle 0° Head Angle 67.5°
Head Angle 22.5° Head Angle 90°
Head Angle 45° Head Angle 112.5°
0 100 200 300 400 500 6000
2
4
6
8
10
12
f(x) = 0.0138888628311969 x
f(x) = 0.0186534768877011 x
f(x) = 0.0205960920629245 x
f(x) = 0.0191304525528288 x
f(x) = 0.0125697872721107 x
f(x) = 0.00801601960126932 x
f(x) = 0.00599112290968966 x
f(x) = 0.00799802051956639 x
f(x) = 0.0136060201187222 x
Displacement U Vs Load P
0 Linear (0)
22.5 Linear (22.5)
45 Linear (45)
67.5 Linear (67.5)
90 Linear (90)
112.5 Linear (112.5)
135 Linear (135)
157.5 Linear (157.5)
180 Linear (180)
Load P (g)
Disp
lace
men
t U (m
m)
0 100 200 300 400 500 6000
2
4
6
8
10
12
f(x) = 0.0138888628311969 x
f(x) = 0.0186534768877011 x
f(x) = 0.0205960920629245 x
f(x) = 0.0191304525528288 x
f(x) = 0.0125697872721107 x
f(x) = 0.00801601960126932 x
f(x) = 0.00599112290968966 x
f(x) = 0.00799802051956639 x
f(x) = 0.0136060201187222 x
Displacement U Vs Load P
0 Linear (0)
22.5 Linear (22.5)
45 Linear (45)
67.5 Linear (67.5)
90 Linear (90)
112.5 Linear (112.5)
135 Linear (135)
157.5 Linear (157.5)
180 Linear (180)
Load P (g)
Disp
lace
men
t U (m
m)
0 100 200 300 400 500 600
-4
-3
-2
-1
0
1
2
3
4
f(x) = − 0.00593326871850167 xf(x) = − 0.00514130912357273 x
f(x) = 0.000995092088433433 x
f(x) = 0.00540229580826522 x
f(x) = 0.00622896791790695 x
f(x) = 0.00412821795343637 x
f(x) = 0.000311126983722081 xf(x) = − 0.00397651140765453 xf(x) = − 0.00651181063038157 x
Displacement V Vs Load P
0 Linear (0)
22.5 Linear (22.5)
45 Linear (45)
67.5 Linear (67.5)
90 Linear (90)
112.5 Linear (112.5)
135 Linear (135)
157.5 Linear (157.5)
180 Linear (180)
Load P (g)
Disp
lace
men
t V (m
m)
Load (N) Left Dial Right Dial U (mm) V (mm) Load (g) Load (N)0 0 0 0 0 0 0
0.981 0.96 0.32 0.91 0.45 100 0.9811.962 1.87 0.48 1.66 0.98 200 1.9622.943 2.74 0.76 2.47 1.40 300 2.9433.924 3.54 1.09 3.27 1.73 400 3.9244.905 4.03 1.44 3.87 1.83 500 4.905
0.7939 dV/dP = 0.3907 mm/N dU/dP = 2.1583
Load (N) Left Dial Right Dial U (mm) V (mm) Load (g) Load (N)0 0 0 0 0 0 0
0.981 1.37 0.39 1.24 0.69 100 0.9811.962 2.98 0.86 2.72 1.50 200 1.9622.943 4.02 1.35 3.80 1.89 300 2.9433.924 5.83 1.80 5.40 2.85 400 3.9244.905 6.08 2.26 5.90 2.70 500 4.905
1.2530 dV/dP = 0.5931 mm/N dU/dP = 2.0065
Load (N) Left Dial Right Dial U (mm) V (mm) Load (g) Load (N)0 0 0 0 0 0 0
0.981 1.63 0.87 1.77 0.54 100 0.9811.962 3.44 1.84 3.73 1.13 200 1.9622.943 5.04 2.80 5.54 1.58 300 2.9433.924 6.97 3.86 7.66 2.20 400 3.9244.905 8.78 5.00 9.74 2.67 500 4.905
1.9863 dV/dP = 0.5476 mm/NdU/dP = 1.5324
Head Angle 67.5° Head Angle 135°
Head Angle 90° Head Angle 157.5°
Head Angle 112.5° Head Angle 180°
0 100 200 300 400 500 6000
2
4
6
8
10
12
f(x) = 0.0138888628311969 x
f(x) = 0.0186534768877011 x
f(x) = 0.0205960920629245 x
f(x) = 0.0191304525528288 x
f(x) = 0.0125697872721107 x
f(x) = 0.00801601960126932 x
f(x) = 0.00599112290968966 x
f(x) = 0.00799802051956639 x
f(x) = 0.0136060201187222 x
Displacement U Vs Load P
0 Linear (0)
22.5 Linear (22.5)
45 Linear (45)
67.5 Linear (67.5)
90 Linear (90)
112.5 Linear (112.5)
135 Linear (135)
157.5 Linear (157.5)
180 Linear (180)
Load P (g)
Disp
lace
men
t U (m
m)
0 100 200 300 400 500 6000
2
4
6
8
10
12
f(x) = 0.0138888628311969 x
f(x) = 0.0186534768877011 x
f(x) = 0.0205960920629245 x
f(x) = 0.0191304525528288 x
f(x) = 0.0125697872721107 x
f(x) = 0.00801601960126932 x
f(x) = 0.00599112290968966 x
f(x) = 0.00799802051956639 x
f(x) = 0.0136060201187222 x
Displacement U Vs Load P
0 Linear (0)
22.5 Linear (22.5)
45 Linear (45)
67.5 Linear (67.5)
90 Linear (90)
112.5 Linear (112.5)
135 Linear (135)
157.5 Linear (157.5)
180 Linear (180)
Load P (g)
Disp
lace
men
t U (m
m)
0 100 200 300 400 500 600
-4
-3
-2
-1
0
1
2
3
4
f(x) = − 0.00593326871850167 xf(x) = − 0.00514130912357273 x
f(x) = 0.000995092088433433 x
f(x) = 0.00540229580826522 x
f(x) = 0.00622896791790695 x
f(x) = 0.00412821795343637 x
f(x) = 0.000311126983722081 xf(x) = − 0.00397651140765453 xf(x) = − 0.00651181063038157 x
Displacement V Vs Load P
0 Linear (0)
22.5 Linear (22.5)
45 Linear (45)
67.5 Linear (67.5)
90 Linear (90)
112.5 Linear (112.5)
135 Linear (135)
157.5 Linear (157.5)
180 Linear (180)
Load P (g)
Disp
lace
men
t V (m
m)
Left Dial Right Dial U (mm) V (mm) dv du0 0 0 0 -0.6981 1.4428
1.28 1.15 1.72 0.09 0.3907 0.79392.91 2.67 3.95 0.17 0.1005 2.15834.52 4.08 6.08 0.31 -0.4028 0.84076.24 5.50 8.30 0.52 0.5931 1.25307.67 7.10 10.44 0.40 -0.5464 2.0065
dV/dP = 0.1005 mm/N 0.0400 0.61780.5476 1.9863-0.6909 1.5324
Left Dial Right Dial U (mm) V (mm)0 0 0 0
0.65 1.19 1.30 -0.381.81 3.21 3.55 -0.992.63 4.70 5.18 -1.463.81 6.77 7.48 -2.095.03 8.75 9.74 -2.63
dV/dP = -0.5464 mm/N
Left Dial Right Dial U (mm) V (mm)0 0 0 0
0.39 0.59 0.69 -0.141.15 2.30 2.44 -0.811.65 4.10 4.07 -1.732.20 5.65 5.55 -2.442.90 7.40 7.28 -3.18
dV/dP = -0.6909 mm/N
Head Angle 135°
Head Angle 157.5°
Head Angle 180°
0 100 200 300 400 500 6000
2
4
6
8
10
12
f(x) = 0.0138888628311969 x
f(x) = 0.0186534768877011 x
f(x) = 0.0205960920629245 x
f(x) = 0.0191304525528288 x
f(x) = 0.0125697872721107 x
f(x) = 0.00801601960126932 x
f(x) = 0.00599112290968966 x
f(x) = 0.00799802051956639 x
f(x) = 0.0136060201187222 x
Displacement U Vs Load P
0 Linear (0)
22.5 Linear (22.5)
45 Linear (45)
67.5 Linear (67.5)
90 Linear (90)
112.5 Linear (112.5)
135 Linear (135)
157.5 Linear (157.5)
180 Linear (180)
Load P (g)
Disp
lace
men
t U (m
m)
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.80.0000
0.5000
1.0000
1.5000
2.0000
2.5000
dU/dP Vs dV/dP
dV/dP (mm/N)
dU/d
P (m
m/N
)
-0.8000 -0.6000 -0.4000 -0.2000 0.0000 0.2000 0.4000 0.6000 0.80000.0000
0.5000
1.0000
1.5000
2.0000
2.5000
Chart Title
0 100 200 300 400 500 6000
2
4
6
8
10
12
f(x) = 0.0138888628311969 x
f(x) = 0.0186534768877011 x
f(x) = 0.0205960920629245 x
f(x) = 0.0191304525528288 x
f(x) = 0.0125697872721107 x
f(x) = 0.00801601960126932 x
f(x) = 0.00599112290968966 x
f(x) = 0.00799802051956639 x
f(x) = 0.0136060201187222 x
Displacement U Vs Load P
0 Linear (0)
22.5 Linear (22.5)
45 Linear (45)
67.5 Linear (67.5)
90 Linear (90)
112.5 Linear (112.5)
135 Linear (135)
157.5 Linear (157.5)
180 Linear (180)
Load P (g)
Disp
lace
men
t U (m
m)
0 100 200 300 400 500 600
-4
-3
-2
-1
0
1
2
3
4
f(x) = − 0.00593326871850167 xf(x) = − 0.00514130912357273 x
f(x) = 0.000995092088433433 x
f(x) = 0.00540229580826522 x
f(x) = 0.00622896791790695 x
f(x) = 0.00412821795343637 x
f(x) = 0.000311126983722081 xf(x) = − 0.00397651140765453 xf(x) = − 0.00651181063038157 x
Displacement V Vs Load P
0 Linear (0)
22.5 Linear (22.5)
45 Linear (45)
67.5 Linear (67.5)
90 Linear (90)
112.5 Linear (112.5)
135 Linear (135)
157.5 Linear (157.5)
180 Linear (180)
Load P (g)
Disp
lace
men
t V (m
m)
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.80.0000
0.5000
1.0000
1.5000
2.0000
2.5000
dU/dP Vs dV/dP
dV/dP (mm/N)
dU/d
P (m
m/N
)
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.80.0000
0.5000
1.0000
1.5000
2.0000
2.5000
dU/dP Vs dV/dP
dV/dP (mm/N)
dU/d
P (m
m/N
)
-0.8000 -0.6000 -0.4000 -0.2000 0.0000 0.2000 0.4000 0.6000 0.80000.0000
0.5000
1.0000
1.5000
2.0000
2.5000
Chart Title
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.80.0000
0.5000
1.0000
1.5000
2.0000
2.5000
dU/dP Vs dV/dP
dV/dP (mm/N)
dU/d
P (m
m/N
)
U Section
Load (g) Load (N) Left Dial Right Dial U (mm) U (m) V (mm) V (m) Load (g)0 0 0 0 0 0 0 0 0
100 0.981 0.51 0.47 0.69 0.000693 0.03 2.83E-05 100200 1.962 0.99 0.98 1.39 0.001393 0.01 7.07E-06 200300 2.943 1.38 1.41 1.97 0.001973 -0.02 -2.1E-05 300400 3.924 1.93 1.90 2.71 0.002708 0.02 2.12E-05 400500 4.905 2.35 2.46 3.40 0.003401 -0.08 -7.8E-05 500
dU/dP = 6.9E-04 dV/dP = -1.3E-05 dU/dP =dU/dP = 6.9E-01 dV/dP = -1.3E-02 mm/N dU/dP =
Load (g) Load (N) Left Dial Right Dial U (mm) U (m) V (mm) V (m) Load (g)0 0 0 0 0 0 0 0 0
100 0.981 0.38 0.46 0.59 0.000594 -0.06 -5.7E-05 100200 1.962 0.80 0.95 1.24 0.001237 -0.11 -0.00011 200300 2.943 1.23 1.45 1.90 0.001895 -0.16 -0.00016 300400 3.924 1.58 1.92 2.47 0.002475 -0.24 -0.00024 400500 4.905 1.97 2.41 3.10 0.003097 -0.31 -0.00031 500
dU/dP = 6.3E-04 dV/dP = -6.3E-05 dU/dP =dU/dP = 6.3E-01 dV/dP = -6.3E-02 mm/N dU/dP =
Load (g) Load (N) Left Dial Right Dial U (mm) U (m) V (mm) V (m) Load (g)0 0 0 0 0 0 0 0 0
100 0.981 0.28 0.38 0.47 0.000467 -0.07 -7.1E-05 100200 1.962 0.66 0.80 1.03 0.001032 -0.10 -9.9E-05 200300 2.943 1.03 1.26 1.62 0.001619 -0.16 -0.00016 300400 3.924 1.33 1.65 2.11 0.002107 -0.23 -0.00023 400500 4.905 1.80 2.13 2.78 0.002779 -0.23 -0.00023 500
dU/dP = 5.7E-04 dV/dP = -4.9E-05 dU/dP =dU/dP = 5.7E-01 dV/dP = -4.9E-02 mm/N dU/dP =
Head Angle 0° Head Angle 67.5°
Head Angle 22.5° Head Angle 90°
Head Angle 45° Head Angle 112.5°
0 100 200 300 400 500 6000
0.5
1
1.5
2
2.5
3
3.5
4
f(x) = 0.00638324576107492 xf(x) = 0.00623282486398615 x
f(x) = 0.00558742922006679 x
f(x) = 0.00509502577062234 xf(x) = 0.00487775114149411 x
f(x) = 0.00520302026083992 xf(x) = 0.00540229580826522 x
f(x) = 0.00620711189012482 x
f(x) = 0.00677022601768793 x
Displacement U Vs Load P
0 Linear (0)
22.5 Linear (22.5)
45 Linear (45)
67.5 Linear (67.5)
90 Linear (90)
112.5 Linear (112.5)
135 Linear (135)
157.5 Linear (157.5)
180 Linear (180)
Load P (g)
Disp
lace
men
t U (m
m)
0 100 200 300 400 500 6000
0.5
1
1.5
2
2.5
3
3.5
4
f(x) = 0.00638324576107492 xf(x) = 0.00623282486398615 x
f(x) = 0.00558742922006679 x
f(x) = 0.00509502577062234 xf(x) = 0.00487775114149411 x
f(x) = 0.00520302026083992 xf(x) = 0.00540229580826522 x
f(x) = 0.00620711189012482 x
f(x) = 0.00677022601768793 x
Displacement U Vs Load P
0 Linear (0)
22.5 Linear (22.5)
45 Linear (45)
67.5 Linear (67.5)
90 Linear (90)
112.5 Linear (112.5)
135 Linear (135)
157.5 Linear (157.5)
180 Linear (180)
Load P (g)
Disp
lace
men
t U (m
m)
0 100 200 300 400 500 600
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
f(x) = − 3.21412173266612E-05 x
f(x) = 0.000552828938018574 x
f(x) = 0.000802244784473465 x
f(x) = 0.000698107240335082 x
f(x) = 0.000223702872593562 x
f(x) = − 0.000201846844811433 xf(x) = − 0.00051425947722658 xf(x) = − 0.000591398398810567 xf(x) = − 5.91398398810566E-05 x
Displacement V Vs Load P
0 Linear (0)
22.5 Linear (22.5)
45 Linear (45)
67.5 Linear (67.5)
90 Linear (90)
112.5 Linear (112.5)
135 Linear (135)
157.5 Linear (157.5)
180 Linear (180)
Load P (g)
Disp
lace
men
t V (m
m)
Load (N) Left Dial Right Dial U (mm) U (m) V (mm) V (m) Load (g) Load (N)0 0 0 0 0 0 0 0 0
0.981 0.35 0.39 0.52 0.000523 -0.03 -2.83E-05 100 0.9811.962 0.62 0.77 0.98 0.000983 -0.11 -0.000106 200 1.9622.943 1.03 1.15 1.54 0.001541 -0.08 -8.49E-05 300 2.9433.924 1.38 1.51 2.04 0.002044 -0.09 -9.19E-05 400 3.9244.905 1.85 1.92 2.67 0.002666 -0.05 -4.95E-05 500 4.905
5.4E-04 dV/dP = -1.2E-05 dU/dP = 5.8E-045.4E-01 dV/dP = -1.2E-02 mm/N dU/dP = 5.8E-01
Load (N) Left Dial Right Dial U (mm) U (m) V (mm) V (m) Load (g) Load (N)0 0 0 0 0 0 0 0 0
0.981 0.29 0.29 0.41 0.00041 0.00 0 100 0.9811.962 0.62 0.62 0.88 0.000877 0.00 0 200 1.9622.943 1.04 0.97 1.42 0.001421 0.05 4.95E-05 300 2.9433.924 1.41 1.29 1.91 0.001909 0.08 8.485E-05 400 3.9244.905 1.91 1.70 2.55 0.002553 0.15 0.000148 500 4.905
5.2E-04 dV/dP = 3.0E-05 dU/dP = 6.5E-045.2E-01 dV/dP = 3.0E-02 mm/N dU/dP = 6.5E-01
Load (N) Left Dial Right Dial U (mm) U (m) V (mm) V (m) Load (g) Load (N)0 0 0 0 0 0 0 0 0
0.981 0.35 0.25 0.42 0.000424 0.07 7.071E-05 100 0.9811.962 0.81 0.61 1.00 0.001004 0.14 0.000141 200 1.9622.943 1.21 0.91 1.50 0.001499 0.21 0.000212 300 2.9433.924 1.62 1.25 2.03 0.002029 0.26 0.000262 400 3.9244.905 2.09 1.58 2.60 0.002595 0.36 0.000361 500 4.905
5.3E-04 dV/dP = 7.1E-05 dU/dP = 6.6E-045.3E-01 dV/dP = 7.1E-02 mm/N dU/dP = 6.6E-01
Head Angle 67.5° Head Angle 135°
Head Angle 90° Head Angle 157.5°
Head Angle 112.5° Head Angle 180°
0 100 200 300 400 500 6000
0.5
1
1.5
2
2.5
3
3.5
4
f(x) = 0.00638324576107492 xf(x) = 0.00623282486398615 x
f(x) = 0.00558742922006679 x
f(x) = 0.00509502577062234 xf(x) = 0.00487775114149411 x
f(x) = 0.00520302026083992 xf(x) = 0.00540229580826522 x
f(x) = 0.00620711189012482 x
f(x) = 0.00677022601768793 x
Displacement U Vs Load P
0 Linear (0)
22.5 Linear (22.5)
45 Linear (45)
67.5 Linear (67.5)
90 Linear (90)
112.5 Linear (112.5)
135 Linear (135)
157.5 Linear (157.5)
180 Linear (180)
Load P (g)
Disp
lace
men
t U (m
m)
0 100 200 300 400 500 6000
0.5
1
1.5
2
2.5
3
3.5
4
f(x) = 0.00638324576107492 xf(x) = 0.00623282486398615 x
f(x) = 0.00558742922006679 x
f(x) = 0.00509502577062234 xf(x) = 0.00487775114149411 x
f(x) = 0.00520302026083992 xf(x) = 0.00540229580826522 x
f(x) = 0.00620711189012482 x
f(x) = 0.00677022601768793 x
Displacement U Vs Load P
0 Linear (0)
22.5 Linear (22.5)
45 Linear (45)
67.5 Linear (67.5)
90 Linear (90)
112.5 Linear (112.5)
135 Linear (135)
157.5 Linear (157.5)
180 Linear (180)
Load P (g)
Disp
lace
men
t U (m
m)
0 100 200 300 400 500 600
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
f(x) = − 3.21412173266612E-05 x
f(x) = 0.000552828938018574 x
f(x) = 0.000802244784473465 x
f(x) = 0.000698107240335082 x
f(x) = 0.000223702872593562 x
f(x) = − 0.000201846844811433 xf(x) = − 0.00051425947722658 xf(x) = − 0.000591398398810567 xf(x) = − 5.91398398810566E-05 x
Displacement V Vs Load P
0 Linear (0)
22.5 Linear (22.5)
45 Linear (45)
67.5 Linear (67.5)
90 Linear (90)
112.5 Linear (112.5)
135 Linear (135)
157.5 Linear (157.5)
180 Linear (180)
Load P (g)
Disp
lace
men
t V (m
m)
Left Dial Right Dial U (mm) U (m) V (mm) V (m)0 0 0 0 0 0
0.46 0.31 0.54 0.000544 0.11 0.0001060.88 0.61 1.05 0.001054 0.19 0.0001911.29 0.95 1.58 0.001584 0.24 0.000241.84 1.37 2.27 0.00227 0.33 0.0003322.28 1.75 2.85 0.00285 0.37 0.000375
dV/dP = 7.6E-05dV/dP = 7.6E-02 mm/N
Left Dial Right Dial U (mm) U (m) V (mm) V (m)0 0 0 0 0 0
0.42 0.39 0.57 0.000573 0.02 2.121E-050.93 0.79 1.22 0.001216 0.10 9.899E-051.42 1.17 1.83 0.001831 0.18 0.0001771.90 1.59 2.47 0.002468 0.22 0.0002192.45 2.05 3.18 0.003182 0.28 0.000283
dV/dP = 6.1E-05dV/dP = 6.1E-02 mm/N
Left Dial Right Dial U (mm) U (m) V (mm) V (m)0 0 0 0 0 0
0.45 0.44 0.63 0.000629 0.01 7.071E-060.86 0.87 1.22 0.001223 -0.01 -7.07E-061.34 1.38 1.92 0.001923 -0.03 -2.83E-051.79 1.82 2.55 0.002553 -0.02 -2.12E-052.27 2.27 3.21 0.00321 0.00 0
dV/dP = -3.1E-06dV/dP = -3.1E-03 mm/N
Head Angle 135°
Head Angle 157.5°
Head Angle 180°
0 100 200 300 400 500 6000
0.5
1
1.5
2
2.5
3
3.5
4
f(x) = 0.00638324576107492 xf(x) = 0.00623282486398615 x
f(x) = 0.00558742922006679 x
f(x) = 0.00509502577062234 xf(x) = 0.00487775114149411 x
f(x) = 0.00520302026083992 xf(x) = 0.00540229580826522 x
f(x) = 0.00620711189012482 x
f(x) = 0.00677022601768793 x
Displacement U Vs Load P
0 Linear (0)
22.5 Linear (22.5)
45 Linear (45)
67.5 Linear (67.5)
90 Linear (90)
112.5 Linear (112.5)
135 Linear (135)
157.5 Linear (157.5)
180 Linear (180)
Load P (g)
Disp
lace
men
t U (m
m)
-8.00E-05 -6.00E-05 -4.00E-05 -2.00E-05 0.00E+00 2.00E-05 4.00E-05 6.00E-05 8.00E-05 1.00E-045.00E-04
5.20E-04
5.40E-04
5.60E-04
5.80E-04
6.00E-04
6.20E-04
6.40E-04
6.60E-04
6.80E-04
7.00E-04
dU/dP Vs dV/dP
dV/dP
dU/d
P
-0.1 -0.05 0 0.05 0.10.5
0.52
0.54
0.56
0.58
0.6
0.62
0.64
0.66
0.68
0.7
dU/dP Vs dV/dP mm/N
dV/dP
dU/d
P
0 100 200 300 400 500 6000
0.5
1
1.5
2
2.5
3
3.5
4
f(x) = 0.00638324576107492 xf(x) = 0.00623282486398615 x
f(x) = 0.00558742922006679 x
f(x) = 0.00509502577062234 xf(x) = 0.00487775114149411 x
f(x) = 0.00520302026083992 xf(x) = 0.00540229580826522 x
f(x) = 0.00620711189012482 x
f(x) = 0.00677022601768793 x
Displacement U Vs Load P
0 Linear (0)
22.5 Linear (22.5)
45 Linear (45)
67.5 Linear (67.5)
90 Linear (90)
112.5 Linear (112.5)
135 Linear (135)
157.5 Linear (157.5)
180 Linear (180)
Load P (g)
Disp
lace
men
t U (m
m)
0 100 200 300 400 500 600
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
f(x) = − 3.21412173266612E-05 x
f(x) = 0.000552828938018574 x
f(x) = 0.000802244784473465 x
f(x) = 0.000698107240335082 x
f(x) = 0.000223702872593562 x
f(x) = − 0.000201846844811433 xf(x) = − 0.00051425947722658 xf(x) = − 0.000591398398810567 xf(x) = − 5.91398398810566E-05 x
Displacement V Vs Load P
0 Linear (0)
22.5 Linear (22.5)
45 Linear (45)
67.5 Linear (67.5)
90 Linear (90)
112.5 Linear (112.5)
135 Linear (135)
157.5 Linear (157.5)
180 Linear (180)
Load P (g)
Disp
lace
men
t V (m
m)
-0.1 -0.05 0 0.05 0.10.5
0.52
0.54
0.56
0.58
0.6
0.62
0.64
0.66
0.68
0.7
dU/dP Vs dV/dP mm/N
dV/dP
dU/d
P
-8.00E-05 -6.00E-05 -4.00E-05 -2.00E-05 0.00E+00 2.00E-05 4.00E-05 6.00E-05 8.00E-05 1.00E-045.00E-04
5.20E-04
5.40E-04
5.60E-04
5.80E-04
6.00E-04
6.20E-04
6.40E-04
6.60E-04
6.80E-04
7.00E-04
dU/dP Vs dV/dP
dV/dP
dU/d
P
-0.1 -0.05 0 0.05 0.10.5
0.52
0.54
0.56
0.58
0.6
0.62
0.64
0.66
0.68
0.7
dU/dP Vs dV/dP mm/N
dV/dP
dU/d
P
-0.1 -0.05 0 0.05 0.10.5
0.52
0.54
0.56
0.58
0.6
0.62
0.64
0.66
0.68
0.7
dU/dP Vs dV/dP mm/N
dV/dP
dU/d
P
Rectangular SectionHead Angle 0°
Load (g) Load (N) Left Dial Right Dial U (mm) U (m) V (mm) V (m) Load (g)0 0 0 0 0 0 0 0 0
100 0.981 0.41 0.31 0.51 0.000509 0.07 7.1E-05 100200 1.962 0.68 0.68 0.96 0.000962 0.00 0.0E+00 200300 2.943 1.10 1.04 1.51 0.001513 0.04 4.2E-05 300400 3.924 1.49 1.39 2.04 0.002036 0.07 7.1E-05 400500 4.905 1.99 1.73 2.63 0.00263 0.18 1.8E-04 500
dU/dP = 0.0005 dV/dP = 3E-05 dU/dP =dU/dP = 0.5326 dV/dP = 0.0280 mm/N dU/dP =
Load (g) Load (N) Left Dial Right Dial U (mm) U (m) V V (m) Load (g)0 0 0 0 0 0 0 0 0
100 0.981 0.31 0.32 0.45 0.000445 -0.01 -7.1E-06 100200 1.962 1.06 0.52 1.12 0.001117 0.38 0.000382 200300 2.943 2.18 0.68 2.02 0.002022 1.06 0.001061 300400 3.924 2.65 0.99 2.57 0.002574 1.17 0.001174 400500 4.905 3.88 1.17 3.57 0.003571 1.92 0.001916 500
dU/dP = 0.0007 dV/dP = 0.0004 dU/dP =dU/dP = 0.7323 dV/dP = 0.4020 mm/N dU/dP =
Load (g) Load (N) Left Dial Right Dial U (mm) U (m) V V (m) Load (g)0 0 0 0 0 0 0 0 0
100 0.981 1.26 0.34 1.13 0.001131 0.65 0.000651 100200 1.962 2.64 0.76 2.40 0.002404 1.33 0.001329 200300 2.943 3.90 1.16 3.58 0.003578 1.94 0.001937 300400 3.924 4.60 1.55 4.35 0.004349 2.16 0.002157 400500 4.905 6.11 1.94 5.69 0.005692 2.95 0.002949 500
dU/dP = 0.0011 dV/dP = 0.0006 dU/dP =dU/dP = 1.1442 dV/dP = 0.5787 mm/N dU/dP =
Head Angle 67.5°
Head Angle 22.5° Head Angle 90°
Head Angle 45° Head Angle 112.5°
0 100 200 300 400 500 6000
1
2
3
4
5
6
7
8
9
f(x) = 0.00519273507129539 x
f(x) = 0.00678051120723246 x
f(x) = 0.0104266109007689 x
f(x) = 0.0146371103705615 x
f(x) = 0.0164280190000031 x
f(x) = 0.0150832304670556 x
f(x) = 0.0113689913927866 x
f(x) = 0.00670851488042074 x
f(x) = 0.00514002347487967 x
Displacement U Vs Load P 0Linear (0)22.5Linear (22.5)45Linear (45)67.5Linear (67.5)90Linear (90)112.5Linear (112.5)135Linear (135)157.5Linear (157.5)
Load P (g)
Dis
plac
emen
t U (m
m)
0 100 200 300 400 500 6000
1
2
3
4
5
6
7
8
9
f(x) = 0.00519273507129539 x
f(x) = 0.00678051120723246 x
f(x) = 0.0104266109007689 x
f(x) = 0.0146371103705615 x
f(x) = 0.0164280190000031 x
f(x) = 0.0150832304670556 x
f(x) = 0.0113689913927866 x
f(x) = 0.00670851488042074 x
f(x) = 0.00514002347487967 x
Displacement U Vs Load P 0Linear (0)22.5Linear (22.5)45Linear (45)67.5Linear (67.5)90Linear (90)112.5Linear (112.5)135Linear (135)157.5Linear (157.5)
Load P (g)D
ispl
acem
ent U
(mm
)
0 100 200 300 400 500 600
-3
-2
-1
0
1
2
3
4
f(x) = − 7.32819755047877E-05 xf(x) = − 0.00372580991250657 xf(x) = − 0.00494460487353357 xf(x) = − 0.00377595021153616 xf(x) = 1.54277843167976E-05 x
f(x) = 0.00403436559884252 x
f(x) = 0.00590755574464034 x
f(x) = 0.00331183103333917 x
f(x) = 0.000254558441227157 x
Displacement V Vs Load P0Linear (0)22.5Linear (22.5)45Linear (45)67.5Linear (67.5)90Linear (90)
Load P (g)
Dis
plac
emen
t V (m
m)
Load (N) Left Dial Right Dial U (mm) U (m) V (mm) V (m) Load (g) Load (N)0 0 0 0 0 0 0 0 0
0.981 0.93 0.56 1.05 0.001054 0.26 0.000262 100 0.9811.962 2.57 1.50 2.88 0.002878 0.76 0.000757 200 1.9622.943 4.40 2.44 4.84 0.004837 1.39 0.001386 300 2.9433.924 5.42 3.11 6.03 0.006032 1.63 0.001633 400 3.9244.905 6.68 3.93 7.50 0.007502 1.94 0.001945 500 4.905
0.0016 dV/dP = 0.0004 dU/dP = 0.00111.5845 dV/dP = 0.4214 mm/N dU/dP = 1.0925
Load (N) Left Dial Right Dial U (mm) U (m) V (mm) V (m) Load (g) Load (N)0 0 0 0 0 0 0 0 0
0.981 1.06 1.10 1.53 0.001527 -0.03 -2.83E-05 100 0.9811.962 2.25 2.25 3.18 0.003182 0.00 0 200 1.9622.943 3.48 3.45 4.90 0.0049 0.02 2.121E-05 300 2.9433.924 4.80 4.77 6.77 0.006767 0.02 2.121E-05 400 3.9244.905 5.75 5.76 8.14 0.008139 -0.01 -7.07E-06 500 4.905
0.0017 dV/dP = 0.0000 dU/dP = 0.00071.6931 dV/dP = 0.0039 mm/N dU/dP = 0.6926
Load (N) Left Dial Right Dial U (mm) U (m) V (mm) V (m) Load (g) Load (N)0 0 0 0 0 0 0 0 0
0.981 0.68 0.96 1.16 0.00116 -0.20 -0.000198 100 0.9811.962 1.43 2.64 2.88 0.002878 -0.86 -0.000856 200 1.9622.943 2.42 4.14 4.64 0.004639 -1.22 -0.001216 300 2.9433.924 3.01 5.10 5.73 0.005735 -1.48 -0.001478 400 3.9244.905 3.88 6.51 7.35 0.007347 -1.86 -0.00186 500 4.905
0.0015 dV/dP = -0.0004 dU/dP = 0.00051.5209 dV/dP = -0.3931 mm/N dU/dP = 0.5309
Head Angle 67.5° Head Angle 135°
Head Angle 90° Head Angle 157.5°
Head Angle 112.5° Head Angle 180°
0 100 200 300 400 500 6000
1
2
3
4
5
6
7
8
9
f(x) = 0.00519273507129539 x
f(x) = 0.00678051120723246 x
f(x) = 0.0104266109007689 x
f(x) = 0.0146371103705615 x
f(x) = 0.0164280190000031 x
f(x) = 0.0150832304670556 x
f(x) = 0.0113689913927866 x
f(x) = 0.00670851488042074 x
f(x) = 0.00514002347487967 x
Displacement U Vs Load P 0Linear (0)22.5Linear (22.5)45Linear (45)67.5Linear (67.5)90Linear (90)112.5Linear (112.5)135Linear (135)157.5Linear (157.5)
Load P (g)
Dis
plac
emen
t U (m
m)
0 100 200 300 400 500 6000
1
2
3
4
5
6
7
8
9
f(x) = 0.00519273507129539 x
f(x) = 0.00678051120723246 x
f(x) = 0.0104266109007689 x
f(x) = 0.0146371103705615 x
f(x) = 0.0164280190000031 x
f(x) = 0.0150832304670556 x
f(x) = 0.0113689913927866 x
f(x) = 0.00670851488042074 x
f(x) = 0.00514002347487967 x
Displacement U Vs Load P 0Linear (0)22.5Linear (22.5)45Linear (45)67.5Linear (67.5)90Linear (90)112.5Linear (112.5)135Linear (135)157.5Linear (157.5)
Load P (g)
Dis
plac
emen
t U (m
m)
0 100 200 300 400 500 600
-3
-2
-1
0
1
2
3
4
f(x) = − 7.32819755047877E-05 xf(x) = − 0.00372580991250657 xf(x) = − 0.00494460487353357 xf(x) = − 0.00377595021153616 xf(x) = 1.54277843167976E-05 x
f(x) = 0.00403436559884252 x
f(x) = 0.00590755574464034 x
f(x) = 0.00331183103333917 x
f(x) = 0.000254558441227157 x
Displacement V Vs Load P0Linear (0)22.5Linear (22.5)45Linear (45)67.5Linear (67.5)90Linear (90)
Load P (g)
Dis
plac
emen
t V (m
m)
Left Dial Right Dial U (mm) U (m) V (mm) V (m)0 0 0 0 0 0
0.37 0.69 0.75 0.00075 -0.23 -0.0002260.79 2.05 2.01 0.002008 -0.89 -0.0008911.17 3.52 3.32 0.003316 -1.66 -0.0016621.59 4.32 4.18 0.004179 -1.93 -0.001931.90 5.43 5.18 0.005183 -2.50 -0.002496
dV/dP = -0.0005dV/dP = -0.5348 mm/N
Left Dial Right Dial U (mm) U (m) V (mm) V (m)0 0 0 0 0 0
0.18 0.73 0.64 0.000643 -0.39 -0.0003890.45 1.51 1.39 0.001386 -0.75 -0.000750.61 2.29 2.05 0.002051 -1.19 -0.0011880.83 2.96 2.68 0.00268 -1.51 -0.0015061.13 3.68 3.40 0.003401 -1.80 -0.001803
dV/dP = -0.0004dV/dP = -0.3730 mm/N
Left Dial Right Dial U (mm) U (m) V (mm) V (m)0 0 0 0 0 0
0.33 0.38 0.50 0.000502 -0.04 -3.54E-050.75 0.72 1.04 0.001039 0.02 2.121E-051.10 1.12 1.57 0.00157 -0.01 -1.41E-051.42 1.50 2.06 0.002065 -0.06 -5.66E-051.82 1.86 2.60 0.002602 -0.03 -2.83E-05
dV/dP = 0.0000dV/dP = -0.0070 mm/N
Head Angle 135°
Head Angle 157.5°
Head Angle 180°
-0.0006 -0.0004 -0.0002 0 0.0002 0.0004 0.0006 0.00080.0000
0.0002
0.0004
0.0006
0.0008
0.0010
0.0012
0.0014
0.0016
0.0018
dU/dP Vs dV/dP m/N
dV/dP
dU/d
P
0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
dV/dP Vs dU/dP mm/N
dU/dP
dV/d
P
0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
dV/dP Vs dU/dP mm/N
dU/dP
dV/d
P
-0.0006 -0.0004 -0.0002 0 0.0002 0.0004 0.0006 0.00080.0000
0.0002
0.0004
0.0006
0.0008
0.0010
0.0012
0.0014
0.0016
0.0018
dU/dP Vs dV/dP m/N
dV/dP
dU/d
P
0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
dV/dP Vs dU/dP mm/N
dU/dP
dV/d
P
0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
dV/dP Vs dU/dP mm/N
dU/dP
dV/d
P
L = 470 mm
1 Fixed-Free Ends
470 mmE = 69 Gpa
Section Details"U" section
Width b (mm) 12.80 12.80 6.49Depth d (mm) 12.80 12.80 12.85
Thickness (mm) 1.80 1.80dU/dP axis crossing 0.52 0.51 0.54dU/dP axis crossing 2.32 0.655 1.7
Dist of Centre from Origin1.420 0.583 1.120
R 0.900 0.073 0.580
1016.88 1523.17 1147.86
964.54 983.45 928.82
267.21 1002.12 292.35
216.19 765.74 295.04
ke =
Le =
Angle Section
Rectangular Section
Ix.theory =
Ix,exp =
Iy.theory =
Iy,exp =𝐼_𝑥=𝐿^3/3𝐸(𝑂𝐶+𝑅) 𝐼_𝑦=𝐿^3/3𝐸(𝑂𝐶−𝑅)
dU/dP dV/dPAngle U Rect Angle U Rect
0 1.44 0.69 0.53 0 -0.6981 -0.0128 0.028022.5 0.84 0.63 0.73 22.5 -0.4028 -0.0628 0.4020
45 0.62 0.57 1.14 45 0.0400 -0.0494 0.578767.5 0.79 0.54 1.58 67.5 0.3907 -0.0122 0.4214
90 1.25 0.52 1.69 90 0.5931 0.0305 0.0039112.5 1.99 0.53 1.52 112.5 0.5476 0.0713 -0.3931
135 2.16 0.58 1.09 135 0.1005 0.0758 -0.5348157.5 2.01 0.65 0.69 157.5 -0.5464 0.0608 -0.3730
180 1.53 0.66 0.53 180 -0.6909 -0.0031 -0.0070Max = 2.16 0.69 1.69 0.59 0.08 0.58Min = 0.62 0.52 0.53 -0.70 -0.06 -0.53
