Motorcycle Chassis Design: Tube Stiffness

Motorcycle Chassis Design: Tube Stiffness

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Indian Larry: Chopper Shaman
The World's Fastest Indian
    Here I will make various observations and comments on how the chassis, swing-arm, forks, brakes &c. function, and in some cases how to diagnose minor faults and make improvements. New material will be added regularly, and eventually better organized. Click below to jump directly to an individual topic.
Frame
Tube stiffness
Forks
Shocks
Steering damper
Engine plates
Wheels
Tires
Chain
Transmission ratio
AHRMA rules
Flywheel inertia
Swing-arm
Brake torque link
Tools, mtl.

    The Tables below are ranked by the stressed dimension in order of OD; select the correct Table first. The values appear below the heading.
    A round tube’s wall thickness in either fractional or U. S. gauge size (Columns 1 & 2), ID (Column 3), stiffness (resistance to bending; Column 4) is calculated by (Π/64) ×((D^4)-(d^4)) or .049087 ×((D^4)-(d^4)), the cross-sectional area (Column 5). The weight is in lbs. per linear foot, with steel at .2836 lbs. per cubic inch (Column 6), and stiffness to weight ratio (× 10,000 to make an easy comparison) (Column 7). Compare tubes of the same wall thickness but different OD for a huge change in stiffness but almost no weight penalty.
    For oval or elliptical tubing*, which Table to use is based on the orientation of the tube in the swing-arm. The long (major) axis is normally the height (vertical); if so, use this Table. If not, use the short (minor) axis.
    For rectangular tubing*, the same rule applies; if the long axis is vertical use this, &c.
    For square tubing* positioned parallel to the ground, use the length of one side.
    For square tubing* rotated 45° (with its corners vertical & horizontal), use the length of one side × 1.4142 (the sine of 45°). Simply turning the tube so that its greatest dimension becomes its stressed axis greatly increases its bending resistance. Since the relative size of this axis (proportionate to the original dimension) is known, the increase in stiffness can be calculated from the relationship without knowing the specific dimension. The math: 1.4142^4 = 4. The tube’s bending resistance in its new orientation is 400% of the “normal” position, or an increase of 300%.
* With these shapes the cross-sectional area, weight, and stiffness/weight values shown in Columns 5-7 are not applicable.

Round tube outside diameter: .875” (7/8”, 22.2mm)

U.S. Gauge
Wall
ID
Stiffness
X-Area
Weight, lbs./ft.
Stiff/Wt. * 10³
1/8”
.125
.6250
.021284
.294524
1.002324
212
11
.120
.6350
.020793
.284628
.968646
215
12
.109
.6570
.019628
.262304
.892673
220
3/32”
.094
.6875
.017808
.230097
.783066
227
14
.083
.7090
.016370
.206516
.702815
233
16
.065
.7450
.013653
.165405
.562906
243
18
.049
.7770
.010882
.127153
.432727
251
20
.035
.8050
.008161
.092363
.314330
260

Round tube outside diameter: .9375” (15/16”, 23.8mm)

U.S. Gauge
Wall
ID
Stiffness
X-Area
Weight, lbs./ft.
Stiff/Wt. * 10³
1/8”
.125
.6875
.026953
.319068
1.085852
248
11
.120
.6975
.026300
.308190
1.048832
251
12
.109
.7195
.024764
.283706
.965508
256
3/32”
.094
.7500
.022387
.248505
.845712
265
14
.083
.7715
.020528
.222813
.758277
271
16
.065
.8075
.017048
.178168
.606341
281
18
.049
.8395
.013538
.136774
.465469
291
20
.035
.8675
.010119
.099235
.337717
300

Round tube outside diameter: 1.000” (1”, 25.4mm)

U.S. Gauge
Wall
ID
Stiffness
X-Area
Weight, lbs./ft.
Stiff/Wt. * 10³
1/8”
.125
.7500
.033556
.343612
1.169380
287
11
.120
.7600
.032711
.331752
1.129018
290
12
.109
.7820
.030731
.305108
1.038344
296
3/32”
.094
.8120
.027747
.267551
.910530
305
14
.083
.8340
.025339
.239110
.813739
311
16
.065
.8700
.020965
.190930
.649773
323
18
.049
.9020
.016594
.146395
.498211
333
20
.035
.9300
.012367
.106107
.361103
342

Round tube outside diameter: 1.125” (1-1/8”, 28.6mm)

U.S. Gauge
Wall
ID
Stiffness
X-Area
Weight, lbs./ft.
Stiff/Wt. * 10³
1/8”
.125
.8750
.049854
.392699
1.336433
373
11
.120
.8850
.048516
.378876
1.289391
376
12
.109
.9070
.045409
.347912
1.184014
384
3/32”
.094
.9375
.04071
.303728
1.033647
394
14
.083
.9590
.037110
.271704
.924663
401
16
.065
.9950
.030516
.216456
.736643
414
18
.049
1.0270
.024021
.165637
.563696
426
20
.035
1.0550
.017818
.119852
.407880
437

Round tube outside diameter: 1.250” (1-1/4”, 31.8mm)

U.S. Gauge
Wall
ID
Stiffness
X-Area
Weight, lbs./ft.
Stiff/Wt. * 103
1/8”
.125
1.0000
.070755
.441786
1.503486
471
11
.120
1.0100
.068762
.426000
1.449763
474
12
.109
1.0320
.064164
.390717
1.329688
483
3/32”
.094
1.0625
.057284
.340544
1.158939
494
14
.083
1.0840
.052065
.304298
1.035587
503
16
.065
1.1200
.042602
.241981
.823510
517
18
.049
1.1520
.033389
.184880
.629184
531
20
.035
1.1800
.024673
.133596
.454654
543

Round tube outside diameter: 1.375” (1-3/8”, 34.9mm)

U.S. Gauge
Wall
ID
Stiffness
X-Area
Weight, lbs./ft.
Stiff/Wt. * 10³
1/8”
.125
1.1250
.096833
.490874
1.670542
580
11
.120
1.1350
.093999
.473124
1.610136
584
12
.109
1.1570
.087497
.433521
1.475359
593
3/32”
.094
1.1875
.077849
.377359
1.284228
606
14
.083
1.2090
.070585
.336892
1.146511
616
16
.065
1.2450
.057525
.267507
.910380
632
18
.049
1.2770
.044924
.204122
.694668
647
20
.035
1.3050
.033093
.147341
.501431
660

Round tube outside diameter: 1.500” (1-1/2”, 38.1mm)

U.S. Gauge
Wall
ID
Stiffness
X-Area
Weight, lbs./ft.
Stiff/Wt. * 10³
1/8”
.125
1.2500
.128663
.539961
1.837595
700
11
.120
1.2600
.124781
.520248
1.770508
705
12
.109
1.2820
.115911
.476325
1.621029
715
3/32”
.094
1.3125
.102836
.414175
1.409520
730
14
.083
1.3340
.093054
.369486
1.257435
740
16
.065
1.3700
.075582
.293032
.997247
758
18
.049
1.4020
.058851
.223364
.760152
774
20
.035
1.4300
.043240
.161085
.548204
789

Round tube outside diameter: 2.000” (2”, 50.8mm)

U.S. Gauge
Wall
ID
Stiffness
X-Area
Weight, lbs./ft.
Stiff/Wt. * 10³
1/8”
.125
1.7500
.325012
.736311
2.505814
1297
11
.120
1.7600
.314399
.708743
2.411994
1303
12
.109
1.7820
.290403
.647542
2.203715
1318
3/32”
.094
1.8125
.255635
.561437
1.910682
1338
14
.083
1.8340
.230048
.499862
1.701130
1352
16
.065
1.8700
.185142
.395134
1.344720
1377
18
.049
1.9020
.142989
.300333
1.022093
1399
20
.035
1.9300
.104317
.216063
.735306
1419

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