# Simple round Bar Sections

### Simple round Bar Sections

Table of Dimensions + Properties

The table includes various useful properties of steel round bar.    The properties are based on the following

Density of mild steel = 7830 kg/m3
2nd Moment of Area ( Ixx = Iyy ) for a round section = πD4 /64 (Used for bending equations )
Polar moment of Area ( Izz ) for a round section = πD4 /32 (used for torsion equations )
Radius of Gyration ( k ) = R /(2) = (D/2) / (2)
Mass Polar Moment of inertia ( Jm ) = m.k2 (used for shaft/ flywheel dynamic inertia calcs

Note: The mass properties provided can easily be converted to another material by mulipling the mass/mm by the ratio of the density of the chosen material to that of steel.

m copper = msteel . [ Densitycopper / Density steel ]

Jm_copper = Jm_steel . [ Densitycopper / Density steel ]

Example 50mm diameter
CSA = 1963mm2
Weight/mm = 0,01571 kg
2nd moment of Area (Ixx = Iyy )= 0,3068 x 106 mm4
Polar M of Area(Izz ) = 0,6136 x 106 mm4
Radius of Gyration (about z axis) = 17.67767 mm
Mass Polar M of I /mm = 4.8044 kg mm2

 Dia Cross Section Area Mass/mm Second Moment of Area of section Polar Moment of Area Torsional Radius of Gyration Mass Polar Moment of Inertia/mm Bending Calcs. Torsion Calcs Dynamic rotation calcs. Dynamic rotation calcs. shafts , flywheels D A m Ixx = Iyy J = Izz k Jm = Im.zz mm mm2 kg/mm mm4 x 106 mm4 x 106 mm kg.mm2 5 0.00001963 0.00015 0.00003068 0.00006136 1.76777 0.0005 10 0.00007854 0.00061 0.00049087 0.00098175 3.53553 0.0077 15 0.00017671 0.00138 0.00248505 0.00497010 5.30330 0.0389 20 0.000314 0.00246 0.00785 0.01571 7.07107 0.1230 25 0.000491 0.00384 0.01917 0.03835 8.83883 0.3003 30 0.000707 0.00553 0.03976 0.07952 10.60660 0.6227 35 0.000962 0.00753 0.07366 0.14732 12.37437 1.1535 40 0.001257 0.00984 0.12566 0.25133 14.14214 1.9679 45 0.001590 0.01245 0.20129 0.40258 15.90990 3.1522 50 0.001963 0.01537 0.30680 0.61359 17.67767 4.8044 55 0.002376 0.01860 0.44918 0.89836 19.44544 7.0342 60 0.002827 0.02214 0.63617 1.27235 21.21320 9.9625 65 0.003318 0.02598 0.87624 1.75248 22.98097 13.7219 70 0.003848 0.03013 1.17859 2.35718 24.74874 18.4567 75 0.004418 0.03459 1.55316 3.10631 26.51650 24.3224 80 0.005027 0.03936 2.01062 4.02124 28.28427 31.4863 85 0.005675 0.04443 2.56239 5.12478 30.05204 40.1271 90 0.006362 0.04981 3.22062 6.44125 31.81981 50.4350 95 0.007088 0.05550 3.99820 7.99640 33.58757 62.6118 100 0.007854 0.06150 4.90874 9.81748 35.35534 76.8708 105 0.008659 0.06780 5.96660 11.93320 37.12311 93.4370 110 0.009503 0.07441 7.18688 14.37377 38.89087 112.5466 115 0.010387 0.08133 8.58541 17.17083 40.65864 134.4476 120 0.011310 0.08856 10.17876 20.35752 42.42641 159.3994 125 0.012272 0.09609 11.98422 23.96845 44.19417 187.6730 130 0.013273 0.10393 14.01985 28.03970 45.96194 219.5508 Dia Cross Section Area Mass/mm Second Moment of Area of section Polar Moment of Area Torsional Radius of Gyration Mass Polar Moment of Inertia/mm Bending Calcs. Torsion Calcs Dynamic rotation calcs. Dynamic rotation calcs. shafts , flywheels D A m Ixx = Iyy J = Izz k Jm = Im.zz mm mm2 kg/mm mm4 x 106 mm4 x 106 mm kg.mm2 135 0.014314 0.11208 16.30441 32.60881 47.72971 255.3270 140 0.015394 0.12053 18.85741 37.71482 49.49747 295.3070 145 0.016513 0.12930 21.69911 43.39822 51.26524 339.8081 150 0.017671 0.13837 24.85049 49.70098 53.03301 389.1587 155 0.018869 0.14775 28.33327 56.66654 54.80078 443.6990 160 0.020106 0.15743 32.16991 64.33982 56.56854 503.7808 165 0.021382 0.16742 36.38360 72.76720 58.33631 569.7672 170 0.022698 0.17773 40.99828 81.99655 60.10408 642.0330 175 0.024053 0.18833 46.03860 92.07720 61.87184 720.9645 180 0.025447 0.19925 51.52997 103.05995 63.63961 806.9594 185 0.026880 0.21047 57.49854 114.99708 65.40738 900.4271 190 0.028353 0.22200 63.97117 127.94234 67.17514 1001.7885 195 0.029865 0.23384 70.97548 141.95096 68.94291 1111.4760 200 0.031416 0.24599 78.53982 157.07963 70.71068 1229.9335 205 0.033006 0.25844 86.69326 173.38652 72.47845 1357.6165 210 0.034636 0.27120 95.46564 190.93128 74.24621 1494.9919 215 0.036305 0.28427 104.88750 209.77500 76.01398 1642.5383 220 0.038013 0.29764 114.99015 229.98029 77.78175 1800.7457 225 0.039761 0.31133 125.80560 251.61120 79.54951 1970.1157 230 0.041548 0.32532 137.36663 274.73326 81.31728 2151.1614 235 0.043374 0.33962 149.70674 299.41348 83.08505 2344.4075 240 0.045239 0.35422 162.86016 325.72033 84.85281 2550.3902 245 0.047144 0.36913 176.86188 353.72376 86.62058 2769.6570 250 0.049087 0.38435 191.74760 383.49520 88.38835 3002.7674 255 0.051071 0.39988 207.55377 415.10753 90.15611 3250.2920 260 0.053093 0.41572 224.31757 448.63514 91.92388 3512.8131 265 0.055155 0.43186 242.07693 484.15385 93.69165 3790.9246 270 0.057256 0.44831 260.87049 521.74098 95.45942 4085.2319 275 0.059396 0.46507 280.73766 561.47532 97.22718 4396.3517 280 0.061575 0.48213 301.71856 603.43712 98.99495 4724.9126 285 0.063794 0.49951 323.85405 647.70811 100.76272 5071.5545 290 0.066052 0.51719 347.18575 694.37150 102.53048 5436.9288 295 0.068349 0.53517 371.75598 743.51196 104.29825 5821.6986 300 0.070686 0.55347 397.60782 795.21564 106.06602 6226.5385 Dia Cross Section Area Mass/mm Second Moment of Area of section Polar Moment of Area Torsional Radius of Gyration Mass Polar Moment of Inertia/mm Bending Calcs. Torsion Calcs Dynamic rotation calcs. Dynamic rotation calcs. shafts , flywheels D A m Ixx = Iyy J = Izz k Jm = Im.zz mm mm2 kg/mm mm4 x 106 mm4 x 106 mm kg.mm2 310 0.075477 0.59098 453.33231 906.66462 109.60155 7099.1840 320 0.080425 0.62973 514.71854 1029.43708 113.13708 8060.4923 330 0.085530 0.66970 582.13761 1164.27522 116.67262 9116.2750 340 0.090792 0.71090 655.97240 1311.94480 120.20815 10272.5278 350 0.096211 0.75333 736.61757 1473.23515 123.74369 11535.4312 360 0.101788 0.79700 824.47958 1648.95915 127.27922 12911.3502 370 0.107521 0.84189 919.97663 1839.95326 130.81475 14406.8340 380 0.113411 0.88801 1023.53874 2047.07748 134.35029 16028.6167 390 0.119459 0.93536 1135.60770 2271.21539 137.88582 17783.6165 400 0.125664 0.98395 1256.63706 2513.27412 141.42136 19678.9364 410 0.132025 1.03376 1387.09219 2774.18437 144.95689 21721.8637 420 0.138544 1.08480 1527.45020 3054.90040 148.49242 23919.8702 430 0.145220 1.13707 1678.20002 3356.40003 152.02796 26280.6123 440 0.152053 1.19058 1839.84232 3679.68464 155.56349 28811.9308 450 0.159043 1.24531 2012.88959 4025.77918 159.09903 31521.8510 460 0.166190 1.30127 2197.86607 4395.73215 162.63456 34418.5827 470 0.173494 1.35846 2395.30781 4790.61562 166.17009 37510.5203 480 0.180956 1.41688 2605.76261 5211.52522 169.70563 40806.2425 490 0.188574 1.47654 2829.79007 5659.58015 173.24116 44314.5126 500 0.196350 1.53742 3067.96158 6135.92315 176.77670 48044.2783 510 0.204282 1.59953 3320.86028 6641.72055 180.31223 52004.6719 520 0.212372 1.66287 3589.08111 7178.16222 183.84776 56205.0102 530 0.220618 1.72744 3873.23080 7746.46161 187.38330 60654.7944 540 0.229022 1.79324 4173.92785 8347.85571 190.91883 65363.7102 550 0.237583 1.86027 4491.80254 8983.60509 194.45436 70341.6278 560 0.246301 1.92854 4827.49694 9654.99387 197.98990 75598.6020 570 0.255176 1.99803 5181.66487 10363.32975 201.52543 81144.8719 580 0.264208 2.06875 5554.97198 11109.94397 205.06097 86990.8613 590 0.273397 2.14070 5948.09567 11896.19134 208.59650 93147.1782 600 0.282743 2.21388 6361.72512 12723.45025 212.13203 99624.6154 620 0.301907 2.36393 7253.31697 14506.63395 219.20310 113586.9438 640 0.321699 2.51890 8235.49665 16470.99329 226.27417 128967.8775 660 0.342119 2.67880 9314.20175 18628.40351 233.34524 145860.3995 680 0.363168 2.84361 10495.55840 20991.11680 240.41631 164360.4446 700 0.384845 3.01334 11785.88119 23571.76238 247.48737 184566.8994 Dia Cross Section Area Mass/mm Second Moment of Area of section Polar Moment of Area Torsional Radius of Gyration Mass Polar Moment of Inertia/mm Bending Calcs. Torsion Calcs Dynamic rotation calcs. Dynamic rotation calcs. shafts , flywheels D A m Ixx = Iyy J = Izz k Jm = Im.zz mm mm2 kg/mm mm4 x 106 mm4 x 106 mm kg.mm2 720 0.407150 3.18799 13191.67322 26383.34643 254.55844 206581.6026 740 0.430084 3.36756 14719.62607 29439.25215 261.62951 230509.3443 760 0.453646 3.55205 16376.61985 32753.23970 268.70058 256457.8668 780 0.477836 3.74146 18169.72313 36339.44625 275.77164 284537.8641 800 0.502655 3.93579 20106.19298 40212.38597 282.84271 314862.9821 820 0.528102 4.13504 22193.47500 44386.94999 289.91378 347549.8184 840 0.554177 4.33921 24439.20323 48878.40647 296.98485 382717.9227 860 0.580880 4.54829 26851.20026 53702.40053 304.05592 420489.7961 880 0.608212 4.76230 29437.47715 58874.95429 311.12698 460990.8921 900 0.636173 4.98123 32206.23344 64412.46688 318.19805 504349.6156 920 0.664761 5.20508 35165.85719 70331.71438 325.26912 550697.3236 940 0.693978 5.43385 38324.92495 76649.84991 332.34019 600168.3248 960 0.723823 5.66753 41692.20177 83384.40354 339.41125 652899.8797 980 0.754296 5.90614 45276.64118 90553.28236 346.48232 709032.2008 1000 0.785398 6.14967 49087.38521 98174.77042 353.55339 768708.4524 Dia Cross Section Area Mass/mm Second Moment of Area of section Polar Moment of Area Torsional Radius of Gyration Mass Polar Moment of Inertia/mm Bending Calcs. Torsion Calcs Dynamic rotation calcs. Dynamic rotation calcs. shafts , flywheels D A m Ixx = Iyy J = Izz k Jm = Im.zz mm mm2 kg/mm mm4 x 106 mm4 x 106 mm kg.mm2