SOLIDWORKS Bridge

{
 "id": "cswa-09-community-stepped-shaft",
 "title": "Community: a stepped hollow shaft - revolved, a groove revolve-cut, a half-depth flat revolve-cut mid-plane",
 "source": "community: built for the bridge's benchmark (no exam publishes it); the key is derived analytically in `derivation`",
 "official": false,
 "units": "MMGS",
 "origin": "the shaft's axis is model X (the Front Plane sketch's x axis), its left end at x = 0; a \u00d86 bore through",
 "material": {
  "name": "6061 Alloy",
  "densityKgM3": 2700
 },
 "expected": {
  "massG": 103.568885,
  "volumeMm3": 38358.8463,
  "centerOfMassMm": [
   46.831491,
   -0.114185,
   0.0
  ],
  "tolerancePct": 0.1
 },
 "keyBasis": "derived analytically (derivation): three coaxial tubes (\u00d820 x 30, \u00d830 x 40, \u00d816 x 25, \u00d86 bore) less a 2-deep x 5-wide groove at x 45..50 and the y > 0 half of a ring r 7..10 over x 0..10 (a 180\u00b0 mid-plane revolve-cut from a profile on +Y sweeps -90\u00b0..+90\u00b0 about +Y); the half ring's centroid is 4(R^3-r^3)/(3\u03c0(R^2-r^2)) off the axis. Exact: held to 0.1 %",
 "exercises": [
  "revolve.360",
  "revolve_cut.360",
  "revolve_cut.midPlane",
  "sketch.construction",
  "sketch.line",
  "sketch.rect"
 ],
 "derivation": [
  [
   "V_body",
   "pi*((10**2 - 3**2)*30 + (15**2 - 3**2)*40 + (8**2 - 3**2)*25)"
  ],
  [
   "Mx_body",
   "pi*((10**2 - 3**2)*30*15 + (15**2 - 3**2)*40*50 + (8**2 - 3**2)*25*82.5)"
  ],
  [
   "V_groove",
   "pi*(15**2 - 13**2)*5"
  ],
  [
   "V_notch",
   "pi*(10**2 - 7**2)*10/2"
  ],
  [
   "yc_notch",
   "4*(10**3 - 7**3)/(3*pi*(10**2 - 7**2))"
  ],
  [
   "volumeMm3",
   "V_body - V_groove - V_notch"
  ],
  [
   "massG",
   "volumeMm3*2.7e-3"
  ],
  [
   "centerOfMassMm",
   "[(Mx_body - V_groove*47.5 - V_notch*5)/volumeMm3, -V_notch*yc_notch/volumeMm3, 0.0]"
  ]
 ],
 "needsOps": [],
 "script": [
  {
   "op": "new_part"
  },
  {
   "op": "sketch",
   "plane": "Front Plane",
   "entities": [
    {
     "polyline": {
      "points": [
       [
        0,
        3
       ],
       [
        0,
        10
       ],
       [
        30,
        10
       ],
       [
        30,
        15
       ],
       [
        70,
        15
       ],
       [
        70,
        8
       ],
       [
        95,
        8
       ],
       [
        95,
        3
       ]
      ],
      "close": true
     }
    }
   ]
  },
  {
   "op": "revolve",
   "axis": "x"
  },
  {
   "op": "sketch",
   "plane": "Front Plane",
   "entities": [
    {
     "rect": {
      "xMm": 45,
      "yMm": 13,
      "widthMm": 5,
      "heightMm": 2
     }
    }
   ]
  },
  {
   "op": "revolve_cut",
   "axis": "x"
  },
  {
   "op": "sketch",
   "plane": "Front Plane",
   "entities": [
    {
     "rect": {
      "xMm": 0,
      "yMm": 7,
      "widthMm": 10,
      "heightMm": 3
     }
    }
   ]
  },
  {
   "op": "revolve_cut",
   "axis": "x",
   "angleDeg": 180,
   "midPlane": true
  },
  {
   "op": "set_material",
   "name": "6061 Alloy",
   "densityKgM3": 2700
  }
 ]
}