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Moments of Inertia

Moments of Inertia

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Moments of Inertia

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  1. Moments of Inertia • Polar moment of inertia – Used when calculating the torsion • Indication of resistance to torsion • Solid Shaft • J = π R4 / 2 • Area moment of inertia – Used when calculating bending stresses • Indication of resistance to bending moments • I = π r4 / 4 • Polar and area moments of inertias use a variety of different formulas • For example, solid versus hollow

  2. Cranes and Slings • Major Causes of Crane Accidents • Contact with power lines • Overturns • Falls • Mechanical failures

  3. Crane Parts

  4. Rated Capacities • Make sure the crane operator can see the: • Rated Load Capacities • Operating Speeds • Special Hazard Warning or Instruction • APPLICABLE OSHA STANDARD • 1926.1501 (a)(2) Rated load capacities, and recommended operating speeds, special hazard warnings, or instruction, shall be conspicuously posted on all equipment. Instructions or warnings shall be visible to the operator while he is at his control station.

  5. Know the Weight of the Load • Refer to shipping ticket or other documentation • Ensure lift calculations are correct • Ensure load is within load chart rating for boom length and load radius of crane • Crane is rated by the maximum weight it will lift at a minimum radius and minimum boom length – the further from its centerpoint, the less it will lift

  6. Load Limiting Factors • Not level • Wind • Side loads • On its wheels • Lifting over the side • Use of extensions, jibs and other attachments • Limits of wire rope, slings and lifting devices

  7. Load Example – 30 ton crane • Will lift 60,000 pounds at 10 feet from the center pin of the crane • Based on level surface, no wind, and outriggers fully extended • At 25 feet from the center pin with an 80 foot boom, the capacity is only 14,950 pounds • At 74 feet from the center pin, the capacity is only 4,800 pounds

  8. Alloy Steel Chains Adapts to shape of the load Can damage by sudden shocks Best choice for hoisting very hot materials Must have an affixed tag stating size, grade, rated capacity, and sling manufacturer

  9. Wire Rope Slings • Used to hoist materials • Selection considerations: • strength • ability to bend without cracking • ability to withstand abrasive wear • ability to withstand abuse Wire Core Center Strand Wire rope

  10. Synthetic Web SlingMarkings • Mark or code to show: • Name or trademark of manufacturer • Rated capacities for the type of hitch • Type of material

  11. OSHA Sling Tables

  12. Sling Stress Example • From the table, a single branch with a 90 degree loading is rated at 3,250 lbs. • If there is a safety factor of 4, the chain could lift 13,000 lbs before breaking. • Two legs at 90 degrees would be rated at 6,500 lbs.

  13. Sling Example • From the table, a two leg sling that forms a 60 degree angle off of the horizontal is rated at 5,560 lbs. • This means the most weight in this configuration the sling should be used to lift is 5,560 lbs. • Preforming this list would result in what type of stress each leg? • What if the sling were used to list 5,560 lbs and the angle off the horizontal were 40 lbs?