Equipment for Rational Securing of Cargo on Railway ... - Vinnova

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MariTerm AB 2004-01-30 jvgRASLA Equilibrium <strong>of</strong> <strong>for</strong>ces: ↑ → R − m ⋅ g = m ⋅ a F f = m ⋅ a Force <strong>of</strong> friction: h v ⇒ ⇒ a h = R = m ⋅ F f m ( a + g) v ( a g) F f = µ ⋅ R = µ ⋅ m ⋅ v + Largest horizontal acceleration that can act on the coil be<strong>for</strong>e it starts to slide is: a ( a + g) µ ⋅ m ⋅ v = = µ ⋅ m ( a g) h v + Transversal direction: The largest allowed transverse acceleration to avoid sliding is calculated according to the <strong>for</strong>mula below. The vertical acceleration according to UIC is –3 m/s 2 . a 2 ( a + g) = 0.3⋅( − 3 + 9.81) 2.0 m / s t = µ ⋅ v = If the vertical acceleration is set to 0 m/s 2 the following calculation is valid: a t = µ ⋅ g = 0.3⋅9.81 = 2.9 m / s 2 Longitudinal direction: The largest allowed longitudinal acceleration to avoid sliding is calculated according to the <strong>for</strong>mula below. No vertical acceleration is to be considered in this case, according to UIC. a 2 ( a + g) = 0.3⋅( 0 + 9.81) 2.9 m / s l = µ ⋅ v = Tipping The figure below shows the <strong>for</strong>ces acting on the cargo during horizontal sliding. 94
MariTerm AB 2004-01-30 jvgRASLA Moment equilibrium around point P: D H D m ⋅ g + av ⋅ − m ⋅ ah ⋅ = 0 ⇒ ah = ⋅ g + a 2 2 H ( ) ( ) v ma h a h a v m(g+a v ) In this analysis the diameter (D) will be 70% <strong>of</strong> the height (H), because it’s the worst case (according to the UIC:s guidelines) when considering tipping. Transversal direction: a D ⋅ H 2 ( g + a ) = 0.7 ⋅( 9.81− 3) 4.8 m / s t = v = P Longitudinal direction: a D ⋅ H 2 ( g + a ) = 0.7⋅( 9.81− 0) 6.9 m / s l = v = 5.6.3 Summery The result is put together in the list below were largest allowed acceleration in respectively transverse and longitudinal direction is shown. The vertical acceleration is taken in account during transverse movement. Longitudinal tipping = 6.9 m/s 2 Longitudinal sliding = 2.9 m/s 2 Transverse tipping = 4.8 m/s 2 Transverse sliding (a v = -3 m/s 2 ) = 2.0 m/s 2 Transverse sliding (a v = 0 m/s 2 ) =2.9 m/s 2 (about 15% <strong>of</strong> general acceleration) (about 7% <strong>of</strong> general acceleration) (about 100% <strong>of</strong> general acceleration) (about 40% <strong>of</strong> general acceleration) (about 60% <strong>of</strong> general acceleration) 5.7 A-frame 5.7.1 Purpose The purpose <strong>of</strong> this analysis is to calculate how large accelerations concrete blocks can be exerted to, when positioned in an A-frame. According to the UIC:s guidelines (RIV Appendix II, Section 2, Loading guidelines 6.2), each <strong>of</strong> the two straps securing the slabs should be able 95
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