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

MariTerm AB 2004-01-30 jvgRASLA
5.11.2 Calculations
The figure below shows the <strong>for</strong>ces acting on the top part <strong>of</strong> the cargo during vertical and
transverse accelerations. The pretension <strong>for</strong>ce (F) <strong>of</strong> the lashings is assumed to be about 10%
<strong>of</strong> the breaking strength.
a t
Force
Acceleration
nF
nF
α
mg
a v
F f
R
Equilibrium <strong>of</strong> <strong>for</strong>ces:
↑
→
R − m ⋅ g − 2 ⋅ n ⋅ F ⋅ sinα
= m ⋅ a
F
f
= m ⋅ a
t
⇒
a
t
=
F
f
m
v
⇒
R = m ⋅
( a + g)
v
+ 2 ⋅ n ⋅ F ⋅ sinα
Force <strong>of</strong> friction:
F
f
[ m ⋅ ( a + g)
+ 2 ⋅ n ⋅ ⋅ α ]
= µ ⋅ R = µ ⋅
F sin
v
Maximum allowed transverse acceleration to avoid transverse sliding:
a
t
=
F
f
m
= µ ⋅
( a + g)
v
µ ⋅ 2 ⋅ n ⋅ F ⋅ sinα
+
m
n = Number <strong>of</strong> lashings
Example:
Sliding in transverse direction (Top part):
The mass <strong>of</strong> the top part <strong>of</strong> the cargo equals 5 ton and is secured by 4 lashings with an angle
(α) <strong>of</strong> 45°. Two <strong>of</strong> the lashings have a breaking strength <strong>of</strong> 10 kN and a pretension <strong>of</strong> 1 kN
(1000 N), the other 2 lashings have a breaking strength <strong>of</strong> 7 kN and a pretension <strong>of</strong> 0.7 kN
(700 N). The coefficient <strong>of</strong> friction is 0.3 and the vertical acceleration acting at the time is –3
m/s 2 .
111