ANSWER TO
RIGGING QUIZ No. 22
Question No. 1:
a.
H
= vertical distance from centerline of
Spreader bar to bearing on the hook = 6.93 ft.
b. Angle of the left sling with the
horizontal =
66.59 deg.
c. L = length of left inclined section of
sling = 7.55 ft.
d. R = length of right inclined section of
sling = 8.00 ft.
e.
Rl = Left reaction = 200.0 kips*4.0/7.0 = 114.29 kips
f.
R2 = Right reaction = 200.0 kips - 114.29 kips = 85.71 kips
g.
C = horizontal compressive stress in the
pipe)
Left end: C
= 114.29 kips*3.0/6.93 = 49.48 kips
Right end: C = 85.71 kips*4/6.93 =
49.48 kips
h. TL = 114.29 kips*7.55/6.93 = 124.52 kips
i. TR =
85.71 kips*8.0/6.93 =
98.94 kips
Question No. 2:
As
the tension in the left sling is the greatest, size the sling for that value
and use the same diameter for both the left and right sling. The SWL (safe working load) for a 2dia.
EIPS wire rope is 79.2 kips. The
end attachment efficiency for a 2sling is .9. The bending ratio for a 2sling bent over the curved end plate of
the spreader bar = 2*12/2= 12 and the strength efficiency = 100-76/12^.73 =
87.6% (refer to a Macwhyte graph for the formula used for strength efficiency
for wire rope). The bending ratio for a
2sling around the trunnion = 12/2=6 and the efficiency = 100-50/SQR(6) =
79.6 %. Using the worst case for
bending efficiency, the SWL for a
doubled 2dia, EIPS sling = 2*79.2 kips*.796 = 126.1 kips > 124.52
kips ==θ Okay
Question No. 3:
The
total length of the left sling = 2(7.55 + 6) +3.14*1/2 = 28.67.
The
total length of the right sling =
2(8.0 + 6) + 1.57 =
29.57
Question No. 4:
Yes,
the horizontal force C does put a bending moment in the pipe. See figure 1
and note that the sling is in contact with the curved end plate for 23.41
degrees and that due to the geometry, the eccentricity E equals 1.69. The bending moment in the pipe is equal to
E*C*IF = 1.69*49.48 k*1.8 = 150.52 k-in. The bending stress fb =
moment/section modulus S = 150.52 k-in./16.81 in^3 = 8.95 ksi < the
allowable of 21.6 ksi. It should be noted that there are other factors to
consider to complete the design of the spreader bar and it is not as simple as
just completing the above step. The 1.8 used above is an impact factor.
Question No. 5:
The
horizontal compression force C is the same through out the pipe spreader
bar. See the calculations for C in
question No. 1 above.
Question No. 6:
See
figure 1 for the location of vertical force V. It is equal to C*Tan(11.71) = 10.26 kips pushing down on the
spreader bar
Question No. 7:
See
figure 1 for the location of the sloping compression force N pushing against
the curved end plate. This force
creates friction between the sling and the curved end plate. The N or normal force = C/Cos(11.71) =
50.53 kips. Using .2 for the coefficient of friction, the friction force =
.2*50.53 kips = 10.11 kips. Note from
question 6 above that V is approximately equal to friction force.
Therefore,
during lifting with this sling configuration, the friction force will almost
keep the spreader bar from slipping down on the slings. To ensure that the spreader does not slip,
clamp plates with half round bars that acts the same way as u-bolts on cable
clamps, are bolted to the bottom of the end plates. A torque value is not
specified for tightening these bolts.
They should be tightened the same way that cable clamps normally are
tightened, so they bite into the cable but not so tight that they damage the
cable.
It
should be noted that for sling angles of 55 degrees or higher, the eccentricity
E occurs below the centerline of the pipe so that the resultant moment from the
compression force C tends to bow the pipe up at the middle of the spreader and
counteracts the downward bowing of the pipe at the middle due to the dead
weight of the pipe. For sling angles below 55 degrees, the eccentricity E
occurs above the centerline of the pipe and the moment due to force C and the
dead weight of the pipe are in the same direction.
Question No. 8:
The
three ways that the pipe spreader bar shown in figure 1 is adjustable are:
a.
Length: Pipe inserts are used to attain the correct
overall spreader bar length required from centerline to centerline of lifting
lugs.
b.
Sling
angle: For a certain length of sling,
the required sling angle can be attained by moving the spreader bar up or down
and then tightening the clamp plate bolts. For a specific length of sling, the
author specifies a vertical distance on the rigging hook up drawing from bearing
on the sling eye at the lug up to the centerline of the spreader bar. Setting
the spreader bar at this distance and then clamping it will set the correct
sling angle above the spreader bar.
c.
Pipe
wall thickness: For example, on a 8
dia. adjustable pipe spreader, pipe inserts of any wall thickness can be used
as the OD remains constant. The
tolerance between the ID of the 10dia. XXS end caps and the 8dia pipe inserts
is 1/8 inch.
COMMENTS ON SPREADER BAR
DESIGN:
There are many ways to design a spreader bar and
some times the design is based on personal preferences and not on good
engineering parameters. But no matter
how it is designed, it should be fabricated, labeled, proof tested and used
according to an approved design. In all cases, the design should conform to
ASME B30.20 and AISC.
If possible, a spreader bar should be designed with
zero moment due to the sling force.
This will produce the greatest SWL for the spreader bar.
See figure 2 for a design that is popular in
Europe. It is similar to the adjustable
pipe spreader design shown in figure 1 except that lugs are welded to the top
of the pipe at each end. Support slings
attach to these lugs to keep the spreader bar positioned during lifting.
See figure 3 for a spreader bar designed for zero
moment. This type of spreader bar has the best capacity of all the spreader
bars shown, but requires four slings to make it work.
See figure 4 for an example where lugs are located
on the spreader bar such that at a 60 degree sling angle the line of force
along the inclined portion of the sling intersects the line of force from the
vertical portion of the sling at the centerline of the spreader bar. This ensures that when a sling angle of 60
degrees with the horizontal is used, the spreader bar will have zero moment due
to the sling force. Using a sling angle greater than or less than 60 degrees
will decrease the SWL of the spreader bar.
Also, for added safety, the top and bottom lug at each end should be
made as one plate and welded into a slot in the pipe. This will eliminate using butt welds to attach the lugs to the
pipe.
Figure 5 shows a spreader bar commonly used in the
construction business where the top lug is located directly over the bottom
lug. For different sling angles, a constant eccentricity E times the
compression force C produces a maximum allowable moment in the pipe. This type
of spreader does not have good capacity compared to the other types. The lug plate should be designed as for Figure
4 above.
See the tables below for a comparison of safe
working loads between the five types of spreader bars that have been discussed.
All spreader bars in the figures are made of 8 dia, std wall pipe, 7 ft long
centerline to centerline of slings and with the center of gravity of the load
at the center of the bars. All values
are based on AISC & ASME B30.20 allowables. A doubled 2 diameter sling was assumed in calculating R for
Figures 1 & 2.
After viewing the Safe Working Loads listed in the
tables for the various types of spreader bars and sling angles, it becomes
apparent that we must be careful when calling out the SWL of a spreader bar on
a drawing, etc. Say the lifting
capacity of a spreader bar is listed as 100 ton. To be absolutely correct and not misleading, detail information
should state at what sling angle, design standard, safety factor, etc, that the
SWL is based on.
TABLE 1:
Sling angle |
SWL |
E |
C |
Moment |
Degrees |
Kips |
Inches |
Kips |
K-in. |
55 |
236 |
.28 |
149 |
-38 |
60 |
226 |
.90 |
117 |
-102 |
65 |
234 |
1.50 |
98 |
-143 |
75 |
308 |
2.67 |
74 |
-194 |
Where: 1. The sling angle is with respect to the
horizontal
2. E is the vertical eccentricity
3.
C
is the horizontal compressive force due to the effect of the sling
4.
A
negative net bending moment indicates that the spreader is being bowed upward
in the middle
___________________________________________________________________________________________
TABLE 2:
Sling angle |
SWL |
E |
C |
Moment |
Degrees |
Kips |
Inches |
Kips |
K-in. |
55 |
145 |
1.68 |
91 |
157 |
60 |
189 |
1.43 |
98 |
144 |
65 |
251 |
1.18 |
106 |
129 |
75 |
512 |
0.70 |
123 |
123 |
___________________________________________________________________________________________
TABLE 3:
Sling angle |
SWL |
E |
C |
Moment |
Degrees |
Kips |
Inches |
Kips |
k-in. |
55 |
262 |
0 |
165 |
4 |
60 |
320 |
0 |
165 |
4 |
65 |
392 |
0 |
165 |
4 |
75 |
684 |
0 |
165 |
4 |
___________________________________________________________________________________________
TABLE 4:
Sling angle |
SWL |
E |
C |
Moment |
Degrees |
Kips |
Inches |
Kips |
K-in. |
55 |
148 |
8.31 |
93 |
148 |
60 |
320 |
0 |
165 |
4 |
65 |
205 |
8.31 |
86 |
-163 |
75 |
125 |
8.31 |
30 |
-286 |
___________________________________________________________________________________________
FIGURE 5:
Sling angle |
SWL |
E |
C |
Moment |
Degrees |
Kips |
Inches |
Kips |
K-in. |
55 |
53 |
8.31 |
33 |
281 |
60 |
64 |
8.31 |
33 |
281 |
65 |
79 |
8.31 |
33 |
281 |
75 |
138 |
8.31 |
33 |
281 |