Stacking Shipping Containers on Land

International Standards Organization (ISO) Series 1
shipping container.

Stacking Shipping Containers on Land for an Off-Axis Detector

Introduction
Fig. 1 shows a typical International Standards Organization (ISO) Series 1
shipping container.

These containers are designed to make vertical contact with each other through
discrete corner fittings; when stacked, all vertical force is transferred
through these fittings, in turn loading the corner posts, and not the walls, of
the container. The number of containers which can be stacked on each other is
determined by the strength of the corner posts.

ISO Standard 1496(1) states that the corner posts of ISO Series 1 containers
should be tested to a load of 86,400 kg (190,480 lbs). This is the load applied
to the posts of the bottom container in an 8-on-1 stack of 24,000 kg (gross
weight) containers, Figure 1. ISO Series 1 Shipping Container corner post
corner post corner fitting 2 multiplied by a factor of 1.8. This extra factor
is used to take into account “conditions aboard ship and the relative
eccentricities between superimposed containers.”(1) The “conditions aboard
ship” were derived from a 1964 study of maximum acceleration values under the
worst sea and wind conditions.(2)

Calculating the safe stacking height for loaded containers on land requires
some understanding of the corner posts, their material properties, possible
failure modes, and what constitutes an adequate factor of safety.

Corner Post Geometry and Compressive Load-Bearing Capacity

Corner post steels typically correspond to the specification ASTM A-572, with a
yield stress of 47,000 psi, and an ultimate stress of 70,000 psi. This is a low
alloy columbium or vanadium steel commonly used for high-strength steel
weldments, such as bridges. The load-bearing characteristics of corners posts
are complex, because in a walled container the posts receive substantial
lateral stability, and compressive cross sectional area, from the participation
of the walls and doors.

The corner post can fail in two ways: The first is collapse, or buckling. This
occurs in a slender column when the compressive load reaches a critical load
Pcr which is so large that the column can no longer recover from small lateral
displacements along its length. The result is sudden and catastrophic loss of
stiffness, and gross deformation of the column and its attached material.

A second type of failure can occur if the compressive load Pcomp exceeds the
value SyA, where Sy is the yield stress of the material, and A is the cross
sectional area of the post. Even a column which is stable against buckling
failure can fail from compressive yielding. Failures of this type are rare for
columns, since the yielding will tend to produce larger cross sectional area
through plastic deformation, and eventually become self-limiting. This self-
limit may not be reached before even a very short column becomes unstable,
however, resulting in a type of collapse that is characterized by large amounts
of plastic deformation.

The most likely failure mode, given the substantial lateral constraint offered
by the walls, is probably a combination of collapse and gross yielding, a type
of failure referred to as elastic/plastic collapse.

The calculation of collapse (buckling) loads for long, slender steel columns
uses the Euler equation:

Pcr = kp2EI/L2

where Pcr = critical (collapse) load E = modulus of elasticity of steel = 30e6
psi I = minimum moment of inertia of section L = length of column k = factor
for end rotational restraint (theoretical range from 1-4)

For the corner posts, the degree of end rotational restraint is difficult to
quantify. The top, bottom, and side rails will serve to provide substantial
restraint, and even the corner fitting contact of the loading container above a
corner post will tend to limit rotation. Therefore, a k factor of 2 is chosen
for calculating the estimates of collapse load.(3) This is less than the
complete rotational restraint (k = 4), but greater than free rotation (k = 1).

In addition to resisting collapse, the corner post must also work at a
compressive stress that is below the yield of the material. Corner posts will
yield at a stress of 47,000 psi. Therefore, the minimum cross sectional area
for resisting the corner post loads is A = 190,840/47,000 = 4.05 in2.

While the minimum performance of a corner post is standardized via ISO, the
actual geometry of the post is not. Manufacturers have explored many different
designs for many different types of containers, all of which will pass the ISO
test load of 86,400 kg or 190,840 pounds. Figure 2 shows the most common corner
post cross-sections at the door and walled ends of a Series 1 container. These
posts are made of 6mm thick pressed steel shapes welded together along the
length of the post. In the case of the door end post, a piece of hot rolled
channel 113 x 40 x 10 mm is welded to the 6mm plate. Both posts in Figure 2
have adequate cross sectional area from the standpoint of compressive stress.
However, the Door End post (a), has a collapse load which is less than the load
required by the ISO standard, and therefore must rely on interaction with the
walls and doors of the container to produce the necessary load-bearing
capacity.

Figure 2. Corner Post Cross Sections — Properties and Load Capacities without
Wall/Door Participation.

Figure 2. Corner Post Cross Sections — Properties and Load Capacities without
Wall/Door Participation

The effect of participation of the walls and doors is illustrated in Fig. 3 The
profile of Fig. 2(a) has been used with a 3-inch wide strip of adjacent
container sidewall (3.6 mm thick) and a 2-inch wide strip of door panel (2 mm
thick), to form a column of considerably higher strength than the profile of
Fig. 2(a) alone. The cross section shown, with walls, has a critical load of
approximately 252,000 lbs, which is well above the 175,000 lbs of the corner
post alone, and well above the 190,480 lbs required by the ISO Standard.

These calculations show that the door is an important part of the load path
under stacking, providing additional cross-sectional area for compression and
stability. The door also acts as a sheer wall, preventing the parallelogram
deformation of the end referred to as “racking” or “sidesway.” For these
reasons, in commercial practice, the doors on a container within a stack are
presumably never opened. This is not a constraint on the way the containers are
used in commerce, since only one container at a time is loaded or unloaded at
terminals, with stacking occurring only during transit.

Figure 3. Corner Post from Fig. 2(a) showing increase in buckling strength due to participation of wall.

The corner fittings shown in Figure 1 are an integral part of the load-bearing
Corner Fittings

column in the container. ISO 1161-1984(E)(4) states “Corner fittings for Series
1 freight containers shall be capable of withstanding the loads calculated in
accordance with the requirements of ISO 1496/1 for Series 1 containers.” This
means that the bottom corner fitting of the bottom container in a stack must
withstand the weight of the containers stacked above it, plus the weight of the
bottom container itself. The maximum load which a single corner fitting must
take is then

Ptot = 190,480 + (52,800/4) = 203,680 lbs

A typical corner fitting is shown in Fig. 4.. The cross sectional area of this
fitting is shown in Fig. 5. The total cross sectional area available for
compression is 10.15 in2. This results in an average compressive stress under
maximum load of 20,067 psi.

Corner fittings are typically cast and machined from A-216 steel, which has a
minimum specified yield stress of 40,000 psi. Therefore, under maximum load, a
corner fitting of the cross section shown below operates with a safety factor
on yield of nearly 2.0

Figure 4. Corner Fitting, Figure 5. Fitting Cross Section 6

A safety factor for the corner posts in the bottom container of a stack can be
Safety Factor for Stacking Containers on Land

defined as
SF = Fcp-fail/Fcp-act

where SF = safety factor Fcp-act = actual operating load on corner post Fcp-
fail = failure load of corner post

The ISO Standard, however, does not define a force Fcp-fail; rather, it
specifies the load that each corner post must withstand without failure. In
this sense, the specified load is a proof load, Fcp_proof, which is simply a
load which each corner post must be shown capable of resisting. For the
purposes of calculating a safety factor, the specified test load can be thought
of as an absolute lower limit on the failure load. Any safety factor calculated
with Fcp-fail = Fcp_proof will be smaller than the actual safety factor, since
Fcp_proof is always smaller than Fcp-fail.

Using the expression above, the safety factor of an 8-on-1 stack of containers
on land is at least 1.8 . Safety factors in engineering commonly range from
1.25 to 2.0 or greater, depending on the amount of confidence the designer has
in material performance and load characterization. The AISC Steel Construction
Code(5), for example, uses a safety factor of 2 for column loading; however,
conservative design in civil structures is necessary because there is typically
no load-testing of the parts; they are designed, manufactured, and set in place
with only the calculation and fabrication standards serving as proof of merit.
Aircraft design, however, uses safety factors closer to 1.25, due to the great
penalties incurred by excess weight. The extremely rigorous materials and
testing programs common in the aviation industry justify these smaller safety
factors.

Because the corner posts of all containers are known to have been tested to the
load stipulated by ISO 1496 with no failures occurring at a load that is less
than the test load, a safety factor of about 1.5 is adequate for a stack of
containers on land. Table I shows the safety factor on the corner post loading
of the bottom container in a stack, for stacks of various heights. This table
is based on the application of the equation for safety factor, with Fcp-fail =
Fcp-proof = 190,480 lbs, and containers of 52,910 lbs gross weight:

Table I. Safety Factors on Land for Various Stack Heights on Land with
Container Corner Post Capacity of 190,480 lbs (86,400 kg)

Number of Containers Stacked on One Total Height of Stack Safety Factor on
Corner Post Loading 8 9 1.80 9 10 1.60 10 11 1.44 11 12 1.31

The table shows that we can stack 9-on-1 on land, and maintain a safety factor
of greater than 1.5.
Possible Modifications

For a final detector design, good engineering practice would require that the
corner posts of several containers be loaded to failure to more precisely
determine Fcp_fail, from which more accurate stacking safety factors could be
calculated. Some advantage might be taken of the fact that while Fcp-fail is
not known, it is certainly higher than 190,480 lbs (86,400 kg). If the measured
failure load is just 4% higher than the test (proof) load, the safety factor on
a 10-on-1 stack becomes 1.5, and stacking to that height becomes defensible.

Some vendors advertise containers with a higher capacity(6) than the ISO Series
1 standard, and advantage could be taken of the greater payload, as well as the
higher post strength, in configuring the detector array. The typical higher
post rating quoted is 214,290 lbs (97,400 kg), allowing exactly 9 on 1 stacking
of 52,910 lb (24,000 kg) containers at sea and therefore allowing 10 on 1 on
land with a safety factor of (9/8)*(1.44) = 1.62.

Similarly, if the Off-Axis detector density is small enough that our standard
gross weight container is less than 52,910 lbs (24,000 kg), then even higher
stacks could be supported. Table II shows the stack heights possible when the
higher strength containers are used. A container volume of 33.2 m3 is assumed
with a tare weight of 2,250 kg and four different detector gross weights of
22,150 kg, 24,000 kg, 26,000 kg and 30,480 kg. The 30,480 kg number is the
vendor quoted maximum gross weight for the higher strength containers.
Comparing Tables I and II shows that the higher strength posts lead to the same
height stacks as the lower strength posts for containers of density 0.75 gm/cc
vs. 0.66 gm/cc.

Table II. Stack Heights on Land forVarious Detector Densities with Container
Corner Post Capacity of 214,290 lbs (97,400 kg)

<table>
Safety Factor on Corner Post Loading Number of Containers Stacked on One Total
Height of Stack (m) with payload density = 0.60 g/cc (22,150 kg gross) with
payload density = 0.66 g/cc (24,000 kg gross) with payload density = 0.75 g/cc
(27,150 kg gross) with payload density = 0.85 g/cc (30,480 kg gross) 8 on 1
23.3 2.20 2.03 1.80 1.60 9 on 1 25.9 1.95 1.80 1.59 1.42 10 on 1 28.5 1.76 1.62
1.43 1.28 11 on 1 31.1 1.60 1.48 1.30 1.16 8
</table>

Conclusion

Stacking ISO containers 10 high on land is reasonable, and stacks as high as 12
may be possible depending on the type of container purchased and on the loading
of the container with Off-Axis detector elements. For a final detector design,
good engineering practice would require that the corner posts of the selected
containers be loaded to failure to more accurately determine the safety factor
of the stacked array.

J. Cooper, J. Kilmer, B. Wands Fermi National Accelerator Laboratory, Batavia,
IL 60510 (May 29, 2003)