Technical Field
[0001] The present invention relates to a bearing device suitable for use as a seismic isolation
device intended for a structure, such as a building or a bridge.
Background Art
[0002] A bearing device, which is known as a seismic isolation device intended for a structure,
such as a building or a bridge, is installed between a superstructure segment and
a substructure segment of the structure, thereby bearing the superstructure segment
while allowing reduction of transfer of vibration of the substructure segment due
to an earthquake or the like to the superstructure segment.
[0003] For example, Patent Literature 1 discloses a bearing device that has no steel plate
layer to be laminated alternating with elastic layers, thereby being overall reduced
in resultant size, and the bearing device is capable of bearing a high load on a small
area. This bearing device has an upper plate (a first rigid component) including a
through hole; a lower plate (a second rigid component) placed facing the upper plate;
an elastic component placed between the upper plate and the lower plate; a shear key
(core) fixed to the lower plate by screw jointing or the like and placed through the
elastic component so as to position its end inside the through hole; and a filler
filled in the through hole so as to be in contact with the end of the shear key.
[0004] According to the bearing device disclosed in Patent Literature 1, the elastic component
can become shear deformed to absorb transferred vibration from the substructure segment
of the structure to the lower plate, thereby ensuring against transfer of vibration
to the superstructure segment of building though the upper plate. The end of the shear
key fixed to the lower plate is placed inside the through hole formed in the upper
plate, therefore limiting relative excessive movement between the upper plate and
the lower plate in horizontal direction; and this protects against damage which otherwise
would be caused to the elastic component by excessive shear deformation.
Citation List
Patent Literature
[0005] Patent Literature 1: Japanese Patent No.
5646383
Summary of Invention
Technical Problem
[0006] Recently, further downsized bearing device has been awaited. However, for the bearing
device disclosed in Patent Literature 1, the shear key is fixed to the lower plate
by screw jointing or the like, and the ability of restraining shear deformation of
the elastic component is dependent on the overlapping amount between the through hole
formed in the upper plate and the end of the shear key placed inside the through hole.
Therefore, ensuring restraint of shear deformation of the elastic component requires
an increase of this overlapping amount or installation of a mechanism of preventing
the end of the shear key from dropping out of the through hole formed in the upper
plate, which makes it difficult to design the bearing device to be short in height.
[0007] The present invention has been made in view of the above situation, and an object
of the invention is to provide a bearing device designable more compactly and capable
of bearing a high load.
Solution to Problem
[0008] In response to the above issue, for a bearing device according to the present invention,
a shear key in the form of round plate is placed inside an elastic component intervening
between a top plate and a base plate in such a manner that one end of the shear key
is situated in a hold section formed in a surface (facing the base plate) of the top
plate and another end in a hold section formed in a surface (facing the top plate)
of the base plate and so that an axis of the shear key can be inclined with respect
to a stacking direction of the top plate and the base plate.
[0009] For example, the present invention provides a bearing device configured to be installed
between a superstructure segment and a substructure segment of a structure and capable
of bearing the superstructure segment while minimizing a transferred vibration from
the substructure segment to the superstructure segment, and the bearing device has
the following:
a top plate configured to be arranged in a position closer to the superstructure segment
than to the substructure segment;
a base plate facing the top plate and configured to be arranged in a position closer
to the substructure segment than to the superstructure segment;
an elastic component bonded to the top plate and to the base plate and intervening
between the top plate and the base plate; and
a shear key having a form of round plate and restraining the elastic component from
shear deforming;
wherein the top plate includes a first hold section formed in a surface facing the
base plate, and a first end of the shear key is situated inside the first hold section;
the base plate includes a second hold section formed in a surface facing the top plate,
and a second end of the shear key is situated inside the second hold section; and
the shear key is placed inside the elastic component while situating the first end
inside the first hold section of the top plate and the second end inside the second
hold section of the base plate and while allowing an axis of the shear key to be inclinable
with respect to a stacking direction of the top plate and the base plate.
Advantageous Effects of Invention
[0010] According to the present invention, shear deformation of the elastic component due
to a relative horizontal movement between the top plate and the base plate causes
one end of the shear key situated inside the hold section of the top plate to be pushed
in a moving direction of the top plate and another end of the shear key situated inside
the hold section of the base plate to be pushed in a moving direction of the base
plate, which is opposite direction to the moving direction of the top plate, thereby
rotating the shear key so as to incline the axis of the shear key with respect to
the stacking direction of the top plate and the base plate. This results in increases
both in the overlapping amount between one end of the shear key and the hold section
of the top plate and in the overlapping amount between another end of the shear key
and the hold section of the base plate, and therefore even shortening the shear key
in height allows the elastic component to be restrained from undergoing shear deformation.
The shear key can not only restrain the elastic component from undergoing shear deformation,
but also bear a vertical load between the top plate and the base plate. Consequently,
according to the present invention, provided is a bearing device designable more compactly
and capable of bearing a high load.
Brief Description of Drawings
[0011]
Fig. 1(A) and Fig. 1(B) are respectively a plan view and a bottom view of a slide
bearing 1 according to one embodiment of the present invention, and Fig. 1(C) is an
A-A cross sectional view of the slide bearing 1 as illustrated in Fig. 1(A).
Fig. 2(A) to Fig. 2(C) are schematic diagrams for explanation about operation of the
slide bearing 1 as illustrated in Fig. 1.
Fig. 3(A) is a view equivalent to Fig. 1(C), for explanation about a modification
1A of the slide bearing 1 according to one embodiment of the present invention, and
Fig. 3(B) is a view equivalent to Fig. 1(C), for explanation about a modification
1B of the slide bearing 1 according to one embodiment of the present invention.
Description of Embodiments
[0012] In the following, one embodiment of the present invention will be described.
[0013] Fig. 1(A) and Fig. 1(B) are respectively a plan view and a bottom view of a slide
bearing 1 according to one embodiment of the present invention, and Fig. 1(C) is an
A-A cross sectional view of the slide bearing 1 as illustrated in Fig. 1(A).
[0014] The slide bearing 1 according to the present embodiment, is to be installed between
superstructure and substructure segments of a structure, such as building or bridge,
thereby bearing the superstructure segment while ensuring that a vibration of the
substructure segment to be caused by an earthquake or the like is prevented from being
transferred to the superstructure segment.
[0015] As illustrated in the figures, the slide bearing 1 according to the present embodiment
has a flange 10; a bearing plate 11 arranged to face the flange 10; an elastic component
12 intervening between the flange 10 and the bearing plate 11; a shear key 13 restraining
the elastic component 12 from undergoing shear deformation; and a slide plate 14 attached
to an undersurface (a surface to face the substructure segment of the structure) 112
of the bearing plate 11.
[0016] The flange 10 is a plate member to act as a top plate arranged in a position (which
is closer the superstructure segment than to the superstructure segment) within the
structure and is to be fixed to the superstructure segment with a bolt (not illustrated)
inserted in each bolt hole 102. A hold section 100 in cylindrical shape with bottom
is formed in an undersurface (one surface facing the bearing plate 11) 101 of the
flange 10 so as to hold one end 130 of the shear key 13 within. The flange 10 is made
of any of the following: metals, including steel materials, such as SS400; ceramics;
hard resins; reinforced plastics; and composites of these materials.
[0017] The bearing plate 11 is a member in the form of round plate to act as a base plate
arranged in a position (which is closer to the substructure segment than to the superstructure
segment) within the structure. A hold section 110 in cylindrical shape with bottom
is formed in a top surface (a surface facing the flange 10) 111 of the bearing plate
11 so as to hold the other end 131 of the shear key 13 within, and the hold section
110 has a diameter equal to or substantial equal to that of the hold section 100 of
the flange 10 and is in a position facing this hold section 100. An attachment recess
113 for attachment of the slide plate 14 is formed in the undersurface 112 of the
bearing plate 11. The bearing plate 11, as with the flange 10, is made of any of the
following: Metals, including steel materials, such as SS400; ceramics; hard resins;
reinforced plastics; and composites of these materials. The bearing plate 11 is covered
with the elastic component 12, except for the attachment recess 113 for attachment
of the slide plate 14.
[0018] The elastic component 12 is bonded to both the undersurface 101 of the flange 10
and the top surface 111 of the bearing plate 11 through vulcanization bonding process
or the like and intervenes between the flange 10 and the bearing plate 11. This allows
shear deformation to occur due to relative movement between the flange 10 and the
bearing plate 11, resulting in minimization of the transferred vibration from the
bearing plate 11 to the flange 10. The elastic component 12 is made of natural rubber,
synthetic rubber, thermoplastic elastomer, or thermosetting elastomer.
[0019] For the elastic component 12, a thickness T1 between the undersurface 101 of the
flange 10 and the top surface 111 of the bearing plate 11, a thickness T2 between
one end 130 of the shear key 13 and a top interior surface 103 of the hold section
100, and a thickness T3 between the other end 131 of the shear key 13 and a bottom
surface 114 inside the hold section 110 are preferably set to meet a relation: T1
≤ (T2+T3), more preferably a relation: T3 = T1*(1/2) and T2 ≥ T3. Meeting the relation
T1 ≤ (T2+T3) makes the elastic component 12 capable of elastically deforming more
easily in the central portion of the slide bearing 1, thereby reducing a compressive
stiffness. This reduces concentration of compressive stress of the elastic component
12 in the central portion of the slide bearing 1, under a compressive load in a vertical
direction (in a stacking direction of the flange 10 and the bearing plate 11) V, thereby
allowing below-mentioned inclination (rotation) of the shear key 13 with respect to
the vertical direction V to be more smooth. Furthermore, meeting the relation T3 =
T1*(1/2) and T2 ≥ T3 ensures adequate thickness of the elastic component 12 between
one end 130 of the shear key 13 and the top interior surface 103 of the hold section
100 of the flange 10 and enables reduced depth of the hold section 110 of the bearing
plate 11, thereby enabling more compact design of the slide bearing 1.
[0020] The elastic component 12 has an outer peripheral surface 120 placed between the flange
10 and the bearing plate 11, which is formed to have a radially inwardly curved shape
in cross section.
[0021] The shear key 13, which is a member in the form of round plate with a diameter smaller
than that of the hold section 100 of the flange 10 and than that of the hold section
110 of the bearing plate 11, is placed inside the elastic component 12 in such a manner
that one end 130 is situated inside the hold section 100 of the flange 10 and the
other end 131 inside the hold section 110 of the bearing plate 11. The shear key 13
is placed through the elastic component 12 to situate respectively its both ends 130
and 131 inside the hold section 100 of the flange 10 and the hold section 110 of the
bearing plate 11, thereby limiting relative movement between the flange 10 and the
bearing plate 11 to restrain the elastic component 12 from undergoing shear deformation.
The shear key 13 is arranged to be inclinable (rotatable) with respect to the vertical
direction V, inside cylindrical space defined by the hold section 100 of the flange
10 and the hold section 110 of the bearing plate 11.
[0022] A corner 134 of the shear key 13 may be preferably chamfered. This avoids the occurrence
of stress concentration at the corner 134 of the shear key 13 and allows the shear
key 13 to incline (rotate) more easily.
[0023] The slide plate 14, which is a member in the form of round plate having a sliding
surface 140 slidable over a placement surface 30 (e.g. a surface of a stainless steel
plate) provided on the substructure segment 3 of the structure, is attached to the
attachment recess 113 of the bearing plate 11 with the sliding surface 140 projecting
downward from the undersurface 112 of the bearing plate 11. When shear force of the
elastic component 12 subjected to shear deformation due to the relative movements
between the flange 10 and the bearing plate 11 overcomes static friction force between
the sliding surface 140 of the slide plate 14 and the placement surface provided on
the substructure segment 3 of the structure, the sliding occurs between the sliding
surface 140 and the placement surface 30.
[0024] Here, the thickness T1 of the elastic component 12 between the undersurface 101
of the flange 10 and the top surface 111 of the bearing plate 11 is designed to be
equal to or substantial equal to one thirtieth of the diameter D3 of the slide plate
14, for example. In case of T1 larger than D3*(1/30), the sinking amount of the slide
bearing 1 becomes excessive correspondingly. Conversely, in case of T1 smaller than
D3*(1/30), the slide bearing 1 becomes correspondingly hard to incline and the distribution
of stress acting on the slide plate 14 subjected to inclination becomes uneven.
[0025] For example, respective diameters D1 of the hold section 100 of the flange 10 and
the hold section 110 of the bearing plate 11 each are set to 284mm when the diameter
D3 of the slide plate 14 is 700mm, and 56mm when the diameter D3 of the slide plate
14 is 200mm.
[0026] Next, an operation of the slide bearing 1 will be described.
[0027] Fig. 2(A) to Fig. 2(C) are schematic diagrams for explanation about the operation
of the slide bearing 1 as illustrated in Fig. 1.
[0028] As illustrated in Fig. 2(A), the slide bearing 1 is arranged on the substructure
segment 3 in such a manner that the flange 10 is fixed to the superstructure segment
2 of the structure with bolts not illustrated and that the bearing plate 11 keeps
the sliding surface 140 of the slide plate 14 in contact with the placement surface
30 provided on the substructure segment 3 of the structure, thereby bearing the superstructure
segment 2 of the structure.
[0029] For the slide bearing 1 as illustrated in Fig. 2(A), when vibration due to an earthquake
or the like is transferred from the substructure segment 3 of the structure to the
bearing plate 11 through the slide plate 14, the elastic component 12 becomes shear
deformed due to relative movement between the flange 10 and the bearing plate 11,
thus minimizing transferred vibration from the bearing plate 11 to the flange 10.
Under such circumstances, as illustrated in Fig. 2(B), one end 130 of the shear key
13 placed inside the hold section 100 of the flange 10 becomes pushed in a moving
direction -F of the flange 10 and the other end 131 of the shear key 13 placed inside
the hold section 110 of the bearing plate 11 becomes pushed in a moving direction
+F of the bearing plate 11, which is opposite direction to the moving direction -F
of the flange 10; therefore the shear key 13 starts rotation so that an axis O of
the shear key 13 can incline with respect to the vertical direction (the stacking
direction of the flange 10 and the bearing plate 11) V. This causes increases both
in the overlapping amount P1 between one end 130 of the shear key 13 and the hold
section 100 of the flange 10 and in the overlapping amount P2 between the other end
131 of the shear key 13 and the hold section 110 of the bearing plate 11, thus ensuring
restraint of shear deformation of the elastic component 12.
[0030] For the shear key 13, its size and arrangement position are set so that the overlapping
amounts P1, P2 can be obtained which are adequate to ensure restraint of shear deformation
of the elastic component 12 upon inclination (rotation) of its axis O with respect
to the vertical direction V. When a diameter D2 and a thickness T4 of the shear key
13 are large, the adequate overlapping amounts P1, P2 are ensured even if an inclination
angle of the axis O of the shear key 13 with respect to the vertical direction V is
small; whereas, when the diameter D2 and the thickness T4 of the shear key 13 are
small, the inclination angle of the axis O of the shear key 13 with respect to the
vertical direction V needs increasing so that the adequate overlapping amounts P1,
P2 are ensured.
[0031] For example, when the respective diameters D1 of the hold section 100 of the flange
10 and the hold section 110 of the bearing plate 11 are 284mm, setting the diameter
D2 and the thickness T4 of the shear key 13 to 260mm and 59. 5mm respectively allows
the axis O of the shear key 13 to rotate up to the maximum of about 5 degrees with
respect to the vertical direction V and therefore ensures, upon rotation of the shear
key 13, the overlapping amounts P1 and P2 adequate to ensure restraint of shear deformation
of the elastic component 12 are ensured. When the respective diameters D1 of the hold
section 100 of the flange 10 and the hold section 110 of the bearing plate 11 are
56mm, setting the diameter D2 and the thickness T4 of the shear key 13 to 50mm and
26.5mm respectively allows the axis O of the shear key 13 to rotate up to maximum
of about 7 degrees with respect to the vertical direction V and therefore ensures,
upon rotation of the shear key 13, the overlapping amounts P1 and P2 adequate to ensure
restraint of shear deformation of the elastic component 12.
[0032] Here, in the event that shear force of the elastic component 12 subjected to shear
deformation due to relative movement between the flange 10 and the bearing plate 11
overcomes static friction force between the sliding surface 140 of the slide plate
14 and the placement surface 30 formed on the substructure segment 3 of the structure,
the sliding occurs between the sliding surface 140 and the placement surface 30 provided
on the substructure segment 3 of the structure, as illustrated in Fig. 2(C). This
reduces transferred vibration of the substructure segment 3 to the slide bearing 1.
[0033] Hereinabove, one embodiment of the present invention has been described.
[0034] In the present embodiment, shear deformation of the elastic component 12 due to relative
movement between the flange 10 and the bearing plate 11 causes the shear key 13 to
rotate such that the axis O of the shear key 13 inclines with respect to the vertical
direction V. This results in respective increases in the overlapping amount P1 between
one end 130 of the shear key 13 and the hold section 100 of the flange 10 and in the
overlapping amount P2 between the other end 131 of the shear key 13 and the hold section
110 of the bearing plate 11, thereby enabling restraint of the elastic component 12
from undergoing shear deformation even if the shear key 13 of short height is used.
Therefore, according to the present embodiment, the bearing device has a more compact
design and enables a high load to be borne.
[0035] In the present embodiment, the attachment recess 113 is formed in the undersurface
112 of the bearing plate 11, and the slide plate 14 is attached to this attachment
recess 113 with the sliding surface 140 projecting from the undersurface 112 of the
bearing plate 11. Consequently, when the elastic component 12 becomes shear deformed
due to relative movement between the flange 10 and the bearing plate 11 and thereby
shear force of the elastic component 12 overcomes static friction force between the
sliding surface 140 and the placement surface 30 formed on the substructure segment
3 of the structure, the slide occurs between the sliding surface 140 and this placement
surface 30, thereby minimizing transferred vibration from the substructure segment
3 to the slide bearing 1.
[0036] According to the present embodiment, the elastic component 12 covers the bearing
plate 11, except for the attachment recess 113 for attachment of the slide plate 14,
therefore being effective in corrosion prevention for the bearing plate 11 even without
additional rust proof treatment against the bearing plate 11.
[0037] In the present embodiment, the hold section 100 of the flange 10 and the hold section
110 of the bearing plate 11, each have a cylindrical shape with bottom. In comparison
with if replacing these hold sections 100 and 110 to through holes, the present embodiment
causes compressive stress of the elastic component 12, which otherwise would be imposed
outside through the through holes, to be more effectively imposed on the shear key
13. This ensures restraint of shear deformation of the elastic component 12.
[0038] In the present embodiment, the elastic component 12 has the outer peripheral surface
120 between the flange 10 and the bearing plate 11, which is formed to have a radially
inwardly curved shape in cross section. Consequently, when the slide bearing 1 is
subjected to compressive load in the vertical direction V, the outer peripheral surface
120 of the elastic component 12 is prevented from expanding and resultantly increasing
surface area, and this ensures against occurrence in ozone cracking into the elastic
component 12. The outer peripheral surface 120 of the elastic component 12 can be
formed into a radially inwardly curved shape in cross section so that the resultant
cross-sectional shape after installation of the slide bearing 1 onto the structure
is flat or slightly inwardly curved.
[0039] The present invention can include, but is not limited to, the above embodiments:
it will be obvious to those skilled in the art that various changes may be made without
departing from the scope of the invention.
[0040] For example, as exemplified by a modification 1A of the slide bearing 1 illustrated
in Fig. 3(A), end faces 132 and 133 of both ends 130 and 131 of the shear key 13 each
may be shaped into a recess with a top portion on the axis O of the shear key 13.
Under such circumstances, the elastic component 12 is thicker in the central portion
of the flange 10 and the bearing plate 11 than otherwise would be, and therefore compressive
stress to be imposed on the elastic component 12 in this central potion is reduced.
This results in decrease in unevenness of distribution of compressive stress of the
elastic component 12 to act on the slide plate 14 through the bearing plate 11, thereby
achieving improved sliding performance of the slide plate 14.
[0041] While the both ends 130, 131 of the shear key 13 herein have the respective end faces
132, 133 each shaped into a recess, the shear key 13 may be used as far as at least
one of the end faces 132, 133 is shaped into a recess.
[0042] As exemplified by a modification 1B of the slide bearing 1 illustrated in Fig. 3(B),
the top interior surface 103 of the hold section 100 of the flange 10 and the bottom
surface 114 inside the hold section 110 of the bearing plate 11, each may be shaped
into a recess with a top portion in corresponding central portion. Even in this case,
as with the modification 1A illustrated in Fig. 3(A), the elastic component 12 is
thicker in central portion of both the flange 10 and the bearing plate 11 and therefore
compressive stress of the elastic component 12 is lower in the central portion; this
results in decrease in unevenness of distribution of compressive stress of the elastic
component 12 to act on the slide plate 14 through the bearing plate 11, thereby achieving
improved sliding performance of the slide plate 14
[0043] While both the top interior surface 103 of the hold section 100 of the flange 10
and the bottom surface 114 inside the hold section 110 of the bearing plate 11 herein
are shaped into a recess, at least one of the surfaces 103, 114 may be shaped into
a recess.
[0044] In the above embodiments, the slide bearing 1 is arranged in the structure in such
a manner that the flange 10 is fixed to the superstructure segment 2 of the structure
and that the slide plate 14 is in contact with the placement surface 30 formed on
the substructure segment 3 of the structure. The scope of the present invention, however,
is not limited in this respect. The slide bearing 1 may be installed in the structure
in such a manner that the slide plate 14 is in contact with a flat surface provided
on the superstructure segment 2 of the structure and that the flange 10 is fixed to
the substructure segment 3 of the structure, namely upside down.
[0045] The above embodiments have been described taking the examples of the slide bearing
1 in which the slide plate 14 is mounted onto the undersurface 112 of the bearing
plate 11; however, the scope of the present invention is not limited in this respect.
The present invention is widely available for any type of bearing device such that
the bearing plate 11 is to be mounted on the substructure segment 3 of the structure
without the slide plate 14 to be mounted on the undersurface 112 of the bearing plate
11.
Reference Signs List
[0046] 1, 1A, 1B: slide bearing; 2: superstructure segment of structure; 3: substructure
segment of structure; 10: flange; 11: bearing plate; 12: elastic component; 13: shear
key; 14: slide plate; 30: placement surface; 100: hold section of the flange 10; 101:
undersurface of the flange 10; 102: bolt hole in the flange 10; 103: top interior
surface of the hold section 100; 110: hold section of the bearing plate 11; 111: top
surface of the bearing plate 11; 112: undersurface of the bearing plate 11; 113: attachment
recess of the bearing plate 11; 114: bottom surface inside the hold section 110; 120:
outer peripheral surface of the elastic component 12; 130, 131: end of the shear key
13; 132, 133: end face of the shear key 13; 134: corner of the shear key 13; 140:
sliding surface of the slide plate 14
1. A bearing device configured to be installed between a superstructure segment and a
substructure segment of a structure and capable of bearing the superstructure segment
while minimizing a transferred vibration from the substructure segment to the superstructure
segment, the bearing device comprising:
a top plate configured to be arranged in a position closer to the superstructure segment
than to the substructure segment;
a base plate facing the top plate and configured to be arranged in a position closer
to the substructure segment than to the superstructure segment;
an elastic component bonded to the top plate and to the base plate and intervening
between the top plate and the base plate; and
a shear key having a form of round plate and restraining the elastic component from
shear deforming;
characterized in that the top plate includes a first hold section formed in a surface facing the base plate,
and a first end of the shear key is situated inside the first hold section;
the base plate includes a second hold section formed in a surface facing the top plate,
and a second end of the shear key is situated inside the second hold section; and
the shear key is placed inside the elastic component while situating the first end
inside the first hold section of the top plate and the second end inside the second
hold section of the base plate and while allowing an axis of the shear key to be inclinable
with respect to a stacking direction of the top plate and the base plate.
2. A bearing device according to Claim 1,
wherein the shear key has, in at least one of the surfaces facing the top plate or
the base plate, a recess with a top portion on the axis.
3. A bearing device according to Claim 1 or 2,
wherein at least one of the first and second hold sections has a bottom surface including
a recess with a top portion in a central portion.
4. A bearing device according to any one of Claims 1 to 3, further comprising a slide
plate attached to a surface of the base plate to face the substructure segment or
to a surface of the top plate to face the superstructure segment, the slide plate
having a sliding surface.
5. A bearing device according to Claim 4,
wherein the base plate includes an attachment recess for attachment of the slide plate,
which is formed in the surface facing the substructure segment; and
the slide plate is attached to the attachment recess with the sliding surface projecting
from the surface of the base plate facing the substructure segment.
6. A bearing device according to Claim 4 or 5,
wherein the base plate is covered by the elastic component, except for an area to
which the slide plate is attached.
7. A bearing device according to any one of Claims 1 to 6,
wherein the elastic component has an outer peripheral surface placed between the top
plate and the base plate, and the outer peripheral surface in absence of compressive
load in vertical direction has a radially inwardly curved shape in cross section.