Proceedma« of the 7th International
Working Conference on Stored-product Protectum - Volume 2
Design of 24-m span hyperbolic shell slab and its application
in the construction of grain depots
Feng
Tianmm1
Abstract
The 24-m span hyperbolic
structure
that integrates
Geometrical figure of hyperbolic shell slab
shell slab IS a space thin-wall
mathematical
Curved surface equation:
model, high-strength
_
steel and high-grade concrete mto one body. It IS a new-type
roof member with slab and truss combmed into one piece. It
has begun to be used in the construction
the gram industry.
roof
member
Practice
features
techmcal and economic
resul ts m use
of storehouses
rational
structure
indices,
and has achieved
and
Where,
m
has proved that this new- type
x2 _
t, a2
Z -
y!:..
fy b2
taking
=
a
b
1485mm,
950mm,
fy =
Fig. 1.
Geometncal figure of slab
fa: =
12000mm,
250mm
advanced
good
Design of Hyperbolic Shell Slab
Design principle
(1) The length of hyperbohc shell slab (24 meters)
larger
than the WIdth (3 meters)
structure
stressed
IS designed
concrete
girder
section IS a parabola,
usually only needs
construction.
(2) The calculation
storehouse
accordmg
IS much
The longitudinal
to the ordinary
member,
pre-
the curve in cross
and the transverse
to be arranged
reinforcement
according
to the
To determine
appropnate
diagram
of hyperbohc
shell slab roof
line which passes through
IS the same as that of the storehouse by usmg
roof truss plus roof boarding as roof,
hyperbohc
assumption
shell
slab
roof
conforms
that it has a cross girder
The pre-stressed
It is considered
that
the
making the gravity of pre-stressed
longi tudmal curvihnear
With walling
the
beam can
as
an
Z
by the gable, the gable column head IS
Immovable
lunged
support,
=
tx
=
A=
Gram Engmeenng Design Institute
1599
IS:
a
i; =
950mm,
the vertical thickness of slab varies
the rule of vanation
IS:
x2
toO + 2")
a
Where,
Beijing
load.
fa: 2
along WIth the parabola,
shell slab at the slab bottom and gable column head.
and
to the bending moment diagram
x2
Where,
and
horizontal tension brace shall be provided for the edge
1
line,
versus the
The equation of the cross section central line parabola
(3) The hyperbolic shell slab roof can bear partial horizontal
regarded
evenly in
mother
reinforcement
under the action of evenly distnbuted
be calcula ted according to the frame.
force transmitted
will be arranged
aXIS vary along the parabola,
making it be proportional
longitudinal
action of connectmg hinged beam and tnmmer
reinforcement
mother
lies in a
at the slab end.
parallel along the two sides of main straight
with unlimited
rigidity and has rehable lunged connection
column head.
to
The main straight
the origin of coordinate
rational position in terms of ItS x-coordmate
their transverse
sections are all calculated according to the bent frame.
The
curve surface equation means to select an
two-way curvature.
"IS an introduced parameter,
ta - to
to
taking
to =
70mm,
taking
t; = 140mm
Proceedings of the 7 th Internaiumal
Working Conference on Stored-product Protection - Volume 2
z
storehouse)
was always built uniformly as a flat-story
with a span below 18 meters.
bin
Along with the development of
reform and openmg- up, the demand for adopting economical
and convenient new type bm and the demand by construction
uruts for building large span flat-story bin have been growing
greater and greater,
fx
x
The
usually
reinforced
roof
The cross section of the shell slab
structural
adopted
plus
large
of variation of slab tluckness
schemes
concrete
roof
boarding,
folded
plate.
For instance,
space IS too low.
nearly 9 meters.
shell slab.
The elimination
of flange bnngs
about
convenience for fabrication, stacking and transportation.
The effective
hoisting are qurte difficult.
the live load IS 0.5kN/
cost.
(1) The
slab
has
supenmposed
concrete
IS adopted,
stones
used for
as pre-stressed
reinforcement
reinforcement
aeon
=
0.72 fptk,
an
artistic
and
company
the hyperbolic
Through demonstration
self-balance
height
for
The slab shape is
the slab joint IS at the slab
waterproofmg
treatment.
to the large roof boarding,
(2) The structural
the slab joint
and the mtegrity is also better.
is small,
and the slab bottom
height IS the very eaves height.
Compared to the roof
truss plus large roof boardmg,
the eaves height
lower by more
as
shape,
facilitates
decreases by third-fifth,
and use Class-I
steel wire
construction.
which
Compared
10.75 (1 x 3 x cp5) fptk =
1>1
reinforcement,
or cold drawn low-carbon
of longitudinal and transverse
Tension control stress
reinforcement
0.75 fe' use
reinforcement
the shell slab
mold.
ridge,
yellow sand IS adopted, It IS strictly
additive
that
will
corrode
the
Use twisted steel wire with
1570N/mm2
to these,
load, and good stability.
helpful to roof dramage,
makmg concrete are m a two-stage allocation, 1. e. 513mm IS approximately 30 %, 13 - 25mm IS approximately
70%, medium-coarse
forbidden
to use
reinforcement.
and the transport
in many ways, It has the following advantages:
nr'.
stone
reinforced
transport and hoist, which results
Compared
shell slab is a more feasible scheme.
m2, and considering that It will act as a thermal insulating
layer and waterproof layer, It should be added WIth 1. OkN/
ratio of building
of pre-stressed
Specialized construction
was required to fabncate,
m much higher
when the
the eaves height IS
utilization
The rigidity
concrete folded plate itself IS poor,
Load and material
C40 fine
above-mentioned
the very height of roof
creating the condition for designmg a large-span
hyperbolic
steel
pre-stressed
truss with 24-m span already reaches 2.5 meters,
IS: making
bottom chord of roof truss IS 6 meters,
,
pre-stressed
and
The
the concrete area of compressed zone enlarged, also being
able to improve the longitudinal and transverse rigidity, thus
The dead weight IS 2. 33kN/m2
are
forms of roof truss plus large boardmg all have
ObVIOUSdisadvantages.
The advantage
roof
concrete roof truss plus large roof boarding,
truss
reinforced
Fig. 2.
thus the selection of roof scheme has
become a problem of utmost importance.
than two meters,
height of enclosure
walling,
thus reducmg
so the utilization
can
the
ratio of
space is high.
(3) There IS only one member - hyperbolic shell slab, and
when pre-stressed
is loosened, the concrete grade reaches ~
two beams of oxygen to cut pre-stressed
alternatrvely.
After the tension IS released,
WIll automatically arch and eject from the
the slab space ngidrty
IS great.
The roof does not
require to be provided with steel brace,
thus saving the
quantity of steel to be used.
(4) The covenng thickness IS enlarged,
the average reduced
thickness of roof truss plus large roof boarding is 8 - 9
A Case History of Application
of Hyperbolic Shell Slab
em concrete,
2 .5cm
hyperbolic
reduced
thickness
of
pre-stressed
hyperbolic slab IS 9. 3cm while the actual thmnest place
of the slab IS 7cm, which IS helpful to waterproofmg
Beijing Gram & Feed Depot IS situated in Niushan Town of
Shunyi County. In the depot, the flat story bm for packed
grain adopts 3 x 24-m pre-stressed
while the actual boarding thickness is only
The
shell slab of
(5) Force transmission
IS Simple. The hyperbolic shell slab
double span and 26-m slab length as the roof, four bins use
transmits
160 slabs m total, amountmg to 12500 square meters,
project was completed and put into use by 1992
the roof truss plus large roof boarding transmits
the
the
past
years,
gram
a load directly to the walhng or column, while
from the boarding to roof truss that transmits
the walling or column.
The selection of roof scheme
In
and
thermal insulation
a load
the load to
The load transmitted
to the
wallmg or column by a hyperbolic shell slab is a linear
system
(especially
load,
gram
1600
while
the
load transmitted
to the walling
or
Proceedmqe of the 7th International
Working Conference on Stored-product Protection - Volume 2
column by the roof truss is a concentrated force. The
problem of local bearing must be considered for the
wallmg at roof truss support, thereby the method of
work is also different. Moreover, the hyperbohc shell
slab can have multi-point connection With the lower
bracmg structure As counted by two pomts for each
slab end, each six meters of spacmg has a four-point
connection, while the roof truss has only one point at
the end. Therefore the connection of hyperbohc shell
slab is more reliable and more effective With respect to
earthquake resistance.
(6) The roof truss plus large roof boardmg (24- m span)
must use concrete bent frame structural system and
mdependent column base, while the hyperbolic shell
slab used as roof boardmg can use bnck-and-remforced
concrete masonry construction and stnp foundation.
The reason is that the hnear load transmitted by the slab
makes the walhng evenly in force, the bearing area is
large, and there is rehable connection between slab and
wallmg. Additional advantageous condition is that the
enclosure height of walhng is reduced, and the
corresponding dead weight of structure is lighter.
(7) According to the current Beijing estimates quota
(1992 ), an analysis and companson is made for the
direct cost of 3 x 24-m hyperbohc slab The direct cost
of one square meter of hyperbohc slab system is lower
than that of reinforced concrete roof truss plus large
roof boardmg by more than 10%, and is lower than that
of steel roof truss plus large roof boardmg by more than
40%. The direct cost of hyperbohc shell slab is about
102 yuan/in", yet without countmg the saved cost of
the upper structure from foundation due to hyperbohc
shell slab.
(8) Hyperbolic shell slab is generally prefabncated on the
construction site, and hoisted and assembled on the very
place, thus savmg a considerable sum of transportation
expenses.
Conclusions
Compared to the traditional system of roof truss and beam-
slab structure, the hyperbolic shell slab has better economic
results and supenor structural behavior. After the project
was completed and put mto use, the relevant leaders and
persons in charge of capital construction of vanous gram
depots went to visit it one after another, and they all gave it
a full affirmation and praise. In the planned construction
projects such as Lishuiqiao Grain Depot, Beijmg Gram
Center Depot (a World Bank loan project}, and Haidian
National Gram Reserve Depot, this roof form will be
adopted As proved by the actual use m a few years past,
the project having adopted the structural design of
hyperbolic shell slab is successful, and it can be said that m
the construction of gram depots from now on, It has played a
demonstrative role to some extent.
It should be pomted out that the hyperbohc shell slab roof
structure With slab and truss combined into one piece has
many advantages. However, there are some mmute
problems m the design and construction yet to be further
studied and solved. Nevertheless,
along with the
dissemmation and use of pre-stressed hyperbohc shell slab m
the construction of storehouses m the gram sector, people's
recognition of it will be contmuously deepemng, and this
structural member pre-stressed hyperbolic shell slab and its
structural system Willsurely be improved day by day.
References
Architecture Research Institute of Mimstry of Metallurgical
Industry, 1973. Hyperbohc shell slab roof (in Chmese).
Metallurgical Industry, 1, 26
Ge Lianfu, 1975 Application of pre-stressed hyperbolic
shell slab and dISCUSSIonof some problems thereof.
Metallurgical Architecture, 5, 31
Foundamental construction committee of Zhejiang province,
1980 Calculation of 24m x 15m prestressed saddle-shaped
shell slab. Prestressed building bloch design and
cmstruction, pubhshed by Architecture Industry Pubhc of
China, 178 -184.
Fen Lei, 1990. Bnef introduction of 27m span saddle-shaped
shell slab project at Luhe Flour Mill. Prestress Technology
Newsletter, 10, 4.
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