UNIT III
CIRCULAR PRESTRESSING
Design of prestressed concrete tanks – Pipes.
3.1 Design of prestressed concrete tanks
This tanks are used in water treatment and distribution systems, waste water collection and treatment system and storm water management. Other applications are liquefied natural gas containment structures, large industrial process tanks and bulk storage tanks. The construction of the tanks is the concrete core is cast and cured. The surface is prepared by sand or hydro blasting. Next, the circumferential prestressing is applied by strand wrapping machine. Shotcrete is applied to provide a coat of concrete over the prestressing strands.
Analysis:
The analysis of liquid storage tanks can be done by IS:3370 – 1967, Part 4 or by the finite element method. The Code provides coefficients for bending moment, shear and hoop tension, which were developed from the theory of plates and shells. In Part 4, both rectangular and cylindrical tanks are covered.
The following types of boundary conditions are considered in the analysis of the cylindrical wall.
a) For base: fixed or hinged.
b) For top: free or hinged or framed.
Base:
Fixed: When the wall is built continuous with its footing, then the base can be considered to be fixed as the first approximation.
Hinged: If the sub grade is susceptible to settlement, then a hinged base is a conservative assumption. Since the actual rotational restraint from the footing is somewhere in between fixed and hinged, a hinged base can be assumed.The base can be made sliding with appropriate polyvinyl chloride (PVC) water-stops for liquid tightness.
Top:
Free: The top of the wall is considered free when there is no restraint in expansion.
Hinged: When the top is connected to the roof slab by dowels for shear transfer,the boundary condition can be considered to be hinged.
Framed: When the top of the wall and the roof slab are made continuous with moment transfer, the top is considered to be framed. The hydrostatic pressure on the wall increases linearly from the top to the bottom of the liquid of maximum possible depth. If the vapour pressure in the free board is negligible, then the pressure at the top is zero. Else, it is added to the pressure of the liquid throughout the depth.
The forces generated in the tank due to circumferential prestress are opposite in nature to that due to hydrostatic pressure. If the tank is built underground, then the earth pressure needs to be considered. The hoop tension in the wall, generated due to a triangular hydrostatic pressure is given as follows.
The hoop tension in the wall, generated due to a triangular hydrostatic pressure is given as follows.
T = CT w H Ri
The bending moment in the vertical direction is given as follows.
M = CM w H3
The shear at the base is given by the following expression.
V = CV w H2
In the previous equations, the notations used are as follows.
CT = Coefficient for hoop tension.
CM = Coefficient for bending moment.
CV = Coefficient for shear.
w = Unit weight of liquid.
H = Height of the liquid.
Ri = Inner radius of the wall.
The values of the coefficients are tabulated in IS:3370 – 1967, Part 4, for various values of H2/Dt, at different depths of the liquid. D and t represent the inner diameter and the thickness of the wall, respectively. The typical variations of CT and CM with depth, for two sets of boundary conditions are illustrated.
The roof can be made of a dome supported at the edges on the cylindrical wall.Else, the roof can be a flat slab supported on columns along with the edges.
IS:3370 – 1967, Part 4, provides coefficients for the analysis of the floor and roof slabs.
Design
IS:3370 – 1967, Part 3, provides design requirements for prestressed tanks.
1) The computed stress in the concrete and steel, during transfer, handling and construction and under working loads, should be within the permissible values as specified in IS:1343 – 1980.
2) The liquid retaining face should be checked against cracking with a load factor of 1.2. σCL/σWL ≥ 1.2 .
Here,
σCL = Stress under cracking load.
σWL = Stress under working load.
Values of limiting tensile strength of concrete for estimating the cracking load are specified in the code.
3) The ultimate load at failure should not be less than twice the working load.
4) When the tank is full, there should be compression in the concrete at all points of at least 0.7 N/mm2. When the tank is empty, there should not be tensile stress greater than 1.0 N/mm2. Thus, the tank should be analysed both for the full and empty conditions.
5) There should be provisions to allow for elastic distortion of the structure during prestressing. Any restraint that may lead to the reduction of the prestressing force, should be considered.
3.2 Pipes
Prestressed concrete pipes are suitable when the internal pressure is within 0.5 to 2.0 N/mm2. There are two types of prestressed concrete pipes: cylinder type and the non cylinder type. A cylinder type pipe has a steel cylinder core over which the concrete is cast and prestressed. A non-cylinder type of pipe is made of prestressed concrete only.
IS:784 – 2001 provides guidelines for the design of prestressed concrete pipes with the internal diameter ranging from 200 mm to 2500 mm. The pipes are designed to withstand the combined effect of internal pressure and external loads. The minimum grade of concrete in the core should be M40 for non-cylinder type pipes.
First, the core is cast either by the centrifugal method or by the vertical casting method.In the centrifugal method the mould is subjected to spinning till the concrete is compacted to a uniform thickness throughout the length of the pipe. In the vertical casting method, concrete is poured in layers up to a specified height.
After adequate curing of concrete, first the longitudinal wires are prestressed (the wires can be pre-tensioned). Subsequently, the circumferential prestressing is done by the wire wound around the core in a helical form. The wire is wound using a counter weight or a die. Finally a coat of concrete or rich cement mortar is applied over the wire to prevent from corrosion. For cylinder type pipes, first the steel cylinder is fabricated and tested. Then the concrete is cast around it.
Prestress concrete pipes
The analysis and design of prestressed concrete pipes consider the stresses due to the different actions. A horizontal layout of the pipe is considered to illustrate them.
Analysis:
The stresses in the longitudinal direction are due to the following actions:
1. Longitudinal prestressing.
2. Circumferential prestressing.
3. Self weight.
4. Transport and handling.
5. Weight of fluid.
6. Weight of soil above.
Longitudinal prestressing:
The longitudinal prestressing generates a uniform compression.
fl1 = Pe/ Ac1
Here,
Pe = Effective prestress.
Ac1 = Area of concrete in the core.
Circumferential prestressing:
Due to the Poisson’s effect, the circumferential prestressing generates longitudinal
tensile stress.
fl2 = 0.284 x Pe/Ac
The above expression estimates the Poisson’s effect.
Self weight:
If the pipe is not continuously supported, then a varying longitudinal stress generates
due to the moment due to self weight (Msw).
fl3 = ± Msw/Zl
Here,
Zl = Section modulus about the centroidal axis.
Transport and handling:
A varying longitudinal stress generates due to the moment during transport and
handling (Mth).
fl4 = ± Mth/Zl
Weight of fluid:
Similar to self weight, the moment due to weight of the fluid inside (Mf) generates
varying longitudinal stress.
fl5= ±Mf /ZI
Weight of soil above:
The weight of soil above for buried pipes is modelled as an equivalent distributed load.
The expression of stress (fl6) is similar to that for the weight of fluid.
The longitudinal stresses are combined based on the following diagram.
Section of pipe
The stresses in the circumferential direction are due to the following actions.
1. Circumferential prestressing.
2. Self weight.
3. Weight of fluid.
4. Weight of soil above.
5. Live load.
6. Internal pressure.
Circumferential prestressing:
The compressive hoop stress (fh1) is given as follows.
fh1 = -Ps/Ac2
= -Ps/1xtc
Here,
Ps = Tensile force in spiral wire in unit length of pipe.
Ac2 = Area for longitudinal section of unit length.
tc = Thickness of the core.
For each of these actions, first the vertical load per unit length (W) is calculated.Moment (M) and thrust (T) develop across the thickness owing to distortion of the section due to W, as shown in the following sketch.
Circumferential prestressing
The hoop stress at a point is calculated by the following equation.
fh = ± M/Zh + T/A
The expressions of M and T due to W are as follows.
M = CM W R
T = CT W
Here,
CM = Moment coefficient.
CT = Thrust coefficient.
W = Vertical load per unit length.
R = Mean radius of pipe.
A = Area of longitudinal section for unit length of pipe.
Zh = Section modulus for hoop stress for same length.
= (1/6)t2 × 1000 mm3/m.
t = Total thickness of core and coat.
Values of CM and CT are tabulated in IS:784 – 2001.
The internal pressure is as follows.
fh6 = pR/At
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