PCA Teoria-Rectangular Concrete Tanks

Rectangular Concrete Tanks

Revised Fifth Edition

b y Javee dA . M u n shi

PCA

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C o n te n ts Chapter 1 Introduction

1-1

Chapter 2 Plate Analysis Results

2-1

Chapter 3 Tank Analysis Results

3-1

Chapter 4 Multicell Tanks

4-1

Chapter 5 Examples

5-1

Appendix

Introduction Conventionally reinforced (non-prestressed) concrete tanks have been used extensively in municipal and indus trial facilities for several decades. The design of these structures requires that attention be given not only to strength requirements, but to serviceability requirements as well. A properly designed tank must be able to withstand the applied loads without cracks that could cause leakage. The goal of designing and constructing a structurally sound tank that will not leak is achieved by providing the proper amount and distribution of rein forcement, the proper spacing and detailing of construction joints, and the use of quality concrete, placed using proper construction practices. A thorough review of the latest report by ACI Committee 350 entitled Environmental Engineering Concrete Structures [11* is essential in understanding the design of tanks. The document recommends that, unless noted otherwise, the structural design should conform to Building Code Requirements for Structural Concrete (ACI 318) [2]. Therefore, a working knowledge of ACI 318 is also necessary. This publication consists of five chapters and an appendix. The contents of these are as follows:

Chapter1

-

Introduction

Except for the notations and the definitions, the topics discussed in this chapter are, for the most part, items presented in ACI 350 that are not addressed in ACI 318: • • • • • • • • • • • • •

Notations and Definitions Design Methods Durability Minimum Reinforcement Loading Conditions Crack Control Formwork Considerations Base Fixity Buoyancy Forces Earthquake Forces Codes, Specifications and Standards References Suggested Literature

Chapter2 Plate AnalysisResults -

This chapter gives the design coefficients for deflection (Cd), shear (Cs) and moments (Ms, M, M,,,) for plates with different end conditions. Results are provided from finite element analyses of two-dimensional plates subject to out-of-plane loads using SAP9O [19]. Convergence analysis was made to ensure the quality of the results. The slab was assumed to act as a thin plate, for which equations and/or the design coefficients are available in some of the references listed [6-10]. However, since only a limited number of cases are available in such literature, this text was prepared to cover a wider range of loading configurations, end-restraint conditions, and width/height ratios. *See the end of this chapter for cited references.

Coefficients for individual panels with fixed side edges apply without modification to continuous walls, pro vided there is no rotation about vertical edges. In a square tank, therefore, moment coefficients can be taken directly from the tables in Chapter 2. For a rectangular tank, adjustments must be made to account for redistri bution of bending moments to adjacent walls. The design coefficients for rectangular tanks are given in Chapter 3.

C h a p te r3 T an kA n alys isR esu lts -

This chapter gives the design coefficients for deflection (Cd) and moments (Mi, M, M,, and M) for tanks with different end conditions. The design coefficients are based on finite element analysis of tanks. The design coefficients (M M, Mx,,) presented in Chapter 2 for design of plates can also be used for tanks that have square plan dimensions. For rectangular tanks, the plate analysis results are not applicable since they do not account for moment distribution that will occur between the walls of different stiffnesses. An adjustment must be made similar to the modification of fixed-end moments in a frame analyzed by moment distribution. The shear coef ficient (C 3) given in Chapter 2 for plates may be used for design of rectangular tanks. If the moment distribution method is used, the common side-edge of adjacent panels is first considered artifi cially restrained, so that no rotation can take place about the edge. Fixed-edge moments taken from the results presented in Chapter 2 are usually dissimilar in adjacent panels, and the differences, which correspond to unbal anced moments, tend to rotate the edge. When the artificial restraint is removed, the unbalanced moments will induce additional moments in the panels. Adding the induced and fixed-end moments at the edge gives final moments, which must be identical on both sides of the common edge. Note, however, that moment distribution cannot be applied as easily to continuous tank walls as it can to framed structures, because bending moments must be distributed simultaneously along the entire length of the side edge so that moments become equal at both sides at any point of the edge. Moreover, tanks will develop in-plane axial compression or tension. Effects of the tension force, if significant, should be recognized. If significant compression forces are developed, the reduction in the effective stiffness of the member may also need to be considered.

C h a p te r4 M ultice llT a nk s -

This chapter provides information on how to modify single-cell coefficients for use in multicell tank design. An appropriate method based on relative wall stiffnesses is given to compute the design moments in intersecting walls of multi-cell tanks.

C hapter5- E xam p les A complete design for a wall and the roof slab of a rectangular tank is presented. Two examples that explain the determination of the bending moments for multicell tanks are also provided.

A pp end ix A design aid that can be used for determining the required reinforcment for a rectangular concrete section subject to a given bending moment is located in the appendix.

N o ta tio n s anDdefin ition s a w q

=

k

=

=

=

height of plate or wall. unit weight of soil or water (for example, lbIft3). k wa, pressure at bottom of plate/wall for triangular load distribution (for example, lb/ft2). k w for uniform pressure along height of plate/wall (for example, lb/ft2). coefficient of active or passive pressure, whichever is applicable [3]. For water, active pressure coefficient ka = 1, while for soil ka = (1 sintb)/(l + sin), where of internal friction of soil [3]. -

=

angle

C5 1 -2

=

shear coefficient given in tables of Chapter 2 for computation of shear: Shear per unit width C 5 q a.

=

RectangularTanks

Cd

=

E

=

t

= =

deflection coefficient given in tables of Chapters 2 and 3 for computation of deflections. Deflection = Cd q a4/1000 D, where D = E t3 / 12(1-!?). modulus of elasticity of concrete (E = w5 33J from ACI 318-95, where w is the unit weight of concrete and is the specified compressive strength of concrete, psi). thickness of plate or wall. Poisson’s ratio, taken as 0.2 for concrete.

(M M, M, M and M )

M

=

=

=

=

X M Coef. q a2/1000

moment per unit width about the z-axis stretching the fibers in the y-direction when the plate or wall is in the y-z plane (see Fig. 1-1). The moment is used to determine steel in the y (vertical) direction of the plate or wall (Fig. 1-1) and is given by: M=MCoef.

M,

X qa/1000

moment per unit width about the y-axis stretching the fibers in the x-direction when the plate or wall is in the x-y plane, or in the z-direction when the plate is in the y-z plane (see Fig. 1-1). The moment is used to determine steel in the x or z (horizontal) direction of the plate or wall (Fig. 11) and is given by: M

M

moment coefficients given in tables of Chapters 2 and 3 for com putation of moments M ,3 M, M, M and respectively. Note that M and coefficients are given in absolute values.

=

moment per unit width about the x-axis stretching the fibers in the y-direction when the plate or wall is in the x-y plane (see Fig. 1-1). The moment is used to determine steel in the y (vertical) direction of the plate or wall (Fig. 1-1) and is given by: M=MCoef.

M

Coef.

=

X

qa/1000

torsion or twisting moments for plate or wall in thex-y and y-z planes, respectively, given by: M=MCoef. =

X

qa/1000

Coef. X q a2/1000

y

y z

y

Platein x-yIane

Figure1-1 CoordinateSystem for Plates

Introduction

1 -3

The twisting moment such as M may be used to add to the effects of orthogonal moments M and M for the purpose of determining the steel reinforcement when the plate is in the x-y plane. can be similarly used for the plate in the y-z plane. These moments should be considered for safe design wherever their effect is deemed to adversely affect the steel requirement. The Principle of Minimum Resistance [4] may be used for determining the equivalent orthogonal moments in this case. The equivalent orthogonal moments M and M, for a plate in x-y plane are computed as follows: Where positive moments produce tension: M2

=

M +jM3,j

=M

+ M E ,I

However, if either M or M is found to be negative, the negative value of the moment is changed to zero (no steel required) and the other moment is given as follows: M2 >0

ifMt0

y

Where negative moments produce tension: M _Mx_MxyI M =My-Mxy However, if either M or M, is found to be positive, the positive value of the moment is changed to zero and the other moment is given as follows: M2

ifMLX.>0,thenMtX=0andMY=M”—

ifM,

>0,thenM31=0andM=

M

M2 -