Degree of external restraint of wall segments in semi‐massive reinforced concrete tanks: Part I rectangular segments

Abstract

This paper presents graphs and formulas serving to define the distribution of the restraint degree of wall segments in rectangular reinforced concrete tanks. The most frequent cases occurring in engineering practice are analyzed, that is, wall segments erected during the first concreting stage and those restrained along three edges. For the latter ones, this paper defines the influence of vertical stiffness in construction joints (depending on the reinforcement degree) on the distribution of the restraint degree. This paper shows a substantial impact of the temperature profile (i.e., imposed strain resulting from the development of hydration heat) on the area where cracks occur first, and on the value and distribution of tensile stresses. A practical aspect of the analysis performed is the possibility of defining the restraint degree for cases and assumptions not included in EN 1992–3.

Degree of external restraint of wall segments in semi‐massive reinforced concrete tanks: Part II: Rectangular and cylindrical segments

“…Part I presents a computational analysis of the degree of restraint of a wall segment restrained along its bottom edge and a segment concreted between the previously executed segments. In addition, it was demonstrated how to model stiffness of a structural joint between wall segments in numerical calculations using linear elastic analysis, taking into account the formulas contained in EN1992:1 .…”

“…The next stage of the analysis of the restraint degree is the issue of its distribution for a case in which a supplementary segment is cracked in the middle of its length. The calculations adopt the same assumptions as presented and proven in Part I . The solution demonstrated in this paper, and also in Part I, is universal and provides a greater possibility to determine the R ax coefficient in relation to the information contained in EN1992:3 .…”

“…The solution demonstrated in this paper, and also in Part I, is universal and provides a greater possibility to determine the R ax coefficient in relation to the information contained in EN1992:3 . Assuming different stiffness in the construction joint between a new and old segments (where the ratio of D 11 / E cm equaled: 0.0, 0.25, 0.5, 1.0, 2.5, ∞ (1/m)) and in a discrete crack (Figure ), the range of a concrete relaxation area and the degree of restraint after cracking can be defined. The length and shape of this concrete relaxation area enable drawing conclusions concerning the area where subsequent cracks might develop.…”

“…The presented analysis regards only one of the coefficients ( R ax ) which are very important in the analysis of stresses and cracks of wall segments of reinforced concrete tanks. In addition, it is equally important to take into account the concrete creep, as described in Part I, using, for example, Bamforth's recommendations or elastic‐viscous model of concrete. Moreover, in a specific computational case, it is necessary to take into account actual stiffness of the foundation, influence of element's changes in temperature on the rate of development of the modulus of elasticity of concrete, type, and amount of cement used, which also influences the size of changes and the course of temperature in time.…”

“…In Part I, the construction joint between the segments was modeled taking into account the contact elements of various normal stiffness D 11 . Based on this approach, for the predetermined geometric parameters of the wall, for a specific stiffness D 11 , it is possible to determine the corresponding degree of reinforcement in the construction joint.…”