The volume changes caused by coupled temperature and moisture variations in early-age concrete elements lead to formation of stresses. If a restraint exists along the contact surface of mature concrete against which a new concrete element has been cast, generated stresses are mostly of a restraint origin. In engineering practice a wide range of externally restrained concrete elements can be distinguished such as tank walls or bridge abutments cast against an old set foundation, in which early-age cracking may endanger their durability or functionality. Therefore, for years methods were being developed to predict early-age stresses and cracking risk of externally restrained concrete elements subjected to early-age thermal-moisture effects. The paper presents the comparative study of the most recognised analytical approaches: the method proposed in EC2, the method proposed by ACI Committee 207 and the method developed at the Luleå University of Technology.

Adetailed tie model of cracking is proposed. The model is dedicated to both semi-massive RC (reinforcement concrete) members subjected to early-age imposed strains and non-massive members in which imposed strains occur after concrete hardening. As distinct from the currently applied European guidelines, the proposed model enables an analysis of crack width changes. These are a function of progressive imposed strain, material and geometry data, but also depend on the scale of cracking which determines the strain conditions of a member. Consequently, the new model takes account of not only the factors determining the cracking development but also the member relaxation effect that results from cracking. For this reason a new definition of restraint factor is proposed, which takes into account the range of cracking of a structural member, i.e. the number and width of cracks. Parametric analyses were performed of both the changes of the degree of restraint after cracking as well as the changes of crack width depending on the adopted type of aggregate, class of concrete and the coefficient of thermal expansion of concrete. These analyses indicate the potential benefits of the application of the presented model for both a more accurate interpretation of research and economical design of engineering structures.

New approach using direct crack width calculations of the minimum reinforcement in tensile RC elements is presented. Verification involves checking whether the provided reinforcement ensures that the crack width that may result from the thermal-shrinkage effects does not exceed the limit value. The Eurocode provisions were enriched with addendums derived from the German national annex. Three levels of accuracy of the analysis were defined - the higher the level applied, the more significant reduction in the amount of reinforcement required can be achieved. A methodology of determining the minimum reinforcement for crack width control on the example of a RC retaining wall is presented. In the analysis the influence of residual and restraint stresses caused by hydration heat release and shrinkage was considered.

Buckling of the stiffened flange of a thin-walled member is reduced to the buckling analysis of the cantilever plate, elastically restrained against rotation, with the free edge stiffener, which is susceptible to deflection.Longitudinal stress variation is taken into account using a linear function and a 2nd degree parabola. Deflection functions for the plate and the stiffener, adopted in the study, made it possible to model boundary conditions and different buckling modes at the occurrence of longitudinal stress variation. Graphs of buckling coefficients are determined for different load distributions as a function of the elastic restraint coefficient and geometric details of the stiffener. Exemplary buckling modes are presented.

The study presents the results of theoretical investigations into lateral torsional buckling (LTB) of bi-symmetric I-beams, elastically restrained against warping at supports. Beam loading schemes commonly used in practice are taken into account. The whole range of stiffness of the support joints, from free warping to warping fully restrained, is considered. To determine the critical moment, the energy method is used. The function of the beam twist angle is described with power polynomials that have simple physical interpretation. Computer programs written in symbolic language for numerical analysis are developed. General approximation formulas are devised. Detailed calculations are performed for beams with end-plate joints. Critical moments determined with programs and approximation formulas are compared with the results obtained by other researchers and with those produced by FEM. Very good accuracy of results is obtained.

Thin-walled bars currently applied in metal construction engineering belong to a group of members, the cross-section resistance of which is affected by the phenomena of local or distortional stability loss. This results from the fact that the cross-section of such a bar consists of slender-plate elements. The study presents the method of calculating the resistance of the cross-section susceptible to local buckling which is based on the loss of stability of the weakest plate (wall). The "Critical Plate" (CP) was identified by comparing critical stress in cross-section component plates under a given stress condition. Then, the CP showing the lowest critical stress was modelled, depending on boundary conditions, as an internal or cantilever element elastically restrained in the restraining plate (RP). Longitudinal stress distribution was accounted for by means of a constant, linear or non-linear (acc. the second degree parabola) function. For the critical buckling stress, as calculated above, the local critical resistance of the cross-section was determined, which sets a limit on the validity of the Vlasov theory. In order to determine the design ultimate resistance of the cross-section, the effective width theory was applied, while taking into consideration the assumptions specified in the study. The application of the Critical Plate Method (CPM) was presented in the examples. Analytical calculation results were compared with selected experimental findings. lt was demonstrated that taking into consideration the CP elastic restraint and longitudinal stress variation results in a more accurate representation of thin-walled element behaviour in the engineering computational model