This paper presents details of an analysis for strength at failure of prestressed beams subjected to a complex system of applied loads consisting of combined torsion, shear and bending. It is based on a modified skew bending approach incorporating the use of strain compatibility over the beam cross-section to permit recognition of a "non-flat" yield region typical for cold drawn reinforcement. A significant feature of this analysis is the use of a biaxial strain criterion to recognize that the magnitude of the limiting strain in the compressed concrete at failure varies with different combinations of torsion, shear and bending. Other contributors working on this problem have used either a constant limiting concrete strain of magnitude 0.003 as for pure flexure, or some constant fraction of this amount throughout all possible load combinations involving torsion, shear and bending. Incorp-orated also in the determination of the ultimate strength is the ' recognition of the presence of shear stresses on the uncracked failure surface. Results of tests made on eighty four beams were used to verify this analysis. An excellent and consistent correlation was obtained between theoretical and test values for bending moments and resisting torques.

A computer-oriented constitutive model for concrete in compresslon, valid at first heating of concrete up to 800 C is described. The total deformation is expressed in terms of thermal, instantaneous stress-related, creep and transient strain components, where the transient strain is a concept introduced to describe the particular behavior under changing temperature. Comparisons with independent tests demonstrate that the material behaviour is described in a very appropriate way. The model is applied in a simple example calculation, showing that thermal stresses due to non-uniform temperature distribution are very insignificant or even nonexistant.Stresses due to restrained thermal expansion cannot in themselves contribute to compression failure of concrete.

The paper presents a model capable of predicting the post-cracking response of reinforced and prestressed concrete members subjected to complex loading. The angles of inclination of the compression diagonals in the walls of the truss model are determined from strain compatibility conditions. These compatibility conditions in conjunction with the equilibrium conditions for the truss and the load-deformation relationships for the members of the truss enable the full response of the model to be determined; i.e. the strain in the longitudinal and web reinforcements as well as the various eformations of the beams at all load levels can be predicted. Experimental results are used to confirm the truss model's predictions. It is shown how the truss model could be used in the design office.

Lapped splices play an important role in the con-struction of reinforced concrete structures. The tensile force at a reinforced bar end is transferred over the concrete to the beginning of the next bar by means of tbe bond action alone. Investigations on the capacity of lapped splices were carried out at the Institute for Structural Engineering, University of Technology, Munich. This research was initiated by Professor Kupfer. The purpose of these tests was to gain more knowledge regarding the stress in the surrounding concrete and to ascertain the force distribution along the spliced bars. The first part of the research program comprised of slab tests with full splicing of reinforced bars with large diame- ters. For the judgement of the capacity of a reinforcing bar the most important criterion is the bond behaviour of the concrete and steel along the lapping length. By means of a new method specially developed for this research it was possible to measure the slip of the spliced bars in comparison to the concrete within short distances along the bar with scarcely any bond disturbance. In connection with the steel strain, measured by bonded wire strain gauges, it was possible to ascertain the bond strain-slip relations (C-A) for different sections of the lapping length. Parallel to these tests, investigations on photoelastic models were carried out. These tests in conjunction with a special technique allowed the spacial course of stress in the vicinity of the reinforced bar to be studied. With the aid of the bond laws derived from reinforced concrete tests and the knowledge gained from the photoelastic tests the splices were calculated on the basis of the finite element method and compared with the results obtained from tests.

A procedure for estimating the inelastic respond\se of reinforced concrete structures to ser\severe ground motion is described. This procedure combines analytical structural engineei\ring methods with interpreitve analyses of response spectra and can be used by practicing engineers without complex computer analysis. The solution results in estimated values for peak structural response, peak ductility demands, equivalent responese periods of vibration, equivalent percentages of creitical damping, and reserve capasities. Examples of the procedure are presented, and their results are compared with data obtained from recorded motion of actual reinforced concrete structures.