2003-2006: ‘Theory of Plasticity for Steel Structures’ by MSc Engineering Thomas Hansen. In this project the theory of plasticity for steel structures is studied with the purpose to establish a new theory with simple calculation models. The project is subdivided into four phases.

1. phase it is the aim to study plasticity methods for connections, primarily for welded connections.

2. phase deals with the most common construction element in steel, the plate girder. After elastic buckling of the web, a system of inclined tension fields comes into existence where the shear force is absorbed in the web by a truss action of the forces together with the flanges and necessary stiffeners.

3. phase it is the aim to use the theory of plasticity to formulate calculation methods for stability problems.  The main part of the studies deals with stability failure of columns, buckling of plates and shells.

4. phase the theory of plasticity assumes that the rotation capacity of the material is sufficiently large. If the rotation capacity is insufficient the load carrying capacity can be exhausted by a brittle fracture before the full plastic load carrying capacity is reached.

For that reason it is the aim in this phase to study the rotation capacity by the theory of crack growth for a selection of solutions developed.

Supervisors
Prof. Dr. techn. M. P. Nielsen (BYG-DTU)
Docent Henning Agerskov (BYG-DTU)
M.Sc. Jesper Gath (ALECTIA, at that time Birch & Krogboe)

Abstract
Research within civil engineering structures has changed considerably along with the development of computer programs. Consequently, at universities it has caused the development of simple hand-calculation methods to cease more or less completely. This is not so convenient for the consulting companies, as the computer programs are often too heavy to work with in normal design projects. Only for very large and important structures can the use of heavy computer programs be justified. Therefore, the aim of the present research project is to derive simple hand-calculation methods within the chosen topics, and thereby create a coherent basis corresponding to what exists for reinforced concrete structures.

The theory of plasticity for steel structures deviates little from the theory of plasticity for concrete structures in the form developed in Denmark. Thus, the present project is a natural extension of the now century old development of concrete structures in Denmark.

The thesis is subdivided into four individual parts concerning the chosen topics. The four parts are: Plasticity Theory of Fillet Welds, The Plastic Tension Field Method, Post-Buckling Strength of Plates in Compression and Patch Loading on Plate Girders.

Initially, simple methods for calculation of fillet welds based on the theory of plasticity are derived.

Currently, static calculations of fillet welds are based on a semi-empirical failure condition, where the effective weld stresses are determined as the mean values of the stresses on the throat section without knowledge of the entire stress field. In the thesis it is shown that fortunately, only small corrections are needed according to a consistent treatment.

The plasticity solutions are compared with yield load tests carried out at the Engineering Academy of Denmark in the early nineties as well as older failure load tests. The new failure conditions are in very good agreement with the yield load tests, while in less good agreement with the older failure load tests.

Furthermore, a calculation method for steel plate girders with transverse web stiffeners subjected to shear is described. It may be used for predicting the failure load, or as a design method, to determine the optimal number of internal web stiffeners.

The new method is called the plastic tension field method. It is based on the theory of plasticity and is analogous to the so-called diagonal compression field method developed for reinforced concrete beams with transverse stirrups. Many other theories have been developed, but the method presented here differs from these by incorporating the strength of the transverse stiffeners and by the assumption that the tensile bands may pass the transverse stiffeners, something that is often observed in tests. Other methods have only dealt with a single web field between two stiffeners.

The load-carrying capacity may be predicted by applying both the lower-bound theorem and the upper-bound theorem. The upper-bound solutions show very good correlation with both old and new tests.

Currently, calculations of plates in compression are based on the semi-empirical effective width method, which was developed by Winter et al. It is a well known fact that plates in compression may carry loads much larger than the load for which elastic buckling will occur. The effective width method takes the post-buckling capacity into account. A new effective width method is established, derived on the basis of a consistent theory. The new method rests on the theory of plasticity, particularly the yield line theory. The emphasis is placed on buckling problems related to plate girders. Two general cases are studied: Plates in uniaxial compression supported along all edges, e.g. the compressed flange in a box girder, and plates with one free edge, e.g. the compressed flange and the internal web stiffeners in an I-shaped girder. The resulting equations are compared with the semi-empirical method developed by Winter et al. The plastic solutions give approximately the same results as Winter’s solutions without any empirical modifications.

Finally, a simplified theory for calculation of steel plate girders subjected to concentrated loads, denoted patch loading, is presented.

The theory is simplified due mainly to the assumption that the whole web panel under the patch load will always be active. The post-buckling strength of the web panel is determined by the effective width approach. The stresses in these effective widths will be uniformly distributed under the flange and utilised in a flange mechanism, which is calculated separately.

The solutions are derived separately for girders with a square web panel and for those with a rectangular web panel.

Both solutions are compared with experimental results, and the theories correlate well with the tests, especially for girders with rectangular web panels.

Additionally, it is shown that the theory is also able to deal with the phenomenon of flange induced buckling.