Plastic Methods for Steel and Concrete Structures

Frontmatter

1. Some General Concepts

Abstract

The teaching of structural analysis follows, in general, traditional lines, the recognised route being statics, simple bending theory, virtual work and, finally, the analysis of rigid jointed structures. The main barrier that has to be crossed is from statically determinate structures (which can be analysed by statics alone) to statically indeterminate structures (which must, effectively, be analysed by a combination of statics and compatibility of deformations). The mathematics involved in the analysis of indeterminate structures frequently presents severe problems for students.

Stuart S. J. Moy

2. Plastic Bending

Abstract

In the previous chapter the behaviour of trusses was discussed. However, a more common form of construction nowadays is the framed structure with joints capable of transmitting bending moments. It will become clear that the ideas already developed can be applied to such structures.

Stuart S. J. Moy

3. Collapse of Simple Frames

Abstract

It was shown in the previous chapter that the formation of a plastic hinge in a framed structure is equivalent to a member yielding in a truss. The purpose of the first part of this chapter is to show what happens in a frame as the load is increased until failure occurs. This means going through an example in the same way as in chapter 1. This example will also be used to illustrate some important theorems which are essential to plastic analysis.

Stuart S. J. Moy

4. Limit Analysis

Abstract

Limit analysis is not related to the limit state philosophy of design. It may seem peculiar to start off this chapter with this statement, but confusion between the two is all too common. Limit state is a philosophy applied to the design of reinforced concrete structures, as embodied in CP 110 [5] and more recently to steel structures, as in the B/20 draft of the Standard for Steelwork Design. [6] Limit analysis is a powerful method for fording the value of, or a range for, the collapse load factor of a structure under a given system of loading, using plastic theory.

Stuart S. J. Moy

5. Design Using Plastic Theory

Abstract

The last two chapters have been concerned with analysis, that is, solving problems where the basic geometry of the structure (length of beams and column heights) and the size of the members is given. This would be the situation when an existing structure is checked for resistance to collapse. More frequently the problem is to find the size of the members, given the loading (or loadings) and the basic geometry, such that the structure has a required load factor against collapse. The sizing of the members is a design problem.

Stuart S. J. Moy

6. Deflections and Stability

Abstract

Methods for finding the collapse loads of steel frames were examined in detail in chapters 3, 4 and to some extent, 5. In the virtual work method, for example, the collapse load was found by considering small (virtual) deformations of the collapse mechanism. However, the shape of the structure before deformation of the mechanism was assumed to be the same as when there was no load on the structure. In other words, all deformation before collapse was ignored. There must be deformation before collapse, but how significant is it?

Stuart S. J. Moy

7. Application of Plastic Methods to Reinforced Concrete Structures

Abstract

At first glance concrete structures bear little resemblance to steel ones. Unexpectedly, reinforced concrete (RC) beams do, in certain circumstances, act similarly to steel beams, because of the characteristics of the steel reinforcement which control the behaviour of the beam. The maximum BM that a section can carry, usually called the moment of resistance of the section, is calculated in a similar way to the plastic moment of a steel beam. Many tests on RC beams have shown that the calculated moment of resistance is very close to the experimental value, confirming the applicability of the theory. Section 7.2 looks in some detail at the analysis of reinforced concrete sections carrying BMs only.

Stuart S. J. Moy

8. Yield Line Analysis and the Hillerborg Strip Method for Reinforced Concrete Slabs

Abstract

The previous chapter showed that plastic theory is usually rather difficult to apply to RC structures because of the limited plastic rotation capacity of concrete sections in bending. However, concrete slabs are almost always very under-reinforced. It is unusual to have sections with more than 1 per cent of reinforcement. Consequently slabs have considerable plastic rotation capacity and can be successfully analysed or designed by plastic methods.

Stuart S. J. Moy

Backmatter