## INTRODUCTION

Structures 1 is designed to give students a basic understanding of structural principles. There are some mathematical skills needed and an understanding of the following topics is essential:

• Fractions (common and decimal)
• Ratio and proportions
• Scientific notation
• Trigonometric functions (sin, cos. & tan)
• First degree equations
• Formula transposition

Students should check their mathematical skills. If you have difficulties with maths you should urgently revise the subject matter; otherwise it will be difficult to complete this subject successfully.

The study of Structure subjects of the National Course provide the students with a basic knowledge of general structural principles. The Learning Outcomes deal with forces and moments, properties and behaviour of structural materials, section properties, beams, columns, structural connections, bracing, trusses and loads. The main emphasis is placed on the understanding of structural principles and the mathematical component is minimised. However, students lacking mathematical skills should make sure that they can cope with all mathematical components of the subject matter.

An understanding of basic geometry (sin and cos function), formulating equation, formula transposition, substitution and scientific notation is a per-requisit for this subject. A short revision on this matter is found in Chapter 1. A self test is included and students who have difficulty to answer the questions need to revise the topics or should enroll in an appropriate mathematical subject to obtain these necessary mathematical skills.

The course notes are designed to assist students whether enrolled in a face to face class or off campus. The notes will accommodate the text listed in the course outline.

Everybody has some understanding of structures and a feeling for the way they sustain load. If we see a very slender (thin, long) column carrying a heavy load we feel that this may not be a safe structure. We know that a piece of timber 100x50 mm and 4 meters long carries more load if it is positioned upright and not laid flat. Often we do not fully understand the reason and cannot explain why the structure behaves in this way. However, there are rules of construction that remove the guesswork and enable a designer to analyses a complex structure accurately. Understanding structural behaviour is the key to understanding structural calculations and design methods. Mathematics is used to quantify our feeling for safe structural components or members.

While these fundamental principles of structural analysis are based on very precise mathematical and physical concepts and calculations, it does not take an expert to understand and use them. After all, we all have some familiarity with structures in our daily lives; we know at what angle to set a ladder so that it will carry our weight without sliding on the floor, and whether the plank over the stream will give way as we walk on it. We know whether the tent pitched at a camp will be blown away by the wind. We should capitalise on our experiences in trying to reach an understanding of how and why a modern structure works.

In Structures 1 a variety of terms, units and Greek symbols (letters) are used. You should make yourself familiar with these units.

Safety and allowable stress design

For purposes of safety knowledge of the stress at which a material will start yielding is of the utmost importance. The yield point in tension or compression for structural steel varies between 250 MPa and 450 MPa. Since structures cannot be allowed to yield under loads, safe stresses are usually assumed as a fraction of the yield point. The safety factors thus introduced depend on a variety of conditions: the uniformity of the material, its yield and strength properties, the type of stress developed, the permanency and certainty of the loads, the purpose of the building. This last factor is of great importance from a social viewpoint: the safety of a large hall is more critical than the safety of a family home, and must be evaluated more conservatively. The calculation of such safety factors involves the use of probability theory, and leads to results that can be gauge in terms of human lives.

Safety factors cannot be established on the basis of the yield point (see stress/strain topic) in cases where the material does not present a well-defined yield point, or does not have any. The first case occurs with concrete, which does not have a clear transition from elastic to plastic behaviour, the second with brittle materials, which behave linearly up to failure. In these cases safety must be measured directly against failure, as far as the material is concerned.

However, there are some advantages in establishing safety factors on the basis of failure, even when the yield point is clearly defined. These safety factors give direct information on the overload the structure can support before it collapses, rather than on the overload that will make the structure unusable because of excessive deformation. Knowledge of both overloads may be useful in establishing higher safety factors for permanent and semipermanent loads on the basis of yield, and lower safety factors for exceptional loads (hurricane winds, earthquakes) on the basis of failure. This criterion is accepted by most codes: a combination of normal vertical loads and of exceptional lateral loads (such as wind or earthquake forces) is usually allowed to stress the structure one third above the stresses due to vertical loads only.

Using factors of safety ensures a satisfactory performance under working loads, but only assumes a reasonable margin against failure, while load factors ensure a definite margin against failure and assume a satisfactory performance under working loads. Both factors operate on the implicit assumption that the determined values, both for the loading which the structure is expected to carry and for the strength of the materials of which the structure is made, remain constant, thus inferring a guarantee of absolute safety. While this may be satisfactory in certain cases, it is generally recognised that a more realistic measure of the safety of a structure can be achieved through an assessment of the probability of its failure.

The Limit State Design method is now introduced in most Australian Design Codes.

To ensure the safety of the structure it is necessary to provide it with sufficient strength, and to safeguard its serviceability it must have adequate stability. For these and other reasons it is necessary to make the design or working stress less than the ultimate stress. This margin is provided by the introduction of the factor of safety, so that

The value of the factor of safety may vary between 1.5 and 2.5 and depends on many circumstances. It has been progressively reduced as the knowledge of structural behaviour of materials has increased. However, the objective of the designer must include a careful control of materials, based on an understanding of their performance.