Structural Design for Architects

A Nash

• Publisher: Routledge
• Year: 2017
• ISBN:
  9781351897433
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Civil Engineering
• Index: Technology & Engineering

First Published in 2017. An architect is not usually responsible for producing detailed structural calculations and drawings, unless the building concerned is very small and simple. Where the architect can be most effective in the field of structural design is in the clarity of the manner in which suggested solutions, in the form of schematic designs, are put to a structural engineer. It is vital that an architect can propose forms from which the structural engineer need not deviate, to the extent that the original design concept is violated. It is also important that he or she is able to make an informed and rational choice between apparently unrelated structural systems. The theme of this book therefore arises from the necessity for an architect to possess an extensive structural vocabulary, based on a clear understanding of the relevant underlying principles. Although written mainly for practising architects, it is hoped that the book will also provide a fresh perspective on the subject for building surveyors as well as for civil and structural engineers.

Chapter 1

PHYSICS AND MATHEMATICS IN ARCHITECTURE

A treatise which sets out to explore the role of structural design in architecture can only evolve out of a clear idea of the meaning of these two terms. It is a widely held belief in those societies which encourage early specialization in schools that architecture belongs in the domain of the arts whilst engineering, whether the discipline be concerned with machines, electricity, aviation or building structures, possesses a collective identity within the world of technology.

Such a dichotomy may work very well in the case of a surrealist painter at one extreme or the engineer responsible for a hidden production process at the other. There are, however, creations of the human intelligence which cannot be judged solely against the single criterion of function or of aesthetics. The practice and profession of architecture, by its very nature, is arguably the most striking example of a field of endeavour where an understanding rooted in both the arts and the sciences is essential.

If architecture is concerned with the spatial organization of man’s activities, then the spaces that emerge from such organization will have their own physical or implied boundaries. In buildings, we call these physical boundaries walls, floors and roofs, often referred to as the enclosing elements of a building. It is not unreasonable to expect these enclosing elements to remain in position once the building is completed. The idea of structural design evolves from this hope of permanence.

Yet many structural elements whose explicit purpose is to maintain the physical integrity of the enclosed space are outstandingly beautiful. The column in Classical architecture and the vaulted ceiling in Gothic architecture are two particular forms which will be explored in later chapters. Neither of these forms can be dismissed simply as responses to the problems imposed by the physical constraints of existing within the earth’s gravitational field. Ably as they fulfil this task, their forms arise from ideas more diverse than those engendered by structural demands alone. Gravity is, nevertheless, an inescapable condition of terrestrial existence, and provides a suitable starting point for the introduction of some of the laws of physics as they affect architecture.

The relevance of Newton’s Laws to built forms

The structures conceived during the Gothic era in Northern European cathedral architecture occupied several centuries before the life span of Sir Isaac Newton (1642–1727). Yet the need to create equilibrium within a complex arrangement of forces was clearly understood, at least at an intuitive if not at a mathematical level. It is idle to speculate on whether the master masons responsible for deciding on the proportions of the structural elements thought of concepts such as force, gravity, and equilibrium in an abstract as well as a physical sense. Whatever the answer to that question, their judgements were in the majority of cases correct. The precise formulation of the laws of mechanics as they affect matter within a gravitational field had to wait for Newton’s Three Laws.

Building on the earlier investigations of Johannes Kepler (1571–1630) and Galileo Galilei (1564–1642), Newton’s Laws defined the relationship that exists between force, mass and acceleration. It is the idea of force that is of most importance in determining the nature and the proportions of structural members. The nature of force, however, can only be fully understood as the description of the experience of a mass trying to accelerate. Newton’s Laws will first be stated, and then illustrated with reference to some familiar objects.

1. Any body remains in a state of rest or uniform motion when no unbalanced force acts upon it.

2. For a mass to undergo an acceleration, a force is required that is equal to the product of mass and acceleration.

3. Every action must have an equal and opposite reaction.

The first law is of more relevance to the study of moving objects, classified by physicists as dynamics and kinematics. These enter the field of structural design when significant movements and oscillations have to be accommodated, such as those arising from wind forces or earthquakes.

In the second law, the term mass may be taken to mean a quantity of matter. The unit of mass is the kilogram. There will be as much mass in a kilogram of lead whether it is located on earth, on the moon, or in outer space. What will vary is the extent to which the lead will be constrained to move to another position. A kilogram of lead in outer space, being remote from any other objects, tends to be almost at rest, being under the influence of minimal unbalanced force. Its condition is very close to that described in Newton’s First Law.

The reason for describing this condition as being almost, rather than totally, at rest lies in Newton’s Law of Universal Gravitation, in which he proved that the force (F) by which one mass (m₁) attracts another mass (m₂) is proportional to the product of the masses, and inversely proportional to the square of the distance between them (r). This can be stated algebraically as:

where G is the gravitational constant applying everywhere in the universe. Even in deepest space, therefore, there are other attractive masses, but the squares of their vast distances from the kilogram of lead will create forces of a very minute order.

Near to the moon, and to a greater extent close to the surface of the earth, the kilogram of lead will experience an appreciable force, and will accelerate according to the relationship expressed in Newton’s Second Law. Although the earth is not a perfect sphere, the acceleration of any mass towards the centre of the earth (g) is very nearly constant for any point on the earth’s surface, and has been confirmed by experiment to be an increase in velocity of 9.81 metres per second for every second, expressed mathematically as:

This property possessed by all objects of falling at the same rate had been established earlier by Galileo in his experiments conducted from the top of the Leaning Tower of Pisa. The implication in Newton’s Second Law is that if the acceleration is constant, the force must vary as the mass. The unit of force adopted in the Système Internationale notation has been appropriately named the Newton, and is defined as that force which will cause a mass of one kilogram to accelerate by one metre per second per second. The consequence for objects within the earth’s gravitational field can be expressed as:

A mass of one kilogram, therefore, will exert a force of 9.81 Newtons towards the centre of the earth, that is downwards. In other words, one kilogram weighs about ten Newtons, which is a good enough approximation in structural design.

Loading on structures

The principle inherent in Newton’s Third Law is that if objects are to have their accelerations prevented and thus remain at rest, the forces which they exert must be balanced by an equal force in the opposite direction. If their gravitational forces are the actions, then the upward forces provided by whatever supports those objects are the reactions. This is the condition of zero unbalanced force for the state of rest in Newton’s First Law.

Forces imposed on all forms of structure must, if stability is to be achieved, eventually be balanced at ground level. A condition must also be reached whereby all of the intervening structural elements transferring those forces to the ground must themselves obey Newton’s First and Third Laws. The first, and often the most tedious proc...