# Stifferness

Topics: Structural engineering, Force, Structural load Pages: 26 (7300 words) Published: March 20, 2013
SE21 p36-42 Ji

29/10/03

3:42 pm

Page 36

paper: ji

Concepts for designing stiffer structures
Synopsis
The paper demonstrates concepts for designing stiffer structures. They are: (a) the more direct the internal force path, the stiffer the structure; (b) the more uniform the internal force distribution, the stiffer the structure; and (c) the smaller the internal forces, the stiffer the structure. These concepts are applicable to the design of many structures. Two ways of implementing the concepts into practice are provided. Simple examples are given to illustrate the implementation and the efficiency of the concepts. Laboratory tests and the demonstration of two physical models further confirm the findings. Several practical designs are also provided to show the applicability and significance of these concepts. An alternative definition of structural stiffness is given which complements the existing definition and allows for designing stiffer structures. It is interesting to note that using the concepts may lead to not only stiffer but also more economical and elegant designs. K= P D

Tianjian Ji
...(3)

Introduction
Buildings have become taller, floors wider and bridges longer in recent years. It is expected that the trend of increasing heights and spans will continue in the future. How can engineers cope with the ever-increased heights and spans, and design structures with sufficient stiffness? The basic theory of structures provides the conceptual relationships between span (L), deflection (∆), stiffness (K) and natural frequency (f) for a single-span structure carrying distributed loads as follows: D = c1 = c2 L4 K f = c3 K = c 4 L2 ...(1) ...(2)

This definition of stiffness provides a means of calculating or estimating the stiffness of a structure, but does not suggest how to find a stiffer structure. How to design a stiffer structure (the form and pattern of a structure) is a fundamental and practical question and may be more important and challenging than how to analyse the structure. It is noted that university courses provide methods for calculating structural responses to different loads, but give little guidance on designing stiffer structures. The work described in this paper is a further development of Ji and Ellis’ earlier work3 on effective bracing systems for temporary grandstands. In the paper the point stiffness and static stiffness of a structure were defined by which the stiffness of a structure can be evaluated. Two concepts for designing stiffer structures based on pin-jointed structures were derived and applied to the arrangement of bracing systems for temporary grandstands. The present work extends the previous work to beam types of structure and provides an additional concept. The paper also focuses on implementing, verifying and demonstrating the concepts, which can be used for designing stiffer structures. The concepts, which are simple but useful in design, are derived based on truss and beam types of structures in the next section The following two sections implement the concepts into possible applications. Simple examples, experiments, demonstration models and engineering cases are provided to show the efficiency of the concepts and the application of the criteria derived. An alternative definition of structural stiffness is given and the applications of the concepts are discussed.The final section summarises the main results and conclusions obtained from this study.

PhD, CEng, MIStructE
Manchester Centre for Civil and Construction Engineering, University of Manchester Institute of Science and Technology, Manchester M60 1QD UK Received: 08/02 Modified: 04 03 Accepted: 05/03 Keywords: Stiffness, Design examples, Structures, Internal forces, Frames, Laboratory tests

Concepts for achieving a stiffer structure
Pin-jointed structures Consider a pin-jointed structure that consists of m bars and n joints, with no limitation on the layout of the structure and the...