Bio-inspired, Flexible Structures and Materials - Biotechnologies and Biomimetics for Civil Engineering - page 272

12.2 The Design Potential of Elastic Construction
Materials

A fundamental pre-requisite in the designing of bending-active structures is the
characteristics of particular building materials which provide a beneficial ratio of
high strength and low bending stiffness. Traditional building materials such as
timber, for example, offer a suitable elastic range. Fibre Reinforced Polymers
(FRP) embody an even greater potential for lightweight bending-active structures
due to their low density and high breaking strain. Constant improvements in the
development and composition of custom-made, high-performing FRPs suggest
that there will be even more materials to choose from in the future.

12.2.1 Material Overview

Among the materials we can consider working with in building and construction,
there is a wide range of strength, stiffness, and densities available. Some materials
are more suitable for bending-active structures than others. Comparing steel with
rubber, for example, one may expect that rubber is the more appropriate choice
due to its compliant nature. However, the low tensile strength of rubber makes it
unsuitable for structural applications. The much stronger steal, in comparison,
offers high tensile strength but is also comparably stiff. As a result neither of these
two materials can really be considered as a favorable option for the design of
bending-active structures.
In the screening process for the most suitable materials it is therefore important not
to focus on one material characteristic only. Instead, the combination of material
properties is much more significant. Choosing the right material parameters necessi-
tates an understanding of the mechanical relationships in large elastic bending
deformations. From the Euler-Bernoulli law we know that the bending curvature is
proportional to the bending moment M (1) (Fertis 2006 , p. 9). For flat sections or plates
the width has no influence on the bending stress which can therefore be expressed
proportional to the thickness t and curvature 1/r as shown in (2). This leads to the
formulation of the minimal bending radius (3) which we can use to analyse different
building materials for their potential use in bending-active structures. The most
important variables to set into relation here are the Young's Modulus E and permissible
bending stress r M,Rk . It can thus be concluded that an optimal material for bending-
active structures would ideally combine low stiffness and high tensile strength.

r ð x 0 Þ ¼ M ð x 0 Þ

1

ð 12 : 1 Þ

E I

r M ¼ E I

r w ¼ E t 2 r

ð 12 : 2 Þ