# A.2.1: Basic Properties of Materials

## Material Stiffness

The stiffness i.e. resistance of a material against deformation is characterized by its Young’s Modulus or modulus of elasticity **“E”**. The higher its value the stiffer the material.

### Table A.2.1.1: Young's Modulus of materials (E-values) for some popular building materials

Type of material | $E [kN/cm^2]$ |

steel | 21000 |

aluminum | 7000 |

reinforced concrete | 3000 |

glass fiber | 7000 |

wood (spruce) | 1000 |

For composite materials – like in the case of rods made from glass fiber and epoxy – it is necessary to defer a mean value for **“E”** using material tests. Karamba3D expects the input for **“E”** to be in kilo Newton per square centimeter ($kN/cm^2$).

If one stretches a piece of material it not only gets longer but also thinner: it contracts laterally. In case of steel for example lateral strain amounts to 30% of the longitudinal strain. In case of beams with a large ratio of cross section height to span this effect influences the displacement response.

In common beam structures however this effect is of minor importance. The shear modulus **“G”** describes material behavior in this respect.

## Specific Weight

The value of **“gamma”** is expected to be in kilo Newton per cubic meter ($kN/cm^3$). This is a force per unit of volume. Due to Earths gravitational acceleration ($a=g=9.81 kg m/s^2$) and according to Newtons law ($f=m \cdot a$) a mass m of one kilogram acts downwards with a force of $f=9.81N$. For calculating deflections of structures the assumption of $f=10N$ is accurate enough. If you want a more precise value change the entry “gravity” in the “karamba.ini”-file. In case of Imperial units the exact value for “gravity” is automatically set – otherwise the conversion from lbm to lbf does not work properly.

Table A.2.1.1 gives specific weights of a number of typical building materials. The weight of materials only takes effect if gravity is added to a load case (see section 3.2.1).

## Theoretical Background of Stiffness, Stress and Strain

Strain is the quotient between the increase of length of a piece of material when loaded and its initial length. Usually one uses the Greek letter $ε$ for strains. Stress is force per unit of area. From the stress in a beam cross-section one can calculate the normal force that it withstands by adding up (integrating) the product of area and stress in each point of the cross-section. Stress is normally symbolized by the Greek letter $σ$ . Linear elastic materials show a linear dependence between stress and strain. The relation is called Hooke’s Law and looks like this:

$σ = E \cdot ε$

Hooke’s law expresses the fact that the more you deform something the more force you have to apply.

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