# 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”](https://manual-1-3.karamba3d.com/troubleshooting/4.3.-miscellaneous-problems/4.1.6-changing-karamba.ini-file)-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](https://manual-1-3.karamba3d.com/3-in-depth-component-reference/3.2-load/3.2.1-loads#gravity)).

## 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.