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.