How is the formulare to calculate Sh and Sc
for a material "carbon steel" ?

You really can't determine allowable stresses for a generic "carbon steel". You need to know what the grade and properties of the material are. I think most of the commonly used carbon steels in petrochem and refining service (A106 B, A53 B, API-5L, A333,etc.) are already covered by the code.

Since you're writing from Germany I'm going to guess that your dealing with some kind of DIN standard. You may first need to do some research to see if it has an equivalent to an ASTM standard for the material you are using and refer to that material in B31.1.

If your material is not listed in that code (Appendix A), then you are using an "unlisted" material. Para. 123.1.2 states some requirements for that material. That paragraph refers you back to Para. 102.3.1(c) for setting allowable stress (Sc & Sh), but that points you to ASME Boiler & Pressure Vesel Code Section II, Part D, Appendix 1. I believe you can use the lower of (1/3.5) times the ultimate tensile strength or 2/3 yield strength. Other criteria, such as creep and rupture strength may apply.
Check the code for a complete definition.