Calculation of Mt_Rd and tau_max in Utilization component

Grasshopper Karamba3D
1

Hello.

I’ve noticed that th the component Utilization of Elements calculates the resistance to a torsion moment:

image
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It also provides the maximum absolute shear stress.

But how are they calculated?

2

Hello @Alfredo_Peña,
The torsional moment Mt is calculated using the formula:
Wt * fy / sqrt(3.0)

The maximum shear stresses in the y- and z-directions are determined as follows:
tau_y_max = std::abs(Mt / Wt_) + std::abs(Vy / Ay);
tau_z_max = std::abs(Mt / Wt_) + std::abs(Vz / Az);

here Ay and Az represent the shear areas in the y- and z-directions, respectively.
–Clemens

3

And how is this term calculated? Is the effect of warping torsion considered?

4

Dear @Alfredo_Peña,
Wt is the maximum shear stresses due to Saint Venant torsion. Warping torsion is currently (Karammba3D 3.1.x) not taken into account.
– Clemens

5

I don’t know if that assumption could be considered as correct for open cross-sections.

Eurocode 3 shows the following:
image

6

Dear @Alfredo_Peña,
The torsional stiffness of open cross-sections is largely governed by warping torsion. Relying solely on St. Venant torsion therefore yields conservative results.
In case of beams which are meant to carry significant torsional moments one would use closed sections rather than I-sections in the first place.
– Clemens