The strength calculation determines the maximum load of the screw with the shear stress hypothesis according to TRESCA:

$$σ_v = \sqrt {(σ_x - σ_y)^2 + 4τ_{xy}^2}$$

The screw fails above this stress. The hypothesis is simplified, because the rotation of the screw generates only torsion stress, neither bend nor normal forces occur, therefore just shear stress takes into account. The occurring shear stress is calculated according to the following formula:

$$τ_{max} = \frac{M_t}{W_t} = \frac{M_t \cdot a_{max}}{l_p}$$

Another influencing factor for the calculation of the screw strength is the radius, which indicates the transition from the bottom of the screw to the flight; a shape number is defined for this geometric influence:

$$K_{t,f} = 1+ \frac{1}{\sqrt{3,4 \cdot \frac{r}{t} + 38 \cdot \frac {r}{d} (1+ 2 \cdot \frac{r}{d})^2 + (\frac{r}{d})^2 \cdot \frac{d}{D}}}$$

In combination with the notch sensitivity number $q$:

$$q = \frac{1}{1+ \frac{8mm}{r} \cdot (1- \frac{R_{p0,2}}{R_m})^3}$$

it is possible in according to THUM to calculate the notch coefficient $K_f$. The following equation describes the influence of the notch on the shear stress:

$$K_f = 1+ (K_t-1) \cdot q$$

Finally, the shape number $K_t$ is multiplied by the calculated shear stress to obtain the maximum stress or rather the characteristic value oft he screw strength.