Shear-Connectors#

General#

Shear-connectors are considered by their load-slip-relationship as well as their position along the beam.

The load-slip relationship is crucial as it assigns a load to a given slip. The position of the shear-connector along the beam matters as in most cases the amount of slip \(s\) depends on the position of the shear-connector within the beam.

Headed Studs#

Headed studs are standardized by Eurocode 4 [1] and implemented in m_n_kappa. For implementation in m_n_kappa a bi-linear load-slip relationship of the headed studs is assumed.

../_images/theory_headed_stud_load_slip_relationship-dark.svg

../_images/theory_headed_stud_load_slip_relationship-light.svg — Assumed load-slip-relationsship of headed stud in `m_n_kappa`#

Where the transition between the linear and the plastic part is assumed at \(s = 0.5\) mm and the maximum slip at \(s_\mathrm{max} = 6.0\) mm.

The maximum resistance of the headed stud is assumed to be the minimum value of the resistance at steel-failure and at concrete failure.

(1)#\[P_\mathrm{R} = \min\{P_\mathrm{m,c}; P_\mathrm{m,s}\}\]

The values for steel- and concrete-failure are assumed to be the mean-values according to Roik et al. [2].

\[ \begin{align}\begin{aligned}P_\mathrm{m,c} &= 0.374 \cdot d^{2} \cdot \alpha \sqrt{f_\mathrm{c} \cdot E_\mathrm{cm}}\\P_\mathrm{m,s} &= f_\mathrm{u} \cdot \pi \cdot \frac{d^{2}}{4}\end{aligned}\end{align} \]

where \(d\) is the diameter of the shank of the headed stud. \(f_\mathrm{c}\) is the concrete cylinder compressive strength and \(E_\mathrm{cm}\) is the mean secant-modulus of the concrete. \(f_\mathrm{u}\) is the tensile strength of the material of the shank of the headed stud. The factor \(\alpha\) depends on the ratio \(h_\mathrm{sc} / d\) as follows:

\[\begin{split}\alpha = \begin{cases} 0.2 \cdot \left( \frac{h_\mathrm{sc}}{d} + 1 \right) & \text{ if } 3 \leq \frac{h_\mathrm{sc}}{d} < 4 \\ 1 & \text{ if } \frac{h_\mathrm{sc}}{d} \geq 4 \end{cases}\end{split}\]

Headed studs with profiled steel sheeting transverse to the supporting beam#

Profiled steel sheeting positioned transverse to the supporting beam reduce the shear-load resistance of the headed studs. Therefore, the shear resistance \(P_\mathrm{R}\) computed in Formula shear_connectors.headed_studs.resistance is reduced by factor \(k_\mathrm{t}\) according to EN 1994-1-1 [1].

\[k_\mathrm{t} = \frac{0.7}{n_\mathrm{r}} \cdot \frac{b_\mathrm{o}}{h_\mathrm{p}} \left( \frac{b_\mathrm{sc}}{h_\mathrm{p}} - 1\right) \leq 1\]

where \(n_\mathrm{r}\) is the number of headed studs in a row, \(b_\mathrm{o}\) is the decisive concrete with in the trough of the profiled steel sheeting, \(h_\mathrm{p}\) is the height of the profiled steel sheeting and \(b_\mathrm{sc}\) is the height of the headed stud.

As indicated above the shear resistance considering the effect of the profiled steel sheeting transverse to the supporting beam is then computed as follows.

\[P_\mathrm{R,t} = k_\mathrm{t} \cdot P_\mathrm{R}\]