Forces by Screw in Main-Connected Beam Joint

Technical Article

RF-/JOINTS Timber - Timber to Timber allows you to design main-connected beam joints. This article explains the determination of forces in screws of a beam connected to a torsionally rigid main beam.

Figure 01 - Structural System

Due to the determination of the forces in the screws, the design is only possible in the main plane of the screw pair. Forces in the other plane of the screw are not considered by the module. So, if there are the internal forces Vy and Vz, the selected plane (usually Vz) is only considered. However, you can select the joint plane in the module (Figure 02).

Figure 02 - Joint Plane

In our example, biaxial bending is defined to show this way of the design. In a spatial system, forces in the y- and z‑direction will inevitably occur. If these forces become too large, it is possible to perform the interaction with $\sqrt{{\mathrm V}_\mathrm z²\;+\;{\mathrm V}_\mathrm y²}$ as a conservative estimation.

System

  • Main beam = 14/26 GL24c
  • Connected beam = 10/16 C24
  • Span of the main beam = 5 m
  • Span of the connected beam = 3 m
  • Load z = 2.2 kN/m (self‑weight by default)
  • Load y = 1.0 kN/m
  • Connecting shear force Vz = 3.38 kN
  • Connecting shear force Vy = 1.13 kN
  • Screw-in angle of screws to each other = 45 °
  • LDC permanent

Design of Screws

In the add‑on module, Joint Type 2 is selected for the main-connected beam joint. Subsequently, connection nodes are selected and loads are defined. General information about the input can be found in the manual for the module. In the Geometry window, the joint plane x‑z is selected for the definition of the first design.

Figure 03 - Joint Type 2

The load bearing capacity of the screw is defined manually according to [1].

$$\begin{array}{l}{\mathrm f}_{\mathrm{ax},\mathrm k}\;=\;0.52\;\cdot\;\varnothing^{-0.5}\;\cdot\;\mathrm l_\mathrm{ef}^{-0.1}\;\cdot\;\mathrm\rho_\mathrm k^{0.8}\;=\;0.52\;\cdot\;8\;\mathrm{mm}^{-0.5}\;\cdot\;90\;\mathrm{mm}^{-0.1}\;\cdot\;350^{0.8}\;=\;11.27\;\mathrm N/\mathrm{mm}^2\\\;{\mathrm F}_{\mathrm{ax},\mathrm{Rk}}\;=\;\frac{{\mathrm n}_\mathrm{ef}\;\cdot\;{\mathrm f}_{\mathrm{ax},\mathrm k}\;\cdot\;\mathrm d\;\cdot\;{\mathrm l}_\mathrm{ef}\;\cdot\;{\mathrm k}_\mathrm d}{1.2\;\cos^2\;\mathrm\alpha\;+\;\sin^2\;\mathrm\alpha}\;=\;\frac{11.27\;\cdot\;8\;\mathrm{mm}\;\cdot\;90\;\mathrm{mm}\;\cdot\;1}{1.2\;\cos^2\;30\;+\;\sin^2\;30}\;=\;7.96\;\mathrm{kN}\\\;{\mathrm f}_{\mathrm{tens},\mathrm k}\;=\;20\;\mathrm{kN}\\\;{\mathrm f}_{\mathrm c,\mathrm k}\;=\;50\;\mathrm{kN}\end{array}$$

For further information regarding the geometry, see the manual.

Design

In the following, the design of forces in the screws is shown. In the program, this is done under the internal design numbers 4103 and 4104.

Force by screw in x‑z plane:

$$\begin{array}{l}{\mathrm F}_\mathrm{def}\;=\;\cos\;(\mathrm\alpha\;{\mathrm N}_\mathrm{def})\;\cdot\;\mathrm N\;+\;\cos\;(\mathrm\alpha\;{\mathrm V}_\mathrm{def})\;\cdot\;\mathrm V\;=\;0\;+\;\cos\;45^\circ\;\cdot\;3.38\;=\;2.39\;\mathrm{kN}\\\;{\mathrm F}_\mathrm{con}\;=\;\cos\;\left(\mathrm\alpha\;{\mathrm N}_\mathrm{con}\right)\;\cdot\;\mathrm N\;+\;\cos\;\left(\mathrm\alpha\;{\mathrm V}_\mathrm{con}\right)\;\cdot\;\mathrm V\;=\;0\;+\;\cos\;45^\circ\;\cdot\;3.38\;=\;2.39\;\mathrm{kN}\end{array}$$

Figure 04 - Forces by Screw in x-z-Plane

Design:

$${\mathrm F}_{\mathrm{ax},\mathrm{Rd}}\;=\;\frac{0.6\;\cdot\;7.96}{1.3}\;=\;3.67\;\mathrm{kN}\;\rightarrow\;\frac{2.39}{3.67}\;=\;0.65$$

Utilization = 65%.

Force by screw in x-y plane:
In the following, the screw pair is located and designed in the plane rotated about 90° due to double bending.

$$\begin{array}{l}{\mathrm F}_\mathrm{def}\;=\;\cos\;\left(\mathrm\alpha\;{\mathrm N}_\mathrm{def}\right)\;\cdot\;\mathrm N\;+\;\cos\;\left(\mathrm\alpha\;{\mathrm V}_\mathrm{def}\right)\;\cdot\;\mathrm V\;=\;0\;+\;\cos\;45^\circ\;\cdot\;1.13\;=\;0.80\;\mathrm{kN}\\\;{\mathrm F}_\mathrm{con}\;=\;\cos\;\left(\mathrm\alpha\;{\mathrm N}_\mathrm{con}\right)\;\cdot\;\mathrm N\;+\;\cos\;\left(\mathrm\alpha\;{\mathrm V}_\mathrm{con}\right)\;\cdot\;\mathrm V\;=\;0\;+\;\cos\;45^\circ\;\cdot\;1.13\;=\;0.80\;\mathrm{kN}\end{array}$$

Design x-y plane:
The diameter is changed to 6 mm and the screw length to 140 mm. Therefore, slightly different load bearing capacity results. The determination of the load bearing capacity is not described again.

$${\mathrm F}_{\mathrm{ax},\mathrm{Rd}}\;=\;\frac{0.6\;\cdot\;5.5}{1.3}\;=\;2.53\;\mathrm{kN}\;\rightarrow\;\frac{0.8}{2.53}\;=\;0.31$$

Utilization = 31%.

Interaction:

$${\mathrm\eta}_\mathrm{ges}\;=\;\sqrt{0.65^2\;+\;0.31^2}\;=\;0.72$$

Summary

Manual superposition allows for considering double bending in two cases with RF‑/JOINTS Timber - Timber to Timber. The tensile resistance and pull‑out strength are only considered in the respective plane.

Reference

[1]   Eurocode 5: Design of timber structures - Part 1‑1: General - Common rules and rules for buildings; DIN EN 1995‑1‑1:2010‑12

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