Design of Timber Composite Concrete Slabs with Screw Connections#

Introduction#

This tutorial covers the design of single-span timber-concrete composite (TCC) slabs with screw connections, using the Rautenstrauch truss model as the analytical framework.

Note

A basic SOFiSTiK knowledge is required for this tutorial. The standard workflow is explained inside the Design of Concrete Building - Beginners Tutorial . Inside this tutorial we show only the project specific workflows, which are different from the basic workflow.

Objectives#

This guide walks you through the process of designing concrete composite ceilings with screw connections using a model truss which can be created in SOFiPLUS or SOFiSTiK Interface for Grasshoppper. By the end of this tutorial, you should be able to:

Create a truss model based on the Rautenstrauch approach using SOFiPLUS(-X) (or alternatively with Rhino Grasshopper).
Input material properties and adjust modulus of elasticity for long-term design.
Create the combination rules for superposition in long-term design.
Perform crack width limitation checks as required by the relevant standards, ensuring verification of compatibility control.
Perform necessary stress, deflection and vibration verifications required for the design of timber-concrete composite (TCC) floors.
Export critical section forces to Excel for verification of screw connections.

Note

This tutorial shares many similarities with the shear notch slab tutorial. Since the general workflow and verification steps are identical, they are not repeated here. Instead, this tutorial focuses primarily on the modeling process specific to screw connections.

Design code#

This tutorial is based on the Eurocode 5 DIN CEN-TS 19103.

Verification Overview#

The DIN CEN/TS 19103:2022-02 defines several verifications required for the design of timber-concrete composite (TCC) floors. These verifications are the same for both screw and shear notch connections. To avoid redundancy, this tutorial links directly to the relevant sections of the shear notch connection tutorial, where each verification step is explained in detail. The same load case numbers and code blocks are used to maintain consistency across both tutorials.

ULS (Ultimate Limit State)

Verification	Shown in this tutorial?
Verification of the timber cross-section	YES
Verification of the concrete cross-section	YES
Verification of connection Load Cases	For the required verifications, Vz-MIN can be obtained from the screw beams of framework model
Verification of concrete for longitudinal shear (including membrane effects)	NO

SLS (Serviceability Limit State)

Verification	Shown in this tutorial?
Crack limitation in concrete cross-section	YES
Deflection	YES
Vibration	YES

Rautenstrauch Truss Model#

DIN CEN-TS 19103 requires accurate calculations of internal forces and deformations that consider the slip between timber and concrete. Therefore, we will use the truss model based on Rautenstrauch, which accurately represents the connectors’ actual positions, allowing for precise internal force calculations and a more realistic depiction of timber-concrete composite system behavior (Grosse K. R., 2003).

Note

Typically, the Gamma method is used for such calculations; it accounts for connector slip by reducing the moment of inertia using the reduction factor Gamma. In this tutorial, we use the Rautenstrauch model because it is easy to implement and allows for direct consideration of moment jumps at the locations of the screw connectors. A key advantage of the truss model approach is the immediate visibility of internal force distributions — no additional calculations or conversions are required.

Truss Model#

Timber beams and concrete slabs are represented as bar elements along the longitudinal axis.
Truss bars connect both elements to ensure equal displacement.
Truss bars should be spaced 10-20 cm apart for accurate internal force calculation; in SOFIPLUS those will be created with a line constrain.
Due to the existing symmetry, it is possible to simplify the model by reducing the system to half (Grosse, Hartnack, & Rautenstrauch, 2004).
At the screw positions, vertical bars (beam elements) with a moment hinge at the height of the composite joint are rigidly connected to the flanges, simulating the screw connectors.

Screw Connection#

The equivalent system represents the connection between timber and concrete by introducing vertical beam elements at the screws. These elements are rigidly connected to the chords while incorporating a moment hinge at the composite joint. This ensures that the connectors are accurately positioned, allowing shear flexibility to be considered through the bending stiffness EI* of the beam element, which can be calculated using the given equation in relation to the connector stiffness KSer.

../../_images/Equivalent_system_shear_notch_connection.png — *Equivalent system for the screw connection*#

../../_images/EI_Cantilever_Formular.png

Modelling#

Starting a new Project#

First, create a new SSD project or use the provided template and save it in a project directory on your local computer. For additional details, refer to the Starting a New Project section in the Beginners Tutorial.

Define Materials#

Generate all necessary materials. The general procedure is explained in chapter Materials and Cross Sections in the Beginners Tutorial.

Maintain the following material order to ensure the truss model generates correctly:

1	Concrete
2	Timber
3	Rigid Truss Beams
4	Shear Beams for Screw Connection (Section 1)
5	Shear Beams for Screw Connection (Section 2)
10	Reinforcing Steel

Concrete/Timber:

Set the nominal weight to 0. We manually define all self-weight loads to ensure that the correct concrete width is considered in the vibration check. This approach provides full control over how the mass distribution is represented.

../../_images/design_code_material_concrete.png — *Task Design Code Material - Modifications Concrete (and Timber accordingly)*#

Shear Beams for Screw Connection:

Define an elastic material for the shear beams simulating the screw connection using Young’s modulus E. Calculate EI* as described in Chapter Screw Connection. In this example, we assume a screw diameter of 10 mm, with six screws per row in the first section and four screws per row in the second section. The cross-section of the shear beam will be defined later such that its moment of inertia is 1·10⁻³ m⁴. Set the nominal weight to 0.

Create an elastic material for the rigid truss beams with a Young’s modulus of 10,000,000 MPa. Set the nominal weight to 0.

../../_images/design_code_material_rigid_truss_beam.png — *Task Design Code Material*#

Define Standard Cross Sections#

In this project we have five rectangular beam cross sections. Please generate the cross sections with the dimensions and material properties needed. The general procedure is outlined in chapter Materials and Cross Sections in the Beginners Tutorial.

Maintain the following cross section order to ensure the truss model generates correctly:

1	Concrete cross section
2	Timber cross section
3	Rigid Truss Beams cross section
4	Shear Beams for Screw Connection cross section (Section 1)
5	Shear Beams for Screw Connection cross section (Section 2)

When creating the cross-sections, consider the following: calculate the effective width (b,eff) in accordance with Section 5.4.1.2 of DIN EN 1994-1-1. Additionally, set the moment of inertia for the cross-section of the shear beams in the screw connection to 1·10⁻³ m⁴, ensuring that the calculated EI* is correct. This can be achieved by setting both the width and height to 0.331 m.

../../_images/cross_section_shear_beams_for_notched_connection.png — *Task Rectangle Beam Cross Section*#

Geometry Generation#

There are two alternative ways to generate the truss model for the screw connection:

Using SOFiPLUS
Using Grasshopper (Rhinoceros)

Both methods result in the same structural model and can be used interchangeably depending on your preferred workflow or software environment.

SOFiPLUS Model#

The following video will show the workflow for generating the truss model in SOFiPLUS.

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Rhinoceros System Input#

Alternatively, the truss model can be generated using a predefined Grasshopper script within Rhinoceros. This parametric approach allows for a high degree of automation and flexibility, especially when working with varying screw connector layouts. More information on the SOFiSTiK interface for Rhinoceros and Grasshopper can be found in the SOFiSTiK Interface for Rhinoceros documentation.

This Grasshopper tool enables the creation of multiple sections with varying screw connector distances along the beam. To define the layout, you specify the X-coordinates that mark the end of each section. The tool interprets these coordinates sequentially: the first segment—up to the first X-position—is always generated without screws. For each subsequent section, a connector spacing must be defined, which is then applied in order.

The final section does not need to end exactly at the beam’s midpoint. Any remaining span beyond the last defined section is automatically generated without screws. To ensure correct structural behavior, it is important that each section is assigned the appropriate section ID from the equivalent cantilever system. If any required parameters are missing or inconsistent, the tool will not be able to generate the truss model.

The workflow is outlined in chapter Rhinoceros Grashopper System Input.

Loads#

Load Definition#

Define the required load cases in SOFiPLUS.

To account for the different connector stiffness values (Kser for SLS and Ku,d for ULS) and material E-moduli (Emean for SLS and Ed for ULS), and to simulate the structural behavior at the two design times (t = 0 and t = ∞), each load must be defined four times:

Twice for t = 0 (initial state)
Twice for t = ∞ (final state after creep and shrinkage)

This separation is necessary because the connection stiffness and the effective E-moduli influence how internal forces are distributed between the timber and concrete components — and these values differ between ULS and SLS. By duplicating the load cases for both time points and stiffness types, the model can correctly superimpose short- and long-term effects for each design situation.

For t = ∞, the effects of concrete shrinkage are modeled using an equivalent temperature load case. This is calculated in accordance with DIN EN 1992-1-1:2011-01, Section 3.1.4.

../../_images/loadcase_overview.png — *Loadcase Overview*#

The following tables list all SLS and ULS load cases used in this example.

SLS

Nr	Description	Load
1	Self-weight timber t = 0	0.565 kN/m
2	Self-weight concrete t = 0	3.00 kN/m
3	Construction load t = 0	2.00 kN/m
4	Live load 1 t = 0	2.40 kN/m
11	Self-weight timber t = ∞	0.565 kN/m
12	Self-weight concrete t = ∞	3.00 kN/m
13	Construction load t = ∞	2.00 kN/m
14	Live load 1 t = ∞	2.40 kN/m
16	Elastic shrinkage concrete t = ∞	-29.00 °C
20	Point load for vibration verification t = 0	2.00 kN

ULS

Nr	Description	Load
101	Self-weight timber t=0	0.565 kN/m
102	Self-weight concrete t=0	3.00 kN/m
103	Construction load t=0	2.00 kN/m
104	Live load 1 t=0	2.40 kN/m
111	Self-weight timber t=oo	0.565 kN/m
112	Self-weight concrete t=oo	3.00 kN/m
113	Construction load t=oo	2.00 kN/m
114	Live load 1 t=oo	2.40 kN/m
116	Elastic shrinkage concrete t=oo	-29.00 °C

Note

The load definition via CADINP is not the only option. For example, loads could also be defined in the Grasshopper script or in SOFiPLUS(-X). We chose the CADINP input in this example to make the tutorial accessible for both modeling methods.

Design Loads#

Design Process#

The following diagram illustrates the design process for the ultimate limit state and the serviceability limit state.

../../_images/Load_Combination_Diagram.png — *Diagram Design Process*#

Linear Analysis t=0#

A linear analysis must be performed for all load cases active at t = 0. This is done using a text task.

The reductions for E_d and K_u,d in ULS are implemented with the FACS command for the corresponding groups in load cases 101–105.

+PROG ASE
HEAD Calculation of forces and moments – SLS at t = 0
LC (1 4 1)
LC 20
END

+PROG ASE
HEAD Calculation of forces and moments – ULS at t = 0
GRP 0    FACS 1
GRP 1    FACS 1/1.5
GRP 2    FACS 1/1.25
GRP 3    FACS 1
GRP 4    FACS 1*(2/3)
LC (101 104 1)
END

Superposition for Combination Rules t=0#

The combination rules follow the requirements of DIN CEN/TS 19103:2022-02.

For the superposition, we use the task task_combine_results_small Combine Results to manually combine load cases. This approach provides more flexibility than the automatic superposition workflow, especially when defining the specific combinations required for the long-term design at t = ∞, as outlined in Section 4.2 “Principles of Limit State Design” of DIN CEN/TS 19103:2022-02.

The resulting load cases are as follows:

t=0

Type	Nr	Description
Load Case	1000	ULS characteristic t=0
Load Case	1100	ULS quasi-permanent t=0
Load Case	1200	ULS fundamental t=0
Load Case	1300	ULS fundamental t=0 (25% additional load to omit the consideration period t=3-7 years)
Load Case	1400	SLS characteristic t=0 (w_inst)
Load Case	1500	SLS quasi-permanent t=0

Check for Necessity of Concrete iteration#

We check for the combination ULS characteristic t=0 if the stresses in the concrete cross section part exceed the limit for tensile stresses ftd. In the wingraf_small Graphic Output “Ultilisation Concrete ULS characteristic t=0” we see that the stresses do not exceed the limit. Otherwise, a iteration with reduced concrete cross sections due to cracks would be necessary.

Elastic Modulus Reduction and Linear Analysis t=oo#

The long-term effect of creep in the construction materials on the stress distribution and deformation of the composite component should be considered in the elastic calculation using the effective moduli of concrete 𝐸conc,fin and timber 𝐸tim,fin, as well as an effective slip modulus of the connection 𝐾ser,fin or 𝐾u,fin, according to DIN CEN/TS 19103:2022-02 4.3.2 (7). The influence of composite action on the effective creep coefficient (creep factor of concrete or deformation coefficient of timber and the connection) is determined using the modification factors for the creep coefficient according to DIN CEN/TS 19103:2022-02 Table 7.1.

For ULS, the design values E_d and K_u,d have to be considered similar to t=0.

The following code demonstrates how to calculate the reduction factors of the elastic moduli, which must be determined for the design time t=oo for the ULS. At the end of the code, an ASE block computes the load cases for t=oo, applying the reduced Young’s moduli. The reduction is implemented by assigning the calculated reduction factors to the corresponding groups and then computing the load cases.

The calculation of the reduction factors for the SLS can be found in the example file.

The following variables must be entered:

#A_Timber (Area content timber)
#I_Timber (Moment of inertia timber)
#NTimber (MAX Axial force timber)
#MTimber (MAX Moment timber)
#A_Concrete (Area content concrete)
#z (Lever arm)
#Phi (Creep coefficient)

+PROG TEMPLATE urs:32.2
HEAD Determination of the E-Modulus (Econc,fin and Etim,fin) at the design time t=oo for ULS

@key MAT_CONC 1
STO#E_Concrete (@EMOD)/1.5 $E-Modulus Concrete kN/m²
PRT#E_Concrete

@key MAT_TIMB 2
STO#E_Timber (@EMOD)/1.25 $E-Modulus Timber kN/m²
PRT#E_Timber

@key MAT_TIMB 2
STO#kdef (@kdef)          $kdef Timber
PRT#kdef

STO#A_Timber        (2*0.24*0.28) $m²
STO#I_Timber ((2*0.24*0.28^3)/12) $m4
PRT#A_Timber
PRT#I_Timber

STO#NTimber         137.30 $kN
STO#MTimber           9.87 $kNm

STO#A_Concrete (0.10*1.20) $m²
STO#z                 0.19 $m
STO#Phi               2.50

STO#EA_Timber (#A_Timber*#E_Timber)
PRT#EA_Timber

STO#EI_Timber (#A_Timber*#I_Timber)
PRT#EI_Timber

STO#EA_Concrete (#A_Concrete*#E_Concrete)
PRT#EA_Concrete


! Determine E_conc,fin, E_tim,fin and the reduced slip modulus and K_u,fin for t = ∞

$ Determine y1 according to DIN CEN/TS 19103:2022-02, Section 7.1.2 (8)
STO#y1                           (#E_Timber*#A_Timber*#E_Timber*#I_Timber*#NTimber)/(#E_Concrete*#A_Concrete*(#E_Timber*#A_Timber*#MTimber*#z-#E_Timber*#I_Timber*#NTimber))
PRT#y1

$ Modify the creep factor to account for composite action based on Table 7.1 of DIN CEN/TS 19103:2022-02

$ --- Design time: t = ∞ ---

$ Phi = 3.5
STO#Psi_c_u_35_06                2.6-0.8*#y1^2
STO#Psi_c_u_35_08                2.3-0.5*#y1^2.6
PRT#Psi_c_u_35_06
PRT#Psi_c_u_35_08

$ Phi = 2.5
STO#Psi_c_u_25_06                2.0-0.5*#y1^1.9
STO#Psi_c_u_25_08                1.8-0.3*#y1^2.5
PRT#Psi_c_u_25_06
PRT#Psi_c_u_25_08

STO#Psi_tim_u                    1.00
STO#Psi_conn_u                   1.00

IF (#kdef < 0.7)
STO#Psi_conc_u                   #Psi_c_u_25_06+(#Psi_c_u_35_06-#Psi_c_u_25_06)/(3.5-2.5)*(#Phi-2.5)
ENDIF

IF (#kdef > 0.7)
STO#Psi_conc_u                   #Psi_c_u_25_08+(#Psi_c_u_35_08-#Psi_c_u_25_08)/(3.5-2.5)*(#Phi-2.5)
ENDIF

PRT#Psi_conc_u

$ --- Calculate reduced E-moduli ---

$  Concrete
STO#n_E_c_f_u_ULS                1/(1+#Psi_conc_u*#Phi)/1.5
PRT#n_E_c_f_u_ULS

$ Timber
STO#n_E_t_f_u_ULS                1/(1+#Psi_tim_u*#kdef)/1.25
PRT#n_E_t_f_u_ULS

$ Reduction of E-modulus for shear beams (indirectly representing the slip modulus)
STO#n_E_Shear_fin_u              1/(1+#Psi_conn_u*#kdef*2)
STO#n_E_Shear_u_ULS              #n_E_Shear_fin_u*(2/3)
PRT#n_E_Shear_u_ULS
END

+PROG ASE urs:36.3
HEAD Calculation of forces and moments – ULS at t = oo
GRP 0   FACS 1
GRP 1   FACS #n_E_c_f_u_ULS      $ Concrete
GRP 2   FACS #n_E_t_f_u_ULS      $ Timber
GRP 3   FACS 1                   $ Truss Beams
GRP 4   FACS #n_E_Shear_u_ULS    $ Shear Notches
LC 111,112,113,114,116
END

Superposition for Combination Rules t=oo#

ULS: Fundamental Combination

Due to different creep behavior of concrete, timber, and the connection system, the load effects at the ultimate limit state for t = ∞ are divided into creep-relevant and non-creep-relevant actions. The resulting stresses in the CLT–concrete composite system are obtained by superimposing:

the internal forces from the quasi-permanent loads (creep-relevant) and the shrinkage-induced stresses, both calculated using the cross-section properties at t = ∞ (𝐸conc,fin, 𝐸tim,fin and effective slip modulus 𝐾u,fin), and
the stresses from the short-term loads (non-creep-relevant), calculated with the cross-section properties at t = 0 (𝐸conc, 𝐸tim, and slip modulus 𝐾u).

../../_images/ULS_fundamental_combination.png

The factor for the permanent portion of the live load t=∞ ULS is γ_Q * ψ_2 = 1.5 * 0.3 = 0.45. The factor for the short-term portion of the live load t=0 ULS is γ_Q * (1-ψ_2) = 1.5 * 0.7 = 1.05.

SLS: Quasi-Permanent Combination for w_fin

For SLS, the final deformation of the composite structure must be calculated under combination of actions 𝐸k by superimposing:

Long-term deformation from quasi-permanent combination 𝐸q,per, calculated with effective moduli 𝐸conc,fin, 𝐸tim,fin and effective slip modulus 𝐾ser,fin.
Short-term deformation from the difference between characteristic combination 𝐸k and quasi-permanent combination 𝐸q,per, calculated with moduli 𝐸conc, 𝐸tim, and slip modulus 𝐾ser.

../../_images/SLS_quasi-permanent_combination.png

t=oo

Load Case	2200	ULS t=oo fundamental
Load Case	2300	ULS t=oo fundamental (25% additional load to omit the consideration period t=3-7 years)
Load Case	2500	SLS t=oo quasi-permanent

ULS Design#

The following verification steps are identical to those described in the shear notch tutorial (Design of Timber Composite Concrete Slabs with Shear Notch Connections) and are applied here in the same way. For detailed instructions and background, please refer to the respective sections in that tutorial.

SLS Design#

The serviceability limit state checks also follow the same procedure as outlined in the shear notch tutorial. Again, please refer to Design of Timber Composite Concrete Slabs with Shear Notch Connections for detailed information.