This tutorial covers the design of single-span timber-concrete composite (TCC) slabs with shear notch 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.
This guide walks you through the process of designing concrete composite ceilings with shear notch connections using a truss model created in the SOFiSTiK Structural Desktop and 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 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 notched connections.
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 with the reduction factor Gamma.
However, this approach is unsuitable for composite floors with notched connections, as it requires a connector spacing of no more than 5% of the span between zero-moment points (notch locations).
Using the Gamma method would lead to an overestimation of internal forces.
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.
Due to the existing symmetry, it is possible to simplify the model by reducing the system to half (Grosse, Hartnack, & Rautenstrauch, 2004).
At the notch flanks, vertical bars (beam elements) with a moment joint at the height of the composite joint are rigidly connected to the flanges simulating the shear notch joints.
The equivalent system represents the connection between timber and concrete by introducing vertical beam elements at the notches.
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.
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.
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
Reinforcing Steel
4
Timber
5
Shear Beams for Notched Connection
6
Rigid Truss Beams
We have to take care of the following modifcations:
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.
Task Design Code Material - Modifications Concrete (and Timber accordingly)#
Shear Notch Beams:
Define an elastic material for the shear beams in the notched connection using Young’s modulus EI*.
Calculate EI* as seen in Chapter Shear Notch Connection, assuming a shear notch depth of 30 mm.
We will define the cross section of the shear notch beam to result in a moment of inertia of 1*10^-3 m^4.
Set the nominal weight to 0.
Task Design Code Material - Modifications Shear Notch Beams#
Rigid Truss Beams:
Create an elastic material for the rigid truss beams with a Young’s modulus of 10,000,000.
Set the nominal weight to 0.
Task Design Code Material - Modifications Rigid Truss Beams#
In this project we have four rectangle 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
Shear Beams for Notched Connection cross section
4
Rigid Truss Beams cross section
Concrete cross section:
Calculate the effective width (b,eff) in accordance with Section 5.4.1.2 of DIN EN 1994-1-1.
Shear Beams for Notched Connection cross section:
Set the moment of inertia for the cross-section of the shear beams in the notched connection to 1*10^-3 m^4, ensuring that the calculated EI* is correct.
This can be achieved by setting both the width and height to 0.331 m.
Deselect the consideration of shear deformations.
To create the truss model according to Rautenstrauch, we use a pre-designed Grasshopper file where you simply input the parameters for the notches, and the model is automatically generated.
The file is flexible, allowing you to set any number of notches as needed, enabling the creation of TCC ceilings with a customizable number of notches.
More information on the Sofistik Interface for Rhinoceros and Grasshopper can be found in the SOFiSTiK Interface for Rhinoceros documentation.
To generate the truss model follow the following steps.
Provide the necessary input parameters:
X-coordinates of the shear notches
X-coordinate of the midpoint of the single-span beam
Height of the concrete slab
Height of the timber beam
Minimum distance between trusses (should be between 10 - 20 cm to ensure optimal results)
The truss model for the calculation is automatically generated and stored in the TEDDY (.dat) file under the name TCC-FloorDesignRhino.dat.
To import the generated TEDDY (.dat) file and create the truss model in SSD, add a Text Task in SSD with Rhinoceros System Input, containing the following code.
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.
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
105
Live load 2 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
115
Live load 2 t=oo
2.40 kN/m
116
Elastic shrinkage concrete t=oo
-29.00 °C
Note
The load definition per CADINP is not the only option. For example, loads could also be defined in the Grashopper Script. We choose the CADINP input in this example to to make the tutorial also accesible for user without Rhino/Grasshopper.
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 1/1.3
GRP 3 FACS 1
GRP 4,5 FACS 1/1.3
LC (101 104 1)
END
The combination rules follow the requirements of DIN CEN/TS 19103:2022-02.
For the superposition, we use the task 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
The “ULS/SLS” at the beginning of the Load Combination descriptions indicates, if the combined load cases are calculated with the cross-section properties for ULS (Ec,d/Et,d/Ku,d) or SLS (Ec,mean/Et/Kser).
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 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=∞#
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 from quasi-permanant t=0)
#MTimber (MAX Moment timber from quasi-permanant t=0)
#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 4
STO#E_Timber (@EMOD)/1.25 $E-Modulus Timber kN/m²
PRT#E_Timber
@key MAT_TIMB 4
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 138.60 $kN
STO#MTimber 9.72 $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
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
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).
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.
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)
The following code demonstrates how the stress check for the timber cross-section can be performed.
The timber cross-section is designed for the fundamental combinations 1200 (t=0) and 2200 (t=∞) in the Ultimate Limit State (ULS) by checking if the stress limits are exceeded.
+PROG AQB
HEAD 'Stress Check of Timber Cross Section in ULS for t = 0'
ECHO STRE,SECT VAL FULL
ECHO NSTR VAL FULL
LC NO 1200
BEAM FROM GRP TO 2
COMB GMAX LCST 63000 TITL 'Stress Check Timber t=0'
STRE B
END
+PROG AQB
HEAD 'Stress Check of Timber Cross Section in ULS for t = oo'
ECHO STRE,SECT VAL FULL
ECHO NSTR VAL FULL
LC NO 2200
BEAM FROM GRP TO 2
COMB GMAX LCST 63001 TITL 'Stress Check Timber t=oo'
STRE B
END
The following code demonstrates how the stress check for the concrete cross-section can be performed.
The stress limits of the concrete material are read from the database via the +PROG TEMPLATE input.
+PROG TEMPLATE
HEAD
@key MAT_CONC 1
STO#fcd ((@fc)/1.5)/1000 $ N/mm²
PRT#fcd
@key MAT_CONC 1
STO#fctd (@ftd)/1000 $ N/mm²
PRT#fctd
END
+PROG AQB urs:51.1
HEAD 'Stress Check of Concrete Cross Section in ULS for t = 0'
ECHO OPT FORC VAL YES
ECHO OPT STRE VAL EXTR
ECHO OPT DESI VAL NO
ECHO OPT NSTR VAL YES
ECHO OPT SSUM VAL YES
LC NO 1200
BEAM FROM GRP TO 1
COMB GMAX LCST 63010 TITL 'Stress Check Concrete ULS t = 0'
STRE SMOD 1,2 SC #fcd ST #fctd SBC #fcd SBT #fctd SBBC #fcd SBBT #fctd SI #fctd SII #fcd
END
+PROG AQB urs:51.5
HEAD 'Stress Check of Concrete Cross Section in ULS for t = oo'
ECHO OPT FORC VAL NO
ECHO OPT STRE VAL FULL
ECHO OPT DESI VAL NO
ECHO OPT NSTR VAL NO
ECHO OPT SSUM VAL NO
LC NO 2200
BEAM FROM GRP TO 1
COMB GMAX LCST 63015 TITL 'Stress Check Concrete ULS t = oo'
STRE SMOD 1,2 SC #fcd ST #fctd SBC #fcd SBT #fctd SBBC #fcd SBBT #fctd SI #fctd SII #fcd
END
In this example, the tensile stresses in the lower part of the concrete cross-section exceed the allowable limit near certain shear notches.
Therefore, reinforcement of the slab is required and will be designed in the next step.
Cross Section Stresses t=∞ at the most critical part of the beam#
Calculation of stress and utilization of the timber cross-section for t=0 and t=oo with a 25% increased load for timber to exclude the consideration period of 3-7 years.
+PROG AQB
HEAD 'Stress Check of Timber Cross Section in ULS for t=0 + 25% Loads'
ECHO STRE VAL FULL
LC NO 1300
BEAM FROM GRP TO 2
COMB GMAX LCST 63020 TITL 'Timber ULS for t=0 + 25% Loads'
STRE B
END
+PROG AQB
HEAD 'Stress Check of Timber Cross Section in ULS for t=oo + 25% Loads'
ECHO STRE,SECT VAL FULL
LC NO 2300
BEAM FROM GRP TO 2
COMB GMAX LCST 63025 TITL 'Timber ULS for t=oo + 25% Loads'
STRE B
END
Crack width limitation (w_k) can be achieved either by following EN 1992-1-1:2004, 7.3.3 or by direct calculation according to EN 1992-1-1:2004, 7.3.4.
Maximum crack width values are read from the database with the +PROG TEMPLATE input.
The Technical Specification also requires verification of compatibility to determine the extent to which the reinforcement can be activated without exceeding the maximum strain in the timber cross-section.
This ensures that the curvature and strain compatibility between the timber and concrete cross-sections is maintained, even under design conditions.
In the following example, this is achieved by verifying whether the strain in the reinforcement exceeds the maximum strain of the timber cross-section, εmax,Timber = 2.08 ‰.
+PROG TEMPLATE
HEAD
STO#RW 0.4
END
!#!Chapter Crack Width Limitation / Minimum Reinforcement t=0
+PROG AQB
HEAD Crack Width Limitation / Minimum Reinforcement t=0
ECHO OPT CRAC VAL YES
ECHO SECT EXTR
DESI STAT NO
REIN MOD SECT RMOD SAVE LCR 15 TITL 'Reinforcement t=0'
LC NO 1500
BEAM FROM GRP TO 1
NSTR SERV CRAC YES CW #RW
NSTR KMOD ULTI CHKR 2.08[o/oo]
END
!#!Chapter Crack Width Limitation / Minimum Reinforcement t=oo
+PROG AQB
HEAD Crack Width Limitation / Minimum Reinforcement t=oo
ECHO OPT CRAC VAL YES
ECHO SECT EXTR
DESI STAT NO
REIN MOD SECT RMOD ACCU LCR 20 TITL 'Reinforcement t=oo'
LC NO 2500
BEAM FROM GRP TO 1
NSTR SERV CRAC YES CW #RW
NSTR KMOD ULTI CHKR 2.08[o/oo]
END
The deflection check for w_inst, and w_fin can be performed by creating a Diagram to visualize the results.
For more details, refer to the Diagram Output tutorial.
For the vibration check, we are following the approach from Hamm (Hamm, 2012).
The figure below provides an overview and a schematic representation of the vibration verification process, which evaluates three key criteria.
The natural frequency should exceed f_limit, which is 8 Hz for floors between different usage units.
We calculate the first eigenfrequency using the Dynamic Eigenmodes task, ignoring modal damping.
For Load-To-Mass Conversion construction load and self-weight loads are needed, since we switched off the self-weight of the materials.
This is to include the self-weigth of the whole concrete width, not only the effective width.
While the concrete cross section only has the effective width, the self-weight loadcase was calculated for the full concrete width.
To check the stiffness, a 2 kN point load is applied at mid-span, and the deflection is measured.
For different usage units, the deflection should remain below the limit value w_limit of 0.5 mm.
3. Structural requirements
A floating wet screed on a heavy fill layer is required.
We assume a construction load of 1.65 kN/m², which ensures the design remains on the safe side for this type of buildup.
To perform the verification of the shear notch connections, the shear forces of the Shear Notch Beams can be exported to Excel.
This can be done by adding the Interactive Lists and Graphics task. For more details, see Export Results to Excel.
First, create a new table.
Use Result -> Selection to add the Beam Element Number of the group and the Beam Element Shear Force Vz to the table.
Under Result -> LC Edit Selection, choose the corresponding load case:
For t=0, select LC 1200
For t=oo, select LC 2200
Under Result -> Filter/Selection -> Groups, select Group 5 to display only the Shear Notch Beams.
DIN CEN/TS 19103:2022-02. (2022-02). Eurocode 5: Bemessung und Konstruktion von Holzbauten Berechnung von Holz-Beton-Verbundbauteilen - Allgemeine Regeln und Regeln für den Hochbau; Deutsche Fassung CEN/TS 19103:2021.
Schänzlin, J. (2021). Entwurf und Entwicklung von Details bei Holz-Beton-Verbundbauteilen für den Einsatz im Hochbau (HIP 1165437). Biberach: Hochschule Biberach, Fakultät Bauingenieurwesen, Institut für Holzbau.
Grosse, K. R. (2003). Modellierung von diskontinuierlich verbundenen Holz-BetonVerbundkonstruktionen, Teil 1: Kurzzeittragverhalten (Bautechnik 80, Heft 8 Ausg.). Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG.
Grosse, M., Hartnack, R., & Rautenstrauch, K. (2004). Modellierung von diskontinuierlich verbundenen Holz-Beton-Verbunddecken, Teil 2: Langzeittragverhalten. Bautechnik 80, Heft 10.
Hamm, P. (2012). Schwingungen bei Holzdecken Konstruktionsregeln für die Praxis. Biberach: Hochschule Biberach, Fakultät Bauingenieurwesen, Institut für Holzbau.