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.
Note
The Rautenstrauch Truss Model can also be adapted for screw connections.
In this example shear notch connections are shown, as they have special design requirements resulting from the irregular arrangement.
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:
Concrete
Reinforcing Steel
Structural Steel
Timber
Shear Beams for Notched Connection
Rigid Truss Beams
For the Wood Concrete Composite Ceilings we have to take care of the following modifcations:
Set the tensile strength and tensile fractile value for concrete to 0.00 to ensure a conservative design, as no tensile strength is considered for cracked concrete.
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 22 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.
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:
Concrete cross section
Timber cross section
Shear Beams for Notched Connection cross section
Rigid Truss Beams cross section
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 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.
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.
Define the required load cases in a CADINP input, ensuring that the appropriate partial safety factors are applied (see example file for detailed input).
In order to analyze the two different points in time, each load has to be defined twice - for t=0 and for t=oo.
For t = oo, represent the shrinkage of the concrete as an equivalent temperature load case, which should be calculated in accordance with DIN EN 1992-1-1:2011-01, Section 3.1.4.
The loads defined in this example are:
Nr
Description
Load
1
Self-weight timber t=0
0.53 kN/m
2
Self-weight concrete t=0
3.0 kN/m
3
Construction load t=0
2.0 kN/m
4
Live load 1 t=0
2.4 kN/m
5
Live load 2 t=0
2.4 kN/m
11
Self-weight timber t=oo
0.53 kN/m
12
Self-weight concrete t=oo
3.0 kN/m
13
Construction load t=oo
2.0 kN/m
14
Live load 1 t=oo
2.4 kN/m
15
Live load 2 t=oo
2.4 kN/m
16
Elastic shrinkage concrete t=oo
-45,65 °C
20
Load for vibration verification
2 kN
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.
The combination rules are determined according to DIN CEN/TS 19103:2022-02.
For the superposition, we are combining results directly using the task Combine Results instead of the automatic superposition workflow.
The manual result combination gives us more flexibility defining the special combinations for t=oo described in DIN CEN/TS 19103:2022-02 4.2 Principles of Limit State Design.
For t=0 the standard combination rules have to be modified in the task Superpositions to include only the t=0 loadcases 1-5.
The combination rules can then be used to automatically create all the relevant result combinations for the system using the automatic generation feature of the task Combine Results
ULS t=0 fundamental (25% additional load to omit the consideration period t=3-7 years)
Load Case
1300-1301
SLS t=0 characteristic (w_inst)
Load Case
1400-1401
SLS t=0 quasi-permanent
Elastic Modulus Reduction and Linear Analysis t=oo#
The following code demonstrates how to calculate the reduction factors of the elastic moduli, which must be determined for the design time 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.
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.
Warning
It is crucial not to recalculate the load cases for t=oo after this step, as doing so would use the Young’s moduli for t=0, overwriting the correct results for t=oo.
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
@key MAT_CONC 1 $E-Modulus Concrete kN/m²
STO#E_Concrete (@EMOD)
PRT#E_Concrete
@key MAT_TIMB 4 $E-Modulus Timber kN/m²
STO#E_Timber (@EMOD)
PRT#E_Timber
@key MAT_TIMB 4 $kdef Timber
STO#kdef (@kdef)
PRT#kdef
STO#A_Timber 0.15 $m²
STO#I_Timber 1.13E-03 $m4
STO#NTimber 68.1 $kN
STO#MTimber 10.8 $kNm
STO#A_Concrete 0.12 $m²
STO#z (0.10/2+0.3/2) $m
STO#Phi 2.5
!*!Determination of the E-Modulus (Econc,fin and Etim,fin) and the slip modulus of the connection (Kser,fin and Ku,fin) at the design time t=oo
$Determination of y1 according to DIN CEN TS 19103:22-02 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
$Modification of the creep factor or deformation coefficient to account for the composite action according to Table 7.1 DIN CEN TS 19103:22-02
$Design time t=oo
$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 == 0.6
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)
else
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
$Design time t = 3 to 7 years (Not required for the current design -> Verification is omitted due to timber cross-section verification with +25% load)
$Phi = 3.5
STO#Psi_c_37_35_06 2.5-#y1^1.1
STO#Psi_c_37_35_08 2.2-0.8*#y1^1.2
$Phi = 2.5
STO#Psi_c_37_25_06 1.9-0.6*#y1^1.1
STO#Psi_c_37_25_08 1.7-0.5*#y1^1.1
STO#Psi_tim_37 0.50
STO#Psi_conn_37 0.65
if #kdef == 0.6
STO#Psi_conc_37 #Psi_c_37_25_06+(#Psi_c_37_35_06-#Psi_c_37_25_06)/(3.5-2.5)*(#Phi-2.5) $r
else
STO#Psi_conc_37 #Psi_c_37_25_08+(#Psi_c_37_35_08-#Psi_c_37_25_08)/(3.5-2.5)*(#Phi-2.5) $r
ENDIF
$Calculation of factors to reduce E-moduli
$E-Concrete
STO#n_E_conc_fin_u 1/(1+#Psi_conc_u*#Phi)
STO#n_E_conc_fin_37 1/(1+#Psi_conc_37*#Phi)
$E-Timber
STO#n_E_tim_fin_u 1/(1+#Psi_tim_u*#kdef)
STO#n_E_tim_fin_37 1/(1+#Psi_tim_37*#kdef)
$EI* Composite
STO#n_E_Shear_fin_u 1/(1+#Psi_conn_u*#kdef*2)
STO#n_E_Shear_fin_37 1/(1+#Psi_conn_37*#kdef*2)
PRT#n_E_conc_fin_u
PRT#n_E_conc_fin_37
PRT#n_E_tim_fin_u
PRT#n_E_tim_fin_37
PRT#n_E_Shear_fin_u
PRT#n_E_Shear_fin_37
PRT#n_E_conc_fin_u
PRT#n_E_tim_fin_u
PRT#n_E_Shear_fin_u
END
+PROG ASE urs:32.1
HEAD Load case calculation with stiffnesses at t=oo
GRP 0 FACS 1
GRP 1 FACS #n_E_conc_fin_u $Concrete Beams
GRP 2 FACS #n_E_tim_fin_u $Wood Beams
GRP 3 FACS 1 $Rigid Truss Beams
GRP 4,5 FACS #n_E_Shear_fin_u $Shear Beams for Notch Connection
LC 11,12,13,14,15,16
END
Due to different creep behavior of concrete, timber, and the connection system, the final stress distribution in the composite structure for ULS (fundamental combination) must be calculated by superimposing:
Quasi-permanent stresses from the quasi-permanent combination of actions 𝐸q,per, calculated with effective moduli (𝐸conc,fin, 𝐸tim,fin) and effective slip modulus 𝐾u,fin.
Short-term stresses from the difference between permanent/temporary design combination 𝐸u (fundamental Combination) and quasi-permanent combination 𝐸q,per, calculated with moduli 𝐸conc, 𝐸tim, and slip modulus 𝐾u.
Fundamental Combination
Quasi-Permanent Combination
ULS: Fundamental Combination – Quasi-Permanent Combination
For SLS, the final deformation of the composite structure must be calculated under the characteristic 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.
The superposition for ULS (Ultimate Limit State) and SLS (Serviceability Limit State) is presented as outlined in DIN CEN/TS 19103:2022-02, Section 4.2. In this example, the factors for residential and office buildings are used. If different actions are selected, the combination factors must be adjusted accordingly and calculated using the provided formulas.
t=oo
Load Case
2100
ULS t=oo fundamental
Load Case
2200
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 governing load cases in the Ultimate Limit State (ULS).
+PROG AQB urs:12
HEAD 'Stress Check of Timber Cross Section in ULS for t = 0'
ECHO STRE,SECT VAL FULL
ECHO NSTR VAL FULL
LC NO 1100,1101,1102
BEAM FROM GRP TO 2
COMB GMAX LCST 63000 TITL 'Stress Check Timber t=0'
STRE B
END
+PROG AQB urs:18
HEAD 'Stress Check of Timber Cross Section in ULS for t = oo'
ECHO STRE,SECT VAL FULL
ECHO NSTR VAL FULL
LC NO 2100
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.
+PROG AQB urs:51.1
HEAD 'Stress Check of Concrete Cross Section in ULS for t = 0'
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 1100,1101,1102
STO#fcd 25.5/1.5
STO#fctd 1.5
BEAM FROM GRP TO 1
COMB GMAX LCST 63004 TITL 'Concrete ULS for 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:27
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 2100
BEAM FROM GRP TO 1
COMB GMAX LCST 63005 TITL 'Concrete ULS for 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 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 urs:12
HEAD 'Stress Check of Timber Cross Section in ULS for t=0 + 25% Loads'
ECHO STRE VAL FULL
LC NO 1200,1201,1202
BEAM FROM GRP TO 2
COMB GMAX LCST 63002 TITL 'Timber ULS for t=oo + 25% Loads'
STRE B
END
+PROG AQB urs:18
HEAD 'Stress Check of Timber Cross Section in ULS for t=oo + 25% Loads'
ECHO STRE,SECT VAL FULL
LC NO 2200
BEAM FROM GRP TO 2
COMB GMAX LCST 63003 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: 0.4 mm for indoor components and 0.3 mm for outdoor components.
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 ‰.
!#!Chapter Crack Width Limitation / Minimum Reinforcement t=0
+PROG AQB urs:22
STO#RW 0.4
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 10
LC NO 1400,1401
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 urs:34
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 11
LC NO 2400
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 manually using the GRAPHIC module or create a Diagram Output to visualize the results.
For more details, refer to the Graphic or 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, only the construction load is needed since the self-weight is included automatically.
To include the self-weigth of the whole concrete width, not only the effective width, 1,25 % of loadcase 2 (self-weigth concrete) is included in the analysis.
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.
+prog SOFILOAD urs:66.2 $ Load definition
HEAD Load input for the vibration verification
PAGE
ECHO FULL VAL NO
ACT TYPE G TITL 'Permanent Actions'
LC 20 TYPE G TITL 'Vibration verification' GAMU 1.35 GAMF 1.00 PSI0 1.00 PSI1 1.00 PSI2 1.00
POIN REF BGRP NO 1 TYPE PG PROJ ZZ P 2.00 X 2.8
END
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 1101
For t=oo, select LC 2100
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.
Combine Results instead of the automatic superposition workflow.
The manual result combination gives us more flexibility defining the special combinations for t=oo described in DIN CEN/TS 19103:2022-02 4.2 Principles of Limit State Design.
