9451x

2021-03-29

Simplified Vibration Design for EC 5

With the RF-/TIMBER Pro add-on module, you can perform the vibration design known from DIN 1052 for the design according to EN 1995-1-1. In this design, the deflection under permanent and quasi-permanent action at the ideal one‑span beam may not exceed the limit value (6 mm according to DIN 1052). If you consider the relation between the natural frequency and the deflection for a hinged single-span beam subjected to a constant distributed load, the 6 mm limit value results in a minimum natural frequency of about 7.2 Hz.

f_{e} = \frac{π}{2 \cdot l^{2}} \cdot \sqrt{\frac{EI}{m}} \Rightarrow \frac{EI}{m \cdot l^{4}} = \frac{f_{e}^{2} \cdot 4}{π^{2}}

f_e	Natural frequency
l	Length of the beam
EI	Bending stiffness of the beam
m	Modal mass

Natural Frequency of Single-Span Beam with Constant Load

w = \frac{5 \cdot m \cdot g \cdot l^{4}}{384 \cdot EI} \Rightarrow \frac{EI}{m \cdot l^{4}} = \frac{5 \cdot g}{384 \cdot w}

w	Deflection
l	Length of the beam
m	Modal mass
g	Acceleration of gravity

Deflection of Single-Span Beam with Constant Load

If both equations are equated, the natural frequency of 7.2 Hz results in a deformation of 6 mm.

\frac{f_{e}^{2} \cdot 4}{π^{2}} = \frac{5 \cdot g}{384 \cdot w}

f_{e, \min, DIN} = \frac{5}{\sqrt{0, 8 \cdot w}} = \frac{5}{\sqrt{0, 8 \cdot 0.6}} = 7.2 Hz

f_e,min,DIN	Minimum natural frequency according to DIN 1052
w	Deflection
g	Acceleration of gravity

Minimum Natural Frequency According to DIN 1052

If we take into account the fact that in most National Annexes of EC 5, a minimum natural frequency of 8.00 Hz is to be considered, we obtain a maximum deflection of about 5 mm.

f_{e, \min, EC 5} = \frac{5}{\sqrt{0, 8 \cdot w}} = \frac{5}{\sqrt{0, 8 \cdot 0.5}} = 8 Hz

f_e,min,EC5	Minimum natural frequency according to EN 1995-1-1
w	Deflection

Minimum Natural Frequency According to EN 1995-1-1

If the structural system deviates from a hinged single-span beam (for example, continuous beams, cantilevers, restraints), this must be taken into account accordingly in the deflection limitation.

Example:

Three-Span Continuous Beam

We analyze a three‑span beam in a dwelling house. To avoid discomfort caused by persons, the system shall have a minimum fundamental frequency of 8 Hz. In order to consider this in RF‑/TIMBER Pro, you can use the formula for three-span beams (see the PDF document below) to determine the maximum allowed deflection of the central span.

w_{\max, 8 Hz} \approx - k_{f}^{2} \cdot \frac{63 \cdot l^{2} \cdot (12 \cdot l_{k}^{3} - 10 \cdot l_{k} \cdot l^{2} - 3 \cdot l^{3})}{f_{e, 8 Hz}^{2} \cdot l_{k}^{4} \cdot (2 \cdot l_{k} + 3 \cdot l)} = - 1.00 mm

w_max,8Hz	Limit deflection of about 8 Hz to be reached
k_f	Correction factor (see PDF file)
l	Length of the middle span
l_k	Length of the outer panels
f_e,8Hz	Minimum natural frequency

Limit Deflection

In this case, the middle span may deform by -1 mm to comply with the frequency criterion. The actual deflection under permanent load (2.1 kN/m) is obtained as -0.683 mm. Thus, the design of the natural frequency is complied with, and the natural frequency of the beam is greater than 8 Hz. A check calculation results in a natural frequency of 9.76 Hz.

f_{e} \approx - k_{f} \cdot \sqrt{\frac{63 \cdot l^{2} \cdot (12 \cdot l_{k}^{3} - 10 \cdot l_{k} \cdot l^{2} - 3 \cdot l^{3})}{w_{0.0683 cm} \cdot l_{k}^{4} \cdot (2 \cdot l_{k} + 3 \cdot l)}} = 9.76 Hz

Natural Frequency

A more precise calculation with the RF‑/DYNAM Pro — Natural Vibrations add-on module results in a natural frequency of 9.86 Hz. The video shows the procedure.

Furthermore, it should be noted that further designs (stiffness criterion, vibration velocity, vibration acceleration) must be performed for the vibration design of apartment ceilings. Notes can be found in [1] or [2], for example.

Knowledge Base

KB 000694 | "Simplified" Vibration Design for EC 5

Author

Mr. Rehm is responsible for developing products for timber structures, and he provides technical support for customers.

Links

Structural Analysis & Design Software for Timber Structures

References

Eurocode 5: Design of Timber Structures - Part 1-1: General – Common Rules and Rules for Buildings; DIN EN 1995-1-1:2010-12
Winter, S.; Hamm, P.; Richter, A.: Schwingungs- und Dämpfungsverhalten von Holz- und Holz-Beton-Verbunddecken. Schlussbericht Juli 2010. München: TU München, Lehrstuhl für Holzbau und Baukonstruktion, 2010

Downloads

Limitation of Deflection (PDF)

7.04 MB

Do you have any questions?

Events

2024-11-20

Online Training

RFEM 6 | Students | Introduction to Timber Design

Videos

Knowledge Base

KB 000694 | "Simplified" Vibration Design for EC 5

Length: 00:01:17 min

RFEM 6 for Students | Introduction to Timber Design

Event

RFEM 6 for Students | Introduction to Timber Design | April 30, 2024

Length: 00:00:00 min

FAQ 005511 | What does each option do under the "Calculation of Torsion" section under the Strength…

FAQ

FAQ 005511 | What does each option do under the "Calculation of Torsion" section under the Strength…

Length: 00:00:16 min

FAQ

FAQ 005494 | How can I model a timber beam with stiffening on both sides? (splice)

Length: 00:01:22 min

Product Feature

Fire Resistance Design of Surfaces for EN 1995, SIA 265, NDS, and CSA O86

Length: 00:00:56 min

Event

Webinar | Timber Floor Calculations in RFEM 6

Length: 00:55:27 min

Event

RFEM 6 for Students | Introduction to Timber Design | November 29, 2023

Length: 01:10:03 min

Product Feature

Cross‑Section Optimization

Length: 00:00:56 min

FAQ

FAQ 005410 | How is the equivalent dimension calculated for round section in the Timber Design ad...

Length: 00:00:28 min

Playlist

Models to Download

1001x

83x

Three-Span Continuous Beam

481x

99x

Timber Frame Building

Model 004809 | Cross-Laminated Timber Building

404x

60x

Cross-Laminated Timber Building

235x

27x

Timber Slab

Model 004717 | Ceiling with Line Releases

287x

31x

Ceiling with Line Releases

Model 004707 | Office Building of Municipal Works in Kirchheim unter Teck, Germany

290x

Office Building Timber Structure with Reinforced Concrete Elements

517x

Timber Industrial Hall Siegrist Igor Carpenteria

491x

51x

Trussed Roof

506x

59x

Timber-Concrete Building

Knowledge Base Articles

KB 001848 | Timber Column Design as per the 2018 NDS Standard in RFEM 6

Using the Timber Design add-on, timber column design is possible according to the 2018 NDS standard ASD method. Accurately calculating timber member compressive capacity and adjustment factors is important for safety considerations and design. The following article will verify the maximum critical buckling strength calculated by the Timber Design add-on using step-by-step analytical equations as per the NDS 2018 standard including the compressive adjustment factors, adjusted compressive design value, and final design ratio.

KB 001825 | WebService & API for Analysis of Construction Stages

When calculating regular structures, data input is often not complicated but time-consuming. Input automation can save valuable time. The task described in the present article is to consider the stories of a house as single construction stages. Data is entered using a C# program so that the user does not have to enter the elements of the individual floors manually.

Our webservice offers users the opportunity to communicate with RFEM 6 and RSTAB 9 using various programming languages. Dlubal's high-level functions (HLFs) allow you to expand and simplify the WebService's functionality. In line with RFEM 6 and RSTAB 9, using our WebService makes the engineer's work easier and faster. Check it out now! This tutorial shows you how to use the C# library by means of a simple example.

Screenshots

Three-Span Continuous Beam

Deformed Cross-Laminated Timber Slab with Point Supports in RFEM 6 | © ATP Architekten Ingenieure

Timber Structure of Lookout Tower

This image shows a user interface of the RFEM 6 software, which is used for the structural analysis and design. In the main area of the interface, there is a complex 3D model of a timber structure, presented in two different styles: before and after the deformation.

Global Deformation – Before and After Position of Timber Structure Due to Wind Forces in RFEM 6 | Knies Magician's Hat in Rapperswil, Switzerland © Ghisleni Partner AG

Global Deformation of Timber Structure Due to Wind Forces in RFEM 6 | Knies Magician's Hat in Rapperswil, Switzerland © Ghisleni Partner AG

RFEM Model of Palazzo Meridia Office and Retail Building in Nice, France | © Architecture-Studio

Tower Structure with Wind Load Generation in RFEM 6

Timber Structure with Wind Load Generation in RFEM 6 | © STATIC Solution s.r.o

Exterior View of Gym | © KL-Architectes

Product Features

Using the "Beam Panel" thickness type, you can model timber panel elements in 3D space. You just specify the surface geometry and the timber panel elements are generated using an internal member-surface construct, including the simulation of the connection flexibility.

Go to Explanatory Video

Feature 002585 | Fire Resistance Design of Surfaces for EN 1995 and SIA 265

You have the option to perform the fire resistance design of surfaces using the reduced cross-section method. The reduction is applied over the surface thickness. It is possible to perform the design checks for all timber materials allowed for the design.

For cross-laminated timber, depending on the type of adhesive, you can select whether it is possible for individual carbonized layer parts to fall off, and whether you can expect increased charring in certain layer areas.

Feature 002615 | Cross-Laminated Timber Manufacturer Library for USA, Canada, and Switzerland

Among others, the following cross-laminated timber manufacturers are available in the layer structure library:

Binderholz (USA)
KLH (USA, CAN)
Kalesnikoff (USA, CAN)
Nordic Structures (USA, CAN)
Mercer Mass Timber
SmartLam
Sterling Structural
Superstructures listed in Lignatec Edition 32 "Cross-Laminated Timber of Swiss Production"

By importing a structure from the layer structure library, all relevant parameters are adopted automatically. The library is continually updated.

The Timber Design add-on for RFEM 6 / RSTAB 9 is multi-purpose and combines a large number of additional elements. [*S16332764*] Timber Design Add-on for RFEM 6

Frequently Asked Questions (FAQ)

What calculation is carried out for the NDS Strength Configuration "Calculation of Torsion" options?

Which Dlubal software products do you recommend for the structural analysis and design of timber structures in particular?

How can I model a timber beam with stiffening on both sides? (splice)

How can I generate an area load on members via cells in RFEM 6 or RSTAB 9?

Which programs do I need for laminate and sandwich structures, or cross-laminated timber (CLT)?

Which Dlubal Software programs can I use to calculate and design timber structures?

Recommended Products for You

RFEM 6 | Main Program RFEM 6

RFEM 6

Main Program

The new generation of 3D FEA software is used for the structural analysis of members, surfaces, and solids.

Price of First License 4,170.00 USD

RFEM 6 | Design

Timber Design for RFEM 6

Add-On

The Timber Design add-on performs the ultimate, serviceability, and fire resistance limit state design checks of timber members according to various standards.

Price of First License 1,930.00 USD

RFEM 6 | Additional Analysis

Structure Stability for RFEM 6

Add-On

The Structure Stability add-on performs stability analysis of structures. It determines critical load factors and the corresponding stability modes.

Price of First License 1,300.00 USD

RSTAB 9 | Main Program RSTAB 9

RSTAB 9

Structural Frame and Truss Analysis Software

Main Program

The modern 3D structural analysis and design program is suitable for the structural and dynamic analysis of beam structures as well as the design of concrete, steel, timber, and other materials.

Price of First License 2,910.00 USD

RSTAB 9 | Design

Timber Design for RSTAB 9

Add-On

The Timber Design add-on performs the ultimate, serviceability, and fire resistance limit state design checks of timber members according to various standards.

Price of First License 1,930.00 USD

RX-TIMBER 2 | Timber Structures

RX-TIMBER Glued-Laminated Beam 2

Stand-Alone Program

Timber design of single-span and wide-span glulam beams according to Eurocode 5 or DIN 1052

Price of First License 1,120.00 USD

RX-TIMBER 2 | Timber Structures

RX-TIMBER Continuous Beam 2

Stand-Alone Program

Timber design of simple, continuous, and Gerber beams with or without cantilever according to Eurocode 5 or DIN 1052

Price of First License 360.00 USD

RX-TIMBER 2 | Timber Structures

RX-TIMBER Column 2

Stand-Alone Program

Timber design of rectangular and circular columns according to Eurocode 5 or DIN 1052

Price of First License 360.00 USD

RX-TIMBER 2 | Timber Structures

RX-TIMBER Purlin 2

Stand-Alone Program

Timber design of coupled purlins and continuous beams according to Eurocode 5 or DIN 1052

Price of First License 360.00 USD

RX-TIMBER 2 | Timber Structures

RX-TIMBER Frame 2

Stand-Alone Program

Timber design of three-hinged frames with finger joint connections according to Eurocode 5 or DIN 1052

Price of First License 360.00 USD

RX-TIMBER 2 | Timber Structures

RX-TIMBER Brace 2

Stand-Alone Program

Timber design of stiffening truss bracing according to Eurocode 5 or DIN 1052

Price of First License 360.00 USD

RX-TIMBER 2 | Timber Structures

RX-TIMBER Roof 2

Stand-Alone Program

Timber design of flat, monopitch, and duopitch roofs according to Eurocode 5

Price of First License 360.00 USD

RFEM 6 | Dynamic Analysis

Modal Analysis for RFEM 6

Add-On

The Modal Analysis add-on allows for the calculation of eigenvalues, natural frequencies, and natural periods for member, surface, and solid models.

Price of First License 1,210.00 USD

RFEM 6 | Dynamic Analysis

Response Spectrum Analysis for RFEM 6

Add-On

The Response Spectrum Analysis add-on performs seismic analysis using multi-modal response spectrum analysis. The spectra required for this can be created in compliance with the standards or can be user-defined. The equivalent static forces are generated from them. The add-on includes an extensive library of accelerograms from seismic zones that can be used to generate the response spectra.

Price of First License 1,390.00 USD

RFEM 6 | Dynamic Analysis

Pushover Analysis for RFEM 6

Add-On

Using the Pushover Analysis add-on, you can analyze the seismic actions on a particular building, and thus assess whether the building can withstand an earthquake.

Price of First License 1,300.00 USD

RFEM 6 | Additional Analysis

Time-Dependent Analysis (TDA) for RFEM 6

Add-On

The Time-Dependent Analysis (TDA) add-on allows you to consider the time-dependent material behavior of members. The long-term effects, such as creep, shrinkage, and aging, can influence the distribution of internal forces, depending on the structure.

Price of First License 1,030.00 USD

RFEM 6 | Design

Concrete Design for RFEM 6

Add-On

The Concrete Design add-on allows for various design checks according to international standards. You can design members, surfaces, and columns, as well as perform punching and deformation analyses.

Price of First License 2,550.00 USD

RFEM 6 | Design

Steel Design for RFEM 6

Add-On

The Steel Design add-on performs the ultimate and serviceability limit state design checks of steel members according to various standards.

Price of First License 2,550.00 USD

RFEM 6 | Design

Masonry Design for RFEM 6

Add-On

The Masonry Design add-on for RFEM allows you to design masonry using the finite element method. It was developed as part of the research project titled DDMaS – Digitizing the Design of Masonry Structures. The material model represents the nonlinear behavior of the brick-mortar combination in the form of macro-modeling.

Price of First License 1,660.00 USD

RFEM 6 | Design

Aluminum Design for RFEM 6

Add-On

The Aluminum Design add-on performs the ultimate and serviceability limit state design checks of aluminum members according to various standards.

Price of First License 1,750.00 USD

RSTAB 9 | Dynamic Analysis

Modal Analysis for RSTAB 9

Add-On

The Modal Analysis add-on allows for the calculation of eigenvalues, natural frequencies, and natural periods for member, surface, and solid models.

Price of First License 1,210.00 USD

RSTAB 9 | Dynamic Analysis

Response Spectrum Analysis for RSTAB 9

Add-On

The Response Spectrum Analysis add-on performs seismic analysis using the multi-modal response spectrum analysis. The spectra required for this can be created in compliance with the standards or can be user-defined. The equivalent static forces are generated from them. The add-on includes an extensive library of accelerograms from seismic zones that can be used to generate response spectra.

Price of First License 1,390.00 USD

RSTAB 9 | Dynamic Analysis

Pushover Analysis for RSTAB 9

Add-On

Earthquakes may have a significant impact on the deformation behavior of buildings. A pushover analysis allows you to analyze the deformation behavior of buildings and compare them with seismic actions. Using the Pushover Analysis add-on, you can analyze the seismic actions on a particular building, and thus assess whether the building can withstand the earthquake.

Price of First License 1,300.00 USD

RSTAB 9 | Design

Concrete Design for RSTAB 9

Add-On

Concrete Design add-on allows for various design checks of members and columns according to international standards.

Price of First License 2,550.00 USD

RSTAB 9 | Design

Steel Design for RSTAB 9

Add-On

The Steel Design add-on performs the ultimate and serviceability limit state design checks of steel members according to various standards.

Price of First License 2,550.00 USD

RSTAB 9 | Design

Aluminum Design for RSTAB 9

Add-On

The Aluminum Design add-on performs the ultimate and serviceability limit state design checks of aluminum members according to various standards.

Price of First License 1,750.00 USD

Display Product Family