📺MasterFrame: Vibration design for composite floors and stairs [WEBINAR RECORDING]

Posted on August 19th, 2019 in Webinars

Summary

This presentation from MasterSeries Software focuses on the vibration design of composite floors and staircases, specifically addressing footfall analysis rather than seismic or natural frequency concerns. It outlines a methodology based on the SDI publication P354, utilising a finite element analysis of a composite floor with steel beams and a concrete slab. Key aspects covered include calculating natural frequencies and their mass participation, determining response factors for various scenarios (including walking on floors and staircases), and assessing vibration dose values and resonant build-up. The demonstration also explores transient loading and the influence of dampening and mesh size, highlighting how to interpret results for human comfort and serviceability limit states.

Key Points

• Vibration Design
• Composite Floors
• Dynamic Analysis
• Response Factors
• Staircase Analysis

Description

This video transcript covers the process of vibration design for composite floors and staircases, specifically focusing on footfall analysis, rather than natural frequencies or earthquakes. The methodology is primarily based on the SDI publication P354.

The analysis uses MasterSeries software and involves several key steps:

• Model Setup:

    ◦ A composite floor with columns, beams, a slab, openings, and a staircase is modelled.

    ◦ The floor is analysed as a finite element (FE) slab, which is recommended by the P354 publication.

    ◦ A fixed rigid analysis is employed because vibration analysis deals with low stresses, unlike ultimate limit state design.

    ◦ Columns are typically modelled as half-length and pinned at the base, restrained horizontally at the top.

    ◦ The analysis focuses on one floor due to the computational intensity.

    ◦ The ribbed deck (e.g., Multi Deck 80) is considered, using the dynamic modulus of elasticity for concrete (e.g., 38 GPa) and a 180mm thick slab.

    ◦ Attached beams are bottom-connected, ensuring the full depth of the beam and concrete contribute.

    ◦ Loading includes live load (2.5 kN) and superimposed dead load (0.5 kN), with slab self-weight handled automatically.

• Dynamic Analysis (Natural Frequencies):

    ◦ This is the initial step to determine natural frequencies, which are then used for vibration design.

    ◦ Mass loads include the full dead load and 10% (0.1) of the live load, as this is a more conservative approach recommended by P354.

    ◦ A 3D analysis is performed to account for columns and staircases.

    ◦ Frequencies up to 30-32 Hz are considered, encompassing the fourth harmonic relevant for walking and stairs.

    ◦ Mass participation is a critical indicator; a global mass participation of 70-75% suggests correct results. The movement forms are normalised to a factor of one.

• Vibration Design Analysis (Response Factors):

    ◦ The focus is on vibration design and response factors, not just natural frequencies, as people react to acceleration rather than the speed of vibration. Fourier coefficients and series are used for a realistic response.

    ◦ Residential Steady-State Walking:

        ▪ Dampening is typically set to 1%.

        ▪ The recommended frequency range for walking is 1.8 to 2.2 Hz.

        ▪ The software calculates a response factor, which is compared against values in Table 5.6 of the SDI guide (e.g., 1 for operating theatres, higher for residential). High response factors (e.g., 18.1) indicate a need for design modification.

    ◦ Staircase Analysis:

        ▪ The frequency range for staircases is higher, 1.2 to 4.5 Hz.

        ▪ Initial response factors can be very high (e.g., 39).

        ▪ To account for the short duration and infrequent nature of staircase loading, a Vibration Dose Value (VDV) analysis is performed, typically over 360 seconds.

        ▪ Considering resonant build-up over a short distance (e.g., 5m) can reduce the VDV to acceptable levels (e.g., 0.25, within the 0.2-0.4 low probability range).

    ◦ Floor Response from Staircase Loading:

        ▪ The impact of staircase excitation on sensitive areas of the floor (e.g., an operating theatre or conference room) can be assessed.

        ▪ Response factors (e.g., 3.0) determine if further action is needed based on the area's sensitivity.

    ◦ Transient Loading:

        ▪ This analysis is used when loading is impulsive and does not build up.

        ▪ It considers the effect of short-duration loads on specific areas, yielding response factors (e.g., 7.8, or 4.0 for office areas).

• General Considerations and Software Requirements:

    ◦ This analysis is for serviceability limit state (comfort), not ultimate limit state structural design.

    ◦ The mesh size affects accuracy and analysis time; a finer mesh increases accuracy but is computationally intensive.

    ◦ The analysis requires MasterFrame, Finite Elements, and Dynamic Analysis modules.

    ◦ While possible, analysing multiple levels is very computationally demanding and is typically reserved for highly sensitive structures (e.g., microsurgery operating theatres below a dance floor).