Seismic Analysis by Generalised Force Method (GFM)
The Generalised Force Method (GFM) is a technique to estimate the dynamic elastic behaviour of a building responding to the seismic actions. The version of GFM introduced herein gives a quick estimate of the dynamic behaviour of a building to assist in decision making at any stages of the design and to verify results as reported by a commercial software. Although the code lateral force method forms part of GFM, it allows vertical irregularities in the building.
1. Input Parameters:
I. No. of Lumped Masses: |
II. Importance Class of Structure: | |
III. Ground Type: |
Note:
- Please provide input for the roof on the first row and follow the descending pattern up to the base.
- The table can be filled manually or by performing a copy (CTRL+C) and paste (CTRL+V) of data from an Excel spreadsheet.
- The 'Lateral Force' can be user-defined or program calculated.
- For program calculated values of EC8 lateral forces, first provide the information: mass and height, and then press the button 'PRESS TO GET LATERAL FORCE'. The lateral force will be calculated based on T1= 0.05 H3/4 and will be generated into the table.
- The generated lateral forces can be used in any software to determine static storey deflections. The results of which are entered into the table.
No. | Mass (tonnes) |
Height above Ground (m) |
(kN) |
User’s estimate of Static Deflection (mm) |
1 (top) | ||||
2 | ||||
3 | ||||
4 | ||||
5 | ||||
6 | ||||
7 | ||||
8 | ||||
9 | ||||
10 | ||||
11 | ||||
12 | ||||
13 | ||||
14 | ||||
15 | ||||
16 | ||||
17 | ||||
18 | ||||
19 | ||||
20 | ||||
21 | ||||
22 | ||||
23 | ||||
24 | ||||
25 |
Note:
- The program requires the ratios of natural periods to determine the solution for higher modes of vibration. T1, T2, and T3 in the table are the natural periods of the first three modes of vibration.
- There are two methods for specifying the ratios of natural periods: user-defined and default.
- By pressing the ‘USER DEFINED’ button, we can specify the preferred ratios of the natural periods into the table.
- Similarly, by pressing the ‘DEFAULT’ button, the program will automatically consider the default ratios provided in the table.
T2 / T1 | T3 / T1 |
T2 / T1 | T3 / T1 |
0.25 | 0.125 |
Note:
- The modal coefficient is the displacement of each lumped mass of the structure under a specific mode of vibration divided by the response spectral displacement corresponding to the natural period of that mode of vibration.
- To determine the solution for higher modes of vibration, the modal coefficients for each normalised height are required.
- The ‘Normalised Height’ is the height of the lumped mass above ground divided by the total height of the building.
- There are two methods for specifying the modal coefficients: user-defined and default.
- By pressing the ‘USER DEFINED’ button, we can specify the preferred modal coefficients into the table.
- Similarly, by pressing the ‘DEFAULT’ button, the program will automatically consider the widely recognised modal coefficients provided in the table.
- The table can be filled manually or by performing a copy (CTRL+C) and paste (CTRL+V) of data from an Excel spreadsheet.
Normalized Height | Modal Coefficients for Second Mode of Vibration | Modal Coefficients for Third Mode of Vibration |
1 | ||
0.9 | ||
0.8 | ||
0.7 | ||
0.6 | ||
0.5 | ||
0.4 | ||
0.3 | ||
0.2 | ||
0.1 | ||
0 |
Normalized Height | Modal Coefficients for Second Mode of Vibration | Modal Coefficients for Third Mode of Vibration |
1 | 0.639 | 0.312 |
0.9 | 0.373 | 0.066 |
0.8 | 0.077 | -0.181 |
0.7 | -0.201 | -0.31 |
0.6 | -0.419 | -0.258 |
0.5 | -0.547 | -0.062 |
0.4 | -0.573 | 0.168 |
0.3 | -0.501 | 0.315 |
0.2 | -0.356 | 0.321 |
0.1 | -0.173 | 0.194 |
0 | 0 | 0 |
mi = mass of each lumped mass 'i',
δi = static deflection of each lumped mass 'i',
n = number of lumped masses,
Fi = inertia force determined based on EC8.
Γ ϕ = modal coefficient for higher modes of vibration,
Mtotal = total mass of the building.
RSD2 and RSD3 = spectral displacement at the second, and third modal natural period,
RSA2 and RSA3 = spectral acceleration at the second, and third modal natural period,
hi and Hi = height of storey 'i', and storey height from ground, respectively.
In Table 2, mi is storey mass, Hi is storey height (above ground), and δi_static is storey static deflection. Similarly, δi_GFM is storey drift, Fi_GFM is storey inertia forces, θi_GFM is inter-storey drift, and Vi_GFM is storey shear determined based on GFM. |
Table 2: Summary of input information of the Floor Mass, Height and Static Displacement (δi), and GFM result of the Floor Inertia Forces (Fi_GFM), Displacement (δi_GFM), Inter-Storey Drift (θi_GFM), Storey Shear (Vi_GFM), Total Base Shear, and Total Overturning Moment:
- Building and Construction Standards Committee (2013). Guidebook for Design of Buildings in Singapore to Requirements in SS EN 1998-1.Building and Construction Standards Committee, Singapore.
- European Commitee for Standardization (2004). EN 1998-1:2004 Eurocode 8: Design of structures for earthquake resistance - Part 1 : General rules, seismic actions and rules for buildings.
- Building and Construction Standards Committee (2013). EXAMPLE CALCULATION – Seismic Actions to BC3: 2013.Building and Construction Standards Committee, Singapore.
- Khatiwada, P.; Lumantarna, E.; Lam, N.; Looi, D. Fast Checking of Drift Demand in Multi-Storey Buildings with Asymmetry. Buildings 2021, 11, 13. https://doi.org/10.3390/buildings11010013