The dymamic analysis is achieved based on the input of the floorplan of the building (drawn to scale). Please upload floor plan (any image file format) below.

Note: Any information outside the boundary of the floorplan and any written text within the floorplan need to be removed before uploading the image. Click ‘More Info’ button to see an example.

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Please verify the dimensions of the structural elements provided in the table below. If the displayed dimensions differ from the actual measurements, kindly update the values by specifying the correct information in the ‘Make Changes’ column.

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Input slab depth (in mm):
Characteristic Compressive Strength of Concrete (MPa):

Input Average Length of Beam in the Direction of Loading (in mm):
Input the Cross-sectional Area of Beam (in mm2):

Confirm system type

B. Details of the Building’s Elevation:

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No. of Lumped Masses:

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2. Results:

2.1 Seismic Design Response Spectrum:

2.2 2D Dynamic Solution Including Higher Modes of Vibration:

The dynamic solution of the seismic response of the building in 2-dimension (no torsion or rotation) is determined as per the following 3 steps.

Step 1. Determination of the mode shape (ϕ_j), participation factor (&#915_j) and period (T_j) of the first 3 modes of vibration:
The modal solution of the building is determined using the free undamped response of the continuum system (having uniform stiffness along height) represented by the Timoshenko Beam, Eqs. (1-3). $$ {ϕ_{j} = C [cos(x a_{j}) – cosh(x \sqrt{{a_{j}}^2+{P}^2}) – D{sin(x a_{j}) – \frac{a_{j}}{\sqrt{{a_{j}}^2+{P}^2}} sinh(x \sqrt{{a_{j}}^2+{P}^2})}]}\tag{1}$$ $$ {&#915_{j} = \frac{m_{i} ϕ_{j}}{ϕ’_{j} m_{i} ϕ_{j}}}\tag{2}$$ $${T_{j} = \left(\frac{2\pi}{a_{j}b_{j}}\right) \times \sqrt{{\frac{M_{total}H^3}{EI}}}}\tag{3}$$ Where: coefficients C and D, and mode shape parameter (a_j) are solved from Eq. (1) using the boundary conditions at the base and roof of the building; P is the stiffness ratio defined as an input; and M_total, H, and EI are the total mass, height, and flexural rigidity of the building.

Step 2. Determination of the effective modal mass (M_j) and modal participation ratio (MPR_j) $$ {M_{j} = \sum^n_{i=1}({m_{i}}\:{{Γ_{j}}\:\:{ϕ_{i,j}}})}\tag{4}$$ $$ {MPR_{j} = \frac{M_{j}}{M_{total}}}\tag{5}$$

Step 3. Determination of the combined storey and inter-storey drift, storey and base shear, and overturning moment
The combination of storey drift (δ_{i,3 modes}), inter-storey drift (θ_{i,3 modes}), storey shear (V_{i,3 modes}), base shear (V_{b,3 modes}), and total overturning moment (OM) of the first three modes of vibration are calculated using Eqs. (6-11). $$ {δ_{i,3\:modes} = \sqrt{\sum^3_{j}{\left({{Γ_{j}}\:\:{ϕ_{i,j}}\:\:{RSD_{j}}}\right)}^2 }}\tag{6}$$ $$ {θ_{i,3\:modes} = \sqrt{\sum^3_{j}{\left(\frac{{{Γ_{j}}\:\:{(ϕ_{i,j}-ϕ_{i-1,j})}\:\:{RSD_{j}}}}{h_{i}}\right)}^2 }}\tag{7}$$ $$ {F_{i,3\:modes} = \sqrt{\sum^3_{j}{\left({m_{i}:\:{Γ_{j}}\:\:{ϕ_{i,j}}\:\:{RSA_{j}}}\right)}^2 }}\tag{8}$$ $$ {V_{i,3\:modes} = \sqrt{{\left(\sum^n_{i}{m_{i}}\:{{Γ_{1}}\:\:{ϕ_{i,1}}\:\:{RSA_{1}}}\right)}^2 + {\left(\sum^n_{i}{m_{i}}\:{{Γ_{2}}\:\:{ϕ_{i,2}}\:\:{RSA_{2}}}\right)}^2 + {\left(\sum^n_{i}{m_{i}}\:{{Γ_{3}}\:\:{ϕ_{i,3}}\:\:{RSA_{3}}}\right)}^2}}\tag{9}$$ $$ {V_{b,3\:modes} = \sqrt{{\left({V_{b,1}}\right)}^2+{\left({V_{b,2}}\right)}^2+{\left({V_{b,3}}\right)}^2}}\tag{10}$$ $$ {OM = \sum^n_{i=1}({{F_{i,3\:modes}} \times H_{i}})}\tag{11}$$ Where: RSA_j and RSD_j are the spectral acceleration and displacement of mode ‘j’ at ‘T_j‘, and h_i and H_i are the height of each storey ‘i’ and it’s height from the base of the building.

Table 1: Effective Modal Mass, Modal Participation Ratio, Effective Stiffness and Natural Period:

2.4 Solution Including 3D Torsional Amplification:

The floor plan of the building provided as an input is scanned here to determine the position of the centre of mass (CM) and centre of rigidity (CR) and the mass radius of gyration as shown in Figure 5. Then the torsional parameters such as the normalised elastic radius (br) and normalised eccentricity (er) are determined as per [1]. Finally, the 3D/2D displacement ratio is determined as per [2]. The torsional parameters and the 3D displacement profile is plotted against the 2D displacement in Figure 5.

Table 2: Summary of input information of the floor mass, height, and GFM results: floor displacements (δ_{i_GFM}), inter-storey drift (θ_{i_GFM}), inertia forces (F_{i_GFM}), storey shear (V_{i_GFM}), total base shear, and overturning moment.