Response Spectrum Method Excel

DYNAMIC ANALYSIS - RESPONSE SPECTRUM METHOD FOR A THREE STOREY BUILDING FOR A SYMME BUILDING (SQUARE IN PLAN) Given Data: Self Weight of concrete Self Weight of Brick infill Grade of concrete used Young's Modulus of concrete

25 kN/m3 20 kN/m3 M w

Dimensions of beam Dimensions of column

25 25000000000 N/m2 d 0.25 0.45

Floor slab thickness Brick infill thickness

0.15 0.12 l

0.4 m 0.45 m m m

w

Slab dimensions Length of the beam Height of the column Height of the brick wall in Roof level parapet No. of beams in one floor No. of columns in one floor No. of walls in one floor

22.5 22.5 3

22.5 m m m

0

m

8 16 8

Live load

3

kN/m2

Step 1: Calculation of Seismic Weights Load due to beam Load due to column Load due to slab Load due to wall Load due to parapet wall in roof

450 243 1898.4375 1296 0

kN kN kN kN kN

0.75

kN

3888.1875 3117.9375

kN kN

Imposed load

Load acting on floors except roof Load acting on roof Floor

Seismic Weight(kN)

Seismic Mass(kg)

Roof Second floor First floor

3117.9375 3888.1875 3888.1875

3.18E+05 3.96E+05 3.96E+05

Step 2: Calculation of stiffness Moment of inertia of column

0.0034171875 m4

Stiffness of one column

3.80E+07

N/m

Total stiffness in the floor

6.08E+08

N/m

Step 3: Calculation of natural frequencies of the system |[K] - ω2 [M]| = 0

[K]

1.22E+09 -6.08E+08 0.00E+00

-6.08E+08 0.00E+00 1.22E+09 -6.08E+08 -6.08E+08 6.08E+08

[M]

3.96E+05 0.00E+00 0.00E+00

0.00E+00 0.00E+00 3.96E+05 0.00E+00 0.00E+00 3.18E+05

ω1 ω2 ω3

71.5617192422 rad/s 50.8093689514 rad/s 18.429611568 rad/s

Step 3: Calculation of mode shapes For

For

For

ω1

71.5617192422 rad/s

a11 a21 a31

1 -1.3411371029 0.7986487288

ω2

50.8093689514 rad/s

a12 a22 a32

1 0.3156964356 -0.9003357605

ω3

18.429611568 rad/s

a13 a23 a33

1 1.7784023607 2.1627149566

Step 4: Calculation of modal mass Mk and modal participation factor Pk

Mode 1

Mode shape Seismic Wiφi Wiφi2 Storey level Weight (Wi) (φi) Roof 3117.94 0.7986487288 2490.1368208825 1988.74461 Second 3888.19 -1.3411371029 -5214.592519332 6993.4835 First 3888.19 1 3888.1875 3888.1875 Sum 10894.3125 1163.7318015505 12870.4156

Modal mass Mk

10.7262

Modal participation factor Pk

0.0904

Mode 2

Mode shape Seismic Wiφi Wiφi2 Storey level Weight (Wi) (φi) Roof 3117.94 -0.9003357605 -2807.190630387 2527.41411 Second 3888.19 0.3156964356 1227.4869347361 387.51325 First 3888.19 1 3888.1875 3888.1875 Sum 10894.3125 2308.483804349 6803.11486

Modal mass Mk

79.8504

Modal participation factor Pk

0.3393

Mode 3

Mode shape Seismic Wiφi Wiφi2 Storey level Weight (Wi) (φi) Roof 3117.94 2.1627149566 6743.2100651423 14583.6413 Second 3888.19 1.7784023607 6914.7618289582 12297.2288 First 3888.19 1 3888.1875 3888.1875 Sum 10894.3125 17546.159394101 30769.0575

Modal mass Mk

1019.9548

Modal participation factor Pk

0.5703

Sum of Pk

1

Sum of Pk

1

Step 5 : Calculation of horizontal acceleration spectrum Ah Time period Tk T1 T2 T3

0.0878 sec 0.1237 sec 0.3409 sec

Zone factor Z Importance factor I Response factor R Sa/g1 Sa/g2 Sa/g3 Ah1 Ah2 Ah3

3

0 0 0

Step 6: Calculation of lateral force and shear in each mode

BUILDING FOR A SYMMENTRIC

kN N g kg

1 1000 9.81 101.936799

4.99E+16 -4E+020 x1 x2 x3

5.12E+03 2.58E+03 3.40E+02

ω1 ω2 ω3

71.5617192 50.809369 18.4296116

8E+023 -2E+026

5.12E+03 4.99E+16 -4.02E+20 2.56E+20 2.58E+03 4.99E+16 -1.46E+20 1.29E+20 4.99E+16 -1.70E+19 x1 x2 x3

5.12E+03 2.58E+03 3.40E+02

7.91E+23 -2.24E+26 -7.47E+23 2.24E+26 4.38E+22 0.00E+00 -4.38E+22 0.00E+00