V. IS 1893 2015 Response Spectrum

Calculate the base shear and its distribution along the height for the response spectrum method in the IS 1893 (Part4): 2015 specification.

Details

A three story frame

Beam and column dimensions: 500 mm × 500 mm

Material: concrete

The structure is modelled in STAAD.Pro considering the following:

Seismic zone factor, Z = 0.16 (ZONE 0.16)
Importance factor, I = 1.5 (I 1.5)
Response reduction factor, R = 5 (RF 5)
Soil site condition = Soft (SOIL TYPE 3)
Minimum factor of total weight for base shear (RSMIN 2.75)

Validation

Table 1. Natural Frequency/Time Period Information & Mode Shapes (Obtained from output file)
Mode	Frequency (cyc/sec)	Time Period (sec)
1	0.229	4.3681
2	0.625	1.59884
3	0.854	1.17043

Table 2. Mode shapes
Mode	Story Level/Joint Numbers	X-Trans
1	Roof/Joints 7 & 8	1
1	2nd Floor/Joints 5 & 6	0.866
1	1st Floor/Joints 2 & 3	0.5
2	Roof/Joints 7 & 8	-1
2	2nd Floor/Joints 5 & 6	0
2	1st Floor/Joints 2 & 3	1
3	Roof/Joints 7 & 8	1
3	2nd Floor/Joints 5 & 6	-0.866
3	1st Floor/Joints 2 & 3	0.5

Story Level	Weight, W_i (kN)	Mode 1			Mode 2			Mode 3
Story Level	Weight, W_i (kN)	ϕ	W_i × ϕ	W_i × ϕ²	ϕ	W_i × ϕ	W_i × ϕ²	ϕ	W_i × ϕ	W_i × ϕ²
Roof	49.035	1	49.035	49.035	-1	-49.035	49.035	1	49.035	49.035
2nd Floor	98.07	0.86603	84.932	73.553	0	0	0	-0.866	-84.932	73.553
1st Floor	98.07	0.5	49.035	24.518	1	98.07	98.07	0.5	49.035	24.518
Summation	245.18		183.00	147.11		49.035	147.105		13.138	147.11

Table 3. Mass participation factor and mod participation factor calculations
	Mode 1	Mode 2	Mode 3
Modal Weight, Mk × g	$\frac{{183.00}^{2}}{147.11} = 227.7$	$\frac{{49.035}^{2}}{147.11} = 16.35$	$\frac{{13.138}^{2}}{147.11} = 1.173$
Modal Weight Participation (In %)	$\frac{227.7}{245.18} \times 100 = 92.85$	$\frac{16.35}{245.18} \times 100 = 6.666$	$\frac{1.173}{245.18} \times 100 = 0.479$
Mode Participation Factor,Pk	$\frac{183.00}{147.11} = 1.244$	$\frac{49.035}{147.11} = 0.333$	$\frac{13.138}{147.11} = 0.089$

Direction factor = $\frac{Z}{2} \times \frac{I}{R} = \frac{0.16}{2} \times \frac{1.5}{5} = 0.024$

	Mode 1	Mode 2	Mode 3
Sa/g	$\frac{1.67}{T} = \frac{1.67}{4.368} = 0.382$	$\frac{1.67}{T} = \frac{1.67}{1.599} = 1.045$	$\frac{1.67}{T} = \frac{1.67}{1.170} = 1.427$
$Ak = \frac{Z}{2} \times \frac{I}{R} \times \frac{Sa}{g}$	$0.024 \times 0.382 = 0.00918$	$0.024 \times 1.045 = 0.0251$	$0.024 \times 1.427 = 0.0342$

Story Level	Weight, W_i (kN)	Mode 1			Mode 2			Mode 3			Story Shear due to all modes (i.e., SRSS of all modes)
Story Level	Weight, W_i (kN)	ϕ	Qi = (Ak × ϕ × Pk × Wi)	Vi = (∑Qi)	ϕ	Qi = (Ak × ϕ × Pk × Wi)	Vi = (∑Qi)	ϕ	Qi = (Ak × ϕ × Pk × Wi)	Vi = (∑Qi)	Story Shear due to all modes (i.e., SRSS of all modes)
Roof	49.035	1	0.560	0.560	-1	-0.410	-0.410	1	0.150	0.150	0.71
2nd Floor	98.07	0.866	0.970	1.530	0	0	-0.410	-0.866	-0.260	-0.110	1.59
1st Floor	98.07	0.5	0.560	2.089	1	0.820	0.410	0.5	0.150	0.040	2.13
Total SRSS Shear											2.13

Minimum base shear per Table 2:

2.75 × 245.18 / 100 = 6.74 kN

The multiplying factor (ratio of minimum base shear to total SRSS base shear): 6.47 / 2.13 = 3.17

Results

Table 4.
Result Type	Reference	STAAD.Pro	Difference
Story shear, roof (kN)	0.71	0.71	none
Story shear, 2nd (kN)	1.59	1.59	none
Story shear, 1st (kN)	2.13	2.13	none
Base shear (kN)	2.13	2.13	none
Minimum base shear (kN)	6.74	6.7423	negligible
Multiplying factor	3.17	3.1668	negligible

STAAD.Pro Input

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\06 Loading\IS 1893\IS 1893 2015 Response Spectrum.std is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 08-Feb-17
END JOB INFORMATION
INPUT WIDTH 79
SET SHEAR
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 3 0; 3 3 3 0; 4 3 0 0; 5 0 6 0; 6 3 6 0; 7 0 9 0; 8 3 9 0;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4; 4 2 5; 5 3 6; 6 5 6; 7 5 7; 8 6 8; 9 7 8;
START USER TABLE
TABLE 1
UNIT METER KN
PRISMATIC
COLLUMN
1e+09 4e-06 0.001 0.001 0.001 0.001 0.5 0.5
TABLE 2
UNIT METER KN
PRISMATIC
BEAM
0.001 1e+09 0.001 0.001 0.001 0.001 0.5 0.5
END
DEFINE MATERIAL START
ISOTROPIC CONCRETE
E 2.17185e+07
POISSON 0.17
DENSITY 23.5616
ALPHA 1e-05
DAMP 0.05
TYPE CONCRETE
STRENGTH FCU 27579
G 9.28139e+06
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 3 TO 5 7 8 UPTABLE 1 COLLUMN
2 6 9 UPTABLE 2 BEAM
CONSTANTS
MATERIAL CONCRETE ALL
SUPPORTS
1 4 FIXED
DEFINE REFERENCE LOADS
LOAD R1 LOADTYPE Mass  TITLE REF LOAD CASE 1
JOINT LOAD
8 FX 49.035
3 6 FX 98.07
END DEFINE REFERENCE LOADS
FLOOR DIAPHRAGM
DIA 1 TYPE RIG HEI 3
DIA 2 TYPE RIG HEI 6
DIA 3 TYPE RIG HEI 9
LOAD 1 LOADTYPE None  TITLE RS_X
SPECTRUM SRSS IS1893 2015-P4 X 0.024 DAMP 0.05 RSMIN 2.75
SOIL TYPE 3
PERFORM ANALYSIS PRINT ALL
PRINT MODE SHAPES
PRINT ANALYSIS RESULTS
FINISH

STAAD.Pro Output

               CALCULATED FREQUENCIES FOR LOAD CASE       1
       MODE            FREQUENCY(CYCLES/SEC)         PERIOD(SEC)
         1                       0.229                  4.36810
         2                       0.625                  1.59884
         3                       0.854                  1.17043
   ***NOTE: Response Spectrum Analysis for IS1893 (Part-4): 2015 should be carried
   out with P-Delta Analysis as per 10.3
 1893 RESPONSE SPECTRUM LOAD     1 
     RESPONSE LOAD CASE      1
            MODAL WEIGHT (MODAL MASS TIMES g) IN KN           GENERALIZED
      MODE           X             Y             Z              WEIGHT
         1       2.276565E+02  0.000000E+00  0.000000E+00    1.471050E+02
         2       1.634500E+01  0.000000E+00  0.000000E+00    1.471050E+02
         3       1.173519E+00  0.000000E+00  0.000000E+00    1.471051E+02
     SRSS          MODAL COMBINATION METHOD USED.
     DYNAMIC WEIGHT X Y Z   2.451750E+02  0.000000E+00  0.000000E+00 KN  
     MISSING WEIGHT X Y Z  -3.177131E-06  0.000000E+00  0.000000E+00 KN  
       MODAL WEIGHT X Y Z   2.451750E+02  0.000000E+00  0.000000E+00 KN  
     RESPONSE LOAD CASE     1
        MODE    SPECTRAL ACCELERATION       DESIGN   SEISMIC   COEFFICIENT
        ----    ---------------------     ------------------------------
                                              X           Y           Z
          1           0.38232                0.0092      0.0000      0.0000
          2           1.04451                0.0251      0.0000      0.0000
          3           1.42683                0.0342      0.0000      0.0000
      STAAD SPACE                                              -- PAGE NO.    6
 PEAK STORY SHEAR 
        STORY           LEVEL IN METE                    PEAK STORY SHEAR IN  KN  
        -----           -------------           -------------------------------------------------- 
                                                  X                  Y                  Z
          3                   9.00               0.71               0.00               0.00
          2                   6.00               1.59               0.00               0.00
          1                   3.00               2.13               0.00               0.00
        BASE                  0.00               2.13               0.00               0.00
   RESPONSE SPECTRUM VALUES - UNITS ( METE SECOND )
   ------------------------
           DIRECTIONAL VALUES:                 SCALE FACTOR =    1.00
    X =  0.02   Y =  0.00   Z =  0.00          DAMPING FACTOR = 0.050
           PERIOD  VS.  ACCELERATION
           4.3681           3.7492
           1.5988          10.2431
           1.1704          13.9924
           MODE                 ACCELERATION-G     DAMPING
           ----                 --------------     -------
              1                      0.38232       0.05000
              2                      1.04451       0.05000
              3                      1.42683       0.05000
      STAAD SPACE                                              -- PAGE NO.    7
 MODAL BASE ACTIONS 
  MODAL BASE ACTIONS        FORCES IN KN   LENGTH IN METE
  -----------------------------------------------------------
                                                             MOMENTS ARE ABOUT THE ORIGIN
   MODE     PERIOD        FX          FY          FZ          MX          MY          MZ
      1      4.368        2.09        0.00        0.00        0.00        0.00      -12.53
      2      1.599        0.41        0.00        0.00        0.00        0.00        1.23
      3      1.170        0.04        0.00        0.00        0.00        0.00       -0.24
 PARTICIPATION FACTORS 
           MASS  PARTICIPATION FACTORS IN PERCENT         BASE SHEAR IN KN  
           --------------------------------------         ------------------
 MODE    X     Y     Z     SUMM-X   SUMM-Y   SUMM-Z       X        Y        Z
   1   92.85  0.00  0.00   92.855    0.000    0.000      2.09     0.00     0.00
   2    6.67  0.00  0.00   99.521    0.000    0.000      0.41     0.00     0.00
   3    0.48  0.00  0.00  100.000    0.000    0.000      0.04     0.00     0.00
                                                    ---------------------------
                                  TOTAL SRSS  SHEAR      2.13     0.00     0.00
                                  TOTAL 10PCT SHEAR      2.13     0.00     0.00
                                  TOTAL ABS   SHEAR      2.54     0.00     0.00
                                  TOTAL CSM   SHEAR      2.13     0.00     0.00
   Minimum Base Shear Per Table 2 IS1893 2015 Part-4:      6.7423 KN  
   NOTE : THE BASE SHEAR (VB) FROM RESPONSE SPECTRUM IS LESS THAN THE
   MINIMUM BASE SHEAR PER TABLE 2. MULTIPLYING FACTOR IS      3.1668