V. IBC 2015 Static Seismic
Calculation of base shear and its distribution along the height for equivalent lateral force method in IBC 2015.
Problem
- Location: Corona, CA, USA (ZIP 92877)
- Site class D (SCLASS 4)
- Long-period transition time = 12s (TL 12)
- Importance factor = 1.0 (I 1.0)
- Response modification factor X = 3 (RX 3)
- Response modification factor Z = 4 (RZ 4)
The seismic weight for each floor is assumed as 200 KN applied as joint weight of 50KN to nodes 2 3 5 6 8 9 11 To 20. Seismic Load as per IBC 2015 specifications are generated along horizontal direction global X. The base shear and its distribution along height reported by STAAD.Pro is verified against hand calculation.
Calculations
ZIP = 92887; Ss = 2.247 & S1 = 0.817
For Site Class D, Fa = 1 (Ss > 1.25) and Fv = 1.5 (S1 > 0.5)
SMS = Ss × Fa = 2.247, SM1 = S1 × Fv = 1.2255
SDS = 2/3 × SMS = 1.498, SD1 = 2/3 × SM1 = 0.817
For concrete moment resisting frames Ct = 0.0466 in metric system & x = 0.9
Height = ha = 16m, Ta = Ct × hax = 0.0466 × 160.9 = 0.565,
Since SD1 = 0.817 > 0.4, Cu = 1.4
Cu × Ta = 1.4 × 0.565 = 0.791
T (from output file) = 1.286, Cu × Ta = 0.791 < 1.286, Tused = 0.791
Csx = SDS/(Rx/I) = 1.498 / (3/1) = 0.49933
Csx lower limit = 0.044 × SDS × I & 0.5 × S1 / (Rx/I),
Csx lower limit = 0.044 × 1.498 × 1 & 0.5 × 0.817 / (3/1)
Csx lower limit = 0.065912 & 0.136166
Csx upper limit = SD1 / (Tused × (Rx/I)) as Tused < TL
Csx upper limit = 0.817 / (0.791 × (3/1)) = 0.34429
Csx used = 0.34429
Seismic Base Shear V = Cs × W = 0.34429 × (200 × 4) = 275.432 KN
Lateral seismic force Fx = Cvx × V where Cvx = Wx × hxk / ∑ Wi × hik
Since Tused = 0.791 sec > 0.5 Sec distribution of Base Shear along story levels would have the value of exponent k linearly interpolated between 1 (less than equal to 0.5 sec) and 2 (greater than equal to 2.5 sec) i.e. power = 1.1455.
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\06 Loading\IBC\IBC 2015 Static Seismic.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 18-May-15
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 4 0; 3 4 4 0; 4 4 0 0; 5 0 8 0; 6 4 8 0; 7 0 0 5; 8 0 4 5;
9 4 4 5; 10 4 0 5; 11 0 8 5; 12 4 8 5; 13 0 12 0; 14 4 12 0; 15 0 12 5;
16 4 12 5; 17 0 16 0; 18 4 16 0; 19 0 16 5; 20 4 16 5;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4; 4 2 5; 5 5 6; 6 6 3; 7 2 8; 8 3 9; 9 5 11; 10 6 12;
11 7 8; 12 8 9; 13 9 10; 14 8 11; 15 11 12; 16 12 9; 17 5 13; 18 6 14;
19 11 15; 20 12 16; 21 13 14; 22 13 15; 23 14 16; 24 15 16; 25 13 17; 26 14 18;
27 15 19; 28 16 20; 29 17 18; 30 17 19; 31 18 20; 32 19 20;
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
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 3 4 6 11 13 14 16 TO 20 25 TO 28 PRIS YD 0.3 ZD 0.3
2 5 7 TO 10 12 15 21 TO 24 29 TO 32 PRIS YD 0.3 ZD 0.25
CONSTANTS
MATERIAL CONCRETE ALL
SUPPORTS
1 4 7 10 FIXED
DEFINE IBC 2015
*DEFINE IBC 2012
ZIP 92887 I 1 RX 3 RZ 4 SCLASS 4 TL 12
JOINT WEIGHT
2 3 5 6 8 9 11 TO 20 WEIGHT 50
*SELFWEIGHT 1
*MEMBER WEIGHT
*2 5 7 TO 10 12 15 UNI 10
LOAD 1 LOADTYPE Seismic TITLE EL-X DIR
IBC LOAD X 1
PERFORM ANALYSIS PRINT LOAD DATA
PRINT ANALYSIS RESULTS
FINISH
STAAD Output
************************************************************ * IBC 2015 SEISMIC LOAD ALONG X : * * CT = 0.047 Cu = 1.400 x = 0.9000 * * TIME PERIODS : * * Ta = 0.565 T = 1.286 Tuser = 0.000 * * TIME PERIOD USED (T) = 0.791 * * Cs LIMITS : LOWER = 0.136 UPPER = 0.344 * * LOAD FACTOR = 1.000 * * DESIGN BASE SHEAR = 1.000 X 0.344 X 800.00 * * = 275.34 KN * ************************************************************ JOINT LATERAL TORSIONAL LOAD - 1 LOAD (KN ) MOMENT (KN -METE) FACTOR - 1.000 ----- ------- --------- 2 FX 5.920 MY 0.000 3 FX 5.920 MY 0.000 8 FX 5.920 MY 0.000 9 FX 5.920 MY 0.000 ----------- ----------- TOTAL = 23.679 0.000 AT LEVEL 4.000 METE 5 FX 13.097 MY 0.000 6 FX 13.097 MY 0.000 11 FX 13.097 MY 0.000 12 FX 13.097 MY 0.000 ----------- ----------- TOTAL = 52.389 0.000 AT LEVEL 8.000 METE 13 FX 20.841 MY 0.000 14 FX 20.841 MY 0.000 15 FX 20.841 MY 0.000 16 FX 20.841 MY 0.000 ----------- ----------- TOTAL = 83.364 0.000 AT LEVEL 12.000 METE 17 FX 28.977 MY 0.000 18 FX 28.977 MY 0.000 19 FX 28.977 MY 0.000 20 FX 28.977 MY 0.000 ----------- ----------- TOTAL = 115.908 0.000 AT LEVEL 16.000 METE