V.IBC 2018 Static Seismic T Less Than 0.5
Verify the program-calculated base shear and its distribution along the height of a three-story frame by using the equivalent lateral force method per IBC 2018. Also, verify the torsional moments to which the floors are subjected to, considering inherent as well as accidental torsion.
Details
A three-story structure is subject to a seismic load from the +X direction. The time period of the structure used is its calculated Rayleigh frequency (taken from STAAD.Pro output).
Assumptions
- Mapped MCER spectral response acceleration parameter at short period, Ss = 2.02
- Mapped MCER spectral response acceleration parameter at a period of 1 s, S1 = 0.795
- Risk Category – I (Hence, From Table 1.5-2, Importance Factor I = 1)
- Site Class – D (SCLASS 4)
- Response Modification Factor (RX & RZ) = 3
- Long-period Transition Time (TL)=12 s
- Seismic weight is composed of UDLs (magnitude -5 kN/m, direction GY) (defined in Reference Load Definition), incident on the beams
- The effect of shear deformation is neglected
Validation
Calculation of Base Shear
Based on Ss and S1, Fa = 1 (per table 11.4-1) and Fv = 1.7 (per table 11.4-2).
Hence:
| SMS = Fa x Ss = 1 x 2.02 = 2.02 | Eq. 11.4-1 |
| SDS = 2/3 × SMS = 1.347 | Eq. 11.4-3 |
| SM1 = Fv x S1 = 1.7 x 0.795 = 1.382 | Eq. 11.4-3 |
| SD1 = 2/3 × SM1 = 0.901 | Eq. 11.4-4 |
| Eq. 12.8-2 |
The time period of the structure is taken as the Rayleigh frequency of the structure (taken from the output file), TR = 0.201 s.
Height of the structure, h = 9 m.
For concrete moment-resisting frames, Ct = 0.0466 and x = 0.9 (per Table 12.8-2).
So the approximate time period, Ta = Ct×hx = 0.0466(9 m)0.9 = 0.3367 s
From Table 12.8-1, Cu = 1.4 (for SD1 > 0.4).
Cu × Ta = 0.4713 s
The time period used, T, is the lesser of TR and Cu×Ta , which is 0.201 s (< TL = 12 s).
| Eq. 12.8-3 |
|
(CS)min1 = 0.044 × SDS × I = 0.0592 | Eq. 12.8-5 |
Since S1 = 0.795 > 0.6g, equation 12.8-6 also needs to be considered for calculating the lower limit of Cs :
| Eq. 12.8-6 |
Therefore, (Cs)min = 0.1325 < Cs.
Cs = 0.4489
The seismic weight, W is taken as the total seismic weight of the beams: = 5 × 3 × 69 = 1,035 kN
So the total base shear, V = CS × W = 0.4489 × 1,035 = 464.6 kN
Vertical Distribution of Lateral Forces
Since, time period of the structure T = 0.201 s < 0.5 s, as per clause 12.8.3, k = 1.
Hence, from equation 12.8-11 and equation 12.8-12, we can find the lateral forces in different story levels, as follows:
| Story Level |
Wx
(kN) |
hx
(m) |
Wx×hx k | Lateral force at story level (kN) |
|
|---|---|---|---|---|---|
| Roof | 5 × 3 × 23 = 345 | 9 | 3,105 | 0.500 | 232.3 |
| 2nd | 345 | 6 | 2,070 | 0.333 | 154.9 |
| 1st | 345 | 3 | 1,035 | 0.167 | 77.40 |
| Σ | 1,035 | - | 6,210 | 1 | 464.6 |
Consideration of Inherent Torsion (Clause 12.8.4.1)
Floor Level – Roof (9 m)
From output file, CRZ = 3. 831 m and CMZ = 3.848 m
Hence, static eccentricity esi = CMZ - CRZ = 0.017 m
Floor Level – 2nd (6 m)
From output file , CRZ = 3.858 m and CMZ = 3.848 m
Hence, static eccentricity esi = CMZ - CRZ = -0.01 m
Floor Level – 1st (3 m)
From output file , CRZ = 3.902 m and CMZ = 3.848 m
Hence, static eccentricity esi = CMZ - CRZ = -0.054 m
Consideration of Accidental Torsion (Clause 12.8.4.2)
At all floor levels:
| 0.05 × Lz = 0.05 × 9m = 0.45 m |
| = |
Hence, total eccentricity to inherent and accidental torsion at roof level er = (0.45 + 0.017) = 0.467 m
Total eccentricity to inherent and accidental torsion at 2nd floor level e2 = (0.45 - 0.01) = 0.44 m
Total eccentricity to inherent and accidental torsion at 1st floor level e1 = (0.45 - 0.054) = 0.396 m
Total torsional moment at roof level = Froof × er = 232.3 x 0.467 = 108.48 kN·m
Total Torsional moment at 2nd floor level = F2nd × e2 = 154.867 x 0.44 = 68.141 kN·m
Total torsional moment at 1st floor level = F1st × e1 = 77.433 x 0.396 = 30.664 kN·m
Results
| Result Type | Reference | STAAD.Pro | Difference | Comments |
|---|---|---|---|---|
| Base shear, V (kN) | 464.6 | 464.6 | none | |
| Lateral force at roof level (kN) | 232.3 | 232.3 | negligible | |
| Lateral force at 2nd floor (kN) | 154.9 | 154.867 | negligible | |
| Lateral force at 1st floor (kN) | 77.4 | 77.433 | negligible | |
| Torsional moment at roof level (kN·m) | 108.48 | 108.523 | negligible | |
| Torsional moment at 2nd floor (kN·m) | 68.141 | 68.092 | negligible | |
| Torsional moment at 1st floor (kN·m) | 30.664 | 30.619 | negligible |
STAAD.Pro Input File
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\06 Loading\IBC\IBC 2018 Static Seismic T Less Than 0.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 08-Mar-19
END JOB INFORMATION
*****************************************************************************
*This problem is created to verify the base shear, distribution of base shear
*And Inherent and Accidental Torsional Moment at different floor levels
*Of the Structure
*****************************************************************************
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 0 3; 6 0 3 3; 7 3 3 3; 8 3 0 3;
9 0 0 6; 10 0 3 6; 11 3 3 6; 12 3 0 6; 13 0 0 9; 14 0 3 9; 15 3 3 9; 16 3 0 9;
17 6 3 0; 18 6 0 0; 19 6 3 3; 20 6 0 3; 21 6 3 6; 22 6 0 6; 25 9 3 3; 26 9 0 3;
27 9 3 6; 28 9 0 6; 33 0 6 0; 34 3 6 0; 35 0 6 3; 36 3 6 3; 37 0 6 6; 38 3 6 6;
39 0 6 9; 40 3 6 9; 41 6 6 0; 42 6 6 3; 43 6 6 6; 45 9 6 3; 46 9 6 6; 49 0 9 0;
50 3 9 0; 51 0 9 3; 52 3 9 3; 53 0 9 6; 54 3 9 6; 55 0 9 9; 56 3 9 9; 57 6 9 0;
58 6 9 3; 59 6 9 6; 70 9 9 3; 71 9 9 6; 72 -3 0 0; 73 -3 3 0; 74 -3 0 3;
75 -3 3 3; 76 -3 0 6; 77 -3 3 6; 80 -3 6 0; 81 -3 6 3; 82 -3 6 6; 84 -3 9 0;
85 -3 9 3; 86 -3 9 6;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4; 4 2 6; 5 3 7; 6 5 6; 7 6 7; 8 7 8; 9 6 10; 10 7 11;
11 9 10; 12 10 11; 13 11 12; 14 10 14; 15 11 15; 16 13 14; 17 14 15; 18 15 16;
19 3 17; 20 7 19; 21 11 21; 23 17 18; 24 17 19; 25 19 20; 26 19 21; 27 21 22;
30 19 25; 31 21 27; 32 25 26; 33 25 27; 34 27 28; 40 2 33; 41 3 34; 42 6 35;
43 7 36; 44 10 37; 45 11 38; 46 14 39; 47 15 40; 48 17 41; 49 19 42; 50 21 43;
52 25 45; 53 27 46; 56 33 34; 57 33 35; 58 34 36; 59 35 36; 60 35 37; 61 36 38;
62 37 38; 63 37 39; 64 38 40; 65 39 40; 66 34 41; 67 36 42; 68 38 43; 70 41 42;
71 42 43; 73 42 45; 74 43 46; 75 45 46; 79 33 49; 80 34 50; 81 35 51; 82 36 52;
83 37 53; 84 38 54; 85 39 55; 86 40 56; 87 41 57; 88 42 58; 89 43 59; 95 49 50;
96 49 51; 97 50 52; 98 51 52; 99 51 53; 100 52 54; 101 53 54; 102 53 55;
103 54 56; 104 55 56; 105 50 57; 106 52 58; 107 54 59; 109 57 58; 110 58 59;
128 45 70; 129 46 71; 132 58 70; 133 59 71; 134 70 71; 135 2 73; 136 6 75;
137 10 77; 139 33 80; 140 35 81; 141 37 82; 143 49 84; 144 51 85; 145 53 86;
147 72 73; 148 73 75; 149 74 75; 150 75 77; 151 76 77; 154 73 80; 155 75 81;
156 77 82; 158 80 81; 159 81 82; 161 80 84; 162 81 85; 163 82 86; 165 84 85;
166 85 86;
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 TO 21 23 TO 27 30 TO 34 40 TO 50 52 53 56 TO 68 70 71 73 TO 75 79 TO 89 -
95 TO 107 109 110 128 129 132 TO 137 139 TO 141 143 TO 145 147 TO 151 154 -
155 TO 156 158 159 161 TO 163 165 166 PRIS YD 0.4 ZD 0.4
CONSTANTS
MATERIAL CONCRETE ALL
SUPPORTS
1 4 5 8 9 12 13 16 18 20 22 26 28 72 74 76 FIXED
DEFINE REFERENCE LOADS
LOAD R1 LOADTYPE Mass TITLE REF LOAD CASE 1
MEMBER LOAD
2 4 5 7 9 10 12 14 15 17 19 TO 21 24 26 30 31 33 56 TO 68 70 71 73 TO 75 95 -
96 TO 107 109 110 132 TO 137 139 TO 141 143 TO 145 148 150 158 159 165 -
166 UNI GY -5
END DEFINE REFERENCE LOADS
FLOOR DIAPHRAGM
DIA 1 TYPE RIG HEI 3
DIA 2 TYPE RIG HEI 6
DIA 3 TYPE RIG HEI 9
DEFINE IBC 2018
SS 2.02 S1 0.795 I 1 RX 3 RZ 3 SCLASS 4 TL 12
LOAD 1 LOADTYPE Seismic TITLE SL +X
IBC LOAD X 1 DEC 2 ACC 0.05
PERFORM ANALYSIS PRINT LOAD DATA
PRINT DIA CR
FINISH
STAAD.Pro Output
***************************************************************************** * EQUIV. SEISMIC LOADS AS PER IBC 2018 * * PARAMETERS CONSIDERED FOR SUBSEQUENT LOAD GENERATION * * SS = 2.020 S1 = 0.795 FA = 1.000 FV = 1.700 * * SDS = 1.347 SD1 = 0.901 * ***************************************************************************** 72. LOAD 1 LOADTYPE SEISMIC TITLE SL +X 73. IBC LOAD X 1 DEC 2 ACC 0.05 74. PERFORM ANALYSIS PRINT LOAD DATA P R O B L E M S T A T I S T I C S ----------------------------------- NUMBER OF JOINTS 67 NUMBER OF MEMBERS 117 NUMBER OF PLATES 0 NUMBER OF SOLIDS 0 NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 16 Using 64-bit analysis engine. SOLVER USED IS THE IN-CORE ADVANCED MATH SOLVER TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 162 TOTAL LOAD COMBINATION CASES = 0 SO FAR. STAAD SPACE -- PAGE NO. 4 LOADING 1 LOADTYPE SEISMIC TITLE SL +X ----------- ************************************************************ * IBC 2018 SEISMIC LOAD ALONG X : * * CT = 0.047 Cu = 1.400 x = 0.9000 * * TIME PERIODS : * * Ta = 0.337 T = 0.201 Tuser = 0.000 * * TIME PERIOD USED (T) = 0.201 * * Cs LIMITS : LOWER = 0.133 UPPER = 1.492 * * LOAD FACTOR = 1.000 * * DESIGN BASE SHEAR = 1.000 X 0.449 X 1035.00 * * = 464.60 KN * ************************************************************ ************************************************************************ ***NOTE: SEISMIC LOAD IS ACTING AT CENTER OF MASS FOR RIGID DIAPHRAGM. TORSION FROM STATIC ECCENTRICITY (esi) IS INCLUDED IN ANALYSIS. DYNAMIC ECCENTRICITY APPLIED = DEC - 1 LOAD NO.: 1 DIRECTION : X UNIT - METE STORY LEVEL DYN. ECC. (dec) ACC. ECC. (aec) DESIGN ECC. ----- ----- --------------- --------------- --------------- X Z X Z X Z dec + aec dec + aec 1 3.00 -0.05 -0.05 0.60 0.45 0.00 0.40 2 6.00 0.01 -0.01 0.60 0.45 0.00 0.44 3 9.00 0.05 0.02 0.60 0.45 0.00 0.47 ************************************************************************ JOINT LATERAL TORSIONAL LOAD - 1 LOAD (KN ) MOMENT (KN -METE) FACTOR - 1.000 ----- ------- --------- DEC + AEC STAAD SPACE -- PAGE NO. 5 2 FX 5.050 MY 1.997 3 FX 5.050 MY 1.997 6 FX 6.733 MY 2.663 7 FX 6.733 MY 2.663 10 FX 6.733 MY 2.663 11 FX 6.733 MY 2.663 14 FX 3.367 MY 1.331 15 FX 3.367 MY 1.331 17 FX 3.367 MY 1.331 19 FX 6.733 MY 2.663 21 FX 5.050 MY 1.997 25 FX 3.367 MY 1.331 27 FX 3.367 MY 1.331 73 FX 3.367 MY 1.331 75 FX 5.050 MY 1.997 77 FX 3.367 MY 1.331 ----------- ----------- TOTAL = 77.433 30.619 AT LEVEL 3.000 METE 33 FX 10.100 MY 4.441 34 FX 10.100 MY 4.441 35 FX 13.467 MY 5.921 36 FX 13.467 MY 5.921 37 FX 13.467 MY 5.921 38 FX 13.467 MY 5.921 39 FX 6.733 MY 2.961 40 FX 6.733 MY 2.961 41 FX 6.733 MY 2.961 42 FX 13.467 MY 5.921 43 FX 10.100 MY 4.441 45 FX 6.733 MY 2.961 46 FX 6.733 MY 2.961 80 FX 6.733 MY 2.961 81 FX 10.100 MY 4.441 82 FX 6.733 MY 2.961 ----------- ----------- TOTAL = 154.867 68.092 AT LEVEL 6.000 METE 49 FX 15.150 MY 7.078 50 FX 15.150 MY 7.078 51 FX 20.200 MY 9.437 52 FX 20.200 MY 9.437 53 FX 20.200 MY 9.437 54 FX 20.200 MY 9.437 55 FX 10.100 MY 4.718 56 FX 10.100 MY 4.718 57 FX 10.100 MY 4.718 58 FX 20.200 MY 9.437 59 FX 15.150 MY 7.078 70 FX 10.100 MY 4.718 71 FX 10.100 MY 4.718 84 FX 10.100 MY 4.718 85 FX 15.150 MY 7.078 86 FX 10.100 MY 4.718 STAAD SPACE -- PAGE NO. 6 ----------- ----------- TOTAL = 232.300 108.523 AT LEVEL 9.000 METE ************ END OF DATA FROM INTERNAL STORAGE ************ 75. PRINT DIA CR DIA CR ************************************************************ CENTRE OF RIGIDITY UNIT - METE ------------------ ----------- DIAPHRAM FL. LEVEL X-COORDINATE Z-COORDINATE 1 3.000 2.393 3.902 2 6.000 2.335 3.858 3 9.000 2.299 3.831 ************************************************************