# V.IBC 2018 Static Seismic T 1.2

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.

### Plan View

Assumptions

1. Mapped MCER spectral response acceleration parameter at short period, Ss = 2.02
2. Mapped MCER spectral response acceleration parameter at a period of 1 s, S1 = 0.795
3. Risk Category – I (Hence, From Table 1.5-2, Importance Factor I = 1)
4. Site Class – D (SCLASS 4)
5. Response Modification Factor (RX & RZ) = 3
6. Long-period Transition Time (TL)=12 s
7. Seismic weight is composed of UDLs (magnitude -5 kN/m, direction GY) (defined in Reference Load Definition), incident on the beams
8. Time Period of the Structure in both directions (PX & PZ) = 1.2 s
9. Time period coefficients, CTX = CTZ = 0.28
10. Exponents in time period equation: XX = XZ = 1
11. 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 natural period of the structure, TN = 1.2 s (TX 1.2, provides as user input).

Height of the structure, h = 9 m.

So the approximate time period, Ta = Ct×hx = 0.28(9m)1.0 = 2.52 s

From Table 12.8-1, Cu = 1.4 (for SD1 > 0.4).

Cu × Ta = 3.528 s

The time period used, TR , is the lesser of TN and Cu×Ta , which is 1.2 s (< TL = 12 s).

 $( C s ) max = S D 1 T × ( R / I ) = 0.25028$ Eq. 12.8-3

 (CS)min1 = 0.044 × SDS × I = 0.059 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 = 1.5× 0.2503 = 0.3754

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 = 0.3754 × 1,035 = 388.56 kN

Vertical Distribution of Lateral Forces

Since, time period of the structure T = 1.2 s > 0.5 s and T < 2.5 s, as per clause 12.8.3, value of k needs to be linearly interpolated.

k = 1.35

Hence, from equation 12.8-11 and equation 12.8-12, we can find the lateral forces in different story levels, as follows:

Table 1. Vertical force distribution
Story Level Wx

(kN)

hx

(m)

Wx×hx k $W x × h x k ∑ i = 1 3 ( W i × h i k )$ Lateral force at story level

(kN)

Roof 5 × 3 × 23 = 345 9 6,700 0.554 1.5×143.48 = 215.22
2nd 345 6 3,875 0.320 1.5×82.999 = 124.50
1st 345 3 1,520 0.126 1.5×32.560 = 48.840
Σ 1,035 - 12,095 1 388.56

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

where
 Lz = the dimension of the structure along the global Z axis

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 = 215.20 × 0.467 = 100.51 kN·m

Total Torsional moment at 2nd floor level = F2nd × e2 = 124.50 × 0.440 = 54.779 kN·m

Total torsional moment at 1st floor level = F1st × e1 = 48.84 × 0.396 = 12.893 kN·m

## Results

Table 2. Comparison of results
Base shear, V (kN) 388.56 388.56 none
Lateral force at roof level (kN) 215.22 215.220 none
Lateral force at 2nd floor (kN) 124.50 124.497 negligible
Lateral force at 1st floor (kN) 48.84 48.839 negligible
Torsional moment at roof level (kN·m) 100.51 100.544 negligible
Torsional moment at 2nd floor (kN·m) 54.779 54.739 negligible
Torsional moment at 1st floor (kN·m) 19.340 19.312 negligible

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\06 Loading\IBC\IBC 2018 Static Seismic T 1.STD is typically installed with the program.

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
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
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 CTX 0.28 CTZ 0.28 PX 1.2 PZ 1.2 TL -
12 XX 1 XZ 1
IBC LOAD X 1 DEC 2 ACC 0.05
PRINT DIA CR
FINISH

*****************************************************************************
* 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                                                *
*****************************************************************************
74. IBC LOAD X 1 DEC 2 ACC 0.05
75. 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
-----------
************************************************************
*  IBC 2018 SEISMIC LOAD ALONG X  :                        *
*     CT =  0.280 Cu =  1.400 x =  1.0000                  *
*  TIME PERIODS :                                          *
*     Ta =  2.520 T =  1.200 Tuser = 1.200                 *
*  TIME PERIOD USED (T) =  1.200                           *
*  Cs LIMITS : LOWER =  0.133 UPPER =  0.375               *
*  LOAD FACTOR          =  1.000                           *
*  DESIGN BASE SHEAR    =  1.000 X  0.375 X      1035.00   *
*                       =       388.56  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        3.185    MY        1.260
3     FX        3.185    MY        1.260
6     FX        4.247    MY        1.679
7     FX        4.247    MY        1.679
10     FX        4.247    MY        1.679
11     FX        4.247    MY        1.679
14     FX        2.123    MY        0.840
15     FX        2.123    MY        0.840
17     FX        2.123    MY        0.840
19     FX        4.247    MY        1.679
21     FX        3.185    MY        1.260
25     FX        2.123    MY        0.840
27     FX        2.123    MY        0.840
73     FX        2.123    MY        0.840
75     FX        3.185    MY        1.260
77     FX        2.123    MY        0.840
-----------        -----------
TOTAL =     48.839             19.312 AT LEVEL     3.000 METE
33     FX        8.119    MY        3.570
34     FX        8.119    MY        3.570
35     FX       10.826    MY        4.760
36     FX       10.826    MY        4.760
37     FX       10.826    MY        4.760
38     FX       10.826    MY        4.760
39     FX        5.413    MY        2.380
40     FX        5.413    MY        2.380
41     FX        5.413    MY        2.380
42     FX       10.826    MY        4.760
43     FX        8.119    MY        3.570
45     FX        5.413    MY        2.380
46     FX        5.413    MY        2.380
80     FX        5.413    MY        2.380
81     FX        8.119    MY        3.570
82     FX        5.413    MY        2.380
-----------        -----------
TOTAL =    124.497             54.739 AT LEVEL     6.000 METE
49     FX       14.036    MY        6.557
50     FX       14.036    MY        6.557
51     FX       18.715    MY        8.743
52     FX       18.715    MY        8.743
53     FX       18.715    MY        8.743
54     FX       18.715    MY        8.743
55     FX        9.357    MY        4.371
56     FX        9.357    MY        4.371
57     FX        9.357    MY        4.371
58     FX       18.715    MY        8.743
59     FX       14.036    MY        6.557
70     FX        9.357    MY        4.371
71     FX        9.357    MY        4.371
84     FX        9.357    MY        4.371
85     FX       14.036    MY        6.557
86     FX        9.357    MY        4.371
STAAD SPACE                                              -- PAGE NO.    6
-----------        -----------
TOTAL =    215.220            100.544 AT LEVEL     9.000 METE
************ END OF DATA FROM INTERNAL STORAGE ************
76. 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
************************************************************