V. NRC 2020 Static Seismic with Torsional Moment
Calculation of base shear and its distribution along the height for equivalent static force method in NBCC/NRC 2020.
References
- National Research Council Canada. National Building Code of Canada 2020. Fifteenth Edition, 2020. Canadian Commission on Building and Fire Codes.
Details
A three-story, concrete structure is subject to seismic loads as calculated by the static seismic method in Division B, Part 4 of NRC 2020 [1].
The SFRS is a conventional construction, moment-resisting frame. Each floor (including roof level) has a seismic weight of 345 kN distributed uniformaly across the floor. Floor-to-floor spacing is 3 m. The structure is considered of high importance.
Use a dynamic eccentricity factor of 2 and an accidental eccentricity factor of 5% of the plan dimension (0.05).
- Seismic acceleration values Sa(0.2) = 0.28 m/s2, Sa(0.5) = 0.17
m/s2, Sa(1.0) = 0.11 m/s2, Sa(2.0) = 0.063
m/s2, Sa(5.0) = 0.04 m/s2, and Sa(10.0) = 0.03
m/s2 (
SA1 0.28,SA2 0.17,SA3 0.11,SA4 0.063,SA5 0.04,SA6 0.03) - Importance factor, I = 1.3 (
I 1.3) - Site class C (
SCL 3) - Ductility-related force modification factor Rdx =
1.5 (
RDX 1.5) - Ductility-related force modification factor Rdz =
1.5 (
RDZ 1l5) - Overstrength-related force modification factor,
Rox = 1.3 (
ROX 1.3) - Overstrength-related force modification factor,
Roz = 1.3 (
ROZ 1.3) - Moment resisting frames in both X and Z directions
(
STX 1,STZ 1) - Provisions to be checked for member strength (
MD 1)
Calculations
Calculations
Weight of the structure, W = 345 kN × 3 = 1,035 kN
Fundamental period
Fundamental lateral period, Ta, as per clause 4.1.8.11-3 of NBC 2020 for concrete moment frames (same in X and Z directions):
Rayleigh method from output file Tc,x = 0.206 sec, Tc,z = 0.211 sec. Per Cl. 4.1.8.11-3(d)(ii):
Design spectral acceleration
Calculate the design spectral accelaration, S(T), from Table 4.1.8.4-C of NBC 2020:
Linearly interpolate the S(Tx) between S(0.5) and S(1.0) for Ta,x = 0.206 sec: S(Ta,x) = 0.278 m/s2.
Linearly interpolate the STz between S(0.5) and S(1.0) for Ta,z = 0.211 sec: S(Ta,z) = 0.276 m/s2.
Higher mode factor
Linearly interpolating from Table 4.1.8.11 for Mv for Ta,x = 0.206 s and Ta,z = 0.211 s:
- Higher mode factor, Mvx = 1
(
MVX 1) - Higher mode factor Mvz = 1
(
MVZ 1)
Lateral earthquake force
Lateral earthquake force, V, in the X direction:
Lateral earthquake force, V, in the Z direction:
The minimum lateral earthquake force, V, per Cl. 4.1.8.11-2b of NBC 2020 (same in X and Z directions):
The maximum lateral earthquake force, V, per Cl. 4.1.8.11-2c of NBC 2020 (same in X and Z directions):
Vertical base shear distribution
Since the fundamental lateral period, Ta < 0.7 s, the portion of the vertical shear concentrated at the top of the building, Ft = 0 per Cl. 4.1.8.11-7(a).
| Story Level | Wi | hi | Wi×hi | (Wi × hi)/∑(Wi × hi) | Fx | Fz |
|---|---|---|---|---|---|---|
| (kN) | (m) | (kN) | (kN) | |||
| 3rd (roof) | 345 | 9 | 3,105 | 0.500 | 64.4 | 64.4 |
| 2nd | 345 | 6 | 2,070 | 0.333 | 42.93 | 42.93 |
| 1st | 345 | 3 | 1,035 | 0.167 | 21.47 | 21.47 |
| ∑ | 1,035 | 6,210 | 128.8 | 128.8 |
Torsional moment
The STAAD.Pro output reports both the center of mass (CM) and center of rigidity (CR) values for each story of the structure. The static eccentricity, SE = CM - CR.
The static eccentricity is then mulitplied by a dynamic factor to obtain the dynamic
eccentricity. This factor is taken as DEC - 1, where
DEC is the multiplying factor for natural torsion given as input
for the static seismic load case. The dynamic eccentricity, DE =
SE×(DEC - 1) = SE×(2-1) = SE.
The accidental eccentricity is obtained by multiplying the story dimension by the accidental torsion factor.
- Accidental torsion along the X direction: AEx = 0.05×Bx = 0.05 (12) = 0.6 m
- Accidental torsion along the Z direction: AEZ = 0.05×BZ = 0.05 (9) = 0.45 m
The total eccentricity due to inherent as well as accidental torsion is the dynamic eccentricity plus the accidental eccentricity. This total eccentricity multiplied by the lateral force at story level gives the total torsional moment in that level.
| Story Level | Center of Mass along Z | Center of Rigidity along Z | Static eccentricity | Dynamic eccentricity | DE + AE | Story force | Torsional moment |
|---|---|---|---|---|---|---|---|
| (m) | (m) | (m) | (m) | (m) | (kN) | (kN·m) | |
| 3 | 3.848 | 3.832 | 0.016 | 0.016 | 0.466 | 64.4 | 30.01 |
| 2 | 3.848 | 3.859 | -0.011 | -0.011 | 0.439 | 42.93 | 18.85 |
| 1 | 3.848 | 3.903 | -0.055 | -0.055 | 0.395 | 21.47 | 8.48 |
| Story Level | Center of Mass along X | Center of Rigidity along X | Static eccentricity | Dynamic eccentricity | DE + AE | Story force | Torsional moment |
|---|---|---|---|---|---|---|---|
| (m) | (m) | (m) | (m) | (m) | (kN) | (kN·m) | |
| 3 | 2.348 | 2.301 | 0.047 | 0.047 | 0.647 | 64.4 | 41.67 |
| 2 | 2.348 | 2.337 | 0.011 | 0.011 | 0.611 | 42.93 | 26.23 |
| 1 | 2.348 | 2.394 | -0.046 | -0.046 | 0.554 | 21.47 | 11.89 |
Results
| Parameter | Hand Calculation | STAAD.Pro | Difference | Comments | |
|---|---|---|---|---|---|
| Story shear, X (kN) | 3rd | 64.4 | 64.400 | none | |
| 2nd | 42.93 | 42.933 | negligible | ||
| 1st | 21.47 | 21.467 | negligible | ||
| Torsional moment, X (kN·m) | 3rd | 30.01 | 29.997 | negligible | |
| 2nd | 18.85 | 18.832 | negligible | ||
| 1st | 8.48 | 8.476 | negligible | ||
| Story shear, Z (kN) | 3rd | 64.4 | 64.400 | none | |
| 2nd | 42.93 | 42.933 | negligible | ||
| 1st | 21.47 | 21.467 | negligible | ||
| Torsional moment, Z (kN·m) | 3rd | 41.67 | 41.654 | negligible | |
| 2nd | 26.23 | 26.238 | negligible | ||
| 1st | 11.89 | 11.898 | negligible | ||
| Base shear (kN) | Vx | 128.8 | 128.800 | none | |
| Vz | 128.8 | 128.800 | none | ||
Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2026\Samples \Verification Models\06 Loading\NRC\NRC 2020 Static Seismic_Torsional Moments.std is typically installed with the program.
STAAD
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 10-OCT-2025
END JOB INFORMATION
INPUT WIDTH 79
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 NRC 2020 LOAD
SA1 0.28 SA2 0.17 SA3 0.11 SA4 0.063 I 1.3 SCL 3 RDX 1.5 RDZ 1.5 ROX 1.3 ROZ -
1.3 SA5 0.04 SA6 0.03 STX 1 STZ 1 MD 1
LOAD 1 LOADTYPE Seismic-H TITLE SL +X
NRC LOAD X 1 DEC 2 ACC 0.05
LOAD 2 LOADTYPE Seismic-H TITLE SL +Z
NRC LOAD Z 1 DEC 2 ACC 0.05
PERFORM ANALYSIS PRINT LOAD DATA
PRINT DIA CR
FINISH
Output
FLOOR DIAPHRAGM
************************************************************************************
FLOOR DIAPHRAGM UNIT - KN METE
--------------- ----------------
NO. TYPE FL. LEVEL FL. WT CENTRE OF MASS CONTROL JOINT NO.
X Z
1 RIGID 3.000 345.00 2.348 3.848 87
2 RIGID 6.000 345.00 2.348 3.848 88
3 RIGID 9.000 345.00 2.348 3.848 89
************************************************************************************
*****************************************************************************
* *
* EQUIV. SEISMIC LOADS AS PER NATIONAL BUILDING CODE OF CANADA 2020 ALONG X *
* CT = 0.075 Ta = 0.390 SEC. Tc = 0.206 SEC. *
* T USED = 0.206 SEC. DESIGN SPECTRAL ACCELERATION = 0.277828 *
* EQUIVALENT LATERAL SEISMIC FORCE (ELASTIC RESPONSE) *
* = 0.124 X 1035.000 = 128.800 KN *
* DESIGN BASE SHEAR = 1.000 X 128.800 *
* = 128.800 KN *
* *
*****************************************************************************
*****************************************************************************
* *
* EQUIV. SEISMIC LOADS AS PER NATIONAL BUILDING CODE OF CANADA 2020 ALONG Z *
* CT = 0.075 Ta = 0.390 SEC. Tc = 0.211 SEC. *
* T USED = 0.211 SEC. DESIGN SPECTRAL ACCELERATION = 0.276089 *
* EQUIVALENT LATERAL SEISMIC FORCE (ELASTIC RESPONSE) *
* = 0.124 X 1035.000 = 128.800 KN *
* DESIGN BASE SHEAR = 1.000 X 128.800 *
* = 128.800 KN *
* *
*****************************************************************************
STAAD SPACE -- PAGE NO. 5
************************************************************************
***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 -0.06 0.60 0.45 0.00 0.39
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
2 FX 1.400 MY 0.553
3 FX 1.400 MY 0.553
6 FX 1.867 MY 0.737
7 FX 1.867 MY 0.737
10 FX 1.867 MY 0.737
11 FX 1.867 MY 0.737
14 FX 0.933 MY 0.369
15 FX 0.933 MY 0.369
17 FX 0.933 MY 0.369
19 FX 1.867 MY 0.737
21 FX 1.400 MY 0.553
25 FX 0.933 MY 0.369
27 FX 0.933 MY 0.369
73 FX 0.933 MY 0.369
75 FX 1.400 MY 0.553
77 FX 0.933 MY 0.369
----------- -----------
TOTAL = 21.467 8.476 AT LEVEL 3.000 METE
33 FX 2.800 MY 1.228
STAAD SPACE -- PAGE NO. 6
34 FX 2.800 MY 1.228
35 FX 3.733 MY 1.638
36 FX 3.733 MY 1.638
37 FX 3.733 MY 1.638
38 FX 3.733 MY 1.638
39 FX 1.867 MY 0.819
40 FX 1.867 MY 0.819
41 FX 1.867 MY 0.819
42 FX 3.733 MY 1.638
43 FX 2.800 MY 1.228
45 FX 1.867 MY 0.819
46 FX 1.867 MY 0.819
80 FX 1.867 MY 0.819
81 FX 2.800 MY 1.228
82 FX 1.867 MY 0.819
----------- -----------
TOTAL = 42.933 18.832 AT LEVEL 6.000 METE
49 FX 4.200 MY 1.956
50 FX 4.200 MY 1.956
51 FX 5.600 MY 2.608
52 FX 5.600 MY 2.608
53 FX 5.600 MY 2.608
54 FX 5.600 MY 2.608
55 FX 2.800 MY 1.304
56 FX 2.800 MY 1.304
57 FX 2.800 MY 1.304
58 FX 5.600 MY 2.608
59 FX 4.200 MY 1.956
70 FX 2.800 MY 1.304
71 FX 2.800 MY 1.304
84 FX 2.800 MY 1.304
85 FX 4.200 MY 1.956
86 FX 2.800 MY 1.304
----------- -----------
TOTAL = 64.400 29.997 AT LEVEL 9.000 METE
************************************************************************
STAAD SPACE -- PAGE NO. 7
***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.: 2 DIRECTION : Z 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 -0.06 0.60 0.45 0.55 0.00
2 6.00 0.01 -0.01 0.60 0.45 0.61 0.00
3 9.00 0.05 0.02 0.60 0.45 0.65 0.00
************************************************************************
JOINT LATERAL TORSIONAL LOAD - 2
LOAD (KN ) MOMENT (KN -METE) FACTOR - 1.000
----- ------- ---------
DEC + AEC
2 FZ 1.400 MY 0.776
3 FZ 1.400 MY 0.776
6 FZ 1.867 MY 1.035
7 FZ 1.867 MY 1.035
10 FZ 1.867 MY 1.035
11 FZ 1.867 MY 1.035
14 FZ 0.933 MY 0.517
15 FZ 0.933 MY 0.517
17 FZ 0.933 MY 0.517
19 FZ 1.867 MY 1.035
21 FZ 1.400 MY 0.776
25 FZ 0.933 MY 0.517
27 FZ 0.933 MY 0.517
73 FZ 0.933 MY 0.517
75 FZ 1.400 MY 0.776
77 FZ 0.933 MY 0.517
----------- -----------
TOTAL = 21.467 11.898 AT LEVEL 3.000 METE
33 FZ 2.800 MY 1.711
34 FZ 2.800 MY 1.711
35 FZ 3.733 MY 2.282
36 FZ 3.733 MY 2.282
37 FZ 3.733 MY 2.282
38 FZ 3.733 MY 2.282
39 FZ 1.867 MY 1.141
40 FZ 1.867 MY 1.141
41 FZ 1.867 MY 1.141
42 FZ 3.733 MY 2.282
43 FZ 2.800 MY 1.711
45 FZ 1.867 MY 1.141
46 FZ 1.867 MY 1.141
80 FZ 1.867 MY 1.141
81 FZ 2.800 MY 1.711
82 FZ 1.867 MY 1.141
STAAD SPACE -- PAGE NO. 8
----------- -----------
TOTAL = 42.933 26.238 AT LEVEL 6.000 METE
49 FZ 4.200 MY 2.717
50 FZ 4.200 MY 2.717
51 FZ 5.600 MY 3.622
52 FZ 5.600 MY 3.622
53 FZ 5.600 MY 3.622
54 FZ 5.600 MY 3.622
55 FZ 2.800 MY 1.811
56 FZ 2.800 MY 1.811
57 FZ 2.800 MY 1.811
58 FZ 5.600 MY 3.622
59 FZ 4.200 MY 2.717
70 FZ 2.800 MY 1.811
71 FZ 2.800 MY 1.811
84 FZ 2.800 MY 1.811
85 FZ 4.200 MY 2.717
86 FZ 2.800 MY 1.811
----------- -----------
TOTAL = 64.400 41.654 AT LEVEL 9.000 METE
************ END OF DATA FROM INTERNAL STORAGE ************
72. PRINT DIA CR
DIA CR
************************************************************
CENTRE OF RIGIDITY UNIT - METE
------------------ -----------
DIAPHRAM FL. LEVEL X-COORDINATE Z-COORDINATE
1 3.000 2.394 3.903
2 6.000 2.337 3.859
3 9.000 2.301 3.832
************************************************************