V. NRC 2020 Static Seismic
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 five-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 ductile moment-resisting frame. Each floor (including roof level) has a seismic weight of 840 kN distributed in plan as shown. Floor-to-floor spacing is 3 m. The structure is considered of high importance.
Input parameters:
- Seismic acceleration values Sa(0.2) = 0.5, Sa(0.5) = 0.2, Sa(1.0) = 0.15,
Sa(2.0) = 0.063, Sa(5.0) = 0.04, and Sa(10.0) = 0.03 (
SA1 0.5,SA2 0.2,SA3 0.11,SA4 0.063,SA5 0.04,SA6 0.03) - Importance factor, I = 1.3 (
I 1.3) - Site class B (
SCL 2) - Ductility-related force modification factor Rdx =
4 (
RDX 4) - Ductility-related force modification factor Rdz =
4 (
RDZ 4) - Overstrength-related force modification factor,
Rox = 1.7 (
ROX 1.7) - Overstrength-related force modification factor,
Roz = 1.7 (
ROZ 1.7) - 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 = 840 kN × 5 = 4,200 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):
Ta =
0.075×(hn)3/4 = 0.075 × 153/4 = 0.572
sec
Rayleigh method from output file Tc,x = 0.641 sec, Tc,z = 0.608 sec. Per Cl. 4.1.8.11-3(d)(ii):
1.5 × Ta,x = 0.857 >
Tc,x so Ta,x = Tc,x = 0.641 sec
1.5 × Ta,z = 0.857 >
Tc,z so Ta,z = Tc,z = 0.608 sec
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 = 0.641 s: S(Ta,x) = 0.186 m/s2.
Linearly interpolate the STz between S(0.5) and S(1.0) for Ta,z = 0.608 s: S(Ta,z) = 0.189 m/s2.
Higher mode factor
Linearly interpolating from Table 4.1.8.11 for Mv for Tax, used = 0.641 sec and Taz, used = 0.608 sec:
- 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:
The maximum lateral earthquake force, V, per Cl. 4.1.8.11-2c of NBC 2020:
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) | |||
| 5th (roof) | 840 | 15 | 12,600 | 0.333 | 49.76 | 50.64 |
| 4th | 840 | 12 | 10,080 | 0.267 | 39.80 | 40.51 |
| 3rd | 840 | 9 | 7,560 | 0.200 | 29.85 | 30.38 |
| 2nd | 840 | 6 | 5,040 | 0.133 | 19.90 | 20.26 |
| 1st | 840 | 3 | 2,520 | 0.067 | 9.95 | 10.13 |
| ∑ | 4,200 | 37,800 | 149.3 | 151.9 |
Results
| Parameter | Hand Calculation | STAAD.Pro | Difference | Comments | |
|---|---|---|---|---|---|
| Story shear, X (kN) | 5th | 49.76 | 49.750 | negligible | |
| 4th | 39.80 | 39.800 | none | ||
| 3rd | 29.85 | 29.850 | none | ||
| 2nd | 19.90 | 19.900 | none | ||
| 1st | 9.95 | 9.950 | none | ||
| Story shear, Z (kN) | 5th | 50.64 | 50.634 | negligible | |
| 4th | 40.51 | 40.507 | negligible | ||
| 3rd | 30.38 | 30.380 | none | ||
| 2nd | 20.26 | 20.254 | negligible | ||
| 1st | 10.13 | 10.127 | negligible | ||
| Base shear (kN) | Vx | 149.3 | 149.250 | negligible | |
| Vz | 151.9 | 151.902 | negligible | ||
Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2026\Samples \Verification Models\06 Loading\NRC\NRC 2020 Static Seismic.STD is typically installed with the program.
STAAD
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 24-Sep-25
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; 23 9 3 0; 24 9 0 0;
25 9 3 3; 26 9 0 3; 27 0 6 0; 28 3 6 0; 29 0 6 3; 30 3 6 3; 31 0 6 6; 32 3 6 6;
33 0 6 9; 34 3 6 9; 35 6 6 0; 36 6 6 3; 37 6 6 6; 38 9 6 0; 39 9 6 3; 40 0 9 0;
41 3 9 0; 42 0 9 3; 43 3 9 3; 44 0 9 6; 45 3 9 6; 46 0 9 9; 47 3 9 9; 48 6 9 0;
49 6 9 3; 50 6 9 6; 51 9 9 0; 52 9 9 3; 53 0 12 0; 54 3 12 0; 55 0 12 3;
56 3 12 3; 57 0 12 6; 58 3 12 6; 59 0 12 9; 60 3 12 9; 61 6 12 0; 62 6 12 3;
63 6 12 6; 64 9 12 0; 65 9 12 3; 66 0 15 0; 67 3 15 0; 68 0 15 3; 69 3 15 3;
70 0 15 6; 71 3 15 6; 72 0 15 9; 73 3 15 9; 74 6 15 0; 75 6 15 3; 76 6 15 6;
77 9 15 0; 78 9 15 3;
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; 22 17 18; 23 17 19; 24 19 20; 25 19 21; 26 21 22;
27 17 23; 28 19 25; 30 23 24; 31 23 25; 32 25 26; 33 2 27; 34 3 28; 35 6 29;
36 7 30; 37 10 31; 38 11 32; 39 14 33; 40 15 34; 41 17 35; 42 19 36; 43 21 37;
44 23 38; 45 25 39; 46 27 28; 47 27 29; 48 28 30; 49 29 30; 50 29 31; 51 30 32;
52 31 32; 53 31 33; 54 32 34; 55 33 34; 56 28 35; 57 30 36; 58 32 37; 59 35 36;
60 36 37; 61 35 38; 62 36 39; 63 38 39; 64 27 40; 65 28 41; 66 29 42; 67 30 43;
68 31 44; 69 32 45; 70 33 46; 71 34 47; 72 35 48; 73 36 49; 74 37 50; 75 38 51;
76 39 52; 77 40 41; 78 40 42; 79 41 43; 80 42 43; 81 42 44; 82 43 45; 83 44 45;
84 44 46; 85 45 47; 86 46 47; 87 41 48; 88 43 49; 89 45 50; 90 48 49; 91 49 50;
92 48 51; 93 49 52; 94 51 52; 95 40 53; 96 41 54; 97 42 55; 98 43 56; 99 44 57;
100 45 58; 101 46 59; 102 47 60; 103 48 61; 104 49 62; 105 50 63; 106 51 64;
107 52 65; 108 53 54; 109 53 55; 110 54 56; 111 55 56; 112 55 57; 113 56 58;
114 57 58; 115 57 59; 116 58 60; 117 59 60; 118 54 61; 119 56 62; 120 58 63;
121 61 62; 122 62 63; 123 61 64; 124 62 65; 125 64 65; 126 53 66; 127 54 67;
128 55 68; 129 56 69; 130 57 70; 131 58 71; 132 59 72; 133 60 73; 134 61 74;
135 62 75; 136 63 76; 137 64 77; 138 65 78; 139 66 67; 140 66 68; 141 67 69;
142 68 69; 143 68 70; 144 69 71; 145 70 71; 146 70 72; 147 71 73; 148 72 73;
149 67 74; 150 69 75; 151 71 76; 152 74 75; 153 75 76; 154 74 77; 155 75 78;
156 77 78;
DEFINE MATERIAL START
ISOTROPIC CONCRETE
E 2.17185e+07
POISSON 0.17
DENSITY 23.5616
ALPHA 1e-05
DAMP 0.05
G 9.28139e+06
TYPE CONCRETE
STRENGTH FCU 27579
END DEFINE MATERIAL
MEMBER PROPERTY
1 TO 28 30 TO 156 PRIS YD 0.4 ZD 0.4
CONSTANTS
MATERIAL CONCRETE ALL
SUPPORTS
1 4 5 8 9 12 13 16 18 20 22 24 26 FIXED
DEFINE NRC 2020 LOAD
SA1 0.5 SA2 0.2 SA3 0.15 SA4 0.063 I 1.3 SCL 2 RDX 4 RDZ 4 ROX 1.7 ROZ 1.7 -
SA5 0.04 SA6 0.03 STX 1 STZ 1 MD 1
JOINT WEIGHT
2 3 17 23 27 28 35 38 40 41 48 51 53 54 61 64 66 67 74 77 WEIGHT 40
6 7 19 25 29 30 36 39 42 43 49 52 55 56 62 65 68 69 75 78 WEIGHT 60
10 11 21 31 32 37 44 45 50 57 58 63 70 71 76 WEIGHT 80
14 15 33 34 46 47 59 60 72 73 WEIGHT 100
LOAD 1 LOADTYPE Seismic-H TITLE SS - X
NRC LOAD X 1
LOAD 2 LOADTYPE Seismic-H TITLE SS - Z
NRC LOAD Z 1
PERFORM ANALYSIS PRINT LOAD DATA
FINISH
Output
*****************************************************************************
* *
* EQUIV. SEISMIC LOADS AS PER NATIONAL BUILDING CODE OF CANADA 2020 ALONG X *
* CT = 0.075 Ta = 0.572 SEC. Tc = 0.641 SEC. *
* T USED = 0.641 SEC. DESIGN SPECTRAL ACCELERATION = 0.185879 *
* EQUIVALENT LATERAL SEISMIC FORCE (ELASTIC RESPONSE) *
* = 0.036 X 4200.000 = 149.250 KN *
* DESIGN BASE SHEAR = 1.000 X 149.250 *
* = 149.250 KN *
* *
*****************************************************************************
*****************************************************************************
* *
* EQUIV. SEISMIC LOADS AS PER NATIONAL BUILDING CODE OF CANADA 2020 ALONG Z *
* CT = 0.075 Ta = 0.572 SEC. Tc = 0.608 SEC. *
* T USED = 0.608 SEC. DESIGN SPECTRAL ACCELERATION = 0.189181 *
* EQUIVALENT LATERAL SEISMIC FORCE (ELASTIC RESPONSE) *
* = 0.036 X 4200.000 = 151.902 KN *
* DESIGN BASE SHEAR = 1.000 X 151.902 *
* = 151.902 KN *
* *
*****************************************************************************
JOINT LATERAL TORSIONAL LOAD - 1
LOAD (KN ) MOMENT (KN -METE) FACTOR - 1.000
----- ------- ---------
2 FX 0.474 MY 0.000
3 FX 0.474 MY 0.000
6 FX 0.711 MY 0.000
7 FX 0.711 MY 0.000
10 FX 0.948 MY 0.000
11 FX 0.948 MY 0.000
14 FX 1.185 MY 0.000
15 FX 1.185 MY 0.000
17 FX 0.474 MY 0.000
19 FX 0.711 MY 0.000
21 FX 0.948 MY 0.000
STAAD SPACE -- PAGE NO. 5
23 FX 0.474 MY 0.000
25 FX 0.711 MY 0.000
----------- -----------
TOTAL = 9.950 0.000 AT LEVEL 3.000 METE
27 FX 0.948 MY 0.000
28 FX 0.948 MY 0.000
29 FX 1.421 MY 0.000
30 FX 1.421 MY 0.000
31 FX 1.895 MY 0.000
32 FX 1.895 MY 0.000
33 FX 2.369 MY 0.000
34 FX 2.369 MY 0.000
35 FX 0.948 MY 0.000
36 FX 1.421 MY 0.000
37 FX 1.895 MY 0.000
38 FX 0.948 MY 0.000
39 FX 1.421 MY 0.000
----------- -----------
TOTAL = 19.900 0.000 AT LEVEL 6.000 METE
40 FX 1.421 MY 0.000
41 FX 1.421 MY 0.000
42 FX 2.132 MY 0.000
43 FX 2.132 MY 0.000
44 FX 2.843 MY 0.000
45 FX 2.843 MY 0.000
46 FX 3.554 MY 0.000
47 FX 3.554 MY 0.000
48 FX 1.421 MY 0.000
49 FX 2.132 MY 0.000
50 FX 2.843 MY 0.000
51 FX 1.421 MY 0.000
52 FX 2.132 MY 0.000
----------- -----------
TOTAL = 29.850 0.000 AT LEVEL 9.000 METE
53 FX 1.895 MY 0.000
54 FX 1.895 MY 0.000
55 FX 2.843 MY 0.000
56 FX 2.843 MY 0.000
57 FX 3.790 MY 0.000
58 FX 3.790 MY 0.000
59 FX 4.738 MY 0.000
60 FX 4.738 MY 0.000
61 FX 1.895 MY 0.000
62 FX 2.843 MY 0.000
63 FX 3.790 MY 0.000
64 FX 1.895 MY 0.000
65 FX 2.843 MY 0.000
----------- -----------
TOTAL = 39.800 0.000 AT LEVEL 12.000 METE
66 FX 2.369 MY 0.000
67 FX 2.369 MY 0.000
68 FX 3.554 MY 0.000
STAAD SPACE -- PAGE NO. 6
69 FX 3.554 MY 0.000
70 FX 4.738 MY 0.000
71 FX 4.738 MY 0.000
72 FX 5.923 MY 0.000
73 FX 5.923 MY 0.000
74 FX 2.369 MY 0.000
75 FX 3.554 MY 0.000
76 FX 4.738 MY 0.000
77 FX 2.369 MY 0.000
78 FX 3.554 MY 0.000
----------- -----------
TOTAL = 49.750 0.000 AT LEVEL 15.000 METE
JOINT LATERAL TORSIONAL LOAD - 2
LOAD (KN ) MOMENT (KN -METE) FACTOR - 1.000
----- ------- ---------
2 FZ 0.482 MY 0.000
3 FZ 0.482 MY 0.000
6 FZ 0.723 MY 0.000
7 FZ 0.723 MY 0.000
10 FZ 0.964 MY 0.000
11 FZ 0.964 MY 0.000
14 FZ 1.206 MY 0.000
15 FZ 1.206 MY 0.000
17 FZ 0.482 MY 0.000
19 FZ 0.723 MY 0.000
21 FZ 0.964 MY 0.000
23 FZ 0.482 MY 0.000
25 FZ 0.723 MY 0.000
----------- -----------
TOTAL = 10.127 0.000 AT LEVEL 3.000 METE
27 FZ 0.964 MY 0.000
28 FZ 0.964 MY 0.000
29 FZ 1.447 MY 0.000
30 FZ 1.447 MY 0.000
31 FZ 1.929 MY 0.000
32 FZ 1.929 MY 0.000
33 FZ 2.411 MY 0.000
34 FZ 2.411 MY 0.000
35 FZ 0.964 MY 0.000
36 FZ 1.447 MY 0.000
37 FZ 1.929 MY 0.000
38 FZ 0.964 MY 0.000
39 FZ 1.447 MY 0.000
----------- -----------
TOTAL = 20.254 0.000 AT LEVEL 6.000 METE
40 FZ 1.447 MY 0.000
41 FZ 1.447 MY 0.000
42 FZ 2.170 MY 0.000
43 FZ 2.170 MY 0.000
44 FZ 2.893 MY 0.000
45 FZ 2.893 MY 0.000
STAAD SPACE -- PAGE NO. 7
46 FZ 3.617 MY 0.000
47 FZ 3.617 MY 0.000
48 FZ 1.447 MY 0.000
49 FZ 2.170 MY 0.000
50 FZ 2.893 MY 0.000
51 FZ 1.447 MY 0.000
52 FZ 2.170 MY 0.000
----------- -----------
TOTAL = 30.380 0.000 AT LEVEL 9.000 METE
53 FZ 1.929 MY 0.000
54 FZ 1.929 MY 0.000
55 FZ 2.893 MY 0.000
56 FZ 2.893 MY 0.000
57 FZ 3.858 MY 0.000
58 FZ 3.858 MY 0.000
59 FZ 4.822 MY 0.000
60 FZ 4.822 MY 0.000
61 FZ 1.929 MY 0.000
62 FZ 2.893 MY 0.000
63 FZ 3.858 MY 0.000
64 FZ 1.929 MY 0.000
65 FZ 2.893 MY 0.000
----------- -----------
TOTAL = 40.507 0.000 AT LEVEL 12.000 METE
66 FZ 2.411 MY 0.000
67 FZ 2.411 MY 0.000
68 FZ 3.617 MY 0.000
69 FZ 3.617 MY 0.000
70 FZ 4.822 MY 0.000
71 FZ 4.822 MY 0.000
72 FZ 6.028 MY 0.000
73 FZ 6.028 MY 0.000
74 FZ 2.411 MY 0.000
75 FZ 3.617 MY 0.000
76 FZ 4.822 MY 0.000
77 FZ 2.411 MY 0.000
78 FZ 3.617 MY 0.000
----------- -----------
TOTAL = 50.634 0.000 AT LEVEL 15.000 METE