The Ontario Building Code | Equivalent Static Force Procedure for Structures Satisfying the Conditions of Article 4.1.8.7.
4.1.8.11. Equivalent Static Force Procedure for Structures Satisfying the Conditions of Article 4.1.8.7.
(1) The static loading due to earthquake motion shall be determined according to the procedures given in this Article.
(2) The minimum lateral earthquake force, V, shall be calculated using the formula,
V = S (Ta) MvIEW/ (RdRo)
except,
(a) for walls, coupled walls and wall-frame systems, V shall not be less than,
S (4.0) Mv IEW/ (RdRo)
(b) for moment-resisting frames, braced frames and other systems, V shall not be less than,
S (2.0) Mv IEW/ (RdRo)
(c) for buildingslocated on a site other than Class F and having an SFRS with an Rdequal to or greater than 1.5, V need not be greater than,
(3) The fundamental lateral period, Ta, in the direction under consideration in Sentence (2) shall be determined as,
(a) for moment-resisting frames that resist 100% of the required lateral forces and where the frame is not enclosed by or adjoined by more rigid elements that would tend to prevent the frame from resisting lateral forces, and where hn is in metres,
(i) 0.085 (hn)3/4for steel moment frames,
(ii) 0.075 (hn)3/4for concrete moment frames, or
(iii) 0.1 N for other moment frames,
(b) 0.025 hn for braced frames where hn is in metres,
(c) 0.05 (hn)3/4for shear wall and other structures where hn is in metres, or
(d) other established methods of mechanics using a structural model that complies with the requirements of Sentence 4.1.8.3.(8), except that,
(i) for moment-resisting frames, Ta shall not be taken greater than 1.5 times that determined in Clause (a),
(ii) for braced frames, Tashall not be taken greater than 2.0 times that determined in Clause (b),
(iii) for shear wall structures, Ta shall not be greater than 2.0 times that determined in Clause (c),
(iv) for other structures, Ta shall not be taken greater than that determined in Clause (c), and
(v) for the purpose of calculating the deflections, the period without the upper limit specified in Subclauses (d)(i) to (iv) may be used, except that, for walls, coupled walls and wall-frame systems, Ta shall not exceed 4.0 s, and for moment-resisting frames, braced frames, and other systems, Ta shall not exceed 2.0 s.
(4) The weight, W, of the building shall be calculated using the formula,
(5) The higher mode factor, Mv, and its associated base overturning moment reduction factor, J, shall conform to Table 4.1.8.11.
Table 4.1.8.11.
Higher Mode Factor, Mv, and Base Overturning Reduction Factor, J(1)(2)
Forming Part of Sentence 4.1.8.11.(5)
| Item | Column 1 Sa(0.2)/Sa(2.0) | Column 2 Type of Lateral Resisting System | Column 3 MV For Ta ≤ 1.0 | Column 4 MV For Ta = 2.0 | Column 5 MV For Ta ≥4.0 | Column 6 J For Ta ≤0.5 | Column 7 J For Ta =2.0 | Column 8 J For Ta ≥4.0 |
| 1. |
| Moment-resisting frames | 1.0 | 1.0 | (3) | 1.0 | 0.9 | (3) |
|
|
| Coupled walls(4) | 1.0 | 1.0 | 1.0 | 1.0 | 0.9 | 0.8 |
|
| < 8.0 | Braced frames | 1.0 | 1.0 | (3) | 1.0 | 0.8 | (3) |
|
|
| Walls, wall-frame systems | 1.0 | 1.2 | 1.6 | 1.0 | 0.6 | 0.5 |
|
|
| Other systems(5) | 1.0 | 1.2 | (3) | 1.0 | 0.6 | (3) |
| 2. |
| Moment-resisting frames | 1.0 | 1.2 | (3) | 1.0 | 0.7 | (3) |
|
|
| Coupled walls(4) | 1.0 | 1.2 | 1.2 | 1.0 | 0.7 | 0.6 |
|
| ≥8.0 | Braced frames | 1.0 | 1.5 | (3) | 1.0 | 0.6 | (3) |
|
|
| Walls, wall-frame systems | 1.0 | 2.2 | 3.0 | 1.0 | 0.4 | 0.3 |
|
|
| Other systems(5) | 1.0 | 2.2 | (3) | 1.0 | 0.4 | (3) |
Notes to Table 4.1.8.11.:
(1) For values of Mv between fundamental lateral periods, Ta, of 1.0 s and 2.0 s and between 2.0 s and 4.0 s, the product S(Ta) · Mv shall be obtained by linear interpolation.
(2) Values of J between fundamental lateral periods, Ta, of 0.5 s and 2.0 s and between 2.0 s and 4.0 s shall be obtained by linear interpolation.
(3) For fundamental lateral periods, Ta, greater than 2.0 s, use the values for Ta = 2.0.
(4) A "coupled wall" is a wall system with coupling beams, where at least 66% of the base overturning moment resisted by the wall system is carried by the axial tension and compression forces resulting from shear in the coupling beams.
(5) For hybrid systems, values corresponding to walls must be used or a dynamic analysis must be carried out as per Article 4.1.8.12.
(6) The total lateral seismic force, V, shall be distributed such that a portion, Ft, shall be assumed to be concentrated at the top of the building, where Ft, is equal to 0.07 TaV but need not exceed 0.25 V and may be considered as zero, where the fundamental lateral period, Ta, does not exceed 0.7 s; the remainder, V - Ft, shall be distributed along the height of the building, including the top level, in accordance with the formula,
(7) The structure shall be designed to resist overturning effects caused by the earthquake forces determined in Sentence (6) and the overturning moment at level x, Mx, shall be determined using the formula,
where,
Jx = 1.0 for hx ≥ 0.6hn, and
Jx = J + (1- J)(hx / 0.6hn) for hx,< 0.6hn
where,
J = base overturning moment reduction factor conforming to Table 4.1.8.11.
(8) Torsional effects that are concurrent with the effects of the forces mentioned in Sentence (6) and are caused by the simultaneous actions of the following torsional moments shall be considered in the design of the structure according to Sentence (10):
(a) torsional moments introduced by eccentricity between the centres of mass and resistance and their dynamic amplification, and
(b) torsional moments due to accidental eccentricities.
(9) Torsional sensitivity shall be determined by calculating the ratio Bx for each level x according to the following equation for each orthogonal direction determined independently:
Bx = δmax / δave
where,
B = maximum of all values of Bx in both orthogonal directions, except that the Bx for one-storey penthouses with a weight less than 10% of the level below need not be considered,
δmax = maximum storey displacement at the extreme points of the structure, at level x in the direction of the earthquake induced by the equivalent static forces acting at distances ± 0.10 Dnx from the centres of mass at each floor, and
δave = average of the displacements at the extreme points of the structure at level x produced by the above-mentioned forces.
(10) Torsional effects shall be accounted for as follows:
(a) for a buildingwith B ≤1.7 or where IEFaSa(0.2) is less than 0.35, by applying torsional moments about a vertical axis at each level throughout the building, derived for each of the following load cases considered separately,
(i) Tx = Fx(ex+ 0.10 Dnx), and
(ii) Tx= Fx(ex – 0.10 Dnx)
where Fx is the lateral force at each level determined according to Sentence (6) and where each element of the building is designed for the most severe effect of the above load cases, or
(b) for a buildingwith B >1.7, in cases where IEFaSa(0.2) is equal to or greater than 0.35, by a Dynamic Analysis Procedure as specified in Article 4.1.8.12.
(11) Where the fundamental lateral period, Ta, is determined by Clause (3)(d) and the building is constructed with more than 4 storeys of continuous wood construction and having a timber SFRS of shear walls with wood-based panels, braced frames or moment-resisting frames as defined in Table 4.1.8.9., the lateral earthquake force, V, as determined by Sentence (2) shall be multiplied by 1.2, but need not exceed that determined by Clause (2)(c).