RAM Structural System Help

NBC of Canada 2015

Equivalent Static Force Procedure is implemented according to Section 4.1.7, Division B of NBC 2015. The specified external pressure or suction (i.e., windward and leeward pressures) is calculated according to the following equation:

p = IwqCeCgCp 4.1.7.3 .(1)

where
p
=
external wind pressure, calculated in kN/m2 (kPa)

Importance Factor for Wind Load (Iw)

It is given in table 4.1.7.3 and this parameter is expected to be provided by the user (no units).

Reference Velocity Pressure ( q )

The reference velocity pressure is referenced in Sentence (4) of Section 4.1.7 and this parameter is expected to be provided by the user. Acceptable units are kN/m2 (kPa) psf, or kg/m2.

Exposure Factor (Ce)

Exposure Factor can be determined based on one of the following three options (in calculations below, h is height above ground level, and it is defined in meters):
  • Use provided value
  • Static procedure: It is given in Sentence 4.1.7.3 (5)
    • Open Terrain: Ce=(h10)0.2>0.9
    • Rough Terrain: C e = 0.7 ( h 12 ) 0.3 > 0.7
    • Intermediate value between these two options (see Commentary I, pg. I-7). This method is not implemented (in this case, the user needs to calculate it manually and enter it)
  • Dynamic procedure: the exposure factor is calculated as follows (4.1.7.8):
    • Exposure A: C e = ( h 10 ) 0.28 and 1.0 ≤ Ce ≤ 2.5
    • Exposure B: C e = 0.5 ( h 12.7 ) 0.50 and 0.5 ≤ Ce ≤ 2.5
    Referring to Figure A-4.1.7.8 (2) and (3), Exposure A is regarded as open terrain and Exposure B as rough terrain. These definitions are used in the current implementation for dynamic procedure.

Topographic Factor (Ct)

The topographic factor is calculated according to a method given in 4.1.7.4. This method is not implemented. Instead, the user is expected to provide Ct values for each direction.

Building Dimensions

For dynamic procedure, building dimensions are needed in calculation of Gust effect factor (Cg) and external pressure coefficient (Cp).

The program provides two options: building dimensions are calculated based on maximum exposed dimensions of building or they are provided as a user input.

If the option to use maximum exposed dimensions selected, effective building width is calculated from the following equation:
w= ∑hiwi∑hi
where
wi
=
the maximum exposed width of building in direction perpendicular to wind's direction (in calculation of the term ∑hiwi, the summation loop starts from top level).
D
=
building depth needed for Cp. D is the maximum exposed depth of building in direction of wind

If static procedure is selected, building depth, D, is needed in calculation of external pressure coefficient (Cp). In this case, the choice selected for building dimensions (either based on maximum exposed dimension or user input) is also used in static procedure.

Gust Effect Factor (Gg)

Gust effect factor can be determined based on one of the following two options (in calculations below, h is mean roof height in meters):
  • Static procedure: 4.1.7.3. Sentence 8
    • Cg = 2.0 for the building as a whole and main structural members
    • Cg = 2.5 for external pressures and suctions on secondary structural members, including cladding
  • Dynamic procedure: 4.1.7.8 (Sentence 4)
    C g = 1 + g p ( σ μ )
    where
    ( σ μ )
    		=
    K C e H ( B + s F β )
    gp
    		=
    statistical peak factor for the loading effect (Figure A-4.1.7.8. (4)-A)
    2ln⁡evT⁡+0.5772ln⁡evT⁡
    v
    		=
    average fluctuation rate
    fnDsFsF+βB
    T
    		=
    3,600 s
    K
    		=
    factor related to surface roughness
    • = 0.08 for Exposure A
    • = 0.10 for Exposure B
    CeH
    		=
    exposure factor at the top of the top of building (mean roof level). It is calculated according to equations given in 4.1.7.8 Sentences 2 and 3.
    B
    		=
    background turbulence factor obtained from Figure 4.1.7-8 as a function of w/H, in which w is building effective width and H is the mean roof height. Both w and H are in meters.
    = 4 3 ∫ 0 914 H [ 1 1 + x H 457 ] [ 1 1 + x w 122 ] [ x ( 1 + x 2 ) 4 / 3 ] ⅆ x
    s
    		=
    size reduction factor obtained from Figure A-4.1.7.8. (4)-B as a function of w/H and reduced frequency, f n H V H . It can be also calculated from the following equation:
    = π 3 [ 1 1 + 8 f n H 3 V H ] [ 1 1 + 10 f n w V H ]
    fn
    		=
    natural frequency of vibration for given direction (in Hz). It is either given by the user or computed by the program
    VH
    		=
    mean wind speed (m/s) at the top of the structure
    = V ¯ C e H
    V ¯
    		=
    2IWqρCeH
    q
    		=
    reference velocity pressure (kPa = kN/m2), which is provided by the user
    ρ
    		=
    air density value used by the program = 1.2929 kg/m3
    F
    		=
    gust energy ratio at the natural frequency of the structure obtained from Figure A-4.1.7.8. (4)-C. It can be also calculated from the following equation:
    = x o 2 ( 1 + x o 2 ) 4 / 3
    x0
    		=
    1,220 fn/VH
    β
    		=
    critical damping ratio in the along-wind direction

External Pressure Coefficient (Cp)

External pressure coefficients Cp for Windward and Leeward surfaces can be either directly provided by the user, or they can be calculated as follows (in the following equations H is the mean roof height and D is the depth of the building in the direction of the wind. See Figure A-4.1.7.5. (2) and (3)):
  • For Windward case:
    C p = { 0.6 H D < 0.25 0.27 ( H D + 2 ) 0.25 ≤ H D < 1 0.8 H D ≥ 1
  • For Leeward case:
    C p = { − 0.3 H D < 0.25 − 0.27 ( H D + 0.88 ) 0.25 ≤ H D < 1 − 0.5 H D ≥ 1

Loading Directions

Loading directions Cases A-D as given in Figure A-4.1.7.9. (1) are implemented. Regarding Case B, it is assumed that only half of the building surface is loaded with indicated wind pressures (see the following figure and note that h is the height of the surface.).

Generated partial wind load cases NBC of Canada 2015

Total Force = (PW + PL) (w/2) h

ex = w/4

Similarly, it is assumed that partial loads are applied to half surface for Case D:

Generated wind load Case D of NBC of Canada 2015

ΣFx = 0.565(PW + PL)wh

ΣFy = 0.565(PW + PL)dh

ex = ±0.082w

ey = ±0.082d

Based on Figure A-4.1.7.9. (1), the following load cases are generated by the program (the load cases indicated with orange color are only generated if Additional Load Cases for Analysis with Tension Only Members option is checked).

Wind Load Case A (NBC of Canada 2015)

Wind Load Case B (NBC of Canada 2015)

Wind Load Case C (NBC of Canada 2015)

Wind Load Case D (NBC of Canada 2015)

Parent topic: Story Forces: Wind