Ice Loading Calculations

Variables needed:

Nominal Ice Thickness in inches, t

Fence Height in feet, h

Height of fencing materials in feet, s       (h minus any gap at the bottom of the fence)

Topographic Factor, K_zt

Importance Factor for Ice, I_i         (not used in ASCE 7-22, so I_i set to 1.0 in that case)

Ice Thickness Modifier, m_t           (corrects for formula differences between ASCE 7 versions)

Height Factor, f_z per Eq. 10.4-4 (½ h substituted for z to average across the vertical surface)                   

f_z = (½ h / 33)^0.10

Design Ice Thickness for Freezing Rain in inches, t_d per Eq. 10.4-5                  

t_d = m_t t I_i f_z K_zt ^0.35

For K_zt = 1.0, Eq. 10.4-5 simplifies to t_d = m_t t I_i f_z

The Density of Ice, I_d = 56 lbs / ft³ per ASCE 7 §10.4.1 (minimum value)

For a solid fence:

Iced Area in ft², A_i = 0.8 s L     (0.8 is reduction factor for vertical plates per §10.4.1)

The Volume of Ice in ft³, V_i = π (t_d / 12)A_i                per Eq. 10.4-1

The Weight of Ice in lbs, D_i = (0.7)V_i I_d         (0.7 ASD reduction factor per ASCE 7 §2.4.3 for Wind on Ice loading)

For open fencing, the ice solidity ratio, ε’ is based on adding the design ice thickness, t_d to each free edge of the fencing members which increases the wind area.  If the iced solidity ratio, ε’ exceeds 0.7, the fence is then considered to be a solid or mostly solid fence.

The cross sectional area of ice on each member is based on the “diameter of the cylinder circumscribing an object”, D_c in inches.  D_c for a variety of cross sections is shown below per ASCE 7, Figure 10-1. This is only used for determining the weight of the ice, not the wind area.

The cross-sectional area of Ice in ft² per Eq. 10.4-1 is A_i = π t_d (D_c + t_d) / 144

The volume of ice on a given member, such as a tube picket on an architectural fence would be:

V_i = A_i x the length of the member in feet.

See above for determining the weight of the ice.