Wind Force Coefficient, C_f

The Wind Force Coefficient, C_f is an aerodynamic adjustment value based on the size and shape of the fencing material, the geometry of the fence, and the location of a given post in both the normal and iced conditions. C_fw is used for wind forces. C_fi is used for wind on ice forces.

If the fence is mostly open (ε or ε’ ≤ 0.7), the C_fw and C_fi values are based on the open fencing / single plane open frame table.  The most common values are shown below.

(ASCE 7 §29 – Open Frame Table)

If the fence is mostly open (ε & ε’ ≤ 0.7) in both the normal and iced condition (if applicable), the information below does not apply so you can skip to the next section. Lateral and Axial Loads

Solid and Mostly Solid Fending

If the fence is solid or mostly solid (ε or ε’ > 0.7), the C_fw and C_fi values for posts away from ends and corners are based on the Case A Solid Wall Table.  The most common values are shown below.

If you want to use the same posts, footings and post spacings for all the posts away from ends or corners, use the B/s value from the shortest fence run as that will be the most conservative Case A C_f value.

(ASCE 7 §29 – Solid Wall Tables)

If the fence is solid or mostly solid (ε or ε’ > 0.7), the C_fw and C_fi values increase as you approach an end or corner and are based on the Case C Solid Wall Table. The variable C_f wind regions that need to be considered are based on the Aspect Ratio, B/s of the straight fence run being designed.

If the Aspect Ratio, B/s falls between the values shown on the table below, use the highest C_f value of the two or interpolate.  Values with an * next to them are subject to the Return Corner Reduction Factor, R₃ if applicable.

(ASCE 7 §29 – Solid Wall Tables)

Case C Reduction Factor, R₂ (See Solid Wall Tables, Note 4)

This is a modifier for solid or mostly solid fencing to adjust the Case C C_f values based on any gap between the ground and the bottom of the fencing material.

The Clearance Ratio, s/h determines which R₂ value is to be used. The R₂ value can be selected from the table below, or calculated directly from the formula at the bottom of the table.

Return Corner Reduction Factor, R₃ (see Solid Wall Tables, Case C, Return Corners)

This is a modifier for solid or mostly solid fencing to adjust the Case C C_f value for the “0 to s” wind region closest to an end or corner. The R₃ values are shown on the table below based on the Return Corner Length, L_r to solid fencing height, s ratio. If the L_r / s value falls between two values on the table, use the highest value, or interpolate.

If there is no return corner, or if the Aspect Ratio, B/s is < 5, R₃ = 1.0.

Equivalent C_f values per Posts near ends and corners

For solid or mostly solid fencing, (ε or ε’ > 0.7) near ends or corners, the spans for each post will have variable loading, so determining the equivalent C_f value for a given fence post takes extra steps.

The fence layout near the ends and corners needs to be sketched, either in a drawing program like AutoCAD or by hand on graph paper, showing the post spacings and the C_f zones. You can either do this just for the longest fence run to save time, or for every fence run for the most economical design.

The C_f values near ends and corners need to be adjusted with the Case C Adjustment Factor, R₂. The 0 to s region also needs to be adjusted with the Return Corner Reduction Factor R₃. If any of these adjusted Case C C_f values are less than the Case A C_f value, the Case A C_f value controls.

The simplest way determine the equivalent C_f value of each post is to use the largest C_f value that is applied to the fence span on either side of the post. This is very conservative but requires less calculation.

The next simplest method is more work, but less conservative. You can calculate a weighted average of all the C_f values applied on each side of the post based on the zone lengths. These values will range from around -7% to +11% of the actual equivalent C_f value for the post, so a 10% adder is used to make sure the weighted average value is above the actual value. This process needs to be done for each post that has variable loading, or just conservatively use the 1^st post loading for all the posts in the Case C area.

Example – 1^st post away from the end gets 6′ of C_f = 3.22, 6′ of C_f = 2.07 and 4′ of C_f = 1.59. Equivalent Post C_f = 1.1 × ((6′ × 3.22) + (6′ × 2.07) + (4′ × 1.59)) / (2 × 8) = 2.62. This is about 18% lower than the simplified method in this particular example.

The most accurate way to determine the equivalent C_f value for a post is to sum the moments about the posts on either side. This is the most involved process, but provides the most economical C_f values.

For the left span, for each C_f zone, you measure the distance from the left post to the center of the C_f zone portion on that span (the moment arm), times the length of the zone portion on that span, times the C_f value to get the moment about the left post for each zone. Add these together to get the total moment about the left post, M_L. Do the same for the right span, measuring from the right post to get M_R.

If the Post Spacing, L is the same on each side of the post in question, the equivalent C_f value for that post = (M_L + M_R) ÷ L²

If the post spacing is different on each side of the post in question, with the left post spacing being L_L and the right post spacing being L_R, the equivalent C_f value for that post = (M_L ÷ L_L²) + (M_R ÷ L_R²)

This process needs to be done for each post that has variable loading, or just conservatively use the 1^st post loading for all the posts with spans in the Case C area.

Example – 1^st post away from the end:

M_L = 3′ × 6′ × 3.22 + 7′ × 2′ × 2.07 = 86.94

M_R = 2′ × 4′ × 1.59 + 6′ × 4′ × 2.07 = 62.4

Equivalent C_f = (86.94 + 62.4) ÷ (8×8) = 2.33. This is about 11% less than the weighted average example above, but could be as much as 20% less depending on the fence geometry.

If you want to economically keep all the posts and footings the same size on a given fence run, start by sizing the Case A line posts away from ends and corners. Then take the Case A C_f value times the post spacing. This is the equivalent allowable load on the Case A post. For the Case C areas, divide that equivalent allowable load by the different case C C_f values which will give you the tributary width that would produce the same forces the Case A posts were designed for. You would need to go through the process a few times to dial in the spacings, but if using a spreadsheet, the extra work may be worth it.

Next – Lateral and Axial Loads