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# 2.5.1 Wind Loading in Piping Stress Analysis

Wind loading is caused by the loss of momentum of the wind striking the projected area of the piping system. The static linear force per foot generated by a steady-state, constant speed wind load can be calculated as:

### f = Peq*S*D*sinθ

Where:

f = "pseudo static" wind force per length of pipe, lb/ft Peq = equivalent wind pressure, psi

= V^2 / 2g

= density of air, lbm/ft^3

= 0.0748 lbm/ft^3 at 29.92 in Hg and 70° F

V = design velocity of wind (usually the 100-year maximum wind speed), ft/sec g = gravitational constant, 32.2 ft/sec^2 S = shape factor (or drag coefficient), based upon Reynolds number of wind and shape of structure; this typically varies between 0.5 and 0.7, with a value of 0.65 characteristic of piping elements, dimensionless D = pipe diameter (including insulation), ft θ = angle of orientation between pipe and wind, where 0° represents the pipe axis parallel to the wind direction

The linear force per foot, f, is calculated for each end of the element and the average taken. The average is assumed to apply as a uniform static load over the entire length of the element.

ASCE #7 (formerly ANSI A58.1) modifies this concept slightly to consider facility importance,proximity of hurricanes, etc. Its formula for wind load is:

### f = 0.00256 Kz (I V)^2 Gh Cd D

Where:

Kz = Exposure coefficient, based upon height above ground level and congestion of local terrain (varies from 0.12 for 0-15 feet height in city environment to 2.41 for 500 feet height in wide open terrain), dimensionless I = importance factor, based upon importance of structure and proximity to hurricane coast (varies from 0.95 for non-essential facility over 100 miles from a hurricane to 1.11 for essential facility on the hurricane coast), dimensionless V = basic wind speed (excluding from the average abnormally high wind loading events such as hurricanes or tornadoes), from ANSI A58.1 map (ranging from 70 to 110), mph

Gh = gusting factor, based upon height above ground level and congestion of local terrain (varies from 1.0 for 500 feet height in wide open terrain to 2.36 for 0-15 feet height in city environment), dimensionless

CAESAR II's ASCE #7 wind input screen requests a number of parameters, from which the coefficients of the equation above are determined

ASCE #7 provides a map of basic wind speeds in the Continental United States. The following is a crude summary of the map:

ASCE #7 adjusts the importance factor according to the site's Distance from Hurricane Ocean line. This typically translates into the distance from the east coast or the Gulf of Mexico in the Continental U.S. If the plant site is greater than 100 miles from either the east or the gulf coasts, then a value of 100 miles should be used (no credit may be taken for any plant site greater than 100 miles from any of these hurricane prone areas).

The importance factor is further influenced by the Structural Classification, where the options are:

The exposure coefficient and gusting factor are influenced by the terrain's Wind Exposure type, where the options are:

1. Large city center

2. Urban and suburban

3. Open Terrain

4. Flat coastal areas

Wind is a static, horizontal uniform load. It may act in any direction, and as such the engineer has several items to consider:

1. How many directions should be analyzed for sensitivity to wind?

2. Should both positive and negative directions be evaluated?

3. Should some skewed direction be evaluated?

4. Do nonlinear supports (i.e. horizontal guides with gaps) and/or friction affect the wind load?

5. Should the wind act on the piping system in the cold or hot condition?

The logic diagram shown in Figure 2-36 should serve as a guideline when setting up and analyzing wind load cases to satisfy piping code requirements. (Note: The load cases shown here only contain the basic analysis components. Other items such as imposed displacements,concentrated loads, etc. may need to be added to the load cases shown above for the user's particular job.)

For nonlinear systems an additional algebraic case may be required to extract the occasional bending moments from the operating bending moments. In perfectly linear systems an occasional load case can be run alone, with this used for the stress component due to the occasional load. With nonlinear systems, the effect the occasional load has on the system is linked to the effect of the operating loads on the system. The algebraic load cases shown in Figure 2-36 permits these two effects to be separated.

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