Wind forces on Emergency Storage Structures (supplement) (NRI) Appendices Apendix 1 Lapse rate Appendix 2 Calculation of wind forces and pressures, with examples Appendix 3 Cyclic load testing

Wind forces on Emergency Storage Structures (supplement) (NRI)

Appendices

Apendix 1 Lapse rate

The expression which describes the relationship between pressure p and density d in the atmosphere is

p= kdn

where n is the index of expansion and k is a constant. If n is less than gamma, the ratio of the specific heats at constant volume and constant pressure, the atmosphere will be stable. If n is equal to gamma the atmosphere is neutrally stable and if n is greater than gamma it is unstable. The index of expansion n is related to the lapse rate mentioned above by the expression

n = g/(g - LR)

where g is the acceleration caused by gravity, L is the lapse rate and R is the gas constant.

Appendix 2 Calculation of wind forces and pressures, with examples

If wind is brought to rest against the windward face of a structure all its kinetic
energy is transferred to a dynamic pressure q, where

q = 0.5dV_S²

d is the density (see Table 5) V_S is design wind speed.

Selection of a design wind speed involves consideration of the maximum gust speed for the geographical area, the building, its immediate location and the probability of high winds occurring during the design life. Then,

where V = the 3-second basic gust speed, from local meteorological data (see Table 1); S₁ is a topographical factor, normally = 1; S₂ is a factor embracing ground roughness, building size and height above ground; and S₃ is a statistical factor which can be obtained from Figure 3. The probability P that a wind speed of greater value will occur at least once in a period of N years is normally taken as P=0.63. Taking a five-year Ifie as a reasonable exposure period for an emergency store, Figure 3 gives S₃=0.83. Lam and Lam (1985) suggest that 3-second gust speeds are adopted as the basis for building design because the natural oscillation period for most structures is only a few seconds, but Robertson (1988) states that 3-second gust speeds are used primarily because of limitations in the response of wind-measuring instrumentation. Research findings support the use of quasi-static loadings - even for plastic film greenhouses. Initial indications are that gusts of about 3 seconds or longer are appropriate design gusts depending on the size of the structure or member in question.

Table 5

Variation of air density d (kg/m3)

Temperature	Pressure (mb)
(°C)	960	980	1000	1020
0	1.225	1.250	1.276	1.302
5	1.203	1.228	1.253	1.278
10	1.182	1.206	1.231	1.255
15	1.161	1.185	1.209	1.234
20	1.144	1.165	1.189	1.213
25	1.122	1.145	1 169	1.192
30	1.103	1.126	1.149	1.172
35	1.086	1.108	1.131	1.153

Source: Eaton (1981)

Figure 3

A statistical factor S₃

Air density d varies with air temperature and pressure (see Table 5). Eaton (1981) suggests that in tropical storms the temperature should be taken as 25°C and the pressure as 960 mbar so that q = 0.5dV_S² becomes

q = 0.561 V_S²

Lam and Lam (1985) suggest that q=0.576V_S² for typhoons.

The pressure p at any point on the external surface of a rigid building can be expressed in terms of q by means of a pressure coefficient C_pe

P = C_pe · q

where e stands for external.

For rigid rectangular buildings with double pitch roofs pressure coefficients for individual external loads are shown in Tables 3 and 4 (BSI 1972, Eaton 1981). Local coefficients can be greater, for example in Table 4 at the corner of roofs with 20° pitch with the coefficient C_pe is double the general figure.

Wind forces have also been measured directly for these buildings and force coefficients derived such that

F = A_e · q · C_f

where F is the force in the direction of the wind, A_e is the effective frontal area of the structure and C_f is the force coefficient in the wind direction. Values of C_f are shown in Figure 4 and an example of force calculation is shown below.

When calculating total wind forces on a structure internal pressures also contribute. On the windward side, open doors and windows will increase the pressure inside and will increase the loading on parts of the roof and walls already subjected to external suction; on the leeward side these openings will decrease the pressure and decrease the force on the roof, but increase the force on the windward wall (see Figure 5). For most design purposes internal pressures are calculated using an internal pressure coefficient C_pi where

C_pi = 0.75 C_pe

Robertson (1986) suggests -0.5<C_pi<0.6 depending on position of dominant opening (-0.5 when in leeward wall, 0.6 when in windward wall). This applies to structures likely to have dominant openings in a storm.

Figure 4

Force coefficients C_f for rectangular buildings

Judicious placing of such openings can ensure that internal forces are always suction forces and therefore reduce total roof and wall loads except for the windward wall, for example by placing a ridge ventilator on a low pitch roof (BSI 1972, Eaton 1980).

Internal pressure in a building with dominant openings

Figure 5

Example of pressure calculation

For a building or structure where the height to width ratio is less than half and the roof angle is 10° calculate the pressure at the gable end, trailing edge, when the basic gust speed is 53 m/s, the temperature is 25°C and pressure 960 mbar

(Assume S₁ = S₂ = S₃ = 1 SO that V = V_s)

Dynamic pressure	q=0.561 VS2
	=0.561 x 532
	=1575.8 Newtons/m²

Local pressure p=Cpe · q where Cpe from Table 4=1.4
	=1.4 x 1 575.8
	=2206 Newtons/m²

Example of force calculation

For a similar building where the breadth to depth ratio is 2.0, C_f = 1.0 and effective areas is 80 m²

F	= Ae · q · Cf
	=80 x 1 575.8 x 1.0
	=126,064 Newtons
	=126 kN

The effective area is the frontal area at right angles to the wind direction.

Appendix 3 Cyclic load testing

In Tonga after Hurricane Isaac in 1982 when damaged structures were inspected it was found that joints between structural members were inadequate, particularly at roof level. A new design was tested at the Cyclone Testing Station in Townsville, Australia. The structure was erected exactly as it would have been in Tonga and simulated wind forces were applied and distributed so that they produced the same structural effect as design loads. Racking forces and uplift forces were applied using hydraulic rams which operated a series of cables, beams and load spreaders. Transducers monitored these loads and deflections all over the structure. A programme of cyclic load tests were conducted to simulate the continual buffeting that a structure receives during a hurricane. Failure of roof-wall straps resulted and therefore these were improved; the modified structure successfully resisted the sequence of cyclic loading that simulated a four-hour hurricane with wind gusts up to the design speed of 62 m/s. Ultimate failure of the structure was caused by fracture of a strap at 1.3 times the design uplift and racking loads. (Eaton and Reardon, 1985).

(1421/89 Hobbs the Printers of Southampton)