## Wind Pressure Calculation For Curved Roof

FIGURE 24.17 Intersection and combination of cylindrical shells.

24.4 Structural Analysis

### 24.4.1 Design Loads 24.4.1.1 Dead Load

The design dead load is established on the basis of the actual loads that may be expected to act on the structure of constant magnitude. The weight of various accessories — cladding, supported lighting, heat and ventilation equipment — and the weight of space frame comprise the total dead load. An empirical

formula is suggested to estimate the dead weight g of double-layer grids:

where q w indicates all dead and live loads acting on double-layer grid except its self-weight (in kN/m2); L is the shorter span (in m); and Z is a coefficient, 1.0 for steel tubes and 1.2 for mill sections.

24.4.1.2 Live Load, Snow, or Rain Load

Live load is specified by the local building code and compared with the possible snow or rain load; the larger one should be used as the design load. Each space frame is designed with uniformly distributed snow load and further allowed for drifting depending on the shape and slope of the structure. Often more than one assumed distribution of snow load is considered. It was recommended by ISO for the determination of snow loads on simple curved roofs, pointed arches, and domes. The intensity of snow load as specified in Bases for Design of Structures: Determination of Snow Loads on Roofs [5] is reproduced as Figure 24.21. For domes of circular plan form, an axially symmetrical balanced load may be given as the corresponding balanced arch load. The drift load may likewise be given by the corresponding arch drift load along the plan diameter being parallel to the wind direction multiplied by a reduction factor (1—a/r) where r is the plan radius and a is the horizontal distance from the wind direction diameter to any parallel plan chord. The snow loads can be calculated by the following formulas:

Balanced load part sb — s0 Ce Ct mb mb — \j cos (Cm 1.5b) for (Cm 1.5b) < 90° (24.5)

md — (2.2Ce — 2.1Ce2) sin(3b) for b < 60° (24.6)

where s0 is the characteristic snow load on the ground (in kN/m2), mb is the slope reduction coefficient, md is the drift load coefficient, Ce is the exposure reduction coefficient, Ct is the thermal reduction coefficient, and Cm is the surface material coefficient.

1 Wind direction

FIGURE 24.21 Snow loads on simple curved roofs and domes.

The exposure coefficient, Ce, defines the balanced load on a flat horizontal roof of a cold building as a fraction of the characteristic load on the ground. For regions where there are not sufficient sinter climatological data available, it is recommended to set Ce = 0.8. However, the designer should always assess whether calm weather conditions (i.e., Ce = 10) during the snowfall season might yield more severe conditions for the structure. The thermal coefficient, Ct, is introduced to account for the reduction of snow load on roofs with high thermal transmittance, in particular glass-covered roofs, from melting caused by heat loss through the roof. For such cases Ct may take values less than unity. For all other cases, Ct = 1.0 applies. The surface material coefficient, Cm, defines a reduction of the snow load on roofs made of surface material with low surface roughness. It varies between 1.333, for slippery, unobstructed surfaces, to 1.0, for other surfaces. Detailed methods for the determination of these coefficients are given in the annexes of the Standard.

Rain load may be important in the tropical climate especially if the drainage provisions are insufficient. Ponding results when water on a double-layer grid flat roof accumulates faster than it runs off, thus causing excessive load on the roof.

### 24.4.1.3 Wind Load

The wind loads usually represent a significant proportion of the overall forces acting on barrel vaults and domes. A detailed comparison of the available codes concerning wind loads has revealed quite a large difference between the practices adopted by various countries. Pressure coefficients for arched roof springing from ground surface that can be used for barrel vault design are shown in Figure 24.22 and Table 24.3. For arched roof resting on an elevated structure like enclosure walls, the pressure coefficients are shown in Table 24.4. It should be noticed that ANSI is no longer used in practice in the United States. The ASCE has issued Minimum Design Loads for Buildings and Other Structures (SEI/ASCE 7-02). In Chapter C6 ''Wind Loads,'' detailed provisions for determining wind loads are given.

The wind pressure distribution on buildings is also recommended by the European Committee for Standardization as European Prestandard [6]. The pressure coefficients for arched roof and spherical domes, either resting on the ground or on elevated structure, are presented in graphical forms in Figure 24.23 and Figure 24.24 respectively.

It can be seen that significant variations in pressure coefficients from different codes of practice exist for three-dimensional curved space frames. This is due to the fact that these coefficients are highly dependent on Reynolds number, surface roughness, wind velocity profile, and turbulence. It may be concluded that the codes of practice are only suitable for preliminary design purposes, especially for the important long-span space structures and those lattice shells with peculiar shapes. It is therefore necessary to undertake further wind tunnel tests in an attempt to establish more accurately the pressure distribution over the roof surface. For such tests, it is essential to simulate the velocity profile and turbulence of the natural wind and the Reynolds number effects associated with curved surface.

### 24.4.1.4 Temperature Effect

Most space frames are subject to thermal expansion and contraction due to changes in temperature and thus may be subject to axial loads if restrained. Potential temperature effect must be considered in the design especially when the span is comparatively large. The choice of support locations — perimeter, intermediate columns, etc. — and types of support — fixed, slid, or free rotation and translation — as

Country code |
Windward quarter |
Central half |
Leeward quarter |
Rise/span, r |

United States: ANSI A 58.1-1982 |
1.4r |
-0.7 - r |

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