General Principles of Roof Design (Case Study)

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The following points should be considered in roof design:

1. The roof should be weatherproof

This implies that the roof should be strong against the effects of weather and it should not be susceptible to hurricane-type and gale-type wind that usually has the capacity to blow off roofs of buildings.

2. The slope of the roof and lap of the roof coverings

This must be considered as well as the degree of exposure. For instance, plain tiles are not suitable for use on slopes of less than 40^oC.

3. Loading

The roof structure or framework must be of adequate strength to carry its own weight together with the superimposed loads of snow, wind, and foot traffic (where applicable). The imposed loads given in Table 2 (an extension of Table 1)are additional to all surfacing materials and include snow and other incidental loads but exclude wind pressure. Minimum loads are given for roofs with no access (other than that necessary for cleaning and maintenance) and for roofs where access is provided as shown in Table 1. Roofs, like floors, should be designed for the worst effects of either the distributed load or the concentrated load. For roofs with access, the minimum load will exceed the snow load in most cases.

Table 1: Imposed roof loadings

If a flat roof is used for purposes such as a café, playground, or roof garden, the appropriate imposed load for such a floor should be allowed.

i. Snow Loads

According to Clause 5.1 (2) of EC 1: Part 1.3, the snow load on the roof can be deposited by

different patterns that are caused by the properties of the roof which include:

a) the shape of the roof;

b) its thermal properties;

c) the roughness of its surface;

d) the amount of heat generated under the roof;

e) the proximity of nearby buildings;

f) the surrounding terrain;

g) the local meteorological climate, in particular its windiness, temperature variations, and likelihood of precipitation (either as rain or as snow).

The snow load on the roof is determined by multiplying the estimated snow load on the ground at the site location and altitude (the site snow load) by an appropriate snow load shape coefficient. The main loading conditions to be considered are:

(a) a uniformly distributed snow load over the entire roof, likely to occur when snow falls with little or no wind;

(b) a redistributed (or unevenly deposited) snow load, likely to occur in windy conditions.

For flat or mono-pitch roofs, it is sufficient to consider the single load case resulting from a uniform layer of snow, as given in Table 2 below.

Table 2: Imposed loads on roofs of buildings

For other roof shapes and for the effects of local drifting of snow behind parapets, reference should be made to BS 6399: Part 3 for further information. In exceptional cases where snow loads occur on the ground, they can be determined as follows (Clause 4.3.1 of EC 1: Part 1.3).

S_Ad = C_esl . S_k

Where,

S_Ad is the design value of exceptional snow load on the ground for the given location;

C_esl is the coefficient for exceptional snow loads (recommended value is 2.0);

S_k is the characteristic value of snow load on the ground for a given location.

For buildings designed to the Eurocodes, snow loads on roofs can be determined by the following (Clause 5.2 (3) of EC 1: Part 1.3):

a) for the persistent/transient design situations

S = μ_i . C_e . C_t . S_k

b) for the accidental design situations where exceptional snow load is the accidental action (except for the cases covered in c) below.

S = μ_i . C_e . C_t . S_Ad

c) for the accidental design situations where exceptional snow drift is the accidental action.

S = μ_i . S_k

Where,

μ_i is the snow load shape coefficient

S_k is the characteristic value of snow load on tile ground

S_Ad is the design value of exceptional snow load on the ground for a given location

C_e is the exposure coefficient

C_t is the thermal coefficient

Note:

1. The load should be assumed to act vertically and refer to a horizontal projection of the roof area.

2. When artificial removal or redistribution of snow on a roof is anticipated the roof should be designed for suitable load arrangements.

3. In regions with possible rainfalls on the snow and consecutive melting and freezing, snow loads on roofs should be increased, especially in cases where snow and ice can block the drainage system of the roof.

4. The exposure coefficient C_e should be used for determining the snow load on the roof. The choice for C_e should consider the future development around the site. C_e should be taken as 1,0 unless otherwise specified for different topographies (see Table 3).

Table 3: Recommended values of C_e for different topographies

5. The thermal coefficient C_t should be used to account for the reduction of snow loads on roofs with high thermal transmittance (> 1 W/m² K), in particular for some glass covered roofs, because of melting caused by heat loss.

6. For all other cases: C_t = 1,0

ii. Wind Pressure

Wind pressure requires special consideration where a light roof covering is laid on a low slope. The greatest suction occurs at slopes below 15^o and this diminishes to around zero at 30^o, with maximum suction at the edges of the roofs. In conditions of high wind pressure, the uplift can exceed the dead weight of the covering so adequate fixing is necessary to prevent stripping of the coverings.

Wind loads are imposed loads whose effect is horizontal in contrast to common permanent actions and variable actions in buildings. Wind loads are obtained from the local wind speed from where the structure is to be situated and converted to wind forces as follows;

Let V be the local basic wind speed, V_s = VS₁S₂S₃ (m/s)

W_k = 0.613 V_s² (N/m²) where V_s is the design wind speed (m/s).

S₁ is the multiplying factor relating to topology which can generally be taken as 1.0. On sites where wind acceleration is known to occur, the value of 1.1 should be adopted and 0.99 is a completely sheltered area.

S₂ = multiplying factor relating to height above ground and wind breaking, obtainable from literature and ranges between 0.55 and 1.27.

S₃ = multiplying factor relating to the life of the structure which again can be taken as 1.0 which corresponds to an excessive speed occurring once in 50 years.

W_k = the wind load in N/m².

Normally, these loads are multiplied by the projected area to determine the wind force on the structure and the wind pressure (W_k) is assumed uniform over the entire surface.

Table 4; Limit state or load combination for roof

4. Durability

The coverings should be able to withstand atmospheric pollution, frost, and other harmful conditions. With large concrete roofs and sheet-metal coverings, provision must be made to accommodate thermal expansion. There should also be effective means for the speedy removal of rainwater from the roof which might otherwise cause deterioration of the roof coverings.

Case Study

My attention was recently brought to a roof of the large open auditorium that has been damaged several times by wind. There is usually a gale-type wind force that passes through the region between April and September each year and each time the wind passes, it blows off the roof. The roof was made of a flat roof with a pitch of about 5.3^o and covering an area of about 1040 m².

When I presented the situation to two experienced engineers; one proposed increasing the pitch of the roof. The other person proposed using steel sections for the roof carcass which has hitherto been made with wood sections and then increasing the gauge of the roof sheets which have hitherto been made with the lowest gauge available in the Nigerian market due to cost implications of using higher gauges. I went for the second option and produced the design sections shown below for the roof solution. I didn’t go for the first option because the columns used in the building are unbraced slender columns and already spanned height close to 6 m. I do not consider it wise to increase the height of those columns further.

Besides using the steel skeleton for the roof, I also thought about the possibility of creating a counter-aerofoil situation at the edges of the roof prone to wind, though its applicability is still vague. The principle of aerofoil which was derived from Bernoulli’s principle and enables the takeoff of aeroplanes also helps to prevent damage to buildings during windstorms or cyclones such that the roof can be blown off while the building remains safe. In accordance with Bernoulli’s principle, the high wind blowing over the roof creates a low-pressure P₁. The pressure under the roof P₂ is greater. Therefore, this pressure difference (P₂–P₁) creates an up thrust and the roof is blown off (see Figure 1).

Comments and suggestions are welcomed for this post on how best to protect roofs from being damaged by strong windstorms.

Thanks for reading and for your comments.

For further reading,

1. Reinforced Concrete Designers Handbook by Reynolds, SteedMan and Threlfall

2. Simplified Reinforced Concrete Design (third edition) by Victor O. Oyenuga

3. Eurocode 1 – Actions on structures – Part 1-3: General actions – Snow loads