What are Structural Calculations ?

If you need to ask this question it is a fair to assume, you have been requested structural calculations by the Building Control Authority to support your Building Regulations Application.

The guidance to the structural aspects of the Building Regulations are contained within Approved Document A http://www.planningportal.gov.uk/uploads/br/BR_PDF_AD_A_2004.pdf This document has become the bible of anything structural to Building Control and anything that falls outside the scope of this document must be justified by structural calculation in accordance with the relevant British Standard or European Code.

Structural calculations can encompass many structural elements that are not included in the Approved Document, but for most domestic applications they relate to steel or timber beams. I have progressed the guidance note to include an example of a structural calculation up to the point the information is input into a structural program.

Firstly I must explain there are two types of loads that can be applied to a structural member. These are dead and live loads, I have listed 4 types of load below but strictly speaking both snow and wind load are classed as imposed loads.

1)                 Dead load               is the weight of the structure being supported

2)                 Imposed load          is a usage load (see wikipedia)

3)                 Snow load             depends upon the shape and pitch of roof

4)                 Wind load               depends upon the height, shape and position of the building.

Dead Load

The dead load of an element such as a roof, floor or wall is calculated by adding the weights of the elements together. The weights of the individual components can be established by product information, such as the weight of a “Marley Modern” roof tile or by reference to BS 648, which is a table weights of common building materials.

Imposed Load

These loads are essentially associated with the use of the structural element. A floor in a domestic house would be subject to people using the room, the weight of furniture and of course clothes and other personal stuff. The British Standard has allowed a load of 1.5kN/m for this use (about 150kg/m2). Some common imposed loads are;

Domestic floor           1.5kN/m2 (about 150kg/m2)

Office floor               2.5kN/m2 (about 250kg/m2)

Domestic loft             0.5kN/m2 (about 50kg/m2)

Snow load This is simply the weight of snow on a roof, it used to be determined by BS6399 part 3 but now has been superceded by Eurocode 1 (EC1). Years ago it was very simple. Snow load was calculated at 0.75kN/m2 on plan area of the roof. Until it was figured out,(not without the odd roof collapse) that snow can accumulate within the valleys of multi pitch roofs and where roofs abut taller buildings. However without getting outside the scope of this explanatory note it is still safe to assume snow load as

Up to 100m altitude               0.75kN/m2 (75kg/m2)

Over  100m altitude              1.00kN/m2 (100kg/m2)

Wind Load

This is simply the load that wind will exert on a structure, it used to be determined by CP3 and then BS6399 part 2 but now has been superceded by Eurocode 1 (EC1). Wind load becomes more of an issue the taller a building becomes, but the shape of a building could make wind load an issue even on a domestic scale. (see diagram 1 of Approved Document A) The two more recent references has made wind load calculations very complex without the use of software to determine the worst case scenarios. However, most Authorities accept CP3 calculations for small structures where wind load is not considered the dominant load. Wind loads vary due to many factors but are generally between the values of

0.4kN/m2 (40kg/m2) for sheltered low rise buildings

up to

1.5kN/m2  (150kg/m2) for low rise factory units with large doors that could remain open in the event of a storm.

Format of structural calculations

For structural calculations to be understood and most important checkable they should follow the following format

1. 1) schedule the weights of the components showing how the loads of the constructional elements have been calculated.
2. 2) a table showing how the loads on the beam have been calculated
3. 3) a diagram of the beam indicating the span, the supports and where the loads are positioned on the beam.
4. 4) the structural analysis, this calculates the max shear, max bending moment and support reactions of the beam.
5. 5) the affects the above values have upon the chosen beam in terms of shear stress, bending stress and deflection.
6. 6) the calculation of supports, such as the padstones, columns or another beam.

It is now common practice for 4, 5 and 6 of above to be carried out using computer software. You only have to “google” structural software to gain an idea of how much there is out there. However, the two products that dominate the domestic market are “superbeam” and for the more experience steelwork designers “prosteel”. Therefore I will concentrate on items 1 to 3 which still appears to be carried out manually by most engineers.

1 – Schedule of loads

Roof (measured on plan)

pitch of roof 30 degrees

Roof tiles (marley modern)                             52kg/m2

Battens and felt                                                5kg/m2

Rafters                                                              8kg/m2

Total                                                                  65kg/m2

This converts the load On plan

65/cos 30                                                         75kg/m2

Convert to kN                                               0.75kN/m2

Snow load                                                    0.75kN/m2

Total Dead + Snow                                      1.50kN/m2

ceiling load

Insulation                                                          2kg/m2
timber                                                               8kg/m2

Plasterboard and skim                                   15kg/m2

Total                                                              25kg/m2

Convert to kN                                             0.25kN/m2

Imposed load for loft                                   0.25kN/m2

Total Dead and Imposed                             0.50kN/m2

Internal Partition Wall

100mm lightweight concrete                       150kg/m2
2 layers of lightweight plaster                      20kg/m2

services (wall hung tv’s ect)                         5kg/m2

Total                                                            175kg/m2

Convert to kN                                            1.75kN/m2

Total dead load                                         1.75kN/m2

Suspended First Floor
22mm floor decking                                     15kg/m2

timber                                                          15kg/m2

plasterboard and skim                                15kg/m2

services                                                        5kg/m2

Total                                                             50kg/m2

Convert to kN                                            0.5kN/m2

Imposed load                                            1.5kN/m2

Total Dead and Imposed load 2.0kN/m2

2 –Table of loads on the beam

In the example I have chosen there is only one uniformly distributed load (udl) that comprises of the above schedule of loads (roof, ceiling , internal wall and floor). For the purposes of this explanatory note I have added the dead and imposed loads together as you would for “Superbeam”. However, if you are using a more sophisticated piece of software the dead and imposed loads must be calculated separate as these loads attract different safety factors for the purpose of limit state design. The example is a typical internal load-bearing wall that is common in 1890 to 1950’s houses.

Table of load on beam

Element                      coverage                         load                          udl on beam

Roof                            7.4/4    (m)                     1.50kN/m2                  2.8 kN/m

Ceiling                         7.4/2   (m)                       0.50kN/m2                 1.8 kN/m

Floor                           7.4/2  ( m)                       2.00kN/m2                 3.7 kN/m

Partition                      2.6      (m)                       1.75kN/m2                 4.6 kN/m

Total                                                                                                   12.9kN/m

3- Beam Diagram

I will leave this explanatory note at this point as once the above information has been established it can be input into a number of structural applications that will assist in the design of the structural member. When dealing with these structural applications it all comes down to the correct data input. Remember garbage in equates to garbage out.