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Software Knowledge Base

 


Note ID: 000070 – Applications: SLABS4

Title: SLABS4 manual – Results – Reactions: Area Method

Description: Detailed notes about the reaction results by the Area Method including numerical examples

See Also:

Date Created: 25/03/2008

Date Modified: 25/03/2008

 


SLABS4 offers two methods of calculating the reactions by the Tributary Area Method. In previous versions of SLABS there was only one method available, and that approach is referred to in SLABS4 as ‘Area Method – Basic’. The new approach introduced in SLABS4 is the ‘Area Method – Advanced’. The Basic approach is kept in the software for the purpose of solving some very olds data files, and the switch between the two options is available under [ Settings > Models and Solvers ] from the Main Menu. A sample screen shot highlighting the switch is shown below;

 

Sample Screen Shot – Switch between Advanced/Basic Area Method calculations

 

 

The Area Method – Advanced is much more precise than the approach taken for the Area Method – Basic. The Area Method - Advanced works in a similar manner as the manual calculations performed by hand when the load is distributed to the surrounding supports. This method will apply appropriate fractions of a point and line loads to the surrounding column and wall supports.

 

The Basic Area method - Basic will ‘snap’ the entire load to the closest support. This is accurate if there is only a UDL load applied. But if there are point or line loads applied to the model then the old Area method will ‘snap’ 100% of the point or line loads to the closest support. This concept is demonstrated using the following example were we consider a rectangular slab, supported by 6 columns and a point load of 50kN (the point load is applied to the Live Load Case to exclude the self weight calculations).

 

 

Sample Screen shot - Geometry and Loading

 

The Area method - Basic will ‘send’ the entire point load to the closest column as shown in the screen shot below;

Sample Screen shot – Reactions calculated by the Area method - Basic

 

 

The new Area method - Advanced will distribute the point load on all columns considering the distance between the point load and each supporting column, and also considering the area of slab that each column supports.

 

Sample Screen shot – Reactions calculated by the Area method - Advanced

 

 

The following generalised procedure outlines the steps and calculations performed by the software in order to determine the reactions in the supporting elements by the Area Method – Advanced.

 

1.)    Determine distance between the supporting elements and the load

2.)    Exclude the elements that will have 0 (zero) reactions due to either a large distance (>15m) between the load and the support or are located within a ‘shadow’ zone.

3.)    Determine the dissecting angle between the supporting elements and the load

4.)    Solve the final equation ‘Fi’ for the reaction

5.)    Repeat steps 1-4 for the next supporting element

 

 

For the numerical example below, the calculations are based on the point load and “Column A” highlighted in the screen shot below;

 

Sample Screen shot – Indicating the point load and supporting column used in the numerical example

 

 

There are two conditions that exclude any supporting elements from the reaction calculations by the Area Method – Advanced. These include either a distance greater than 15m between the load and the supporting element, or if the support is located with a shadow zone.

 

The screen shot below indicates that in this example the distance (d) between the point load and each supporting column is within the maximum 15m;

 

 

 

The second condition is to determine if any of the supporting elements are located within a shadow zone. A shadow zone is created for each supporting element by a 120 degree angle placed at each supporting element as shown in the screen shot below;

 

 

Sample Screen shot – Shadow zone concept used in the reaction calculations by the Area Method – Advanced

 

The dashed orange coloured lines in the screen shot above indicate the placement of the 120 degree angles relative to the 50kN point load. The grey coloured zones are the shadow zones, and all supporting elements that are within these zones are excluded from the calculations. Note: the coordinates of the bottom right column coincide with the shadow zone boundary and is therefore excluded in the rest of the Area method calculations.

 

Once the supporting elements that satisfy the exclusion conditions are known, the next step in the calculations is to determine the bisecting angle (a) between these supporting elements.

 

Using the parameters calculated in the previous steps, the following equation is solved for each supporting element to determine the reaction;

 

 

In the case of “Column A”, the step by step calculations are;

F = 50kN

d=4.243m

a =110.1° (1.922 rad)

(Note: 0.0355 below is the sum of all  for each supporting column).

 = 35.43kN

 

In the case of supporting walls, the shadow zones are generated in a similar manner with the only difference being that are two 120 degree angles placed at each end of the wall. The screen shot below is an example that illustrates this concept;

 

Sample Screen shot – Shadow zone concept example for supporting walls

 

 

Sample Screen shot – Shadow zone concept example: 120 degree lines at each wall end

 

 

The process outlined above is repeated for each point load in every Load Case. All line loads and pressure loads in a model (in each Load Case) are reduced to point loads and the entire procedure is again repeated for each supporting element.

A Report containing a tablulated output of the Area Method – Advanced is available by selecting [ Reports > Reactions – Area Method ] from the Main Menu.