mat foundations

5/27/2018 Mat Foundations

1/10

Mat foundations


2/10


3/10

1

Description

STAAD has the ability to generate supports for structures like slabs

on grade, which also go by the name mat foundations. A mat

foundation is a large concrete slab sitting on soil. The support for

the structure is the soil itself. The resistance of the soil is

represented through a term called Modulus of Subgrade Reaction,

the definition of which may be found in many textbooks onfoundation analysis.

The general approach to solving such problems is to sub-divide the

slab into several plate elements. Each node of the meshed slab will

then have an influence area or a contributory area, which is to say

that soil within the area surrounding that node acts like a spring.

The influence area is then multiplied by the subgrade modulus to

arrive at the spring constant. Subgrade modulus has units of force

per length^3 . So, the spring will have units of force/ length.

The problem with using this method is that, for irregularly-shaped

or large slabs with many nodes, computing the influence area for

each node can become quite tedious and time-consuming. The

model below exemplifies the problem.


4/10

STAAD.Pro 2004 Training Manual Advanced Topics

2

This is where the Foundation type of support can be useful.

STAAD will calculate the influence areas of all the nodes by itself

and derive the spring constants for you. In STAAD, we refer to

facility as SPRING SUPPORT GENERATION.

STAAD has two options for such supports:

a) The ELASTIC MAT option

b) The PLATE MAT option

The ELASTIC MAT option :

When the spring support generation facility was first introduced in

STAAD, it was based on this method. In fact, this was the only

method available until and including STAAD.Pro 2002 Build 1004.

This method calculates the influence area of the various nodes

using the Delaunay triangle method.


5/10


3

The distinguishing aspect of this method is that it uses the joint-

list that accompanies the ELASTIC MAT command to form a

closed surface. The area within this closed surface is then

determined and the share of this area for each node in the list is

then calculated.

Hence, while specifying the joint-list, one should make sure that

these joints make up a closed surface. Without a proper closedsurface, the area calculated for the region may be indeterminate

and the spring constant values may be erroneous. Consequently, the

list should have at a minimum, 3 nodes.

While forming the closed surface, namely, a polygon, the sides of

the polygon have to be assembled by lining up points along the

edges. The edge detection aspects of this method are very sensitive

to out-of-straightness, which may occur if the coordinates of the

nodes aren't precise to a significant number of digits.

Also, the internal angle formed by 2 adjacent lines connecting 3

consecutive nodes in the list should be less than 180 degrees,

which is to say that, the region should have the shape of a convex

polygon.

Failure to form straight edges and convex polygons can lead to

erroneous influence area values and consequently, erroneous spring

constants. This is the limitation of this feature.

The example below explains the method that may be used to get

around a situation where a convex polygon is not available.

For the model comprised of plate elements 100 to 102 in the figurebelow, one wishes to generate the spring supports at nodes 1 to 8.

However, a single ELASTIC MAT command will not suffice

because the internal angle between the edges 1-8 and 8-7 at node 8

is 270 degrees, which violates the requirements of a convex

polygon.


6/10


4

So, one should break it up into 2 commands:

1 2 3 8 ELASTIC MAT DIREC Y SUBG 200.

3 4 5 6 7 8 ELASTIC MAT DIREC Y SUBG 200.

Joints 3 and 8 will hence get the contribution from both of the

above commands.

Because this method uses nodes to generate contours, it may be

used whether the mat is defined using plates, or solids. This is the

advantage of this method.


7/10


5

The PLATE MAT option :

If the foundation slab is modeled using plate elements, the

influence area can be calculated using the principles used in

determining the tributary area of the nodes from the finite element

modeling standpoint. In other words, the rules used by the program

in converting a uniform pressure load on an element into fixed end

actions at the nodes are used in calculating the influence area of thenode, which is then multiplied by the subgrade modulus to obtain

the spring constant. This feature has been available since

STAAD.Pro 2002 Build 1005.

The advantage of this method is that it overcomes one of the major

limitations of the Delaunay triangle method, which is that the

contour formed by the nodes of the mat must form a convex hull.

Example

SUPPORTS

17054 TO 17081 PLATE MAT DIR YONLY SUBGRADE 5000.0

PRINT

YR -.01 0.01 PLATE MAT DIR YONLY SUBGRADE 5000.0

The first of the above 2 commands instructs STAAD to internally

generate supports for the nodes at the corners of plate elements

17054 TO 17081.

The second example instructs STAAD to internally generate

supports for the nodes at the corners of plate elements which lie in

the global XZ plane bound by the YRANGE value of -0.01 and

+0.01 length units.

Another advantage of the PLATE MAT method is that it enables us

to view soil pressure contours beneath the base of the slab. After

the analysis, go to the post-processing mode, and click on the

Plates page. In the selection box for choosing the type of result to

plot , choose base pressures. This is not currently available with the

ELASTIC MAT method.


8/10


6

Question : How do I tell STAAD that my soil spring is effective only inCOMPRESSION, and should not be considered when it goes into

tension?

Answer : This may be done by using the ELASTIC MAT or PLATE MATcommand in conjunction with the SPRING COMPRESSION

command. The program iteratively solves the problem so that thefinal answer reflects the condition corresponding to actual contact

between slab & soil . Example problem 27 il lustra tes this .

Question : Is it possible to get a report which shows the influence areagenerated by STAAD for each support node?

Answer : Yes. Use the PRINT option available with the ELASTIC MAT orPLATE MAT commands. This will produce a report of the

influence areas. An example of such a report is shown below.

To get a report of the spring constants themselves, use the

command

PRINT SUPPORT INFORMATION


9/10


7

Question : Is it possible to find out the base pressure at each node for eachload case?

Answer : Yes. In the post-processing mode, go to the Node Base pressurepage. A table will appear along the right side of the screen showing

these values. The Summary tab will show the maximum and

minimum pressure along with the associated node for each of the 3global directions.

Question : How does subgrade modulus differ from soil bearing capacity?

Answer : A soil must be capable of carrying the loads it is subjected to,without undergoing a shear failure, or excessive settlements. This

capacity is referred to as the soil bearing capacity.

The modulus of subgrade reaction is a measure of the stiffness of

soil if it were to behave like a spring. It is the relationship between

bearing pressure and soil deflection.

The modulus of subgrade reaction is the quantity by which the

influence area of a support node is multiplied by to get the

equivalent spring constant which can be used at the analysis stage.

One would provide this as an input item when one wishes STAAD

to generate spring supports using the ELASTIC MAT command, as

explained in section 5.27.3 of the STAAD.Pro Technical Reference

manual.

At the end of the mat foundation analysis, the maximum soil

pressure you get from STAADs soil pressure diagram should be

within the limits of the soils bearing capacity. If the actualpressure exceeds the capacity, it is an indication of fa ilure.


10/10


8

Question : If you have the value for soil bearing pressure, how do you usethat to come up with the subgrade modulus that STAAD uses for

elastic mat definitions?

Answer : One doesn't use the bearing capacity of soil to determine thesubgrade modulus. Instead, it is a separate attribute of soil. If you

have a look at the text book "Foundation Analysis and Design" byJoseph Bowles, you will find a few sections devoted to that topic,

with specific values listed for specific types of soil.

The basic difference between these 2 attributes is that, bearing

capacity (or bearing pressure) is the pressure at which the soil fails,

either in shear or compression. It hence has units of force per unit

area. Subgrade Modulus on the other hand is a measure of the

"spring constant" of soil. It is the distance that a unit area of soil

would deflect under a unit load.

mat foundations

Documents