MAT FOUNDATION USING FEM

STAAD has the ability to generate supports for structures like slabs on grad

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 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..

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.

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 closed surface, 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 figure below, 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

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.

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 the node, 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.

Modelling of SOIL:

The soil is represented by elastic springs located at the nodes as shown in

fig. below. The elastic spring of the constant is named as spring stiffness (K1,K2

etc.) ( KN/m)

Fig. 1 Showing modeling of soil

Fig. 2 Definition of coefficient of sub grade reaction

1

Fig. 3 Finite element model for raft foundation

Problem:

MAT FOUNDATION USING FEM

Data: Width l : 9.50m Length : 10.0m No. of columns : 9 Load on each columns : Dead load =250 KN Live load -150KN Mat Thickness : 0.45m Concrete Grade : M20 Steel Grade : Fe 415 SBC of soil : 120 KN/m2

(9.50m x 10.m)

1 .Creation of Geometry :

File New Project Select space File Name= Mat foundation

Unit KNS Met. Next Add plate Finish.

Type minimum Data on Data area.

Node X Y Z

1 0 0 0

2 0.50 0 0

3 0.0 0.0 0.50

4 0.50 0.0 0.50

Add 4 noded plates. Pick node 1,3,4,2.

1

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1 No. Plate created

(Note: Plate shall be preferably connected in anticlockwise direction.)

Select Plate 1 created. Click Translational Repeat icon.

Global direction X

No. of steps =18 (9.50-0.50)/0.5 =18)

Default spacing =0.50m Ok.

19 Plate elements created in X direction.

Select 19 Plates created.

Click Translational Repeat icon.

Global Direction Z

No. of steps =19 (10.0-0.50)/0.5 =19)

Default spacing =0.50m Ok.

2. Member Property :

Main menu Commands Property Thickness Plate 1 =0.45 Add.

Select all the plates using Plate cursor Assign to selected plates Assign

Yes.

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3. Supports :

Calculation of Sub grade reaction :

SBC =120KN/m2

Elastic mat subgrade reaction value is KN/m2/m

As per Bowels subgrade modulus =40 x FOS x SBC

(for 25mm settlement)

FOS =2.5 to 3

Sub grade modulus =40 x (2.5 to 3) x SBC

= 100 to 120 tomes SBC = X

For 50mm settlement =X/2

For 75mm settlement = X/3 (OR)

Subgrade reaction = SBC/ settlement of 25 mm

=120KN/m2/0.025 =4800 KN/m2/m.

Ks =subgrade reaction = 100 to 120 times SBC say 100 x 120

=100x120 =12,000KN/m2

Ka= End plate = area x ks

= (0.50/2 x 0.50/2) x 12000

= 0.0625 x 12000 = 750 KN/m3

Kb = Middle plate = area x ks

= (0.50 x 0.5/2) x 12000

=0.125 x 12000 = 1500 KN/m3

Kc = Interior plate = area x ks

= (0.50x 0.50) x 12000

=0.25 x 12000 = 3000 KN/m3

General Support Create Click Fixed but

For ka ky =750 KN/m3

For kb ky = 1500 KN/m3

For kc ky = 3000 KN/m3

Select corner node ka Ky=750KN/m3 Assign.

Select intermediate end plates for kb Ky =1500KN/m3 assign.

Select all intermediate node kc for Ky=3000KN/m3 Assign.

4. Loading :

Main menu Commands Loading Click Load case Details Add.

Primary Number :1 Loading type: Dead Title: Dead load Add .

Click Load case details Add. Number 2 Loading type: Live

Title: LL Add close .

Click Load case 1 (Dead) details Add.

Self weight Factor=-1 Y Add.

Dead Load (from column reaction) Fy=-250KN Add.

Select Fy =-250 KN Select all column support node Assign.

Select Load case 2 (Live load) Add .

Fy=-150KN Add.

Select Fy =-150KN Select all column support nodes Assign.

Click Load case details Add.

Click Load Combination Load Number: 4

Name: 1.5 (DL+LL) Normal Factor Default :1.5

Load case 1 α1=1.5

Load case 2 α2=1.5 Close.

Main menu Commands Loading Load list (selecting design load) Ok Close.

5. Analysis Type: Main menu Commands Analysis Perform Analysis No Print Ok. 6 .Post Analysis print:

Main menuCommands Post analysis print Support reactions Ok. 7 . Design:

Main menu Commands Design Concrete Design Current code=IS456

Main menu Tools Set current input unit= length=mm;

Force =N OK. Select all plate elements Define Parameters

Fc=25 Assign

Fymain=415 Assign

Fysec=415 Assign

Max Main=16 Assign

Min Main=10 Assign Close.

Click Commands Design slab elements AddClose

Go to top view & select entire plate using plate cursor Assign to selected plates

Assign Yes.

8 .Analysis:

Main menu Analysis Run Analysis Done. 9. Results: POST PROCESSING

Go to post processing mode. Maximize screen. Select Load case

and see the deflections.

Click Bending Moment Mz icon.

Results View valueBeam results

Bending Moment □ Ends □ Mid span Annotate Close

Click Shear Force Fy icon

Results View valueBeam results

Shear Force □ Ends Annotate Close

Click Axial Force icon FX

Results View valueBeam results.

Axial Force □ Ends Annotate Close.

Report:

Click Report set up.

Available Selected

Input Sections Supports Loadings Output Beam End Forces Reactions Beam max. Axial Forces Beam Max. Moments

Beam Force Details Summary Ok Report Preview Report. To Take picture:

Click take picture icon Enter the title of the sketch. Then Go to report set up.

Select picture Album. If you want to change the sketch title enter the title in

caption. Adjust the picture size by adjusting height & width. Select □ Full page.

To export Results in word file:

File Export Report MS word file. Click save.