Staad Pro- Mat Foundation

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-ofstraightness, 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

2

1

Y X Z

3

4

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

Default spacing =0.50m

(9.50-0.50)/0.5 =18)  Ok.

19 Plate elements created in X direction.

Y X Z

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

Y

 Ok.

X

Z

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.

Y X Z

R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1

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

Subgrade reaction

= SBC/ settlement of 25 mm

(OR)

=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 menuCommands 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  AddClose 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 valueBeam results Bending Moment □ Ends □ Mid span Annotate Close Click Shear Force Fy icon Results View valueBeam results Shear Force □ Ends Annotate Close Click Axial Force icon FX Results View valueBeam 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.