MAT MAT FOUNDATION USING
FEM
STAAD STAAD has the ability to generate supports for structures 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 structure is the soil itself. itself. The resistance of the soil is represented represented through through a term called called Modulus of Subgrade Reaction. The general approach approach to solving such problems problems is to sub-divide the slab into several plate elements. ach node of the meshed slab will then have an in!uence area or a contributory area" which is to say that soil within the area surrounding surrounding that node acts like a spring. The in!uence area is then multiplied by the subgrade modulus to arrive at the spring constant. Subgrade modulus has units of force per length#$. So" the spring will have units of force%length. force%length.
The problem with using this method method is that" for irregularly irregularly-shaped -shaped or large large slabs with
many nodes" computing the in!uence area for each node can become &uite tedious and time-consuming. The model below e'empli(es the problem..
This is where the )oundation type of support can be useful. STAAD will calculate the in!uence areas of all the nodes by itself and derive the spring constants for you. *n STAAD" we refer to facility as SPRING SUPPORT GENERATION. STAAD has two options for such supports+ a, The AST* MAT option b, The /AT MAT option The ELASTIC MAT option : 0hen the spring support generation facility was (rst introduced in STAAD" it was based on this method. *n fact" this was the only method available until and including STAAD./ro 1221 3uild 4225. This method calculates the in!uence area of the various nodes using the Delaunay triangle method. The distinguishing aspect of this method is that it uses the 6oint-list that accompanies the AST* 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.
7ence" while specifying the 6oint-list" one should make sure that these 6oints make up a closed surface. 0ithout a proper closed surface" the area calculated for the region may be indeterminate and the spring constant values may be erroneous. onse&uently" the list should have at a minimum" $ nodes. 0hile 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 aren8t precise to a signi(cant number of digits. Also" the internal angle formed by 1 ad6acent lines connecting $ consecutive nodes in the list should be less than 492 degrees" which is to say that" the region should have the shape of a conve' polygon. )ailure to form straight edges and conve' polygons can lead to erroneous in!uence area values and conse&uently" erroneous spring constants. This is the limitation of this feature. The e'ample below e'plains the method that may be used to get around a situation where a conve' polygon is not available. )or the model comprised of plate elements 422 to 421 in the (gure below" one wishes to generate the spring supports at nodes 4 to 9. 7owever" a single AST* MAT command will not su:ce because the internal angle between the edges 4-9 and 9-; at node 9 is 1;2 degrees" which violates the re&uirements of a conve' polygon So" one should break it up into 1 commands+ 4 1 $ 9 AST* MAT D*R < S=3> 122. $ 5 ? @ ; 9 AST* MAT D*R < S=3> 122.
oints $ and 9 will hence get the contribution from both of the above commands. 3ecause this method uses nodes to generate contours" it may be used whether the mat is de(ned using plates" or solids. This is the advantage of this method. The PLATE MAT option : *f the foundation slab is modeled using plate elements" the in!uence area can be calculated using the principles used in determining the tributary area of the nodes from the (nite element modeling standpoint. *n other words" the rules used by the program in converting a uniform pressure load on an element into ('ed end actions at the nodes are used in calculating the in!uence area of the node" which is then multiplied by the subgrade modulus to obtain the spring constant. This feature has been available since STAAD./ro 1221 3uild 422?. The advantage of this method is that it overcomes one of the ma6or limitations of the Delaunay triangle method" which is that the contour formed by the nodes of the mat must form a conve' hull. Example
SUPPORTS 17!" TO 17#1 PLATE MAT DIR $ONL$ SU%GRADE !& PRINT $R '&1 &1 PLATE MAT DIR $ONL$ SU%GRADE !& The (rst of the above 1 commands instructs STAAD to internally generate supports for the nodes at the corners of plate elements 4;2?5 TB 4;294. The second e'ample instructs STAAD to internally generate supports for the nodes at the corners of plate elements which lie in the global C plane bound by the value of -2.24 and F2.24 length units. Another advantage of the PLATE MAT method is that it enales us to vie! soil "ressure #ontours eneath the ase of the sla. After the analysis" go to the post processing mode" and click on the /lates page. *n the selection bo' for choosing the type of result to plot" choose base pressures. This is not currently available with the AST* MAT method. Mo(ellin) o* SOIL: The soil is represented by elastic springs located at the nodes as shown in (g. below. The elastic spring of the constant is named as spring stiGness HI4"I1 etc., H IE%m,
)ig. 4 Showing modeling of soil
)ig. 1 De(nition of coe:cient of sub grade reaction
1
Fi)& + Finite element mo(el *o, ,a*t *o-n(ation
/roblem+ MAT FOUNDATION USING
FEM
Data: 0idth l + J.?2m ength + 42.2m Eo. of columns + J oad on each columns + Dead load K1?2 IE ive load -4?2IE Mat Thickness + 2.5?m oncrete >rade + M12 Steel >rade + )e 54? S3 of soil + 412 IE%m1
HJ.?2m ' 42.m, 1 &C,eation o* Geomet,. : )ile
Eew
/ro6ect
=nit IES Met.
Select space
Ee't
Add
)ile
plate
Type minimum Data on Data area. Eode
C
<
4
2
2
2
1
2.?2
2
2
$
2.2
2.2
2.?2
5
2.?2
2.2
2.?2
Add 5 noded plates. /ick node 4"$"5"1.
EameK Mat foundation
)inish.
1
2
1
$ / 0 3
4
4 Eo. /late created HEote+ /late shall be preferably connected in anticlockwise direction., Select /late 4 created. lick Translational Repeat icon. >lobal direction Eo. of steps
C
K49
Default spacing K2.?2m
HJ.?2-2.?2,%2.? K49,
Bk.
4J /late elements created in C direction.
$ / 0
Select 4J /lates created. lick Translational Repeat icon. >lobal Direction
Eo. of steps
K4J
H42.2-2.?2,%2.? K4J,
Default spacing K2.?2m
$
Bk.
/
0
& Mem2e, P,ope,t. : Main menu ommands
/roperty
Select all the plates using /late cursor
Thickness /late 4 K2.5? Add.
Assign to selected plates
Assign
R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1
$ / 0
R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1 R1
+. S-ppo,t3 + alculation of Sub grade reaction + S3 K412IE%m1 lastic mat subgrade reaction value is IE%m1%m A3 pe, %o4el3 subgrade modulus K52 ' )BS ' S3 Hfor 1?mm settlement, )BS K1.? to $ Sub grade modulus K52 ' H1.? to $, ' S3 K 422 to 412 tomes S3 K C )or ?2mm settlement
KC%1
)or ;?mm settlement
K C%$
Subgrade reaction
K S3% settlement of 1? mm
HBR,
K412IE%m1%2.21? K5922 IE%m1%m.
Is Ksubgrade reaction K 422 to 412 times S3 say 422 ' 412 K422'412 K41"222IE%m1 IaK nd plate K area ' ks K H2.?2%1 ' 2.?2%1, ' 41222 K 2.2@1? ' 41222 K ;?2 IE%m$
Ib K Middle plate K area ' ks K H2.?2 ' 2.?%1, ' 41222 K2.41? ' 41222 K 4?22 IE%m$
Ic K *nterior plate K area ' ks K H2.?2' 2.?2, ' 41222 K2.1? ' 41222 K $222 IE%m$
>eneral Support
reate
lick )i'ed but
)or ka
ky K;?2 IE%m$
)or kb
ky K 4?22 IE%m$
)or kc
ky K $222 IE%m$
$
Select corner node ka
IyK;?2IE%m
Select intermediate end plates for kb
Assign.
Iy
K4?22IE%m$
Select all intermediate node kc for IyK$222IE%m$
assign.
Assign.
"& Loa(in) : Main menu /rimary
ommands oading lick
Eumber
+4 oading type+ Dead
Click Load case details Title: LL
Add.
Add close
oad case Details
Add.
Title+ Dead load Add .
Number 2 Loading type: Live
.
lick oad case 4 HDead, details Add. Self weight
)actorK-4
< Add.
Dead oad Hfrom column reaction,
)yK-1?2IE
Add.
Select )y K-1?2 IE Select all column support node Assign. Select oad case 1 Hive load, Add . )yK-4?2IE Add. Select )y K-4?2IE Select all column support nodes Assign. Click Load case details
Add.
Click Load Combination Name: 1.5 !L"LL#
Load case 1
&1'1.5
Load case 2
&2'1.5
Load
Number: 4
Normal $actor !e%ault :1.5
Close.
Main menu ommands oading oad list Hselecting design load, Bk lose.
!. Anal.3i3 T.pe+ Main menu ommands
Analysis /erform
Analysis Eo /rint
Bk.
5 .Po3t Anal.3i3 p,int+ Main menuommands /ost analysis print Support reactions Bk. 7 . De3i)n:
Main menu
ommands Design oncrete
Design
urrent
codeK*S5?@ Main menu )orce KE )cK1?
Tools Set
BI.
current input unitK lengthKmmL
Select all plate elements De(ne /arameters
Assign
)ymainK54? Assign )ysecK54? Assign Ma' MainK4@ Assign Min MainK42 Assign lose. lick
ommands Design slab elements Addlose
>o to top view select entire plate using plate cursor Assign to selected plates Assign o
to post processing mode. Ma'imiNe screen. Select oad case
and see the de!ections. lick %en(in) Moment Results
Oiew
MN icon.
value3eam results
3ending Moment P nds P Mid span Annotate lose lick Shea, Fo,e )y icon Results
Oiew
value3eam results
Shear )orce P nds
Annotate lose
lick Axial Fo,e icon )C Results
Oiew
value3eam results.
A'ial )orce P nds
Annotate lose.
Report+ lick Report set up. Available
Selected
*nput
Sections Supports oadings
Butput
3eam nd )orces Reactions 3eam ma'. A'ial )orces 3eam Ma'. Moments 3eam )orce Details Summary
Bk
Report /review Report. To Take picture+ lick take picture icon nter the title of the sketch. Then >o to report set up. Select picture Album. *f you want to change the sketch title enter the title in caption. Ad6ust the picture siNe by ad6usting height width. Select P )ull page. To e'port Results in word (le+ )ile
'port
Report
MS
word (le. lick save.
