DESIGN OF MAT (RAFT) FOUNDATIONS Design Steps and Equations For an example on Design of Mat Foundations click here 3D View of Mat (Raft) Foundation
y L1
L2
B
A Pu1
C Pu3
Pu2 ex
Column dimensions l i x bi
B1
Pu ey
B
E
D Pu4
Pu5
x
F Pu6 B2
Pu7 G
Pu8
H
Pu9 I
L Top View of Mat (Raft) Foundation 1 of 6
Foundation Engineering 2 Design of Mat (Raft) Footings Dr. Adnan A. Basma
STEP 1 – CHECK SOIL PRESSURE FOR SELECTED DIMENTION Allowable load P = !Pi Ultimate load
Piu = ! [1.4DLi + 1.7LLi]
Ultimate ratio
ru =
Pu , Ultimate pressure qu = qa x ru P
Locate the resultant load Pu In x- direction:
!My-axis = 0,
ex &
In y- direction:
!Mx-axis = 0,
ey &
"Pu3 $ Pu9 # L2
% "Pu1 $ Pu7 # L1 Pu
"Pu1 $ Pu3 # B1
% "Pu7 $ Pu9 # B2 Pu
,P My x Mx y ) ' Applied ultimate pressure, qu,applied = * u Iy Ix ' *A + ( Where
A = Area = BL Mx = Pu ey
and
My = Pu ex
Ix = ! B L
and
Iy = ! L B
3
3
For the mat shown in Top View, the following sign convention is used to estimate qu,applied x (+)
x (%) A
B
C y (+)
D
E
F
G
H
I
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y (%)
Foundation Engineering 2 Design of Mat (Raft) Footings Dr. Adnan A. Basma
The following values for x and y along with the sign conventions are used to estimate qu,applied Point A
B
C
D
E
F
G
H
I
x
L1
0
L2
L1
0
L2
L1
0
L2
y
B1
B1
B1
0
0
0
B2
B2
B2
For the dimensions L and B to be adequate, qu,max . qu
and
qu,min / 0
STEP 2 – DRAW SHEAR AND MOMENT DIAGRAMS (L - DIRECTION) The mat is divided into several strips in L-direction as shown below where B' = B/4. y L2
L1 B
A B'
C
I
K
J
B1
B' B D
II
E
x
F
B' B2 M
L B'
III
G
H
I
L
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Foundation Engineering 2 Design of Mat (Raft) Footings Dr. Adnan A. Basma
Calculations for Strip ABC: a) The average uniform soil reaction, quI =
q uA $ quC 2
b) Total soil reaction Q = quI x (B1 x L) where B1 = B' c) Total Column loads Pu, ABC = Pu1 + Pu2 + Pu3 d) Average load Pu, avg(ABC) =
Q $ Pu,
e) Load multiplying factor FABC =
ABC
2 Pu,
avg( ABC )
Pu,
ABC
f) The modified loads on this strip P'ui = (FABC) x (Pui) , Pu, avg( ABC ) ) g) Modified Average soil pressure qu, modified = quI x * ' Q *+ '( h) The pressure distribution along the length of the strip qu, L (ABC) =
0 P' ui L
Note that the same can be done for strips DEF (B2 = 2B') and GHI (B3 = B') where: quII = quIII =
q uD $ q uF 2 q uG $ q uI 2
Steps (b) to (h) are repeated as above
The shear and bending moment diagrams for strip ABC is shown below. Other strips will have similar plots.
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Foundation Engineering 2 Design of Mat (Raft) Footings Dr. Adnan A. Basma
P'u1
P'u3
P'u2 L1
L2 B
A
C qu, L (ABC)
+ V(kN)
%
Top Steel between Column 2 and 3
Top Steel between Column 1 and 2
% M(kN.m)
+ Bottom Steel under Column 2
Moment drawn on tension side
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Foundation Engineering 2 Design of Mat (Raft) Footings Dr. Adnan A. Basma
Similar plots should be made for strips in B-direction as shown below A
B I
C III
II
D
E
F
G
H
I
STEP 3 – DEPTH OF CONCRETE, d' Estimate d' for: a) Column 1, 3, 7 and 9 by 2-way punching shear (p' = l + w). b) Column 2, 4, 6 and 8 by 3-way punching shear (p' = 2l + w). c) Column 5 by 4-way punching shear (p' = 2l + 2w). (Use Equations For Punching Shear or approximate d' by Structural Depth of Concrete table for punching shear failure). Select the largest d' from (a), (b) or (c)
STEP 4 – REINFORCEMENT The calculations below are repeated for every strip in L and B direction. a) Select the appropriate moments for each strip (refer to moment diagram) and estimate the moment per meter by Mui/m = Mu/Bi or Li b) Using Mui/m, d', fc' and fy estimate the reinforcement As (refer to Equations for Reinforcement or the percent reinforcement can be obtained directly from Percent Steel Tables).
For an example on Design of Mat Footings click here
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Foundation Engineering 2 Design of Mat (Raft) Footings Dr. Adnan A. Basma
