HOMEWORK SOLUTION

 

HW #7

 

CE 455

FOUNDATION AND EARTH STRUCTURE

 

(Question no. 5.1, 5.2, 5.6, 5.9, & 5.13 ..Braja M. Das textbook)

 

 


5.1 cu = 2500 lb/ft2, f = 0o, B = 20 ft, L = 30 ft, Df = 6.2 ft

Net ultimate bearing capacity:

qnet(u) = qu q

From eq. 5.9:

 

5.2 Mat foundation 6.5 m x 6.5 m

Df = 1.5 m, allowable settlement = 50.8 mm, g = 16.5 kN/m3

We have,

For large width and from eq. 5.12:

 

 

 

 

Depth (m)

Field value NF

sv (ton/ft2)

cN = Ö(1/sg)

Ncor

1.5

9

0.26

1.96

17.64

3.0

12

0.52

1.39

16.68

4.5

11

0.78

1.13

12.43

6.0

7

1.03

0.98

6.93

7.5

13

1.29

0.88

11.44

9.0

11

1.55

0.80

8.8

10.5

13

1.81

0.74

9.62

Average = 11.93

We have Fd = 1.099

 

5.6 Precosolidation pressure (Pc) = 105 kN/m2

20 x 10 m

 

Sand

g = 16 kN/m3

 
 

 

 


2 m

 

 

 

 

 

 

 

 



We have:

Po = 4.2*16+2*(18-9.81)+2.6*(17.5-9.81) = 103.574 kN/m2

and:

DPav = 1/6 * (DPt+4DPm+DPb)

For top: DPt = ((30*103)/(12*10))* Ic, from table 4.3 Ic = 0.606

DPt = 151.5 kN/m2

For center: Ic = 0.755, DPm = 188.75 kN/m2

For bottom: Ic = 0.755, DPb = 188.75 kN/m2

DPav = 182.54 kN/m2

Overconsolidated clay:

 

5.9 We have:

Q = 400+500+450+3000+1200+3000+1200+900+350 = 11,000 kN

Also Ix = 1/12 * 16.5*21.53 = 13665.3 m4

Iy = 1/12 * 16.53*21.5 = 8048.4 m4

SMy = 0

11000 x = -3800*8.25+3200*8.25

x = 0.45 m

SMx = 0

11000 y = 4200*3.5+1350*10.75-4200*3.5-1250*10.75

y = 0.098 ~ 0.1 m

Mx = Qey = 11000*0.1 = 1100 kNm

My = Qex = 11000*(-0.45) = -4950 kNm

From eq. 5.25:

 

Point

A : x = -8.25, y = 10.75 m qA = 36.93 kN/m2

B : x = 0, y = 10.75 m qb = 31.86 kN/m2

C : x = +8.25, y = 10.75 m qC = 26.79 kN/m2

D : x = -8.25, y = -10.75 m qD = 25.07 kN/m2

E : x = 0, y = -10.75 m qE = 30.14 kN/m2

F : x = -8.25, y = -10.75 m qF = 35.21 kN/m2

 

5.13 Subgrade reaction = 18 kN/m2

Plate 1 m x 0.7 m

For a foundation of 5 m x 3.5 m :

From eq. 5.49:

Subgrade reaction of rectangular plate is a function of B/L ratio

and we have:

B/L (plate) = 0.7/1 = 0.7

and for foundation

B/L = 3.5/5 = 0.7

kfoundation = 18 kN/m2