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