The document is a lecture handout for a geotechnical engineering course, focusing on stress distribution under uniformly loaded rectangular and trapezoidal areas using Boussinesq's equation. It includes various cases for calculating vertical stress at different points under loaded areas and provides practice problems for students. Reference material cited includes an introductory text on geotechnical engineering.

1. 1
Geotechnical Engineering–II [CE-321]
BSc Civil Engineering – 5th Semester
by
Dr. Muhammad Irfan
Assistant Professor
Civil Engg. Dept. – UET Lahore
Email: mirfan1@msn.com
Lecture Handouts: https://groups.google.com/d/forum/geotech-ii_2015session
Lecture # 8
29-Sep-2017

2. 2
STRESS UNDER UNIFORMLY LOADED
RECTANGULAR AREA
Bousinesq equation can be extended for uniformly loaded
rectangular area as;
),( nmIq recz 
where,
IZ = Shape function/ Influence factor
m = b/z; n=l/z
x
z
q
A
y
z
dx
dy

3. 3
STRESS UNDER
UNIFORMLY
LOADED
RECTANGULAR
AREA
•3
z
L
n
z
B
m  ,
Log scale

4. 4
STRESS UNDER UNIFORMLY LOADED
RECTANGULAR AREA
This methods gives stress at the corner of rectangular area
),( nmIq recz 
A B
D C
Case I
E
F
G
A B
D C
Case II
σz due to ABCD =
4 x σz due to EBFG

5. 5
E
FH
G
E
FH
I
STRESS UNDER UNIFORMLY LOADED
RECTANGULAR AREA
G
A B
D C
A B
D C
I
A B
D C
Case I Case II
σz due to ABCD =
4 x σz due to EBFG
Case III
σz due to ABCD = σz due to
(EBFI + IFCG + IGDH + AEIH)

6. 6
E
I
STRESS UNDER UNIFORMLY LOADED
RECTANGULAR AREA
A B
D C
EF
GH
F
A B
D
C
Case IV
σz due to ABCD = 2 x σz due to ABEF
Case V
σz due to ABCD = 2 x σz due to EBCF
Case VI
σz due to ABCD = σz due to
(AEGI – BEGH – DFGI + CFGH)
A BE
D CF

7. 7
A rectangular footing with load intensity of 20 t/m2 is shown.
Find z at 2.5 m depth for point
a) R
b) S
c) T
d) U
Practice Problem #9

8. 8
STRESS UNDER
UNIFORMLY
LOADED
RECTANGULAR
AREA
•8
z
L
n
z
B
m  ,
Log scale

9. 9
The uniform contact pressure under a rectangular footing of 6m
x 5m is 200kPa. Compute the vertical stress component under
points A and B at a depth of 2m.
Practice Problem #10

10. 11
STRESS UNDER
UNIFORMLY
LOADED
TRAPEZOIDAL AREA
Stress distribution under
a very long embankment;
length = ∞
(U.S. Navy, 1986, after
Osterberg, 1957)
Ref: Holtz & Kovacs
(2nd Ed.)
Fig. 10.6 (pp #474)

11. 12
STRESS UNDER
UNIFORMLY
LOADED
TRIANGULAR AREA
Influence values for vertical
stress under the corners of a
triangular load of limited
length.
(U.S. Navy, 1986)
Ref: Holtz & Kovacs
(2nd Ed.)
Fig. 10.7 (pp #475)

12. 13
CONCLUDED
REFERENCE MATERIAL
An Introduction to Geotechnical Engineering (2nd Ed.)
Robert D. Holtz & William D. Kovacs
Chapter #10