# (Assg-1)………Direct & Bending stresses - WordPress.com

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29 Νοε 2013 (πριν από 4 χρόνια και 7 μήνες)

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S.A.
-

I

(
130604
)

Civil Branch (Sem.

III)

Direct & Bending
Stresses.

Assignment
-

1

01.08.2013

Department of
Civil Engineering.

| Darshan Institute Of Engineering & Technology.

Contact me for any quarry on Blog Add
ress
:
-

1

-

: FORMULAE SUMMARY :
-

1.

Maximum & Minimum
Stresses
.

Maximum stress (
σ
max
)

M
inimum

stress (
σ
m
in
)

σ
max

=
σ
d

+
σ
b

=

For rectangular section

(

)

σ
max

=
σ
d

-

σ
b

=

For rectangular section

(

)

2.

Sign Convension

Compression = Positive (+’ve)

Tension = Negative (
-
‘ve)

3.

To tension condition

e

<= Z/A

4.

Core OR Kernel of section

e

=

Z

/

A

For rectangular = e
x

= b / 6 & e
y

= d / 6

;where
b & d are the width & depth of rectangular section

For rectangular hollow section e
x

= [(DB
2

-

bd
3
)]/[6D(BD
-
bd)]

e
y

= [(BD
2

-

db
3
)]/[6D(BD
-
bd)]

;where B & D are external width & depth & b & d are internal width &
depth of hollow section. respectively

For Circular section e
x

= e
y

= d / 8

;where
d is the
diameter of circular section.

5.

Stresses in Dams

Weight of dam

W

=

(a+b)*h
1
*
γ

C.G. of weight of dam

X

=

Pressure of water

P

=

Pressure of earth

P =

Distance of resultant form A

Z

=

Eccentricity

e

=

z

b/2

Maximum stress

σ
max

=

(

)

Minimum Stress

σ
min

=

(

)

Stability Check

1.

No. Tension Condition

OR

2.

No Overturning

3.

No Sliding

4.

No Crushing

σ
max

<
σ
c

Minimum Base Width

of base for no tension

1.

6.

Chimney

Weight of chimney W =

;
Where
?

= Unit weight of chimney material.

Direct Stress (σ
o
) =

Uniform wind pressure (P)

acting on a side of width b = P = p*b*h

Moment induce @ base = M =

Bending stress (σ
b
) =

The extreme stresses on the base are

σ
max

= σ
o

+ σ
b

σ
max

= σ
o

-

σ
b

(Ph)/(w3)

Z

b/2

b/2

h1

h

wh

a

x

A

B

C

D

E

F

P

R

W

h/3

σ
m
in

σ
max

b

d

h

Wind
Pressure
"P"

S.A.
-

I

(
130604
)

Civil Branch (Sem.

III)

Direct & Bending
Stresses.

Assignment
-

1

01.08.2013

Department of
Civil Engineering.

| Darshan Institute Of Engineering & Technology.

Contact me for any quarry on Blog Add
ress
:
-

2

1

Explain the limit of eccentricity and core of section

2

Draw the ‘core’ for the following section:
-

1.

Square

2.

Rectangular

3.

Circular

4.

Hollow circular

3

Explain the
condition to avoid tensile stresses at the base of a masonry dam when
subjected to hydrostatic pressure.

March
2010

04

4

A masonry pier of size 3 m x 4 m is subjected to a compressive load of 600 kN as shown
in figure.

Find the stresses produced at each
be placed at the center of the pier to avoid tension in the pier section?

March
2010

08

5

A masonry dam 4.5 m high, 1 m wide at the top and 3.5 m wide at the base retains water
to the full
height. The water face of the dam is vertical. Determine the extreme pressure
intensities at the base. Water and masonry weigh 9810 N/m3 and 22500 N/m3
respectively. Find also the extreme pressure intensities at the base when the dam is
empty.

Dec
2009

07

6

A masonry pier of 3 m x 4 m supports a vertical load of 80 kN as shown in figure. Find
the stresses developed at each corner of the pier.

Dec
2009

07

7

A concrete block has the cross
-
section as shown in figure. The block weighs 90kN
& a
vertical downward load of 20kN at P on the axis XX but eccentric about YY axis.
Calculate the distance of the point P from the axis YY, if the pressure under the block
along the edge AD is just twice the pressure under the edge BC & determine these
pre
ssures.

Dec
2012

07

8

A masonry retaining wall is 6 m high, 0.75 m wide at top and 2 m wide at bottom. The
wall is retaining soil up to top. The face of the wall on soil side is vertical. The lateral
pressure due to soil varies from
zero at top to 3.2 kN / m2at bottom. Specific weight of
masonry is 24 kN/m3. Draw stress distribution at base of wall due to self weight of wall
alone and due to self weight of wall and soil pressure.

May
2012

07

S.A.
-

I

(
130604
)

Civil Branch (Sem.

III)

Direct & Bending
Stresses.

Assignment
-

1

01.08.2013

Department of
Civil Engineering.

| Darshan Institute Of Engineering & Technology.

Contact me for any quarry on Blog Add
ress
:
-

3

9

A horizontal wooden cantilever, 3 meters

long is 40mm wide and 100mm deep and is
hinged at the wall end. A wire is connected to it at 1m from the free end and the other
end is attached to the wall. The wire makes an angel of 30 degree with the cantilever
which carries a uniformly distributed lo
ad of 1.5kN/m over the entire length. Find the
maximum compressive stress in it and the position of the section where it occurs.

Practice Numerical

10

A timber beam 100mm wide X 200mm deep is simply supported on 2.5m span carries a

of its self
-
weight. It is supported in tilted position so that its
100mm face makes an angle of 20 degree with the horizontal. Determine the maximum
flexural stresses at all four corners.

11

The section of masonry pier 5 meters high is a hollow rectangl
e, external dimensions
3.6mX1.5m, internal dimension 3mX0.9m. A horizontal trust of 25k is exerted at the top
of the pier in the vertical plane bisecting the length. If the unit weight of masonry is
23kN/sqm, calculate the maximum and minimum stresses at t
he base.

12

A 325mm X 165mm I
-
section when used as a short column can carry safely an axial load
of 500kN. It the column is strengthened by riveting a 250mm X 12mm steel plate to each
flange in order that the load of 500kN may be permitted to act in a
direction parallel with
the axis of the column through a point in the centre line of the web, find the maximum
eccentricity possible if the compressive stress in the compound section is not to exceed
that when the axial load acts on the unplated section. F
or a 325mmX165mm I
-
section A
= 54.9sqcm, Ixx = 9874.6 cm
4
.

13

A trapezoidal retaining wall has the following data:

Top Width = 2.0m; Bottom width = 6.0m; height of wall = 10m; Soil retained up to the
top of wall; Density of earth = 15kN/m
3
; Density of ma
sonry = 20kN/m
3
; Angle of
respose = 32°; Coefficient of friction = 0.6;

Calculate the maximum and minimum stresses at the base of the wall and check the
stability.