Combination of Direct Stress and

Bending Stress

CC205 MECHANICS OF STRUCTURES

Introduction

Axial Load

Bending Moment

Body

Direct

Stress

Bending

Stress

Single

resultant

stress

Eccentric Loading

A load, whose line of action does not coincide

with the axis of a column or a strut is known as an

eccentric load

A load imposed on a structural

member at some point other than

the centroid of the section.

Columns With Eccentric Loading

Load P acts at eccentric, e

Load P causes moment (P x e)

and also produces bending stress

Where e is a distance from

centroid to the ecentric point

e

P

P

d

b

e

Eccentric axial load

The combination of direct and bending

stresses is a result of eccentric axial load

Direct

Stress

A

Pd y

I

Mb

Bending

Stress Max/Min

Stress

min/max

Eccentric axial load

yI

M

A

P

min/max

Moment caused by eccentric loading

ePM .

Columns With Eccentric Loading about

One Axis

e

P

max min

y

x x

e y

P

A B

C D

The maximum

stress will be at

the corners which

near to the load

Columns With Eccentric Loading about

Two Axes

e

P

ex = Eccentricity of the load of about x-x axis

ey = Eccentricity of the load of about y-y axis

y

x x

ey

ex

y

P

A B

C D

y

x x

ey

ex

y

P d

b

b = width of the column section

d = thickness of the column

ex = Eccentricity of the load of about x-x axis

ey = Eccentricity of the load of about y-y axis

Formulae

Bending stress about x-x axis

12

3bdI x

2

dy

xx ePM .

Bending stress about y-y axis

12

3dbI y

2

bx

yy ePM .

Formulae

xI

My

I

M

A

P

yx

min/max

Combination stress about x-x and y-y axis

bybxd min/max

Example on column

with eccentric loading

about one axis

Example 1

A column with a cross section

width of 200mm and thickness

350mm, carries an eccentric

load of 20kN, 5mm from the

centroid as shown in figure

below . Determine the maximum

and minimum stress that occur

in the cross section.

e

P

350mm

200mm

A rectangular column 200mm

wide and 150mm thick is

carrying a vertical load of

120kN at an eccentricity of

50mm as shown in Figure

below. Determine the maximum

and minimum intensities of

stress in the section

e P

150mm

200mm

Example 2

A rectangular hollow column

has a cross section of 0.45m x

0.6m. An eccentric load of 2MN

is applied at an eccentricity of

100mm from the geometric axis

of the section. Calculate the

maximum and minimum stress

intensities in the section.

0.45m

y

x

0.3m

0.45m

0.6m

e

Example 3

Example on column

with eccentric loading

about two axes

A short column 800mm x

600mm is subjected to an

eccentric axial load of 60 kN

as shown in figure below.

Find the stresses developed

at each diagonal of the cross

section.

800mm

600mm 50mm

25mm

A B

C D

Example 4

A short column 350mm x

500mm is subjected to an

eccentric axial load of 120 kN

as shown in figure below.

Find the stresses developed

at each diagonal of the cross

section.

Example 5

350mm

500mm

2cm

3cm

A B

D C

End of Chapter