1. Course No: CE 416
Course Title :pre-stressed concrete
WELCOME TO MY PRESENTATION
Presented by
Md.Sohel Rana
ID: 10.01.03.043
2.
3.
A beam is a structural element that is capable of withstanding load
primarily by resisting bending. The bending force induced into the
material of the beam as a result of the external loads, own weight, span
and external reactions to these loads is called a bending moment.
Beam of rectangular cross sections are known as rectangular beams.
4. Concrete is good in compression and bad in tension.
Tensile strength of concrete is about 1/10 of f’c.
longitudinal reinforcement is placed
closed to the bottom side of the beam
5. WSD
or working stress design is based on
elastic theory, assuming a straight line
distribution along the depth of concrete.
The actual or working load are estimated
such that the member are proportioned so
that stresses in the concrete and steel
resulting from the service load are within
the allowable limit.
6. Flexure – WSD Method
Assumptions:
• Plane sections remain plane
• Hooke’s Law applies
• Concrete tensile strength is
neglected
• Concrete and steel are totally
bonded
Allowable
Stress
Levels
• Concrete = 0.45f’c
• Steel = 20 ksi for gr. 40 or gr. 50
= 24 ksi for gr. 60
Transformed
Section
• Steel is converted to equivalent
concrete.
n
Es
Ec
7. Effect of
steel ratio)
The behavior of the beam at failure (mode of
failure) is determined by the relative amount of
steel present – measured by .
As
bd
=0
No steel used. Brittle (sudden) failure.
min
Just enough steel to prevent brittle failure
200
min
< balance
Steel fails first – ductile failure (desirable)
'
0 . 18 f c
balance = max
Steel and concrete both stressed to allowable
limit
fy
max
> balance
Concrete fails first – brittle failure (not
desirable)
fy
balanced
8.
9. “Internal Couple” Method
As
bd
• Uses the internal force couple T & C
to determine the moment
• Defines factors k and j that can be
used to find depth of stress block and
moment arm of couple
• Provides equations for analysis or
design.
n
Es
Ec
10.
11.
Reinforcement in both tension and compression zone.
If concrete can not develop to required compressive
force to resist the maximum moment ,then additional
reinforcement is added in the compression zone.
12. Double
Reinforcement
- Increase steel area
- Enlarge section
When Mreq’d > Mallow
- Double RC
only when no choice
A’s
d’
M
As
s
T’ = A’s f’s
c
s
C = fc k b d
T = As fs
As fs
As fs
13. T’ = A’s f’s
T’ = A’s f’s
C = fckbd
C = fckbd
d-d’
jd
T = As fs
T = As fs
Moment strength
M=M
M
Steel area
As
M1
Mc
1
2
f c kjbd
T = As fs
2
M2
As 1
f s jd
Mc
As 2 f s ( d
A s 1 f s jd
Mc
M
As f s ( d
As 2
M
fs (d
d )
d )
Mc
d )
15. A’s
Force equilibrium [ Fx
T’ = A’s f’s
T’ = T
d-d’
A’s f’s = As fs
T = As fs
Substitute
As
1
2
As 2
1
k
fs
k
d d
2 fs
k
d d
1
k
16. Advantages of Using WSD method
• This design usually results in relatively large
sections of structure members.
• Experienced engineers are used to this
method.
• In past it was the only method for design
purposes.
17. Disadvantages of Using WSD
method
• This method deals with only the elastic
behaviour of the structure.
• Same factor of safety is used for
different loads.
• Failure mode is not directly predicated.
• The failure mode can not be observed.
