Concrete Design Ali N. Attiyah, Ph.D.
Fourth Year 2015-2016
1
Lecture eleven
Prestressed Concrete
The prestressed concrete member is that preloaded to counteract the effect of applied
loads to a given degree.
Concrete Design Ali N. Attiyah, Ph.D.
Fourth Year 2015-2016
2
Strands are used to apply pre-stress on the concrete members, and strands are cables
consist of certain number of wires.
Concrete Design Ali N. Attiyah, Ph.D.
Fourth Year 2015-2016
3
There are two methods to pre-stress concrete:
1- Pre-tensioned prestressed concrete. 2- Post-tensioned prestressed concrete.
Some of stresses are lost due to different reasons, and according to ACI 318-14:
There are three types of forces in strands because of losses: jacking force P
j
(which is
before any losses), initial force P
i
(which is after initial losses), and effective force P
e
(which
is after total losses).
The losses (a), (b), (d), and (f) are initial losses and (c) and (e) are long-term losses.
Concrete Design Ali N. Attiyah, Ph.D.
Fourth Year 2015-2016
4
Serviceability Requirements:
According to ACI 24.5, the concrete stresses in prestressed concrete members shall be
limited to permissible values. For simply supported beam, stresses shall be checked at
two sections: the middle and end of beam. For example, the stresses at the middle of
beam are found from the following figure:
Concrete Design Ali N. Attiyah, Ph.D.
Fourth Year 2015-2016
5
Concrete Design Ali N. Attiyah, Ph.D.
Fourth Year 2015-2016
6
Concrete Design Ali N. Attiyah, Ph.D.
Fourth Year 2015-2016
7
There are two loading stages:
1) Initial loading stage:
It is the stage after transfer of force from steel to concrete (i.e. after initial
prestress losses). Stress distribution is shown in Figs. (a) and (b) below.
2) Service loading stage:
It is the stage of applying all superimposed loads (i.e. dead loads except self-
weight and live loads) and after all losses. Stress distribution is shown in Fig. (c)
below.
Concrete Design Ali N. Attiyah, Ph.D.
Fourth Year 2015-2016
8
Where
P
i
is the initial prestress force in steel,
P
e
is the effective prestress force in steel,
e is the steel eccentricity,
A
c
is the area of beam section,
I
c
is the moment of inertia of beam section,
c
1
is the distance from the centroid to the top fiber,
c
2
is the distance from the centroid to the bottom fiber,
r is the radius of gyration,
M
o
is the bending moment due to self-weight only,
M
d
is the bending moment due to dead load except self-weight,
M
l
is the bending moment due to live load.
Kern points are those points where the prestress forces will be applied without causing
tension and they are found from:
Concrete Design Ali N. Attiyah, Ph.D.
Fourth Year 2015-2016
9
Concrete Design Ali N. Attiyah, Ph.D.
Fourth Year 2015-2016
10
Example: