This document discusses the deflection of prestressed concrete beams. It defines deflection as the vertical displacement of a beam under loading. Methods for calculating short-term and long-term deflection are presented, including the double integration method, moment area method, and conjugate beam method. Factors that influence deflection, such as imposed loads, prestressing force, modulus of elasticity, and creep are also described. The document provides equations to calculate deflection due to different prestressing tendon profiles and load cases. Serviceability limits for deflection are specified as span/300 for upward deflection and span/250 for total deflection.

1. PROF. SHREETEJ P.G.
JAIN COLLEGE OF ENGINEERING,BELAGAVI
Department of Civil Engineering
JCE e CONNECT

2. DESIGN OF PRESTRESSED
CONCRETE ELEMENTS (17CV82)
M O D U L E - I I
D E F L E C T I O N O F B E A M S

3. DEFLECTION OF BEAMS
Deflection:
It is defined as the vertical
displacement of a point on
a loaded beam.
The maximum deflection
occurs where slope is zero.

4. DEFLECTION OF BEAMS
Since a prestressed concrete member is smaller in depth than an
equivalent reinforced concrete member, the deflection of a prestressed
concrete member tends to be larger.

5. METHODS OF CALCULATION OF DEFLECTION
Double Integration Method
Moment Area Method
Conjugate Beam Method
Principal of Virtual Work

6. Short term
deflection
Long term
deflection
TYPES OF DEFLECTION

7. Short term deflection (at transfer) is caused by the initial prestressing force,
dead load and live load.
Long term deflection (under service loads) is caused by the prestressing
force, dead load, live load and the effect of Creep and Shrinkage.
The deflection of a flexural member is calculated to satisfy the limit state of
serviceability.

8. The total deflection is the resultant of the upward deflection due to
prestressing force and downward deflection due to gravity loads.
Only flexural deformation is considered and any deformation due to shear
force is neglected in the Calculation of Total deflection.

9. FACTORS INFLUENCING DEFLECTION
1. Imposed load and self weight.
2. Magnitude of Prestressing force.
3. Cable profile.
4. Modulus of Elasticity.
5. Moment of Inertia.
6. Shrinkage and Creep.
7. Span of member.
8. Support conditions.

10. PERMISSIBLE DEFLECTION
Clause 19.3.1 of IS:1343 – 1980 specifies limits of deflection such that the efficiency
of the structural element and the appearance of the finishes or partitions are not
adversely affected.
total upward deflection due to prestressing force should
not exceed span / 300.
Upward deflection = Span/300 (only PSF)
The total deflection due to all loads, including the effects of
temperature, creep and shrinkage, should not exceed span / 250
= Span/250

11. SHORT TERM DEFLECTION
1. Due to gravity loads i.e. DL and LL
2. Due to Prestressing force

12. DUE TO GRAVITY LOADS (DD & LL)
Simply supported Beams

13. DUE TO GRAVITY LOADS (DD & LL)
Cantilever Beams

14. DUE TO GRAVITY LOADS (DD & LL)
W W W
A1 A2
x1
x2
By Mohr’s Theorem
𝜹 = 𝜟 =
𝐴.𝑥
𝐸.𝐼
(By Mohr’s moment area
method)

15. DUE TO PRESTRESS
Deflection of PSC beam depends on the tendon profile. The prestressing force causes
a deflection only if the CGS is eccentric to the CGC.
1. Straight cable
(-)
𝜹 = 𝜟 =
𝐴.𝑥
𝐸.𝐼

16. 2. Parabolic cable
(-)
𝜹 = 𝜟 =
𝐴.𝑥
𝐸.𝐼
5/8

17. 3. Sloping Tendon
(-)
𝜹 = 𝜟 =
𝐴.𝑥
𝐸.𝐼

18. 4. Trapeziodal cable
(-)
𝜹 = 𝜟 =
𝐴.𝑥
𝐸.𝐼
𝜟 =
−𝑃.𝑒
6.𝐸.𝐼
( 2𝑙1
2
+6 𝑙1𝑙2+3 𝑙2
2
)

19. e1
5. Sloping Tendon with end eccentricity
(-)
𝜹 = 𝜟 =
𝐴.𝑥
𝐸.𝐼
e2
(+)
P.e1
-P.(e1+e2)
𝜟 =
𝑃.𝑙2
24.𝐸.𝐼
( 𝑒1 − 2𝑒2)
Here, the resultant deflection at the
centre is obtained as sum of the
upward deflection due to (e1+e2)
and downward deflection due to e1

20. (-)
e1
e2
P.(e1+e2)
(+)
P.e1
6. Parabolic tendon with end eccentricity Here, the resultant deflection at the
centre is obtained as sum of the
upward deflection due to (e1+e2)
and downward deflection due to e1
𝜟 =
𝑃.𝑙2
48.𝐸.𝐼
( 𝑒1 − 5 𝑒2)

21. LONG TERM DEFLECTIONS