1

Design of Prestressed Concrete Bridges

Design of RC structure - Objectives

2

(i) have acceptable probability of performing satisfactorily during their intended life,

(ii) sustain all loads with limited deformations during construction and use,

(iii) be durable, (iv) adequately resist the effects of misuse and

fire.

The objectives can be fulfilled by:

3

(i) understanding the strength and deformation characteristics of concrete and steel, (ii) following the clearly defined standards for materials, production, workmanship and maintenance, and use of structures in service, (iii) adopting measures needed for durability.

Methods of design of reinforced concrete structural elements

4

The three methods are: (i) limit state method, (ii) working stress method, (iii) method based on experimental approach

Which of the three methods is the best?

5

Limit state method is the best of the three methods when clearly applicable.

What is the basis of the analysis of structures to be designed?

6

The basis of the analysis is the employment of linear elastic theory.

How to estimate the design loads in (i) limit state method, and (ii) working stress method?

7

(i) In limit state method, Design loads = Characteristic loads multiplied by the partial safety factor for loads (ii) In working stress method, Design loads = Characteristic loads

characteristic load.

8

Characteristic load is that load which has a ninety-five per cent probability of not being exceeded during the life of the structure

What are the main (i) loads, (ii) forces and (iii) effects to be considered while designing the structures?

9

(i) The main loads are: (a) Dead loads (b) Imposed loads or live loads (c) Wind loads (d) Snow loads (e) Erection loads (ii) The main force is: (a) Earthquake force

(iii) The main effects are: (a) Shrinkage, creep and temperature effects (b) Foundation movements (c) Elastic axial shortening (d) Soil and fluid pressures (e) Vibration (f) Fatigue (g) Impact (h) Stress concentration effects due to application of point loads

What are the basis of combining different loads for the design?

10

Natural phenomenon and common sense are the basis of selecting the combination of different loads acting on the structure while designing.

11

Limit State is condition of potential failure.Failure being defined as any state that makes the design to be infeasible.Structures limit states are of major two categories, Strength and Serviceability. The procedures of Limit State Design let the Engineer to examine conditions which may be considered as failure – referred to as limit states.These conditions are classified into Ultimate and Serviceability Limit States.Within each of these classifications, various aspects of the behavior of the concrete structure may need to be checked.Ultimate Limit States concern, such as load carrying resistance and equilibrium, when the Structure reaches the point where it is substantially unsafe for its intended purpose.The designer checks to ensure that the maximum resistance of a structure (or element of a structure) is adequate to sustain the maximum actions (loads or deformations) that will be imposed upon it with a reasonable margin of safety.For RCC & PSC design the aspects which must be checked are resistance (including yielding, buckling, and transformation into a mechanism) and stability against overturning.

Limit State Concept / Philosophy

12

Serviceability Limit State

In contrast to reinforced concrete, the design of prestressed concrete members is initially based upon the flexural behaviour at working load conditions.

The ultimate strength of all members in bending, shear and torsion is then checked, after the limit states of serviceability have been satisfied.

The prime function of prestressing is to ensure that only limited tensile stresses occur in the concrete under all conditions within the working range of loads.

To satisfy the limit state of cracking it is necessary to satisfy the stress limitations for the outermost fibres of a section.

13

Limit State Design procedures require formal examination of different conditions which might lead to collapse or inadequate performance.The effect of various actions is compared with the corresponding resistance of the structure under defined failure criteria (limit states).The most important failure criteria are the ultimate limit state (collapse) and the serviceability limit state of deflection.In checking each limit state, appropriate design models must be used to provide an accurate model of the corresponding structural behavior.Separate partial safety factors are introduced for loading and material. These factors are variable quantities and the precise values to be used in design to reflect the degree of variability in the action or resistance to be factored.Different combinations of actions may also require different values of safety factor.This flexible approach helps provide a more consistent level of safety compared with other design approaches. Both concrete and steel structures are to be designed on ‘Limit State Design’ based on IRC 112-2011 and IS 800-2007 respectively.

14

Design Procedure

15

Structures designed by limit state of collapse are of comparatively smaller sections than those designed employing working stress method. They, therefore, must be checked for deflection and width of cracks. Excessive deflection of a structure or part thereof adversely affects the appearance and efficiency of the structure, finishes or partitions. Excessive cracking of concrete also seriously affects the appearance and durability of the structure. Accordingly, cl. 35.1.1 of IS 456 stipulates that the designer should consider all relevant limit states to ensure an adequate degree of safety and serviceability. Clause 35.3 of IS 456 refers to the limit state of serviceability comprising deflection in cl. 35.3.1 and cracking in cl. 35.3.2. Concrete is said to be durable when it performs satisfactorily in the working environment during its anticipated exposure conditions during service. Clause 8 of IS 456 refers to the durability aspects of concrete. Stability of the structure against overturning and sliding (cl. 20 of IS 456), and fire resistance (cl. 21 of IS 456) are some of the other importance issues to be kept in mind while designing reinforced concrete structures.

16

Class of PSC Structure

azlanfka/utm05/mab1053 17

Basic Theory

azlanfka/utm05/mab1053 18

Basic Inequalities

Stresses at transfer condition

Top fibre 'minfZ

M

Z

eP

A

P

t

i

t

i

c

i

Bottom fibre 'maxf

Z

M

Z

eP

A

P

b

i

b

i

c

i

azlanfka/utm05/mab1053 19

Basic Inequalities

Stresses at service condition

Top fibre maxfZ

M

Z

eP

A

P

t

s

t

i

c

i

Bottom fibre minfZ

M

Z

eP

A

P

b

s

b

i

c

i

azlanfka/utm05/mab1053 20

Inequalities for Zt and Zb

Re-arranging the above inequalities by combining, the expressions for Zt and Zb can be obtained.

These two inequalities may be used to estimate the preliminary section for design.

'

minmax ff

MMZ ist

min

'max ff

MMZ isb

azlanfka/utm05/mab1053 21

Inequalities for Prestress Force P

eAZ

MfZP

ct

iti

'min

eAZ

MfZP

cb

ibi

'max

eAZ

MfZP

ct

sti

max

eAZ

MfZP

cb

sbi

min

PRESTRESSED CONCRETE BRIDGES - problems

PRESTRESSED CONCRETE BRIDGES - problems

TYPICAL CROSS SECTIONS OF

PRETENSIONED

PRESTRESSED CONCRETE

BRIDGE DECKS

TYPICAL CROSS SECTIONS OF

PRETENSIONED

PRESTRESSED CONCRETE

BRIDGE DECKS

TYPICAL CROSS SECTIONS OF

POST -TENSIONED

PRESTRESSED CONCRETE

BRIDGE DECKS

TYPICAL CROSS SECTIONS OF

POST -TENSIONED

PRESTRESSED CONCRETE

BRIDGE DECKS

CANTILEVER METHOD OF CONSTRUCTION OF

PRESTRESSED CONCRETE BRIDGESCANTILEVER METHOD OF CONSTRUCTION OF

PRESTRESSED CONCRETE BRIDGES