Ministry Of Higher EducationN.C.AFUNDAMENTAL OF PRESTRESSED CONCRETE Eng/Ahmed esa

INTRODUCTON

Historical development of prestressing :Prestressed concrete is not a new concept, the first attempt to develop a prestressing system was in 1872 by P.H. Jackson an American engineer .

Today prestressed concrete is used in large constructions around the world

Concept of prestressed concrete :

Advantages of prestressed concrete :Reduces the concrete section dimensions.Prevent or reduce tension cracks in concrete elements.Increase durability of concrete elements.Protect steel in concrete elements from corrosion.Reduces deflection in concrete elements.High resistance against dynamic loads.

Disadvantage of prestressed concreteHigh costs of materials and equipments .

The lack of experience in design and construction of prestressed concrete.

Economics of prestressed concrete:

the depth of a prestressed concrete member is usually about 65 to 80 percent of the depth of the equivalent reinforced concrete member .

the prestressed member requires about 20 to 35 percent of the amount of reinforcement of equivalent reinforced concrete member.

Higher quality materials needed in prestressed concrete result in higher costs .

Prestressing operations themselves result in added cost.

The total initial cost depends on the number of units made .

The long term cost savings are the most effective in prestressed concrete.

Materials of prestressed concrete:Concrete :The most important properties required in prestressed concrete :

high compressive and tensile strength.

early high strength

high density.

Small permanent deformations (shrinkage & creep)

Cement :Cement used is High grade Portland cement.High alkali content cement must be avoided.

Aggregates: Aggregate shall be supplied from controlled and approved sources.Samples must be subjected to specified tests.Admixtures:Its used if needed to :Accelerate hardening .Minimize water content .

Pre-stressing reinforcement: The steel used in prestressing is high tensile steel which have much greater tensile strength and tensile strain than mild steel used in reinforcement concretestress-strain diagram for pre-stressing steel strandsIn comparison mild steel bar steel

stress-strain diagram for pre-stressing steel

Prestressing cables (tendons):Prestressing cables could take many shapes :Wires bars strands Different types of prestressing cables

Types of anchors:

pre-stressed systems: The main classification of prestressed concrete is pretensioned & post tensioned concrete. Other classifications can Be made according to particular attributes:External pre-stressing: In external prestressing tendons are placed outside the concrete member.example of external pre-stressed toStrengthen an old bridge

Circular pre-stressing: The term circular pre-stress applies to pipes, pressure vessels and tanks .

Types of prestressing Pre-tensioning: In pretensioning The tendons are tensioned before the pouring of concrete .Typical pre-tensioning bed and abutments showing beams with straight tendons

Post-tensioning In post tensioning the tendons are tensioned after the pouring of concrete.

SLAB CONFIGURATION

From the structural design point of view, floors are classified according to their internal structural system, such as:

one- or two-way spanning Solid or ribbed Which elements are post-tensioned?

PRESTRESS LOSSES

We can categorized this losses as following:Immediate losses (short term)which occur during the stressing operation

Time dependent loses (long term )which occur at a gradually decreasing rate over the life of the member

Elastic shortening of concrete: For Pretensioned Elements How to calculate this loss?

For post-tensionedThere is new losses in case of all tendons are simultaneously tensioned or there is a single tendon

the tendon that was tensioned last does not suffer any losses due to elastic shortening, while the tendon that was tensioned first suffers the maximum amount of loss.

How to calculate this loss?

Friction losses:Loss of prestressing occurs in post-tensioning members due to friction between the tendons and the surrounding concrete ducts causes a gradual reduction in prestress along tendon from jacking end

The magnitude of this loss is a function of the tendon form or alignment, called the curvature effect and the local deviations in the alignment, called the wobble effect

Anchorage seating LossHow to calculate this loss ?

Creep lossHow to calculate this loss ?

Shrinkage loss:

The magnitude of the shrinkage of concrete is affected by several factors: type of aggregate type of cement time between the end of external curing and the application of prestressing, Size and shape of the member How to calculate this loss ?

Relaxation of tendon loss: Relaxation is defined as gradual decrease of stress in a material under constant strain

The magnitude of the decrease in the prestress depends on the duration of the sustained prestressing force and on the ratio of the initial prestress to the yield strength of the reinforcement (pi/py ) . How to calculate this loss ?

BEHAVIOR OF PRESTRESSED COCNCRETE UNDER FLEXURE

Flexural analysis of prestressed concrete :typical load-deflection curve of a prestressed beam (under reinforced; bonded tendons; first loading).

effect of bonded versus unbonded tendons on load-deflection curve

Flexural types of failures:Fracture of the steel immediately after concrete cracking and thus sudden failure

Crushing of the concrete compressive -zone, preceded by yielding and plastic extension of the steel

Crushing of the concrete compressive zone before yielding of the steel

Minimum Reinforcement Ratio: where fy is in pounds per square inch min = 200/fy min = 1.4/fy Using megapascals

Maximum Reinforcement Ratio: Where:

Shear strength design

Different between The behavior of prestressed concrete beams at failure in shear from their behavior in flexure: They fail abruptly without sufficient advance warning.

The diagonal cracks that develop are considerably wider than the flexural cracks .

The shear forces result in shear stress this stress can result in principal tensile stresses at the critical section.

Modes of failure of beams without diagonal tension reinforcement Flexure failure .

Diagonal Tension Failure (Flexure Shear)

Shear Compression Failure (Web Shear)

SHEAR REINFORCEMENT AFTER CRACKING

ACI CODE DESIGN CRITERIA FOR SHEAR

Shear Strength Provided by Concrete The smaller of them

Another equation by ACI

Required Area of Shear Reinforcement

Limitations and Special Cases Maximum spacing. The spacing s of shear reinforcement measured parallel to the axis of the member shall not exceed 3h/4 or 24 in (61 cm). In common practice the spacing is taken not less than 3 in (75 mm)

Maximum shear. The value of shall not exceed

Minimum shear reinforcement

Critical Sections for Shear

Comparison between Codes

General considerations: ACI code :

The design investigation should include all stages that may be significant. The three major stages are: (1)-jacking stage (2)-Service load stage (3)-The factor load stage.

provisions shall be made for effects on adjoining construction of elastic and plastic deformations, deflection, change of length and rotation due to prestressing. Effects of temperature and shrinkage shall also be included.

The possibility of buckling in a member between points where there is intermittent contact between the prestressing steel and an oversize duct, and buckling in thin web and flanges shall be considered.

Egyptian code:The prestressing members shall be designed to strengthen the load and the actions that act on it and must be investigation the conditions of case of the maximum strength and the conditions of cases of working.

The prestressing members shall be designed with effects of joining members. Euro code: The prestressed forces are permanent effects due to controlled forces and controlled deformations imposed on a structure. Various types of prestresse shall be distinguished from each other as relevant (for ex: prestressed by tendon, prestressed imposed deformation at supports.

For lightweight aggregate concrete, the prestress losses will, in general, be greater than those for dense aggregate concrete.

Design assumptions: ACI code:The strength of a member computed by the strength design of the code requires that two basic condition be satisfied:-(1)-static equilibrium and (2)-compatibility of strains. Equilibrium between the compressive and tensile forces acting on the cross sections at nominal strength should be satisfied.

The maximum concrete compressive strain at crushing of concrete has been observed in tests of various kinds to vary from 0.003 to higher than 0.008 under special condition.

Prestressed flexural member shall be classified as class U, class C, or class T based on (Ft). The computed extreme fiber stress in tension in the pre-compressed tensile zone calculated at service loads, as follows:-

(a)-Class U: (b) Class T:

(c) Class C:

Prestressed two-way slab systems shall be designed as class U with For class C and class T flexural members deflection calculations shall be based on a cracking transformed section analysis. It shall be permitted to base computations on a bilinear moment-deflection relationship.

Egyptian code:The prestressed concrete designed to satisfied the loads acting on it according to design cases and the kind of effects that affect on members and take factors of reduces maximum strength (ps).

The relation between the maximum stress Fpu and the yield stress Fpy for prestressed concrete according to the kind of steel:

Fpy/Fpu=0.8 for deformed bars

Fpy/Fpu=0.85 for normal relaxation stress- relieved strands, wires and smooth bars.

Fpy/Fpu=0.9 for low relaxation stress-relieve strands and wiresthe methods of elastic analysis can be used to Sure from the stresses when transfer the prestresse to concrete and when the external load act on the concrete and when the concrete relieve to cracking load.

Immediate deflection and camber for fully prestressed beams calculated as the elastic theory with taken Ig.

The value of deformation must be not exceed on: L/250 for the beams and one-way slabs L/450 for the cantilevers.Euro code :In the assessment of the likely behavior of the prestressed concrete structure or element, the amount of flexural tensile stress allowed under service load defines its class as follows:-

Class (1):- No flexural tensile stresses.

Class (2);- flexural tensile stresses but no visible cracking

Class (3):- flexural tensile stresses but surface width of cracks not exceeding 0.2 mm for all members

Serviceability requirements flexural members: (a)-Extreme fiber stress in compression:- - 0.6Fci' in ACI code. - 0.45 Fcui in Egyptian code. (b)-Extreme fiber stress in tension except as permitted in (c):- - 3Fci' in ACI code. - 0.22Fcui in Egyptian code. (c)-Extreme fiber stress in tension at ends of simply support members:- - 6Fci' in ACI code. - 0.44Fcui in Egyptian code. Euro code:- -In flexural members compressive stresses should not exceed 0.33 Fcu at the extreme fiber, except in continuous beams and other statically indeterminate structures where they may be increased to 0.4 Fcu within the rang of support moments. In direct compression the stress should not exceed 0.25 Fcu.

Permissible stresses in prestressing steel: Tensile stress in prestressing steel shall not exceed the following :-(a)-Due to prestressing steel jacking force :- - 0.94Fpy0.8Fpu in ACI code. - 0.9Fpy 0.7Fpu in Egyptian code. (b)-Immediately after prestress transfer :- - 0.82Fpy 0.74Fpu in ACI code. -0.7Fpu in Egyptian code. (c)-post-tensioning tendons, at anchorage devices and couplers, immediately after force transfer:- - 0.7Fpu in ACI code. -0.8Fpy0.7Fpu in Egyptian code.Euro code: The jacking force should not normally exceed 75% of the characteristic strength of the tendon but may be increased to 80% provided additional consideration is given to safety and to the load/extension characteristics of the tendon. At transfer, the initial prestress should not normally exceed 70% of characteristics of the tendon, and in no case should it exceed 75%.

Flexural strength: For members with bonded tendons:- ACI and Egyptian code In ACI code- Where is y/c`, ` is `y/c`, and p is 0.55 for py/pu not less than 0.8, 0.4 for py/pu not less than 0.85, and 0.28 for py/pu not less than 0.9. In Egyptian codeWhere w is y/cu, w` is `y/cu, and p is 0.68 for py/pu not less than 0.8, 0.5 for py/pu not less than 0.85, and 0.35 for py/pu not less than 0.9.

ps = se + 10,000 + c`/100 p. In ACI codeBut ps shall not be taken greater than the lesser of y and (se+60000)(b)- For members with un-bonded tendons and with a span-to-depth ratio of 35 or less:-ps = pe + 70 + cu/125 p. In Egy. Code.But ps shall not be taken greater than the lesser of y and (pe + 420). In Euro code For bonded tendons, values of ps may be obtained from table (4.4) in BS code.- For un-bonded tendons, values of ps may be obtained from following eq:- - ps = pe + 7000/l/d(1- 1.7 pu.Aps/ cu.b.d).- The value of ps should not be taken as greater than 0.7 pu.

Minimum bonded of reinforcement: ACI and Egyptian code :Minimum area of bonded reinforcement shall be computed by: - As= 0.004Act.Total amount of prestressed and non prestressed reinforcement shall be adequate to develop a factored load at least 1.2 times the cracking load computed on the bases of the modulus of rupture r, this provision shall be permitted to be waived for:- (a)- Two way, un-bonded post-tensioned slabs. (b)- Flexural members with shear and flexural strength at least twice that required by computations.In Euro code :In the absence of a rigorous analysis, the area of reinforcement (As) may be replaced by an equivalent area of prestressing tendons As* fy/fu

The length of bonded and transferred of prestressed steel:-ACI code :-Minimum length of bonded reinforcement required by the equations of calculates (As).-In positive moment areas, minimum length bonded reinforcement shall be one-third the clear span length (ln) and centered in positive moment area.-In negative moment areas, bonded reinforcement shall extend one-sixth the clear span (ln) on each side of support.Egyptian code: -For the 3 to 7 wire pre-stressing strands (Ld) taken as following equation: - Ld = Lt + La = ( ps 2/3.pe)./7.-Where Lt is the transfer length and it is calculated by following equation: - Lt = (pe /3)./7.- And La is the length after critical section and calculated by: - La = (ps pe)./7.-Where is diameter of tendon by units mm

Euro code: For calculating the transmission length Lt in the absence of experimental evidence, the following equation may be used for initial prestressing forces up to 75% of the characteristic strength of the tendon when the end of the units are fully compacted: - Lt = Kt./ciWhere:- - ci. Is the concrete strength at transfer. - is the nominal diameter of the tendon. - Kt is a coefficient for the type of the tendon.