Prestressed-concrete-lecture-1.pdf

PRESTRESSED CONCRETE (LECTURE 1)

q BASIC CONCEPTS q MATERIALS q ADVANTAGES AND LIMITATIONS q PRESTRESSING METHODS q FLEXURAL ANALYSIS

BASIC CONCEPTS 1.1 INTRODUCTION

PRESTRESSING –

can be defined as in general terms as the preloading of a structure, before application of the service loads, so as to improve its performance in specific ways.

PRESTRESSING OF CONCRETE –

involves application of a compressive loading, prior to applying the anticipated service loads, so that tensile stresses that otherwise would occur are reduced or eliminated.

???Why do we need prestressing for concrete???

BASIC CONCEPTS Ø

Concrete’s tensile strength is only 8-15% of its compressive strength.

•

Cracks develop at early stages of loading in flexural member (beams, slabs)

Ø

To prevent such crack, compressive forces can be suitably applied in the longitudinal direction, either concentrically or eccentrically (linear prestressing).

Ø

The prestressing enhances not only the bending capacity, but it also enhances the shear and the torsional capacities of the flexural members.

BASIC CONCEPTS PRESTRESSING OF CONCRETE

MATERIALS q CONCRETE - a composite material composed of gravels which are the coarse aggregates, sand which is the fine aggregates and hydrated cement which is the binder

q PROPERTIES of HARDENED CONCRETE The concrete in prestressed applications has to be of good quality. It requires the following properties: 1)

high strength with low water-to-cement ratio

2)

durability with low permeability, proper mixing, compaction and curing

3)

minimum shrinkage and creep, by limiting the cement content

MATERIALS q STRENGTH of CONCRETE For prestressed concrete applications, high strength concrete is required for the following reasons. 1)

to sustain high stresses at anchorage regions

2)

to have high resistance in compression, tension, shear and bond

3)

to have higher stiffness for reduced deflection

4)

to have reduced shrinkage crack

q PROPERTIES OF HIGH STRENGTH CONCRETE 1)

High strength

2)

Minimum shrinkage and creep

3)

High durability

4)

Easy to cast

5)

Cost effective

MATERIALS

Typical compressive stress-strain curves for normal density concrete with wc= 145 pcf

Typical compressive stress-strain curves for lightweight concrete with wc= 100 pcf

MATERIALS q TIME DEPENDENT DEFORMATION OF CONCRETE 1) CREEP - defined as the increase in deformation with time under constant load. Due to the creep of concrete, the prestress in the tendon is reduced with time. The rate of strain increase is rapid at first, but decreases with time, until after many months, a constant value is approached assymptotically.

2) SHRINKAGE of CONCRETE - defined as the contraction due to loss of moisture. The study of shrinkage is also important in prestressed concrete to calculate the loss in prestress. Just like creep, the shrinkage is also a phenomenon which varies with time. It has also the same effect, i.e. it will have a reduction in the prestressing force with time, and also it will lead to an increased deflection. Hence, the study of creep and shrinkage is important in prestressed concrete to calculate the loss in prestress.

MATERIALS q PRESTRESSING STEEL The development of prestressed concrete was influenced by the invention of high strength steel. It is an alloy of iron, carbon, manganese and optional materials. During the early stages of prestressing concrete, it was noticed that the effective prestress reduced with time, and the reason was the creep and shrinkage of concrete. In order to overcome this problem, high strength steel was developed. Restressing of concrete became successful only after the development of the high strength steel.

MATERIALS q TYPES of PRESTRESSING STEEL 1) Round Wires

MATERIALS 2) Stranded Cable

MATERIALS 3) Alloy Steel Bars

MATERIALS

MATERIALS qPROPERTIES of PRESTRESSING STEEL 1) High Strength 2) Adequate ductility 3) Bendability, required at harping points at ends 4) High-bond, required for prestressed member 5) Low relaxation to reduce losses 6) Minimum corrosion

MATERIALS q STRESS-STRAIN PROPERTIES OF STEEL

MATERIALS

MATERIALS q RELAXATION OF STEEL - defined as the decrease in stress with time under constant strain. Due to the relaxation of steel, the prestress in the tendon is reduced with time. Hence, the study of relaxation is important in prestressed concrete to calculate the loss in prestress. The relaxation of steel depends on the type of steel, the amount of initial prestress, and the temperature to which the steel is subjected.

ADVANTAGES OF USING PRESTRESSED CONCRETE 1) Section remains uncracked under service loads • Reduction of steel corrosion Ø Increase in durability • Full section is utilized Ø Higher moment of inertia (higher stiffness) Ø Less deformation (improved serviceability) • Increase in shear capacity • Suitable to be used in pressure vessels and in liquid retaining structures • Improved performance due to resilience under dynamic and fatigue loading.

ADVANTAGES OF USING PRESTRESSED CONCRETE 2) High span-to-depth ratios • Larger spans possible with prestressing (Bridges, building with large column-free spaces) Typical values of span to depth ratios in slabs are given below: Ø Non-prestressed slab: 28:1 Ø Prestressed slab: 45:1 3) Suitable for precast construction The advantages of precast constructions are as follows: • Rapid construction • Better quality control • Reduced maintenance • Suitable for repetitive construction • Multiple use of formwork • Availability of standard shapes

LIMITATIONS OF PRESTRESSING Although prestressing has advantages, some aspects need to be carefully addressed. •

Skilled technology(hence, not as common as reinforced concrete)

•

Use of high-strength materials is costly

•

There is additional cost in auxiliary equipment

•

Need for quality control and inspection

PRESTRESSING METHODS 1) PRETENSIONING -

stretching the tendons between external anchorages before the concrete is placed. As the fresh concrete hardens, it bonds to the steel. When the concrete has reached the required strength, the jacking force is released, and the force is transferred by bond from steel to concrete.

2) POST-TENSIONING – the tendons are stressed after the concrete has hardened and achieved sufficient strength, by jacking against the concrete member itself. - usually hollow conduits containing the tendons are placed in the beam forms, to the desired profile, before pouring the concrete.

PRESTRESSING METHODS (PRETENSIONING)

PRESTRESSING METHODS (POSTTENSIONING)

AGAS-AGAS BRIDGE (LEYTE)

CHACO CORRIENTES BRIDGE (ARGENTINA)

WISCASSET BRIDGE (MAINE)

FLEXURAL ANALYSIS q FLEXURAL ANALYSIS – the process by which a given prestressed beam with known concrete dimensions, as well as the magnitude and line of action of the prestressed force are already known.

q FLEXURAL DESIGN – material properties are known and specified, the designer must determine concrete and steel dimensions as well as the magnitude and the line of action of the prestressing force.

PARTIAL LOSS OF PRESTRESS The jacking tension, Pj, initially applied to the tendon is reduced at once to what is termed the initial prestress force Pi. A part of this loss in jacking tension that due to friction between a post-tensioned tendon and its encasing duct, usually occurs before the transfer of prestress force to the concrete. The remainder due to elastic shortening of the concrete and due to slip at post-tensioning anchorages as the wedges take hold, occurs immediately upon transfer. Additional losses occur over an extended period, because of concrete shrinkage and creep, and because of relaxation of stress in the steel tendon. As a result the prestressed force is reduced from Pi to its final or effective value, Pe after all significant time-dependent losses have taken place. P The effectiveness ratio, R= e Pi

Pi−Pe or 1−R= Pi

NOTE: Pi = fpi x Aps Pe = fpe x Aps Where: Pi = initial prestressing force fpi = initial prestress before losses Aps = area of prestressing tendons Pe = effective prestressing force fpe = effective prestress after losses

FLEXURAL ANALYSIS Both analysis and design of prestressed concrete may require the consideration of several load stages as follows: 1) Initial prestress immediately after transfer, when Pi alone may act on the concrete 2) Initial prestress plus self-weight of the member 4) Effective prestress, Pe, plus service loads consisting of full dead and expected live loads 5) Ultimate load, when the expected service loads are increased by load factors, and the member is at incipient failure

ELASTIC STRESSES (UNCRACKED BEAMS) 1. INITIAL CONDITION Initial Prestressing force 1

plus Self-weight

−P# A

+

P# ec' I

-

−P# A

-

P# ec) I

+

M+c' I

c1 CL

e

2

c2 M+c) I

ELASTIC STRESSES (UNCRACKED BEAMS) 2. FINAL CONDITION Final Prestressing force 1

and full Service Load

−P# A

+

P# ec' I

-

−P# A

-

P# ec) I

+

M+c' I

-

M,-.c' I

c1 CL

e

2

c2 M+c) I

+

M,-.c) I

PERMISSIBLE STRESSES IN CONCRETE IN PRESTRESSED FLEXURAL MEMBERS (NSCP 2010) 1. Stresses in concrete immediately after prestress transfer before time-dependent prestress losses):

fci= fci=

fti= fti=

2. Stresses in concrete at service loads (based on uncracked section properties, and after allowance for all prestress losses) shall not exceed the following:

fcs =

Concrete tensile stress limits at service loads: Load Condition

Concrete tensile stress limit

Prestress plus total load

fts =

fc’

Where: f 'c = compressive strength of concrete at 28 days (MPa) f 'ci = compressive strength of concrete at time of initial prestress (MPa)

Example 1: For the floor plan shown, consider the highlighted beam that is made up of normal weight concrete having unit weight of 24 kN/m3. Listed below are the superimposed loads:

Light Storage -

6 kPa

The beam will be pre-tensioned using multiple seven-wire strands; eccentricity is constant and equal to 175 mm. The initial prestress force Pi immediately after transfer is 750 kN. Time dependent losses due to creep and some other factors total to 15% of the initial prestress force. Assuming simple support, find the concrete flexural stresses at midspan and support sections under initial and final condition.

200

12 m 200

A

1000

5m

5m

500 mm

300

A 250

SECTION A-A

Example 2: A rectangular concrete beam of width 275mm & depth h = 700mm is post tensioned using parabolic tendon having eccentricity e = 195mm at midspan & zero at the supports. The initial prestress force is 1485.6 kN & the effectiveness ratio is 0.80. (Assume ɣc = 24 kN/m3 and fixed supports) Check if the stresses exceed the ACI stress limits. Loads: WD+L = 4.38 KN/m +14.59 KN/m L= 12.20m

Example 3: A pretensioned beam has rectangular section of 200 mm and 500 mm depth. It is built using normal weight concrete (Ɣc = 24 KN/m3). Stress limits are as follows: fti = 1.139 Mpa fci = -12.42 Mpa fts = 2.62 Mpa fcs = -12.42 MPa The effectiveness ratio, R is equal to 0.80. For these conditions, find the initial prestress, Pi and eccentricity, e to maximize the superimposed dead and live load moment, MD+L that can be carried without exceeding stress limits. What uniformly distributed load can be carried on a 9 m span? What tendon profile would you recommend?

Example 4: A post tensioned bonded with a prestress transfer force of 1560 kN is being wrongly picked up at its mid-point. The parabolic tendons used is placed at a distance of 175mm from the bottom at the midspan and at the center of the beam at its ends. The beam has a span of 12m. Modulus of rupture fr=0.62√f’c. Dimension of the beam is 300 mm x 600mm, f’c = 34 Mpa, unit weight of concrete = 24 kN/m3. a)

Compute the stress at the top fibers at its midspan.

b)

Compute the eccentricity at the midspan so that the stress of concrete will not crack.

c)

Determine the distance from both ends where the beam should be picked up to avoid any possibility of damage to the beam during handling.

Example 5: The flooring of a warehouse is made up of double-tee joists (DT) as shown. The joists are simply supported on a span of 7.5 m and are pre-tensioned with one tendon in each stem with an initial force of 745 kN each, located at 75 mm from the bottom of the fiber, loss of stress at service load is 18%. Load imposed on the joists are: Dead Load = 2.3 kPa Live Load = 6 kPa Properties of DT: A = 200, 000 mm2 I = 1880 x 106 mm4 yt = 88 mm yb = 267 mm a = 2.4 m a)

Compute the stress at the bottom fibers of the DT at mid-span due to the initial pre-stressing force alone.

b)

Compute the resulting stress at the bottom fibers of the DT at midspan due to the service loads and prestress force.

c)

What additional super imposed load can the DT carry such that the resulting stress at the bottom fibers at midspan is zero.