CE 537, Spring 2014 Introduction to Prestressed 1 / 7

In prestressed concrete, compressive stresses are applied to the concrete prior to loading. Under service loads, the entire cross section is essentially in compression, which takes advantage of concrete’s considerable compressive strength but minimal tensile strength. Therefore cracking under service loads is minimized or eliminated (depending on the design). Also, since the entire concrete section resists (unlike in “normally” sections where most of the section is in tension and therefore unused) service load deflections are greatly reduced.

Prestressed concrete components are constructed in two different ways. In pretensioned concrete components, the prestressing steel is tensioned before the concrete is placed, as illustrated in Figure 1 below. The prestressing tendons are typically un‐sheathed so that the concrete bonds to the tendons.

Pretensioning frame anchored to ground Prestressing steel is tensioned Pretressing tendons P P

Concrete is placed

Prestressing force is transferred to the concrete

Figure 1. Construction sequence for Pre‐tensioned concrete

In post‐tensioned concrete, the concrete is prestressing steel is tensioned after the concrete is placed, as illustrated in Figure 2 below. The prestressing tendons are sheathed or placed in ducts so that the concrete and tendons are unbounded.

Since concrete deforms under sustained loads (creep), prestressed concrete was not practical until the advent of high‐strength prestressing bars and strands. Typical prestressing strands have a tensile strength of 270 ksi, compared to 90 ksi for grade 60 . With high‐strength prestressing, large initial prestress forces can be applied to the concrete, so that when the concrete shortens over time and causes a decrease in prestress force, there is still sufficient prestressing force applied to the concrete to keep the cross section in compression under service loads. Typical stress‐strain curves of prestressing strands are shown in Figure 3.

CE 537, Spring 2014 Introduction to Prestressed Concrete 2 / 7

The sizes of prestressing reinforcement are listed in the appendix of the ACI code and are shown in Table 1 below. Seven‐wire Grade 270 ½‐inch diameter strand is very common, and Grade 270 0.60 inch diameter strand is becoming more popular.

post‐tensioning cable (sheathed)

Concrete forms are erected and prestressing strands are positioned form shoring existing column

Concrete is placed

Cables are tensioned

Figure 2. Construction sequence for Post‐tensioned concrete beam

CE 537, Spring 2014 Introduction to Prestressed Concrete 3 / 7

Figure 3. Stress‐strain curves of 7‐wire strands (from PCI Manual).

CE 537, Spring 2014 Introduction to Prestressed Concrete 4 / 7

Table 1. Diameters and areas of typical prestressing reinforcement (from ACI 318‐11).

CE 537, Spring 2014 Introduction to Prestressed Concrete 5 / 7

Design of prestressed concrete beams consists of selecting the depth of the concrete beam and the amount and layout of prestressing tendons to:

• prevent or limit flexural tensile cracking in the concrete under service loads • limit service‐load deflections • prevent flexure failure under over‐load (ultimate strength) conditions

It’s possible to use too much prestressing resulting in excessive compressive stress in the concrete (usually at locations with high service‐load stresses) and/or resulting in excessive tensile stress in the concrete (usually at locations with little or no service load stresses).

Chapter 18 of ACI 318 on prestressed concrete presents limits on stresses in prestressing and concrete, which are summarized in Figure 4 below. Please refer to Chapter 2 (p 19) in ACI 318 for explanations of notation.

The stress on the concrete due to prestressing is calculated using the equations from strength of materials for normal stresses due to an eccentric axial load (see Figure 5). The effect of the eccentric axial load is equivalent to the axial load applied at the centroid of the concrete section plus a moment equal to the axial load times the eccentricity. The normal stress at any location in the concrete cross section can then be calculated using the familiar formula:

P My ! = ± A I

CE 537, Spring 2014 Introduction to Prestressed Concrete 6 / 7

Prestressing Steel: The following criteria are specified by ACI for the prestressing steel (Section 18.5.1, pg 287):

Max stress due to jacking force = min( 0.94 fpy , 0.80 fpu )

Max stress at transfer = min( 0.82 fpy , 0.74 fpu )

Stage Design Criteria

1. Concrete at ends elsewhere stresses at wSW transfer of PT max tension ' ' 6 f c 3 fc force to i i concrete ' ' max comp. 0.7 f 0.6 f P P (ACI 18.4.1, ci ci pg 290)

2. Concrete Sustained All loads stresses under loads service loads max tension ' (ACI Table 12 f ci R18.3.3, pg 291) max comp. 0.45 f ' 0.60 f ' ci ci

2. Deflections L max ΔLL = under service 360 loads L (ACI Table 9.5b, max Δafter erection = pg 129) 240

3. Flexure strength φ M n ≥ M u

under ultimate φ M n ≥1.2 M cr loads (ACI 18.7 and 8, pp 294 - 296)

Figure 4. Relevant design criteria in ACI 318‐11

CE 537, Spring 2014 Introduction to Prestressed Concrete 7 / 7

Figure 5. Calculation of concrete stresses due to prestressing