• Example GIVEN: The rectangular prestressed concrete beam as shown below. Use the following:. Concrete f’ c = 5000 PSI. Concrete strength = 75%(f’ c) at time of prestressing. A ps = 3 – ½” dia. 7-wire strands @ 0.153 in 2 per strand = 0.459 in2. f pu = 270 KSI (using an ordinary 7-wire strand). Initial prestress force, P s = 70%(f.
• Sl.No Contents Page No. PRESTRESSED CONCRETE STRUCTURES UNIT I - THEORY AND BEHAVIOUR 1.1 Pre-stressed concrete 2 1.2 Types of pre-stressing 2 1.3 Losses 3 UNIT II - DESIGN CONCEPTS 2.1 Analysis of beam section - concept 18 2.2 Elastic Design for flexure 38 2.3 Permissible stresses for flexure member 41 2.4 End block 54 UNIT III CIRCULAR PRESTRESSING.
• Design process starts with the choice of a preliminary geometry. By trial and adjustment, it converge to the final section with geometrical details of the concrete section and the alignment of the prestressing strands. The section has to satisfy the flexural (bending) requirements of concrete stress and steel stress limitations.
• Design a simply supported prestressed concrete Y beam which carries a 150mm thick concrete slab and 100mm of surfacing, together with a nominal live load udl of 10.0 kN/m 2 and kel of 33kN/m. The span of the beam is 24.0m centre to centre of bearings and the beams are spaced at 1.0m intervals.

(6 points) Prestressed Concrete Second Exam Solution Page 3 of 4 Problem 2: Design, for service load condition, a post-tensioned T-section to carry a total service load of 15 kN/m (not including self weight) on a 12m simply supported span.

Fundamentals of Prestressed Concrete Bridge (with solved example)

Introduction: In prestressed concrete, a prestress force is applied to a concrete member and this induces an axial compression that counteracts all, or part of, the tensile stresses set up in the member by applied loading. In the field of bridge engineering, the introduction of prestressed concrete has aided the construction of long-span concrete bridges. These often comprise precast units, lifted into position and then tensioned against the units already in place, the process being continued until the span is complete. For smaller bridges, the use of simply supported precast prestressed concrete beams has proved an economical form of construction. The introduction of ranges of standard beam section has simplified the design and construction of these bridges. Methods of Prestressing:

1. Pre-tensioning

2. Post-tensioning

Serviceability Limit State

• In contrast to reinforced concrete, the design of prestressed concrete members is initially based upon the flexural behavior 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 fibers of a section.

Stress Limitation BS8110

• Class 1 : No tensile stresses;
• Class 2 : Flexural tensile stresses, but no visible cracking;
• Class 3 : Flexural tensile stresses, but surface crack widths not exceeding a maximum value (0.1mm for members in aggressive environments and 0.2mm for all other members)

Prestress Losses:

1. Elastic deformation of concrete
2. Anchorage draw-in
3. Friction losses
4. Concrete shrinkage
5. Concrete creep
6. Steel relaxation

Total Prestress Losses: If the initial prestress force applied to a member is Pi, then the effective prestress force at transfers is aPi, while that at service load is bPi. The value of a reflects the short-term losses due to elastic shortening, anchorage draw-in and friction.Total loss coefficient b accounts for the short term and long-term time-dependent losses due to concrete shrinkage and creep and steel relaxation. Magnel Diagram The relationship between 1/P_i and e are linear and if plotted graphically, they provide a useful means of determining appropriate values of P_iand e. These diagrams were first introduced by a Belgian engineer, Magnel and hence the name Magnel Diagram.

Cable Zone and Cable Profile

• Once the prestress force has been chosen based on the most critical section, it is possible to find the limits of the eccentricity e at sections elsewhere along the member.
• An allowable cable zone is produced within which the profile may take any shape.
• The term ‘cable’ is used to denote the resultant of all the individual tendons.
• As long as the ‘cable’ lies within the zone, the stresses at the different loading stages will not exceed the allowable values, even though some of the tendons might physically lie outside the cable zone.

Shear in Prestressed Concrete Beam

• The shear resistance of prestressed concrete members at the ultimate limit state is dependent on whether or not the section in the region of greatest shear force has cracked.
• The mode of failure is different for the two cases. If the section is uncracked in flexure, then failure in shear is initiated by cracks which form in the webs of I or T sections once the principal tensile strength has been exceeded.
• If the section is cracked, then failure is initiated by cracks on the tension face of the member extending into the compression zone, in a similar manner to the shear mode for reinforced concrete members.

Shear reinforcement If the shear resistance of a prestressed concrete member is not sufficient, then shear reinforcement must be provided in the form of links, similar to those used in reinforced concrete members. Ultimate Strength of Prestressed Concrete: After designing a member to meet the stress limitations for serviceability, it is necessary to check the ultimate limit state. Deflection of Prestressed Beams The deflection of prestressed beams is difficult to assess in practice since it is dependent upon many variables as follows:

1. Elastic deflection due to prestress
2. Elastic deflection due to initial loading
3. Creep deflection under sustained stresses
4. Deflection due to loss of prestress
5. Additional deflection due to live load

The deflection due to prestress may be calculated by treating the prestress as an equivalent normal loading. Since concrete deforms both instantaneously under load and also with time, due to creep, the deflections of concrete structures should be assessed under both short-term and long-term conditions. End Block Design

• There are 2 problems associated with end-block design namely, the assessment of the bursting tensile stresses and the compressive bearing stresses directly beneath the bearing plate.
• For post-tensioned members, the prestressing force in a tendon is applied through the anchorages as a concentrated force.
• By St. Venant’s principle, the stress distribution in a member is reasonably uniform away from the anchorage but in the region of the anchorage itself the stress distribution is complex.

Composite Construction:

• Many applications of prestressed concrete involve the combination of precast prestressed concrete beams and in-situ reinforced concrete slab.
• A common example is the in-situ infill between precast bridge beams. The beams are designed to act alone under their own weights plus the weight of the wet concrete of the slab. Once the concrete in the slab has hardened, provided that there is adequate horizontal shear connection between the slab and beam, they behave as a composite section under service load. The beam acts as permanent formwork for the slab, which provides the compression flange of the composite section.
• The section size of the beam can thus be kept to a minimum, since a compression flange is only required at the soffit at transfer. This leads to the use of inverted T sections.

Prestressed Concrete Design Example

Complete topic is covered in the form of a PowerPoint presentation embedded below along with the solved example on post-tensioned Concrete Slab Bridge.

The CivilWeb Prestressed Concrete Beam Design Excel Spreadsheet is a powerful design spreadsheet which can be used to complete the design of prestressed concrete beams in accordance with BS EN 1992. The spreadsheet includes unique design charts and graphs which show the designer exactly where the beam design can be optimised. Using this spreadsheet and the unique tools the designer can complete a fully optimised prestressed concrete beam design in minutes. The CivilWeb Prestressed Concrete Beam Design Excel Spreadsheet can be purchased at the bottom of this page for only £20.

The CivilWeb Reinforced Concrete Beam Design Excel Bundle including the Prestressed Concrete Beam Design Excel Spreadsheet, Design of Singly Reinforced Beam in Excel Spreadsheet and T Shaped RCC Beam Design Excel Sheet design spreadsheets is available for only £30. This bundle also includes our Beam Analysis spreadsheets for a total discount of more than 60%. Alternatively why not purchase our best value bundle, the full Concrete Design Suite which includes all of our reinforced concrete design spreadsheets. This is our best value design bundle and can be purchased at the bottom of this page for only £50.

Prestressed Concrete Beam Design

Prestressed concrete beams work by effectively transferring some of the tensile stresses in a beam into compressive stresses. Concrete is strong in compression but weak in tension. Concrete is around ten times stronger in compression and for this reason the tensile strength of concrete is usually ignored when designing a concrete beam subjected to tensile stresses from bending. Normally the reinforcing steel is designed to accommodate all of the tensile stresses which can lead to large quantities of steel being required for heavily loaded or long span concrete beams.

This is done by prestressing the beam with a compressive force using steel tendons installed through the beam. When the beam is stressed using the tendons this puts the whole of the beam (both top and bottom) into compression.

Then when the beam is subjected to a bending moment some of the tensile stresses which would be induced in the bottom of the beam are effectively cancelled out by the compressive prestressing. This effectively reduces the maximum tensile stresses and therefore reduces the amount of reinforcing steel which is required. Prestressing is also often used to reduce the beam depth which would otherwise be required. This can be done for aesthetic reasons or to reduce self-weight, leading to longer beam spans than would otherwise be possible.

Prestressed Beam Design - Inputs

First the designer must input the type of beam which is to be designed. These inputs include the section shape and dimensions, concrete specification, the type of prestressing and some other minor factors such as curing time and damping factors.

Next the designer must enter the size and number of spans and the forces which will act on the beam. The CivilWeb Prestressed Concrete Beam Design Excel Spreadsheet allows the designer to enter the loadings and partial action factors in accordance with BS EN 1991. The designer can enter loads as UDLs, partial UDLs and up to two different point loads. These can be different for each span. The CivilWeb Prestressed Concrete Beam Design Excel Spreadsheet includes useful dynamic diagrams of the beam spans and loading arrangements.

After these loads have been input by the designer, the CivilWeb Prestressed Concrete Beam Design Excel Spreadsheet then automatically calculates the bending moments and MOR acting on the beam under the input loads. The spreadsheet includes a handy summary table of these forces and draws a bending moment diagram showing the envelope of moments and MOR acting on the beam.

Next the prestressed beam design spreadsheet xls assists the designer to design the tendons. The designer can input the tendon strand area and number of tendons for each span along with the strand strength and the design properties. The designer can also input the height for the strand at the centre of each span and each support. The CivilWeb Prestressed Concrete Beam Design Excel Spreadsheet draws a handy diagram showing the designer the tendons chosen profile.

The spreadsheet then calculates the tensile and compressive stresses acting on the beam and the tendons. These stresses are calculated both at the top and at the bottom of the section. The results of this analysis are plotted on a graph which shows the designer exactly how close the stresses are to their maximum values and exactly where along the beam these stresses are highest.

Prestressed Concrete Design Example Pdf

If these expected stresses are acceptable, next the spreadsheet can be used to design the conventional reinforcement required. The prestressed beam design spreadsheet xls calculates the stresses in the beam and calculates the reinforcement required at the top and bottom of each span and at each support. The designer can either design each reinforcement section individually or choose to use the worst case throughout the beam. The designer selects the bar size and quantity, then the spreadsheet checks whether this is both higher than the required reinforcement and suitable with maximum and minimum steel requirements.

Prestressed Concrete Column Design Example

Finally the prestressed beam design spreadsheet xls checks the shear forces present in the beam and allows the designer to add conventional shear reinforcement if required. The spreadsheet checks the shear forces at either side of each support along the beam, where shear forces are highest.

Prestressed Concrete Pile Design Example

In order to simplify and speed up the design process, the CivilWeb Prestressed Concrete Beam Design Excel Spreadsheet includes numerous additional tools and graphs which illustrate to the designer exactly what state the design is in at each design stage. This includes a handy summary table showing the utilisation of each part of the design.

This table is shown at several stages through the design process and shows the designer exactly where the beam design is not valid and also shows the designer at a glance any areas where the beam design is under-utilised and therefore exactly where there may be scope for beam design optimisation. This makes a very complicated design process much clearer and saves a great deal of time for the designer who doesn't need to check every area where the beam design is valid. It also allows the designer to check at a glance that any changes to one area of the design does not have a detrimental effect on any other parts of the design.

CivilWeb Prestressed Concrete Beam Design Excel Spreadsheet

Prestressed Concrete Design Example

The CivilWeb Prestressed Concrete Beam Design Excel Spreadsheet is a powerful design spreadsheet for prestressed concrete beam design. The spreadsheet completes all the calculations instantly in accordance with BS EN 1992. The spreadsheet also includes unique design analysis graphs and tools which show the designer at a glance exactly where the beam design can be improved. This allows the designer to complete a fully optimised prestressed concrete beam design in minutes.

Buy the CivilWeb Prestressed Concrete Beam Design Excel Spreadsheet now for only £20.

Prestressed Concrete Examples

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