Case CIE4160 page 1

Faculty of Civil Engineering and Geosciences

Department of Design and Construction

Case study Prestressed Concrete CIE4160. 2014 - 2015

Name : ......................................................................................

Identification number : ......................................................................................

E-mail address : ......................................................................................

Guidelines for elaborating the case study

Explain briefly how calculations/calculation parts are executed.

Make your ideas clear by adding proper drawings or sketches on a sufficiently large scale, completed with text and dimensions.

Summarise relevant results in tables.

Refer to page numbers with corresponding information

Be aware that other persons should be able to read and check your calculations.

General information

A 3 span continuous prestressed concrete bridge is cast in-situ. It has a box-shaped cross-section. The

bridge is longitudinally prestressed by tendons that have a curved profile. Tendons are stressed from both

ends.

Goal:

Estimating the prestressing force required to have no tensile stresses at the level of the prestressing

steel at permanent load + a percentage of the variable load.

The analysis is to be performed according to EN 1992-1-1 and the textbook Prestressed Concrete

(CIE4160).

The input data set follows from the student identification number:

Identification number = ABCDEFG

A defines the width of the deck bdeck: bdeck = ( 10 + A/2 ) m

B defines mid span length l: l = ( 40 + B ) m

C defines the coefficient of friction of the tendon : = 0,16 + C0,02

D defines the coefficient of the wobble effect k: k = ( 0,01 + D0,001 ) rad/m

E defines the wedge set wset: wset = ( 5 + E0,2 ) mm

F defines the minimum tendon radius at the intermediate support Rmin: Rmin = ( 6 F0,2 ) m

G defines the variable load on the bridge Qk: Qk = ( 110 + G4 ) kN/m

Case CIE4160 page 2

Geometry specification bridge mid span : l

end span : 0,80 x mid span

height viaduct : 0,04 x mid span

width deck : bdeck

The dimensions follow from design rules:

1) The top flange thickness dftop is:

minimum 1/30 of the box width bbox and

minimum 1/10 of the cantilever length.

In addition, minimum flange thickness is 200 mm. The box width bbox can be derived from these

requirements. (A proper choice for bbox should result in the same thickness for the box flange and the

cantilever flange).

2) Minimum web thickness dweb is based on concrete cover, stirrups, longitudinal reinforcement, duct diameter and duct spacing. Assume that two ducts per web can be required at the same level. Provide

a clear horizontal spacing between two tendons (min. 200 mm) to cast and compact the concrete.

3) Bottom flange thickness dfbot is to be chosen as small as practically possible ( 200 mm).

4) It is not necessary to apply a varying thickness or height along the box girder length. As a result, in this case study, webs, top and bottom flange have constant dimensions.

Case CIE4160 page 3

Material data:

Prestressing (strands) : Y1860S7, strand = 15,7 mm (Ap = 150 mm2), see table 1

Friction losses : coefficient of friction

wobble-factor k

The wedge set of strands : wset

Minimum radius of curvature at a mid support: Rmin

Environmental classes : Exposure class XC4, XD3, XF4 (EC2; table 4.1)

Density of concrete : 2500 kg/m3

Cover on prestressing steel : EC2; cl. 4.4.1.2; table 4.5N

Cover on reinforcing steel : EC2; cl. 4.4.1.2; table 4.4N

Table 1 Geometric properties prestressing system

Number of strands 3 4 7 12 19 22 31 37 43 55

Internal/external diameter 45/50 50/55 60/67 80/87 95/102 110/117 130/137 140/150 150/160 170/180

duct (mm)

Loads

In this case study, variable loading can be assumed to be present over the full bridge length; it is not

required to include combinations of loaded not loaded spans. The bending moment and shear diagrams may be calculated with FEM/beam/frame programs.

Tasks to do

The design of a continuous prestressed girder bridge is in general an iterative process where a number of

input data (such as cross-section dimensions and the magnitude and profile of the prestressing) are to be

determined. Since they are interrelated, the design process may be rather time consuming.

Therefore, a simplied approach is followed:

1) Make girder height equal to 1/25 of the mid span.

2) Determine the web width and the flange thickness using the design rules (2) and (1) given. Estimate the reinforcing bar diameters.

3) Calculate the selfweight Gk.

4) Estimate the theoretical maximum eccentricities of the centroid of the prestressing steel at span and support cross-sections (to maximise the flexural capacity, it is advised to locate the tendon(s)

as high as possible over the intermediate supports and as low as possible in the spans).

Assumption: At end sections, the centroid of the prestressing steel coincides with the centroid of

the concrete cross-section at end sections.

5) Choose a parabolic tendon profile that results (at t = 0) in a constant upward load from tendon curvature in both end spans and mid span (engineering model). Estimate mean direct losses from wedge set and friction at end span and mid span as a percentage of the tendon force Pm0 at the

anchor. The result is a ratio between tendon drape at end span and at mid span (drape f1 at end span

and f2 at mid span).

Note: The influence of the prestressing sequence (losses from elastic deformation of the concrete)

has not to be taken into account

6) Use the tendon drape ratio f1 end span / f2 mid span to calculate the tendon position at three points, namely at the end span, support and mid span cross-sections. Then use end span length

Case CIE4160 page 4

0,8l, mid span length l and minimum tendon radius Rmin as input to calculate the exact tendon

profile. (Geometric relationships for parabolic segments at end span, intermediate support and mid

span are in a file uploaded to Blackboard).

7) Time-dependent prestress losses are now assumed to be 10%. Calculate the bending moment and shear force curves from the working prestressing load Pm, (use the exact tendon profile), the

selfweight Gk and the variable load Qk.

8) Calculate the working prestressing force Pm, required to have no tensile stresses at the level of the prestressing steel at the intermediate support at permanent load Gk + 30% of the variable load Qk.

9) Calculate the required cross-sectional area of prestressing steel, the number of strands and tendons (recommended:12 to 19 strands per tendon) from Pm, and check whether the assumed web width

and tendon eccentricity at the intermediate support are correct. Note: Only a check is required; in

case assumptions are not correct, the calculation procedure has not to be repeated.

Drawings should contain:

Side view and the prestressing profile.

Prestressing detailing at the intermediate support cross-section.