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ENGM031/Spring 2009/5pp (1 handout)

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UNIVERSITY OF SURREY ©

Faculty of Engineering and Physical Sciences

Postgraduate Programmes in Civil Engineering

Level MSc Examination

Module ENGM031; 15 Credits

PRESTRESSED CONCRETE BRIDGE DESIGN

Time allowed: Three hours Spring 2009

Answer 3 questions ONLY

All questions carry equal marks unless otherwise stated; where appropriate the mark carried by an individual part of a question is indicated in brackets [].

Additional materials:

Data Sheets (26 Pages)

Candidates may use Casio FX115MS, FX115W or FX115S calculators or any other model

with lower functionality (i.e. non-programmable, no alphanumeric memory and no

communication devices).

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ENGM031/Spring 2009/5pp 2

1. A simply supported foot bridge having an effective span of 25 m consists of a pre-

tensioned U beam, shown in Figure 1, with a top slab of 2500mm wide and 150mm

deep. For design purposes, it is designated as a category 1 (class 1) member.

Some additional details are given below.

• Assume 10% immediate losses and another 15% losses in the long term.

• C40/50 concrete consisting of CEM 42,5R is used for both the beam and slab. • Prestressing will be carried out 10-days after casting the concrete. • Density of concrete is 25kN/m3. • Live Load on the bridge is 5kN/m2. • For simplicity, ignore the differential shrinkage and creep effects between the

top slab and U beam, i.e. full box- section must be considered for both the

transfer and service stages. • Assume suitable values for parameters not provided here.

Figure 1: U beam details for the bridge in Question 1

(a) Draw Magnel’s diagram for the mid span of the bridge and use this to estimate

the no. of strands, and their location (i.e. eccentricity), to satisfy stresses at the

serviceability limit state. [12]

(b) Assume a straight tendon profile along the length of the member, i.e. the

eccentricity of strands is the same at the support and mid span. Also assumethat 40 - 13mm diameter super strands are placed in two layers in the soffit at

75mm and 125mm, respectively, from the base of section. Establish the de-

stressing arrangement (i.e. no. of strands requiring de-stressing) over the

supports to satisfy the stresses at the serviceability limit state. [4]

(c) What are various methods of prestressing? Discuss the advantages and

limitations of each method. [4]

970 mm

1180 mm

800 mm

351,9 mm

Centroidal axis for U beam alone

U- Beam Properties:

Cross-sectional area = 490130 mm2

Second moment of area = 29,4 x 109 mm4

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2. (a) The section of a simply supported prestressed concrete box girder footbridge

is shown in Figure 2. The maximum ULS shear on the deck section is

3250 KN, the co-existent ULS torsion is 2500 kNm and the co-existent ULS

moment is 8,000 kNm (sagging). Determine the maximum shear plus torsional

stress in the webs and compare with the maximum shear and torsion stress

allowed in accordance with BS5400 part 4. [6]

(b) For the situation in a) above, determine the area of reinforcement required in

the webs to provide sufficient capacity to resist both the shear and torsion. [9]

(c) Precast concrete segmental box girder construction with match-cast joints has

become a very popular choice for longer bridge decks. Describe the technique

of match-cast joints and how they are achieved on site. Compare the

difference between match-cast joints and in-situ concrete joints for precast

segmental construction. [5]

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4000mm

300mm

2200mm

200mm

200mm

2500mm

150mm

200mm

Tendons in75mm dia ducts

f cp = 3.0 N/mm unfactored

f pt = 8.0 N/mm2

unfactored

f cu =50 N/mm2 Concrete cover = 40mmReinforcement, f y =460 N/mm

2

Figure 2: Cross-sectional details for Question 2

Area of deck =3.0m2

I =2.1m4

N-A =1.3m above soffit

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3. (a) Calculate the required reinforcement for the prestressed anchorage blister

shown in Fig. 3. [16]

Elevation on blister

Figure 3: Cross Section showing blisters for Question 3

Tendon stressing force = 3000 kN

Assume tendons alignment in plan is straight, parallel to the webs.

(b) Produce a sketch showing the reinforcement arrangement for the blister. [4]

5m radius

300 x 300mmanchor plates

250mm

250mm Angle =14º

6000mm

300mm

250mm

300mm300mm

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4. A three span continuous prestressed concrete beam consists of two tendons as shown

in Figure 4. The straight tendon has an effective prestressing force (β Pi ) of 1000 kN,

whereas the draped tendon has an effective prestressing force of 2500 kN.

(a) Calculate and sketch out the equivalent loading on the beam due to prestressing only. Also draw the primary bending moment diagram due to the

prestressing. [5]

(b) If the secondary moments (Msec) at the intermediate supports are 1300 kN-m,

show a plot of the effective tendon profile in relation to the actual tendon

profile. [4]

(c) The moment due to the applied loads at midspan of the 30m span is 1583 kN-

m, and at intermediate supports it is -2354 kN-m. Calculate and draw the

stress profiles at these sections for the serviceability limit state and comment

on the results. [6]

(d) Sketch a typical force profile along the span showing various types of losses in

a prestressed concrete member. Discuss, with the aid of the sketch, how you

would calculate the tendon elongation during stressing operation and which of

the losses you would consider for this purpose. [5]

Figure 4: Longitudinal and cross section of the beam for Question 4

Internal Examiner: Dr. M I Rafiq

N HewsonExternal Examiner: Prof J G A Croll

500

700Centroidal axis

Area of section = 0,7 m2

Second moment of area = I = 0,094 m4

300 mm

20 m 30 m

300 mm

8.8m 1.2m

300 mm

20 m

590 mm

300 mm

1.2m

640 mm

200 mm

13.8m

r p1 =100.3 m r p2 =73.3 m r p3 =10.3 m r p4 =116.2 m

1 2

3

4 4

3

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