CE-702-A Prestressed Concrete Structures - Nov 2022 Question Paper

Under each question, How to answer lists the points an answer should cover, outlined by CampusPrep from the syllabus. Check the details against your textbook.

1. 4 Marks
   aClassify the Pre-stressed concrete. OR Explain Freyssinet's system of pre-stressing.
   How to answer

   • Define classification criteria (source, timing, shape, etc.)
   • List types: pre-tensioning vs post-tensioning, etc.
   • Brief features of each type
   • OR alternative: components of Freyssinet system
   • Anchorage and jacking operation with sketch
2. 10 Marks
   bA simply supported pre-stressed concrete beam of rectangular cross section $400\, \text{mm} \times 600\, \text{mm}$ is loaded with a total uniformly distributed load of $256\, \text{kN}$ over a span of $6.0\, \text{m}$. Sketch the distribution of stress at mid span and at end section, if the pre-stressing force is $1920.0\, \text{kN}$ and the tendon is concentric with beam section. OR Explain in detail the load balancing concept of pre-stressed structures with suitable sketches.
   How to answer

   • Compute cross-sectional properties A, I, Z
   • Compute direct stress P/A at end and mid
   • Compute bending stress My/I due to 256 kN UDL
   • Superpose to get extreme fibre stresses
   • Sketch stress distribution at mid-span and end section
3. 4 Marks
   aWrite down the merits and demerits of pre-stressed concrete. OR What are the basic assumptions of pre-stressed concrete theory?
   How to answer

   • Define pre-stressed concrete merits (crack control, economy, etc.)
   • List demerits (high strength materials, skilled labour, etc.)
   • Brief explanation of each
   • OR alternative: state basic assumptions (plane sections, elastic behaviour, etc.)
4. 10 Marks
   bA post tensioned unbounded beam section $120\, \text{mm} \times 300\, \text{mm}$ is pre-stressed by 7 wires of $5\, \text{mm}$ diameter with an effective cover of $50\, \text{mm}$ and effective stress of $1200\, \text{N/mm}^2$. The beam is of $7.50\, \text{m}$ span. If M40 concrete is used and $f_p = 1600\, \text{N/mm}^2$. Find the ultimate flexural strength of the section. OR A post tensioned unbounded T-section has a flange width of $800\, \text{mm} \times 250\, \text{mm}$. The size of web of beam is $200\, \text{mm} \times 1000\, \text{mm}$. The area of high tensile wire is $4000\, \text{mm}^2$, located at $1200\, \text{mm}$ from top of flange. The characteristics strength of steel and concrete are $1500\, \text{N/mm}^2$ and $40\, \text{N/mm}^2$ respectively. Calculate the ultimate moment capacity of section using IS 1343 recommendations.
   How to answer

   • Compute steel area from 7 wires of 5 mm dia
   • Determine effective depth and reinforcement ratio
   • Check IS 1343 provisions for unbonded post-tensioned section
   • Compute ultimate flexural strength / moment capacity
   • OR alternative: analyse T-section flange width, neutral axis, Mu per IS 1343
5. 4 Marks
   aWrite a short note on Anchorage zone stress. OR Explain end zone reinforcement.
   How to answer

   • Define anchorage zone / end block stress
   • Describe bursting, spalling and bearing stresses
   • Guyon / Magnel distribution concept
   • OR alternative: purpose and detailing of end zone reinforcement
6. 10 Marks
   bThe end block of post tensioned beam of $500\, \text{mm} \times 1000\, \text{mm}$ is pre-stressed by 2 cables each comprising of 5 wires of $7\, \text{mm}$ diameter. The cable is anchored by square anchor plate of $400\, \text{mm} \times 400\, \text{mm}$ with their center located at $250\, \text{mm}$ from the top and bottom edge of beam. The jacking force in the cable is $3000\, \text{kN}$. Design a suitable anchorage zone reinforcement as per the provisions of IS 1343. OR Explain the important factors influencing the deflection in a pre-stressed concrete beam and also describe differences between short term deflection and long term deflection.
   How to answer

   • Compute jacking force per cable and bearing stress
   • Determine bursting tension per IS 1343
   • Design stirrups / helical reinforcement for anchorage zone
   • Detail spacing and arrangement sketch
   • OR alternative: factors affecting deflection, short-term vs long-term difference
7. 4 Marks
   aExplain the methods of achieving continuity in continuous pre-stressed beam. OR What is meant by primary moments, secondary moments and resultant moments in pre-stressed concrete?
   How to answer

   • Define continuity in prestressed beams
   • Methods: cap cables, added reinforcement, etc.
   • Construction sequence and advantages
   • OR alternative: define primary, secondary and resultant moments with expressions
8. 10 Marks
   bIn the pre-stressed beam shown below, pre-stressing is done by a parabolic cable carrying an effective pre-stress of $200\, \text{kN}$. The beam supports a uniformly distributed load of $15\, \text{kN/m}$ including self weight over whole span. Use $f_{ck} = 40\, \text{N/mm}^2$. Find the shear resistance of un-cracked section at the support. OR Explain the concordant cable and concept of linear transformation in pre-stressed concrete beam.

   How to answer

   • Determine beam properties and prestress eccentricity from diagram
   • Compute shear due to UDL and vertical component of cable
   • Compute principal tensile stress / shear capacity of uncracked section
   • Apply f_ck = 40 N/mm2 formula for shear resistance
   • OR alternative: define concordant cable and linear transformation with sketches
9. 4 Marks
   aExplain composite construction in Pre-stressed concrete members. OR Describe the merits and demerits of partial pre-stressing.
   How to answer

   • Define composite construction with precast + in-situ
   • Stages of loading and propping
   • Stress distribution and shear connection
   • OR alternative: merits (economy, etc.) and demerits of partial prestressing
10. 10 Marks
    bA composite T-beam is made up of pre-tensioned web $100\, \text{mm}$ wide and $200\, \text{mm}$ deep with a cast in situ slab of $400\, \text{mm}$ wide and $40\, \text{mm}$ thick, having a modulus of elasticity $28\, \text{kN/m}^2$. If the differential shrinkage is $100 \times 10^{-6}$ units, determined shrinkage stress developed in the precast and cast in situ units. OR What are the methods of achieving partial pre-stressing? Explain in details.
    How to answer

    • Compute modular ratio and transformed section properties
    • Compute differential shrinkage strain effect
    • Compute shrinkage stresses in precast web and in-situ slab
    • State nature (tensile/compressive) and magnitude
    • OR alternative: methods of partial prestressing (untensioned steel, etc.)
11. 14 Marks
    A post tensioned concrete beam $100\, \text{mm} \times 300\, \text{mm}$ of $10\, \text{m}$ span is pre-stressed successively tensioned and anchored by 3 cables each having cross sectional area $200\, \text{mm}^2$. Initial pre-stress is $1200\, \text{N/mm}^2$. First cable is parabolic with $e = 50\, \text{mm}$ at mid span and $50\, \text{mm}$ above neutral axis at support. Second cable is also parabolic with $e = 50\, \text{mm}$ at mid span and zero eccentricity at support. Third cable is straight with $50\, \text{mm}$ eccentricity. Calculate the loss of pre-stress due to elastic deformation. Take $m = 6$. OR Define loss of pre-stress. Explain different losses of pre-stress in pre-tensioned and post-tensioned concrete.
    How to answer

    • Compute prestress force per cable (A x initial stress)
    • Compute concrete stress at cable levels due to successive tensioning
    • Apply m=6 for elastic loss in each cable
    • Sum losses for three cables with different profiles
    • OR alternative: define loss, list friction, anchorage, elastic, creep, shrinkage, relaxation
12. 14 Marks
    Design a post-tensioned girder, which is spaced $2.40\, \text{m}$ c/c and has an effective span of $9.0\, \text{m}$. The dead load over beam is $3.0\, \text{kN/m}^2$ excluding self weight. The beam is subjected to a live load $15\, \text{kN/m}^2$ over whole span. The permissible compressive stress at transfer stage and at working stage is $14\, \text{N/mm}^2$ and $12\, \text{N/mm}^2$ respectively. The permissible tensile stress at all stages of loading is $1.0\, \text{N/mm}^2$. Consider loss ratio of $0.80$. Determine number of $7.0\, \text{mm}$ wires required if permissible tensile stress in wire is $1000\, \text{N/mm}^2$. Assume cover equal to $100\, \text{mm}$. OR Design a pre-stressed concrete I-beam to carry load of $12\, \text{kN/m}$ over simply supported span of $25.0\, \text{m}$. The permissible stress in concrete at transfer stage and at working stage is $14\, \text{N/mm}^2$ and $12\, \text{N/mm}^2$ respectively. Initial stress in cable is $1000\, \text{N/mm}^2$. Loss of pre-stress is $20.0\%$. Adopt Freyssinet cable 12 numbers and $5.0\, \text{mm}$ diameter.
    How to answer

    • Compute design load from spacing, dead + live + self weight
    • Determine required section modulus using permissible stresses and loss ratio
    • Select section and compute prestress force and eccentricity
    • Determine number of 7 mm wires with 1000 N/mm2
    • OR alternative: design I-beam for 12 kN/m over 25 m similarly
13. 6 Marks
    aWrite short notes on any two: $2 \times 3 = 6$

    1. i)Stress concept in pre-stress
    2. ii)Tendon and tendon profile
    3. iii)Guyon's method
    4. iv)Concept of stress distribution in end block
    How to answer

    • Define stress concept / tendon profile / Guyon method / end block distribution
    • Explain with formulas and sketches
    • State applications
    • Select any two items as required
14. 8 Marks
    bWrite short note on any two: $2 \times 4 = 8$

    1. i)Types of flexural failures in concrete
    2. ii)Hoye's system of pre-stressing with neat sketch
    3. iii)Differences between pre-tensioned and post-tensioned
    4. iv)Why mild steel cannot be used in pre-stressing
    How to answer

    • Define types of flexural failures / Hoye system / pre vs post tension / mild steel issue
    • Explain with neat sketch where needed
    • Compare characteristics
    • Select any two items