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Note for Design of Concrete Structures - DCS by Chandan Kumar Ray

• Design of Concrete Structures - DCS
• Note
• Civil Engineering
• B.Tech
• 2 Topics
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Chandan Kumar Ray
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Prestressed Concrete Structures Dr. Amlan K Sengupta and Prof. Devdas Menon 2.3 Losses in Prestress (Part III) This section covers the following topics. • Creep of Concrete • Shrinkage of Concrete • Relaxation of Steel • Total Time Dependent Losses 2.3.1 Creep of Concrete Creep of concrete is defined as the increase in deformation with time under constant load. Due to the creep of concrete, the prestress in the tendon is reduced with time. The creep of concrete is explained in Section 1.6, Concrete (Part II). information is summarised. Here, the For stress in concrete less than one-third of the characteristic strength, the ultimate creep strain (εcr,ult) is found to be proportional to the elastic strain (εel). The ratio of the ultimate creep strain to the elastic strain is defined as the ultimate creep coefficient or simply creep coefficient θ. The ultimate creep strain is then given as follows. (2-3.1) εcr,ult = θεel IS:1343 - 1980 gives guidelines to estimate the ultimate creep strain in Section 5.2.5. It is a simplified estimate where only one factor has been considered. The factor is age of loading of the prestressed concrete structure. The creep coefficient θ is provided for three values of age of loading. Curing the concrete adequately and delaying the application of load provide long term benefits with regards to durability, loss of prestress and deflection. In special situations detailed calculations may be necessary to monitor creep strain with time. Specialised literature or international codes can provide guidelines for such calculations. The loss in prestress (∆fp ) due to creep is given as follows. ∆fp = Ep εcr, ult Indian Institute of Technology Madras (2-3.2)

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Prestressed Concrete Structures Dr. Amlan K Sengupta and Prof. Devdas Menon Here, Ep is the modulus of the prestressing steel. The following considerations are applicable for calculating the loss of prestress due to creep. 1) The creep is due to the sustained (permanently applied) loads only. Temporary loads are not considered in the calculation of creep. 2) Since the prestress may vary along the length of the member, an average value of the prestress can be considered. 3) The prestress changes due to creep and the creep is related to the instantaneous prestress. To consider this interaction, the calculation of creep can be iterated over small time steps. 2.3.2 Shrinkage of Concrete Shrinkage of concrete is defined as the contraction due to loss of moisture. Due to the shrinkage of concrete, the prestress in the tendon is reduced with time. The shrinkage of concrete was explained in details in the Section 1.6, Concrete (Part II). IS:1343 - 1980 gives guidelines to estimate the shrinkage strain in Section 5.2.4. It is a simplified estimate of the ultimate shrinkage strain (εsh). Curing the concrete adequately and delaying the application of load provide long term benefits with regards to durability and loss of prestress. In special situations detailed calculations may be necessary to monitor shrinkage strain with time. Specialised literature or international codes can provide guidelines for such calculations. The loss in prestress (∆fp ) due to shrinkage is given as follows. ∆fp = Ep εsh (2-3.3) Here, Ep is the modulus of the prestressing steel. 2.3.3 Relaxation of Steel Relaxation of steel is defined as the decrease in stress with time under constant strain. Due to the relaxation of steel, the prestress in the tendon is reduced with time. The relaxation depends on the type of steel, initial prestress (fpi) and the temperature. To Indian Institute of Technology Madras

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Prestressed Concrete Structures Dr. Amlan K Sengupta and Prof. Devdas Menon calculate the drop (or loss) in prestress (∆fp), the recommendations of IS:1343 - 1980 can be followed in absence of test data. Example 2-3.1 A concrete beam of dimension 100 mm × 300 mm is post-tensioned with 5 straight wires of 7mm diameter. The average prestress after short-term losses is 0.7fpk = 1200 N/mm2 and the age of loading is given as 28 days. Given that Ep = 200 × 103 MPa, Ec = 35000 MPa, find out the losses of prestress due to creep, shrinkage and relaxation. Neglect the weight of the beam in the computation of the stresses. 100 300 50 Solution Area of concrete A = 100 × 300 = 30000 mm2 Moment of inertia of beam section I = 100 × 3003 / 12 = 225 × 106 mm4 Area of prestressing wires Ap = 5 × (π/4) × 72 = 192.42 mm2 Prestressing force after short-term losses P0 = Ap.fp0 = 192.4 × 1200 = 230880 N Indian Institute of Technology Madras CGS

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Prestressed Concrete Structures Dr. Amlan K Sengupta and Prof. Devdas Menon m = Ep / Ec Modular ratio = 2 × 105 / 35 × 103 = 5.71 Stress in concrete at the level of CGS P0 P0e e A I 230880 230880 =×502 4 6 3×10 225×10 fc = - = – 7.69 – 2.56 = – 10.25 N/mm2 Loss of prestress due to creep (∆fp)cr = Ep εcr, ult = Ep θεel = Ep θ (fc/Ec) = m θ fc = 5.71 × 10.25 × 1.6 = 93.64 N / mm2 Here, θ = 1.6 for loading at 28 days, from Table 2c-1 (Clause 5.2.5.1, IS:1343 - 1980). Shrinkage strain from Clause 5.2.4.1, IS:1343 - 1980 εsh = 0.0002 / log10(t + 2) = 0.0002 / log10 (28 + 2) = 1.354 × 10-4 Loss of prestress due to shrinkage (∆fp)sh = Epεsh = 2 × 105 × 1.354 × 10-4 = 27.08 N/mm2 Indian Institute of Technology Madras