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CIVL4333 Advanced Concrete Design

THE UNIVERSITY OF QUEENSLAND

SCHOOL OF CIVIL ENGINEERING

CIVL4333 Advanced Concrete Design

Question

A simply-supported beam with a rectangular cross section as shown in Fig 1 spans 12 m and carries two point live loads, each of which is P = 50 kN.  The beam is post-tensioned with 2 cables, each of which consists of six 7-wire ordinary strands.  The tendon profile is parabolic, with no eccentricity at both ends and a maximum eccentricity e of 150 mm at the mid-span.  All strands are stressed to 70% of their characteristic breaking loads.

  1. Determine the stress distribution at mid-span during transfer and service.  Check if the critical stresses are within the allowable design limits given below. (ii) Calculate the location of line of pressure at mid-span at service.
  2. Determine the maximum live loads P that the beam can sustain within the allowable stress limits if the initial prestress is kept at 70% of the breaking load.
  3. Determine the minimum possible initial prestress (without any loss) that would satisfy the allowable stress limits for the given loading arrangement, i.e. P = 50 kN.

Given the following material properties:

Concrete

Characteristic compressive strength fc = 50 MPa

Strength at transfer fcp = 35 MPa

Density of concrete (with steel) = 24 kN/m3

Allowable stress limits

Compressive stress at transfer = 0.5fcp

Tensile stress at transfer = 0.4fcp

Compressive stress at service = 0.4fc

Tensile stress at service = 0.4fc

Strands

Characteristic breaking load of a 7-wire ordinary strand = 185 kN

Nominal steel area of a 7-wire ordinary strand = 100 mm2

Loss of prestress

At transfer = 15%

At working load = 30%

CIVL4333 Advanced Concrete Design img1

Fig 1 A post-tensioned prestressed concrete beam

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