Department of Civil Engineering
Ryerson University
CV8313 Prestressed Concrete
Final Examination
Time: 3 Hours December 11, 2015
Notes:
1) For missing information, make certain assumtions and clearly state your assumptions
2) This is an open book examination
3) Problem 1- Part A, 16 marks, Part B, 6 marks, Part C, 12 marks, Part D, 6 marks
Problem 2- Part A 10 marks, Part B, 10 marks- Total = 60 Marks
1- A pre-tensioned prestressed untopped double-tee beam (total depth 610 mm) as shown.
It has a span of 14 m and is subjected to a service superimposed dead load of 1.0 kN/m2
and a superimposed service live load of 2.4 kN/m2. The prestressing tendon is harped at
1/3 of the span with eccentricities e of 350 mm over the middle section and 200 mm at
the ends. It is assumed that the stresses are tensioned to 0.75fpu in the pretensioning bed.
The following data are given:
Ac = 260,000 mm2 ec = 350 mm
Ic = 8,735 X 106 mm4 ee = 200 mm
Ct = 174 mm (yt) f’c = 34.5 MPa, normal-weight concrete
St = 50,194x103 mm3 f’ci = 24.1 MPa
Cb = 436 mm (yb) fyt for stirrups = 400 MPa, 10M stirrups
Sb = 20,058x103 mm3 fpu = 1,860 MPa, low-relaxation strands
wd = 2.5 kN/m2 or 6.1 kN/m Aps =6-1/2in. dia (12.7 mm dia) 7-wire
member self-weight tendons= 592mm2 total
bw= 150 mm each (assume uniform web
width) with one leg of stirrups in each web
1
Part A- Design for shear at dv from the face of the support- Use the Code’s Simplified
Method (A23.3-2004).
i)Calculate the vertical component of prestressing force
ii)Calculate the factored shear force and bending moment
iii) Calculate the maximum spacing of 10M stirrups- Assume the cross-section is
adequate to carry the shear.
Part B- Elastic stresses
Determine the stresses at the top and bottom fibre at the center of gravity of the beam
cross-section at the time of prestress transfer (initial). Determine whether these stresses
satisfy the Cod’s minimum requirements.
Part C-Moment and curvature
Calculate the strain and curvature at the center of the beam corresponding to dead load
moment (beam self-weight plus superimposed dead laod). Determine the corresponding
strains and stresses at the extreme fibres of concrete.
Part D- Deflection
Calculate the defalcation due to only tendon eccentricity at the center of the beam.
2- At about the turn of the century, a number of people attempted to produce prestressed
concrete by pretensioning ordinary plain reinforcing bars with fy about equal to 300 MPa
and casting low-quality concrete around the reinforcement. Assume the pretensioned
member has a square cross-section of 200 mm x 200 mm with four 20 M bars (one at
each corner) with a total area of 1200 mm2, and Es= 200,000 MPa.
Part A
a) Calculate the stress and the strain in the concrete immediately after release of the bars
assuming that Ec = 14000 MPa and also assuming the steel was stressed to 250 MPa at
the time the concrete was cast.
b) Calculate the stress in the concrete after creep and shrinkage have occurred assuming
that in this case Ec,eff = 4000 MPa and the free shrinkage strain is -0.6 x 10-3.
Comment on why these early attempts to produce prestressed concrete failed.
Part B
Estimate the maximum crack width that will occur when this section is subjected to a
short-term axial load of 230 kN. Assume a clear cover of 40 mm for the bars. Try an
initial strain of εc in the concrete = 1 x 10-3 and no further iteration is necessary. In your
calculations, use the Gergely-Lutz equation.
