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CONCORDIA UNIVERSITY
Department of Building, Civil and Environmental Engineering
CIVI 6011 – Winter 2015
PRECAST AND PRESTRESSED CONCRETE STRUCTURES
ASSIGNMENT 1 (Due Monday Feb. 16th)
Problem 1:
The following figure shows an unreinforced T-beam made of normal-weight concrete with fc' = 35MPa.
(a) If the beam is simply-supported, what is the maximum span length possible if the beam is not to
undergo flexural cracking under its own weight?
(b) What is the curvature at mid-span?
(c) At mid-span, what is the flexural stress at a point 350 mm from the top of the beam?
(d) For the span length computed in part (a), what is the minimum prestressing force, applied at an
eccentricity of 60mm, that would be required to prevent tension in the beam at the mid-span
section?
(e) For the span length computed in part (a) and considering that the beam will carry additional load
equal to its self-weight, what is the minimum prestressing force, applied at an eccentricity of
60mm, that would be required to prevent concrete cracking in the beam at the mid-span section?
500 mm
100
600
100
Problem 2:
Referring to Example 1 of Chapter 3 of the course notes, it is required to draw the variation of the
flexural stresses at the top and bottom fibres of the concrete CPCI girder along the beam span (from the
support till the mid-span) at the transfer and service stages for the following cases:
(a) ec = ee = 500mm
(b) ec = 500mm and ee = 200mm
Problem 3:
The I-beam shown in the following figure is to be used in a roof support system spanning 12m between
simple supports. It will carry a superimposed dead load of 6 kN/m and service live load of 10 kN/m, in
addition to its own weight. The member will be post-tensioned with a force Pi = 1000 kN. At mid-span,
the eccentricity is 300mm. Time-dependent losses of 25% (from initial to service stage) will be
assumed. Normal weight concrete is specified with fc' = 40MPa, and at time of stressing, with fci' =
25MPa. It is required to:
500
(a) Find concrete flexural stresses at mid-span at
the initial stage and compare with CSA A23.375
04 limits. Propose any necessary modification to
meet the code limits, if needed.
(b) Find concrete stresses at full service load and
compare with CSA A23.3-04 limits.
100 mm
(c) Compute the upper and lower central kern
800
Concrete
limits.
centroid
[Hint: you may use gross-section properties]
Ap = 650 mm2
150
250 mm
Problem 4:
The simply supported concrete I-girder shown in the figure below is pre-tensioned with straight bonded
tendons having constant eccentricity ‘e’. The effective prestress force after losses is 80% of the initial
prestress force ( Pf  0.80 Pi ). The concrete strength is 50MPa; however, the strength at transfer is only
30 MPa. Using CSA A23.3-04 concrete and tendon stress limits;
(a) Find the initial prestress force Pi (at transfer) and the eccentricity ‘e’ that would correspond to
full use of the allowable stresses.
(b) What is the super imposed uniform service load (kPa) that could be placed on the beam without
over stressing the concrete during service loading?
500
100
100 mm
750
150
400 mm
Problem 5:
The following figure shows the cross section of a pre-tensioned simply supported box girder. The fully
bonded pre-stressing tendons are at a constant eccentricity of 900 mm throughout the length of the
girder. The initial total pre-stressing force on the section immediately after transfer is Pi  6500 kN,
and it is expected that there will be a further 20% pre-stress loss over time.
(a) Use a strain compatibility analysis to calculate the factored flexural resistance moment M r .
(b) Calculate the cracking moment M cr for the section, and compare it to M r found in part (a).
(c) Does this section satisfy the flexural ductility requirements associated with the prestress concrete
sections? If the requirements for ductile behaviour are not satisfied, suggest possible solutions to
insure a ductile behaviour.
DATA
f ci'  30MPa;
f c'  40MPa;
f pu  1860MPa;
Aps  5000mm 2 ;
f y  400 MPa
All dimensions are in mm