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CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Semester 1 Examinations 2010/
Module Title: Prestresssed Concrete
Module Code: CIVL
School: Building and Civil Engineering
Programme Title: Bachelor of Engineering (honours) in Structural Engineering
Programme Code: CSTRU_8_Y
External Examiner(s): Dr. Mark G. Richardson
Mr John O’Mahony
Internal Examiner(s): Mr. Brian D. O’Rourke
Instructions: Three Question are to be attempted
Questions 1 and 2 are compulsory
Attempt either Question 3 or Question 4
Total 100 marks
Duration: 2 hours
Sitting: Winter 2010
Requirements for this examination: Mathematics Tables.
Students may use their Extracts to the British Standards PP 7312, Extracts to the Structural
Eurocodes, and the Approved Design Aids booklet.
Note to Candidates: Please check the Programme Title and the Module Title to ensure that you have received the correct examination paper. If in doubt please contact an Invigilator.
L L
W - 0.125 W
0.375^ 1.25 0.
0.070 (^) 0.
Moment = coefficient x W x L Reaction = coefficient x W W = total load on one span
Coefficients for equal span continuous beams with uniform loading
Q1 Stress limits (40 marks)
A cross-section through a prestressed concrete foot bridge is shown in Figure Q1. The foot bridge is to be constructed with a precast, prestressed U shaped beam with a 250mm in-situ concrete deck poured on site. Formwork will be required for the deck construction, but it may be ignored in the design. The manufacturer of the precast U beam has specified that the U beam is capable of supporting its own weight over the design span but that it must be propped at mid-span on site while the deck concrete is poured, and that this propping must remain in position until the deck concrete reaches its specified strength.
From consideration of top and bottom fibre stresses at mid-span only , check (a) Transfer stresses
(b) Site stage stresses (assume imposed loading due to workmanship = 1.5 kN/m^2 )
(c) Service stresses
Allowable stresses Transfer f o max = 17.5 N/mm^2 f o min = -2.66 N/mm^2
Service f s max = 16.5 N/mm^2 f s min = 0 N/mm^2
Beam span 17m c/c simply supported
Loading (in addition to self-weight) Imposed loading at service = 10 kN/m^2
Concrete properties f ci precast U beam= 35 N/mm^2 f cu precast U beam = 50 N/mm^2 f cu in-situ concrete topping = 40 N/mm^2 E (^) f cu = 50 N/mm^2 (short-term) = 33 kN/mm^2 E (^) f cu = 40N/mm^2 (short-term) = 30 kN/mm^2 Unit weight of concrete = 24 kN/m^3
Strand data 40 no. x 12.5mm diameter standard strands to BS
Eccentricity of prestress force = 300mm below neutral axis of the precast U beam
Strand breaking load = 164 kN
Initial transfer force = 73% of breaking load
Prestress losses at service = 15% (α =0.85)
Q2 Magnel lines (40 marks)
Figure Q 2 shows the section of a precast, prestressed concrete I beam. The beam is simply supported at transfer and service to a span of 14 metres. The beam is required to carry an unfactored imposed load of 10 kN/m at service excluding self-weight. The self-weight is the only load acting at transfer.
Concrete properties f ci = 35 N/mm^2 f cu = 50 N/mm^2
Strand data 12.5 mm diameter Nominal cross-sectional area = 93 mm^2 Strand breaking load = 164 kN Transfer prestress force = 73% of breaking load Prestress losses at service = 20%, hence α =0.
Allowable stresses Transfer f o max = 17 N/mm^2 f o min = -1 N/mm^2
Service f s max = 16.67 N/mm^2 f s min = 0 N/mm^2
For the mid-span section of the beam:
(a) Write the Magnel inequalities and hence draw the Magnel diagram to obtain the feasible zone for the applied prestressing force and eccentricity. (25 marks)
(b) Choose a suitable prestressing force and eccentricity for the section. (5 marks)
(c) Distribute the prestressing strands in the section to achieve the eccentricity chosen in (b). Maintain a minimum concrete cover of 30 mm to the strands. (10 marks)
250mm 30mm strand inset
25mm strand inset
1200mm
Q3 Prestress Losses (20 marks)
Figure Q3 shows the cross-section of a 250mm deep prestressed hollow-core floor slab. The slab is subject to indoor conditions of exposure.
Figure Q
FIGURE Q.2 Beam Section (mm)
B = 500mm
H = 950
mm
00mm
Figure Q
t = 100mm
T = 1
00mm
00mm
B = 400mm
T = 1
00mm
00mm
Q4 Feasible Section Modulus (20 marks)
Figure Q4 shows the cross section of simply supported inverted prestressed concrete I- Beam that is required to span 8 metres. The service mid-span maximum bending moment is 400 kNm in addition to self-weight, which is the only force acting at transfer.
From consideration of limiting stresses at the extreme top and bottom fibres:
(a) Derive inequalities that can be usefully used to check if the section is acceptable for any level of prestress force, and
(b) Show that the cross-section in Figure Q4 satisfies these inequalities for:
Transfer limiting stresses f o max = 22 N/mm^2 f o min = -1 N/mm^2
Service limiting stresses f s max = 16.67 N/mm^2 f s min = 0 N/mm^2
Prestress loss factor (effective prestress) at service α = 0. Take the unit weight of concrete = 24kN/m^3
