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CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Semester 1 Examinations 2008/
Module Title: Prestresssed Concrete
Module Code: CIVL 8013
School: Building and Civil Engineering
Programme Title: Bachelor of Engineering (honours) in Structural Engineering
Programme Code: CSTRU_8_Y
External Examiner(s): Mr. P. Anthony and Prof. P. O’Donoghue
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 2008
Requirements for this examination: Mathematics Tables. Students may use their
Extracts to the British Standards PP 7312 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
Figure Q1: Coefficients for equal span continuous beams with uniform l di
Q1 Stress limits (40 marks)
A precast and prestressed concrete 75mm thick solid plate floor slab with a composite 100 mm in-situ concrete topping screed is to span 6.0 m simply supported. The over-all depth of the composite slab is 175 mm. In addition to its self-weight, the imposed design load on the slab is 4.0 kN/m^2. The precast slab is manufactured in standard widths of 2.4 m and is prestressed with 18 x 9.3mm steel strands over that width. The manufacturer of the precast slab specifies that the precast slab must be propped at mid-span on site before topping screed is placed and that this propping must remain in position until it reaches its specified strength. Figure Q1 gives design coefficients for prop reactions and moments.
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
BS 8110 class II limits of stress should be applied.
Design Data:
Precast slab data Design width = 2400 mm I (^) xx precast slab = 84.375 x 10^6 mm^4 Depth to neutral axis from top of Precast slab = 37 mm Cross-sectional area, A = 180000 mm^2
Concrete properties f ci = 35 N/mm^2 f cu Precast slab = 50 N/mm^2 f cu in-situ concrete topping = 35 N/mm^2 E (^) f cu = 50 N/mm^2 (short-term) = 30 kN/mm^2 E (^) f cu = 35 N/mm^2 (short-term) = 27 kN/mm^2 Unit weight of concrete = 24kN/m^3
Strand data 18 x 9.3 mm diameter standard strands to BS Strand inset = 25 mm from bottom of precast slab Nominal cross-sectional area = 52 mm^2 Strand breaking load = 92 kN Initial jacking force = 70% of breaking load Prestress losses at service = 20% (hence α =0.8)
300 225 1500 225 300
450
100
Dimensions (mm)
4 strands @ 250
4 strands @ 200
4 strands @ 150
4 strands @ 100
4 strands @ 50
Full Section
Possible strand locations mm
from bottom of each rib
(Part section)
Per rib
Per rib
Per rib
Per rib
Per rib
Figure Q
250mm 30mm strand inset
25mm strand inset
1 2 0 0 m m
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
Section data Design width = 1200 mm I (^) xx = 1195.2 x 10^6 mm^4 Z (^) bottom = -9521 x10 3 mm^3 Z (^) top = 9602 x 10^3 mm^3 Cross-sectional area, A = 157.6 x 10^3 mm^2
Concrete properties f ci = 35 N/mm^2 f cu = 50 N/mm^2 E concrete (short-term) = 30 kN/mm^2 Concrete creep coefficient, Φ = 2 Shrinkage strain (indoor exposure) = 300 x 10-
Strand data 12.5 mm diameter, 10 no. total: 8 @ 30mm inset from bottom and 2 @ 25mm inset from top Nominal cross-sectional area (A (^) ps ) = 93 mm^2 per strand Strand characteristic (failure) strength = 164 kN per strand Initial prestress force (jacking force) = 70% of breaking load E steel = 195 kN/mm^2 Strand 1000 hour relaxation value = 2% Strand relaxation factor = 2.2 (Table 4.6 BS 8110)
(a) Show from first principles that the loss of prestress force due to elastic shortening of
the concrete is:
ps c
s (^) A E
E
I
e A A
P
loss inforce P
2 1
