DESIGN EXAMPLE

1
DESIGN EXAMPLE
Dr. Bijan Aalami
Structural Engineer, California
Emeritus Professor, San Francisco State
University

Corporation

Adapt Structural Engineering Consultants


2
POST-TENSIONG DESIGN STEPS
PRELIMINARY STEPS

• Member thickness
• Cover to rebar and prestressing

COMPUTATIONAL STEPS

1. Geometry and Structural System
2. Material Properties
3. Loading
4. Design Parameters
5. Actions and Stresses Dead and Live Loading
6. Actions due to Post-Tensioning
7. Stress Check for Serviceability
8. Minimum Passive Reinforcement
9. Strength Calculation for Bending
10. Shear Design
11. Deflection Check
12. Stresses at Transfer
13. Tendon and Reinforcement Layout

3
THREE SPAN, SINGLE LEVEL PARKING STRUCTURE

T-BEAM EXAMPLE

ROSTAM 1 PARKING

GEOMETRY OF THE BEAM

Figure 1
-
1




1
SEM-018M
A good natured legendary strongman of Persian
culture


4
JAVA 3-D VIEW OF ROSTAM PARKING BEAM
5
1 GEOMETRY AND STRUCTURAL SYSTEM
Dimensions and Support Conditions

One-way slab


Supported on parallel beams


Total tributary width 5 m typical


Columns extend below deck only

Effective Width

• Less than the total tributary width 5000 mm
• Assume effective width 24 times flange
  thickness plus the stem width

Effective Width 24 125 460 3460 mm
6
ACI-318 code is mute on the effective width of
prestressed beams.
Effective width depends on

• Bending
• Axial Forces

• The practice among many engineers is to
  assume 12 times the flange thickness on each side
  of the stem, but not greater than the tributary
  of the beam.
• The restriction of effective width being less
  than one quarter of span is not strictly adhered
  to.

Section Properties
Area 7.246e5 mm2 Moment of Inertia
3.555e10 mm4 Yt 215.7 mm from top of
section Yb 544.3 mm from bottom of section
7
2 MATERIAL PROPERTIES
Concrete
f
28 MPa
c
weight
2400 kg/m
3
Elastic Mod.
24870
MPa
Creep Coef.

2
Prestressing
Low Relaxation, Unbonded System
12 mm
Strand
Diam.
99 mm2
Strand Area
200,000
MPa
Elastic Mod.
1860 MPa
f
pu
Nonprestressed (Passive) Reinforcing
460 MPa
f
y
Elastic Mod.
200,000 MPa
8
3 LOADING
Dead Load
Selfweight Slab 0.125 m 2400 kg/m3
9.806/1000 14.71 kN/m Stem 0.635
0.460 2400 9.8061000 6.87 kN/m
Total Dead Load due to Selfweight 14.71
6.87 21.58 kN/m
Superimposed Dead Load due to Mechanical, Sealant
and Overlay 0.5 kN/m2 5 m 2.5 kN/m
Total Dead Load 21.58 2.5 24.08 kN/m
9
Live Load
2.395 kN/m2, reducible per UBC

• UBC (Uniform Building Code) gives
• R Percentage of Live Load Reduction
• 0.861 (A 13.94)
• R Reduction factor equal to or less than 40
• A Tributary of member in square meters

1st Span Reduction 0.861 (20 m 5 m
13.94) 74.1 gt 40 max Live Load (1.0
0.40) 2.395 kN/m2 5m 7.19 kN/m
10
2nd Span Reduction 0.861 (17 m 5 m
13.94) 61.0 gt 40 max Live Load (1.0
0.40) 2.395 kN/m2 5m 7.19 kN/m
3rd Span Reduction 0.861 (5 m 5 m
13.94) 9.5 Live Load (1.0 0.095)
2.395 kN/m2 5m 10.84 kN/m
MaxLL/DL ratio 10.84/24.08 0.45 lt 0.75 ?
Do Not Skip Live Loading

• Strictly speaking, live loading must be skipped
  to maximize the design values. But, when the
  ratio of live to dead loading is small, for hand
  calculations it is adequate to determine the
  design actions based on live loading on all
  spans. The ratio used is 0.75.

11
4 DESIGN PARAMETERS

• Cover to rebar and prestressing strands

Minimum Rebar Cover 50 mm, Top and
Bottom

• The cover selected is higher than the minimum
• Code requirement to allow for top bars over the
• Beam cage in the transverse direction.

Minimum Prestressing CGS 70 mm, All Spans

• The cover cover and hence distance to the CGS
  (Center of Gravity Strand) is determined by the
  fire requirements and corrosion protection ACI
  423, 1996. The CGS distance (70 mm) is slightly
  higher than the minimum required. Its selection
  is based on ease of placement.

12

• Effective stress in prestressing strand

Fse 1200 MPa

• Effective prestress (after all losses) is
  assumed 1200 MPa, if
• Members with dimensions common in building
  construction
• Tendons equal or less than 36 m long stressed at
  one end, or for tendons up to 72 m when stressed
  at both ends
• Generic 12 mm extruded tendons with industry
  common friction coefficients and
• Tendons stressed to 0.8 fpu.

13

• The design prestressing force in each span is
  chosen based upon the following assumptions

• A constant effective force is assumed for each
  span. The design prestressing force is chosen as
  a multiple of the average force in each tendon.
• Force/tendon 1200 Mpa 99 mm2/1000
• 118.8 kN/tendon
• ? Use multiples of 119 kN when selecting
  the post- tensioning forces for design.
• Tendon profiles are chosen to be simple parabolas
  are such that in each span a uniform upward force
  will result.

14
BALANCED LOADING OF A PARABOLIC CABLE
W
b
W d
W c
b
b
P
P
b
a
d
c
L
a
a
c
1
b
b
2Pa
W
b
c
2
SEM-019
15
COMPARISON OF SIMPLIFIED AND ACTUAL
TENDON PROFILES
Figure C4-2
SEM-023M
16

• Other Design Parameters

• Minimum Avg. Precompression 1.4 Mpa
• Target Balanced Loading 60 of Total Dead Load
• Allowable Stresses 0.45 fc Compression
  (final)
• 0.75 v fc Tension, Top
• 1.00 v fc Tension, Bottom
• Minimum Rebar Reqd 0.004 A(Tensile Zone)
• Load Combinations
• Service 1 DL 1 LL 1 PT
• Strength 1.4 DL 1.7 LL 1 HYP

• Observe
• Dead (DL) and live (LL) loading with same values
  in the serviceability and strength load
  combinations.
• For serviceability the post-tensioning (PT)
  actions are used.
• For strength combination, the hyperstatic (Hyp)
  actions (secondary) is used.

17
5 ACTIONS AND STRESSES DUE TO
DEAD AND LIVE LOADING
STRUCTURAL FRAME AND ITS
DEAD AND LIVE LOADING (kN/m m)
LL10.84
DL24.08
LL7.19
3.0
20
17
5
Figure 5-1
SEM-026M
18

Center to center of support distances are used


Moments are reduced to the face-of-support

• The computed moments from the frame analysis are
  reduced to the face of the support using statics
  of each span. The face-of-support moments and
  the moments at midspan are summarized in Table
  5-1.

TABLE 5-1 MOMENTS AT FACE-OF-SUPPORT AND MIDSPAN
(kN-m)
19
DL LL MOMENT DISTRIBUTION (kN-m)
-1184
-1038
-435
-382
-176
333
820

• The critical design moments are not generally at
  midspan. However, in the common hand
  calculation, the midspan location is approximated
  for design check.

SEM-027M
20
6 ACTIONS DUE TO POST-TENSIONING

• Guidelines
• Determine the number of strands to satisfy the
  minimum average precompression.
• Position the strands selected with the maximum
  drape in the critical span.
• Assuming a simple and continuous parabola between
  the supports, determine the upward force of the
  prestressing tendons.
• From the upward force, calculate the percentage
  of the balanced loading in the critical span. If
  the value is more than 60, accept the trial.
  Else, increase the force to balance 60 of dead
  loading. If it is more than 90, increase the
  value of CGS to reduce the percentage to 70 and
  use it as first trial.
• Having selected the first trial for
  post-tensioning of the critical span, use
  engineering judgment to reduce its value in other
  spans if necessary, or raise the drape in other
  spans.

21

• Post-tensioning Design
• Tendon Forces and Balanced Loading
• Tendon Force Based on Minimum
• Precompression
• 1.4 N/mm2 Minimum Precompression
• 1.19 kN Average Effective Force per Tendon
• 1.4 N/mm2 724600 mm2/1000 1014.4 kN
• Equivalent of strands 1014.4/119
• 8.52
• ? say 9 strands
• Force in 9 strands 9 119
• 1071 kN

22

• Design Forces and Balanced Loading
• Span 1

• For hand calculation tendon profile is chosen to
  give uniform upward force.

Try maximum drape and force based upon P/A above
a 544 70 474 mm b 690 70 620
mm L 20.0 m c 474/6200.5/1(474/620)0.5
20.0 9.32 m Wb 1071 kN 2
0.474/9.32 2 1071 0.01091/m 11.68
kN/m DL balanced 11.68/24.08 49 lt
60 No Good
23
Span 1 (Continued)
Prorated of strands 60 / 49 9 11.02
strands Try 11 strands 119 kN 1309
kN  Wb 1309 0.01091/m 14.28 kN/m
?   DL balanced 14.28/24.08 60
OK    Balanced Load Reaction, Left 14.28
kN/m 9.32 133.09 kN?  Right 14.28
kN/m 10.68 152.51 kN?
24
TENDON AND
BALANCED LOADING FOR SPAN 1
W 14.28 kN/m
b
133.09 kN
152.51 kN
(a) BALANCED LOADING
TENDON
620 mm
474 mm
9.32 m
10.68 m
20.0 m
(b) SIMPLE PARABOLA
SEM-030M
25
BALANCED LOADING
W 1.137 klf
b2
W 0.875 klf
b1
36.38 k
28 k
B
A
C
EQ
EQ
32.00'
32.00'
(a) DOUBLE PARABOLA
W 1.033 klf
b
30.89 kips
35.23 kips
29.90'
34.10'
(b) SINGLE PARABOLA
SEM-021
26
Span 2
Continuous Tendons

• This span is shorter. 9 tendons are adequate
  to satisfy the minimum precompression. A lower
  percentage of selfweight (50) is balanced
  because the dead load in span 2 helps with the
  actions of span 1.
• Note that the tendon low point is located at the
  span midpoint.

  Wb 50 24.08 kN/m 12.04 kN/m ? a Wb
L2/8 P (12.04 172) / (8 1075.5)
1000 405 mm CGS 690 405 285
mm   Balanced Load Reactions 12.04 kN/m 8.5
m 102.34 kN ? (Left and
Right)
27
Span 2 (continued)
Added (discontiued) Tendons   a 690 544
146 mm c 0.20 17 3.4 m Wb 2
119.5 (2 0.146 / 3.4) 2 119.5 0.02526
6.01 kN/m ?   Concentrated Force _at_ Dead
End 6.01 3.4 m 20.44 kN ?
28
Span 3

• Tendons in this span are chosen to be straight.

CGS Left 690 CGS Right 594 CGS Center (690
594)/2 617 say 620

• The Vertical Balanced Loading forces are
  limited to concentrated forces acting at the
  supports only they are equal and opposite

Wb 1075.5 kN (690 544) / (5 1000)
31.27 kN ?(right) ? (left)
29
TENDON, FORCE AND BALANCED LOADING
ADDED
TENDON
690
690
620
544
544
70
285
8.5 m
10.68 m
9.32 m
8.5 m
20 m
17 m
5 m
(a) SIMPLIFIED TENDON PROFILE
1309 kN
3.4 m
1071 kN
11 STRANDS
9 STRANDS
(b) FORCE DIAGRAM
14.28 kN/m
12.04 kN/m
31.27 kN
6.01 kN/m
31.27 kN
152.51 kN
20.44 kN
102.34 kN
133.09 kN
102.34 kN
(c) BALANCED LOADING
SEM-020M
30
Verify the computed balanced loading
(i) Sum of vertical forces must add up to
zero   -133.09 152.51 14.28 20 102.34
20.44 6.01 3.4 12.04 17 102.34 31.27
31.27 0.006 OK      (ii) Sum of
moments of the forces must be zero. Taking
moments about the first support gives   -152.51
20 14.28 202 /2 102.34 20 6.01 3.4
12.04 17 102.34 31.27 31.27 -2.97
OK  
31

• Many engineers use the expression given bellow
  to compute hyperstatic moments. This expression
  gives the correct answer, only if the balanced
  loading used in the determination of Mpt
  satisfies equilibrium.
•  
• Mhyp Mpt Pe

Actions due to Post-Tensioning Actions due to
post-tensioning are calculated using a standard
frame analysis program. The same frame geometry
used for dead and live loading (Fig. 5-1) is
subjected to the balanced loading shown in Fig.
6-2(c). The results shown in Fig. 6-3. The
moments shown in the figure are reduced to the
face of support. Midspan moments are also marked.
32
POST-TENSIONING MOMENT
DISTRIBUTION (kN-m)
-379.0
125.2
81.7
148.9
132.3
457.4
528.7
  Figure 6-3
SEM-028M
33
DEAD AND LIVE LOAD MOMENTS
Moments Diagrams
Data rostamhm
Dead Load
Live Load Min
Live Load Max
-1000
-750
-500
-250
Moments kNm
0
250
500
Span 1
Span 2
Span 3
34
BALANCED AND HYPERSTATIC (SECONDARY) MOMENTS
Moments Diagrams
Data rostamhm
Post-Tensioning
Secondary
-400
-300
-200
-100
0
100
Moments kNm
200
300
400
500
600
Span 1
Span 2
Span 3
35
7 STRESS CHECK FOR SERVICEABILITY
CRITICAL LOCATIONS FOR ANALYSIS
A
B
C
D
E
20.0 m
17.0 m
5.0 m
SEM-001M
36
Stresses
? (MD ML MPT)/S P/A S I/Yc where I
3.555e10 mm4 YT 216 mm YB 544
mm   Stop 3.555e10/216 1.646e8 mm3 Sbot
3.555e10/544 6.536e7 mm3
Stress Limits
Top Tension 0.75 ?28 3.97 MPa Bottom
Tension 1.0 ?28 5.29 MPa Compression
0.45 28 -12.60 MPa  
37
Point A MD ML MPT (631.5 188.7
379.0) 441.2 kN-m P/A
-13091000/72460 -1.81 MPa   Top Fiber ?
(MD ML MPT)/S P/A ? -441.210002/1.646e
8 1.814 MPa -4.49 MPa Compression lt12.60
MPa OK Bottom ?
441.210002/6.535e7 1.814 MPa 4.94 MPa
Tension lt 5.290 MPa OK Stresses
at the other sections are calculated in a similar
manner and listed in the Table 7-1.
38
TABLE 7-1. SERVICE EXTREME FIBER STRESSES AT
SELECTED POINTS

• Note Ft and Fb are the respective top and
  bottom allowable stresses.
• Since the post-tensioning selected satisfies the
  stresses, no revision in post-tensioning is
  necessary.

39
ADAPT-PT v6.0 INTERACTIVE GRAPHS
40
SERVICE TOP STRESSES AND LIMITS
Stresses Diagrams
Data rostamhm ()Tension (-)Compression
Combined Top Max-T
Combined Top Max-C
Allowable Stresses
2
1
-0
-1
Stresses N/mm²
-2
-3
-4
Span 1
Span 2
Span 3
Combined stresses factors 1DL1LL1PT
41
SERVICE BOTTOM STRESSES AND LIMITS
Stresses Diagrams
Data rostamhm ()Tension (-)Compression
Combined Bottom Max-T
Combined Bottom Max-C
Allowable Stresses
5.0
2.5
0.0
-2.5
Stresses N/mm²
-5.0
-7.5
-10.0
-12.5
Span 1
Span 2
Span 3
Combined stresses factors 1DL1LL1PT
42
8 CODE REQUIRED MINIMUM NONPRESTRESSED
REINFORCEMENT

• Use 22 mm bars (Area 387 mm2 Diameter
  22 mm)
• Minimum Required, Top
• As 0.004 ATens
•  
• Atens is the area of the section between the
  tension fiber and the section centroid.
•  
• 0.004 125 3460 (216 125) 460
• 1897 mm2
• Bars 1897/387 4.90
• Use 5 22 mm bars
• As 5 387 1935 mm2
•  
• Minimum Required, Bottom
• As 0.004 ATens
• 0.004 (460 544)
• 1001 mm2
• Bars 1001/387 2.58

43
9 STRENGTH CALCULATIONS

• Mu is the factored combination of dead, live
  and hyperstatic moments.

Hyperstatic Moments The hyperstatic moments are
determined from the reactions of the frame
analysis when the frame is subjected to balanced
loading.

• The hyperstatic (secondary) reactions must be in
  self-equilibrium, since the applied loading
  (balanced loading) was in self-equilibrium.

Check the validity of the solution for static
equilibrium.   ?Vertical Forces 13.68 30.30
19.07 2.45 0 OK ?Moments about Support
1 -102.90 82.00 29.18 - 5.02
(30.3020) (19.0737) (2.4542)
-0.05 ? 0 OK  
44

• Support reactions due to post-tensioning are
  applied to the beam in order to construct the
  hyperstatic moment diagram shown 9-1(b). The
  support reactions are shown in part (a) of the
  figure.

45
HYPERSTATIC (SECONDARY) ACTIONS
-102.90 kN-m
81.66 kN-m
-5.00 kN-m
29.05 kN-m
-30.18 kN
13.62 kN
-2.44 kN
19.00 kN
(a) SUPPORT REACTIONS DUE TO PT
-16.64
-5.42
11.1
102.42
289.40
374.76
(b) HYPERSTATIC MOMENT DISTRIBUTION
SEM-002M
46
Design Moments (Mu)MU 1.4 MD 1.7 ML
1.0 MHYP
47
Capacity and Reinforcement Calculations
For hand calber can be approximated for most
common sections by assuming a conservative
ultimate stress for the prestressing tendons. The
approximated solution is validated by ensuring
that the reinforcing index is not exceeded. The
approximate procedure is based on the following
limitations

• fc ? 28 Mpa
• P/A ? 1.72
• a/de ? 0.4, where de is the depth of the
  center of the tensile force from the compression
  fiber
•  Tendon Length ? 38 m for single end stressing
• ? 76 m for double end stressing

• fps is conservatively assumed to be 1500 MPa
  if span is less than 11 m in slabs
• fps is conservatively assumed to be 1350 MPa
  if span is greater than 11 m in slabs
• fps is conservatively assumed to be 1400 MPa
  if span is less than 11 m in beams
• fps is conservatively assumed to be 1300 MPa
  if span is greater than 11 m in beams

48
GEOMETRY AND REINFORCEMENT
b
f
d'
A '
s
a
h
f
d
p
d
d
e
r
h
A
ps
A
s
b
SEM-031
49
DISTRIBUTION OF FORCES
IN PRESTRESSED MEMBER
a
c
d
d
d
p
r
e
T
P
T
S
SEM-032
50
At Point A (Midspan of Span 1) h 760
mm Aps 11 99 1089 mm2 dp 760 70
690 mm As 1161 mm2 (from minimum
computation) dr 760 50 22 / 2 699
mm Span gt 11 m fps 1300 MPa   Total Tension
Force Tp Ts (1089 1300 1161 460) /
1000 1415.7 534.06 1949.76 kN   a
1949.76 1000 / (3460 0.85 28) 24
mm de approximately 695 mm a/de 24/695 lt
0.4 OK to use approximation ?Mn
0.91415.7(69024/2)534.06(699-24/2)/1000
1194.1 kNm lt Mu 1443.5 kNm No Good
51

• Add Supplemental Rebar
• Since supplemental rebar must be added the depth
  of compression zone must be prorated to
  approximate the added compressive stress in the
  section.
•  
• Prorated a 24 1477 / 1194 30 mm
• Msupplemental 1476.6 1194 275.9 kN-m
• Asupplemental 282.5 kN-m10002 /
  0.9460ksi(699-30/2)
• 998 mm2 99 mm2 (10 more for
  conservatism) 1097 mm2
• Since this is an approximate method for
  expeditious hand calculation, add 10 more rebar
  in lieu of iterating the solution.
•  
• As 1161 1097 2257 mm2
• Bars 2257/ 387 5.8 Say 6-22
  mm bars
• As 6 387 2322 mm2
• Ts 2322 460/100 1068.12 kN

52

• At Point B (Right Face of Support, Span 1)
• Ap 11 99 1089 mm2
• dp ? 670 mm
• At the face of support the tendon height is
  approximated to be slightly less than the maximum
  tendon height.
•  
• As 1935 mm2
• ds 760 50 22 / 2 699 mm
• Span gt 11.0 m ? fps 1300 MPa
•  
• Total Tension Force Tp Ts
• (1089 1300 1935 460) / 1000
• 1415.7 890.10
• 2305.8 kN
•  
• a 2305.8 kN 1000 / (460 0.85 28 MPa)

53

• Add Supplemental Rebar
•  
• Prorated a 211 mm 1369.5 / 1194.7 245 mm
• Msupplemental 1369.5 1194.7 172.4 kN-m
• Asupplemental 174.8 kN-m10002 / 0.9460
  MPa(699-245/ 2)
• 732 mm2 73 mm2 (10 more for
  conservatism) 805 mm2
•  Again for expeditious hand calculation 10 more
  rebar is added in lieu of iteration.
•  
• As 805 1935 2740 mm2
• Bars 2740/387 7.1 Say 8-22 mm bars
• As 8387 3096 mm2
•  Ts 3096 460 / 1000 1424.2 kN-m

54
At Point D (Midspan of Span 2)   Aps 9
99 891 mm2 dp 760 285 475 As 1161
mm2 dr 760-50-22 / 2 699 Span gt 11.0 m
fpu 1300 MPa   Total Tension Force TP
TS (8911300 1161460)/1000
1158.3 534.1 1692.4 kN   a
(1692.41000) / (3460 0.85 28 MPa) 21 mm
a/de lt 0.4 by inspection, OK to use
approximation   ?Mn 0.91158.3(475 21 /
2) 534.1(699-21 / 2) / 1000 815.2 kN-m
gt Mu 642.8 kN-m OK
55
FACTORED MOMENT DISTRIBUTION
Moments Diagrams
Data rostamhm
Factored Min
Factored Max
-1500
-1000
-500
0
Moments kNm
500
1000
1500
Span 1
Span 2
Span 3
Factored moments factors 1.4DL1.7LL1PT
56
DISTRIBUTION OF REBAR REQUIREMENTS
57
Chosen bars

• Bar lengths are based upon the ACI-318 minimum
  requirements that state that bars at midspan be
  1/3 span length and bars over supports extend 1/6
  of span length into each span, except when needed
  for strength. When required for strength, one
  third of bars at exterior spans, and one-fourth
  at interior spans should extend the supports.

Point Abar length 20000/3 6667 say
6700 mm   Chosen bar at midpoint span 1 4 22
mm x 6700 mm 2 22 mm
continuous   Points B Cbar length
2(2000017000) / (26) 6167 say 6200
mm   Chosen bar at support 2 8 22 mm x 6200
mm
58
Summary of bar lengths

• Strength computations performed herein were
  limited to points considered critical by
  inspection. When spans and loading are not
  regular, the selection of critical points by
  inspection become difficult. In such cases,
  stress and strength checks must be performed at a
  greater number of locations.

59
10 SHEAR DESIGN
Distribution of design shear is shown in Figure
10-1. The Design shear (Vu) is computed from the
results of the standard frame analysis performed
for the loading conditions D, L and PT. The
following combination was used.  Vu 1.4 VD
1.7 VL 1.0 VHYP  
DISTRIBUTION OF SHEAR (kN)
522.38
353.47
-9.60
-258.51
-396.32
-427.43
SEM-017M
60
Span 1 point of zero shear 396.3220 /
(396.32 522.38) 8.63 m Design at
distance (column width h) / 2 (350
760) / 2 555 mm from exterior column CL
(450 760) / 2 605 mm from interior column
CL   Vu -396.32(8.63-0.555) / 8.63 -370.83
kN _at_ exterior 522.38(20-8.63-0.605) /
(20-8.63) 494.58 kN _at_ interior
522.38(20-8.63-20/3) / (20-8.63) 216.09 kN _at_
distance 1/ 3L from interior column   bw 460
mm d 0.8h 0.8760 608 mm   vcmin
0.166?28 0.878 MPa vcmax 0.420?28 2.222
MPa
61
vc 0.05?fc 4.8Vud/ Mu   vc ext.
0.05?28 4.8370.83608/ (157.101000) 7.15
MPa use 2.22 MPa at exterior column   vc int.
0.05?28 4.8494.58608/ (1367.21000) 1.32
MPa at interior column   vc 1/3. 0.05?28
4.8216.09608/ (9001000) 0.96 MPa at 1/3 L
from interior column     vu (358.481000) /
(0.85460608) 1.50 MPa exterior
(463.661000) / (0.85460608) 1.95 MPa
interior (192.211000) / (0.85460608) 0.81
Mpa _at_ 1/3 point
62
Assume 13 mm stirrups w/ 2 legs Ay 2129
mm2 258 mm2     At exterior column vu lt vc
? Use minimum specified spacing 570 mm
(0.75h)   At interior support s Ay fy/ bw
(vu vc) 258460/460(1.95-1.25) 368
mm ? Use 350 spacing from interior support to
1/3 point.   At point 1/3 from interior support
vu ? vc ? Use minimum specified spacing
570 mm
63
11 DEFLECTION CHECK
The deflections are calculated from the frame
analysis program for each of the load cases of
dead, live and post-tensioning, using the gross
cross-sectional area and linear elastic
relationship. The critical location is in span 1.
The values for span 1 are as follows
Span 1 Deflection   Dead Load 25
mm Post-Tensioning -15 mm Dead Load
PT 10 mm   Reduction in moment of inertia due
to cracking   Ie 1 0.30(fmax 0.5 ?fc)
/ 0.5 ?fc I 1 0.30(4.94-2.646) /
2.646 I 0.74 I
64
Hence deflection due to dead load and PT
10 mm / 0.74 13.5
mm   Long-term deflection due to creep
(12)13.5 40.5 mm   Ratio of
deflection to span 40.5 / (201000)
1 / 494 OK

• Service stress exceeded the cracking limit of
  0.5sqrtfc, the stiffness of the member must be
  reduced to allow for the effects of cracking.

Ie 1 0.3(fmax 0.5sqrtfc)/0.5sqrtfc
I Live load deflection 7.4 mm from frame
analysis   Live load deflection with cracking
allowance 7.4 / 0.74 10 mm
65
Total long-term deflection due to dead, live and
prestressing 40.5 10 50.5
mm   Deflection ratio 50.5 / (201000)
1 / 396 OK

• Deflection does not generally govern the design
  for members dimensioned within the limits of the
  recommended tables and balanced within the
  recommended range, and when subject to loading
  common in building construction. For such cases,
  deflections are almost always within the
  permissible code values.

66
SERVICE DEFLECTIONS
Deflections Diagrams
Data rostamhm
0.0
2.5
5.0
7.5
Deflections mm
10.0
12.5
15.0
17.5
Span 1
Span 2
Span 3
Combined deflection factors 1DL1LL1PT
67
12 STRESSES AT TRANSFER
Load Case 1.0DL 1.15PT fcl ¾ fc ¾
28 21 Mpa ? ?(MD 1.15MPT) / S
1.15P/A S I/Yc Stress Limits Tension
0.25 ?21 MPa 1.146 MPa Compression
0.60 21 Mpa -12.6 MPa
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70
13 TENDONS AND REINFORCEMENT LAYOUT
The final tendon and reinforcement layout for
Band-B is shown in figures 13-1 and 13-2
BEAM ELEVATION
1
2
3
4
5.0m
17.0m
20.0m
2500
1200
9-12mm
3100
3100
STRANDS
11-12mm STRANDS
5-22mm
4-22mm
x 3400
2-22mm CONT.
6-22mm x 6200
4-22mm x 1000
x 3700

544
544
690
280
3.4m
690
2-22mm
2-22mm x
1-22mm
CONT.
x 1700
6700
1-22mm x
5700
13mm_at_570mm O.C.
13mm_at_570mm O.C.
13mm_at_570mm O.C.
STAGGER TOP TIE
STRAIGHT PROFILE
NOTE FOR LAYOUT OF TENDON AND
REBAR SEE THE ATTACHED DETAILS
SEM-042M
71
PROFILE FOR TENDONS
TERMINATED TENDONS
CONTROL POINTS AS
STAGGER AT 300MM AT BANDS
SHOWN ON PLAN
(ANCHOR AT CENTROIDAL AXIS)
STRESSING
END
TYP. UNO
CENTROID
CENTROID
CGS
LOW
a
SPAN/5
POINT
TYP. UNO
TYP.
0.5L2
0.4L1
0.6L1
0.5L2
0.4L3
0.6L3
L1
L2
L3
INTERIOR SPAN
EXTERIOR SPAN
EXTERIOR SPAN
WITH STRESSING
NO STRESSING
a 0.1 L
NOTES
SEM-046M
72
PLACEMENT OF TENDONS IN BEAM
STIRRUPS OR ,
(a) BUNDLING OF TENDONS
10mm REBAR
(b) TENDONS SUPPORT CHAIRS
SEM-047M
73
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