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-180
-160
-140
-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
140
160
180
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0
Shearforce(kN)
Distance from left hand support (m)
DESIGN SHEAR FORCE AND RESISTANCEChanges in resistances at holes and notches occur at a distance
of one centroid height from change of section
Ultimate shear
Shear capacity Vco or Vcr
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0
20
40
60
80
100
120
140
160
180
200
220
240
260
280
300
0.0 2.0 4.0 6.0 8.0 10.0 12.0
Moment(kNm)
Distance from left hand support (m)
DESIGN MOMENTS AND RESISTANCESChanges in resistances at holes and notches occur atone transmission length from the change in section
Service moment Ultimate moment
Service resistance Ultimate resistanc
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-30
-20
-10
0
10
20
30
40
50
0.0 2.0 4.0 6.0 8.0 10.0 12.0
Deflection(mm)
x axis = Distance from left hand support (m)
INSTALLATION, FINAL & LIVE LOAD DEFLECTIONSNo holes or notches included
Final deflection span/250 limit
At installation Deflection after install
span/350 or 20 mm limit
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-8
-6
-4
-2
0
2
4
6
8
10
12
14
16
18
20
22
24
0.0 2.0 4.0 6.0 8.0 10.0 12.0
Servicebendingstress(N/mm2)
Distance from left hand support (m)
SERVICE STRESS AND LIMITS Bottom stress Top stress
Bottom limit Top limit
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Project title Designed by
Job ref Checked by
Location Date
Floor level Revision A Date
Load (kN) Distance* (m)
mm
hour %
Load (kN/m) Start* (m) End* (m)
PRETENSIONING DATA
Stress in tendons (N/mm2)
Initial prestress force (kN)
Initial force x axis height (kNmm)
Mean axis height = 41,049 / 1,118.82 = 36.7 mm * Distances measured from the left hand end to centre of supp
Eccentricity = 123 - 36.7 = 86.3 mm
Mean initial stress in all tendons = 1,118,817 / 903 = 1,239.0 N/mm2
LOSSES
Immediate steel relaxation loss = 1.2 x 0.02 = 0.024Elastic shortening after relaxtion loss = (0.976 x 12.50 x 195,000) / (1,239.0 x 27,000) = 0.0711
where initial stress in concrete at centroid of tendons = (1,118,817 / 175,000) + (1,118,817 x 86.3 / 15,814,939) = 12.50 N/mm2
Residual after initial losses R = - . = .
Page 2 of 10
Transmission length coefficient 240
1,118.82
41,049
TOTAL
1,239 1,239 1,239 708
26,789 14,259 0 0
903
0.00.0345.7773.1
00
5.00
3.00
4.00
Line load 3
Line load 4
0.00
0.00
Program by K S Elliott, Nottingham University Consultants Ltd. 20
0.00
2.00 DEAD
DEAD
DEAD
DEAD
3.00
4.00
DEADPoint load 4
Line load 1
Line load 2
LINE LOADS PARALLEL WITH SPAN
0.00
1.00
2.00
4.00
0.00
Point load 3
DEAD
DEAD
DEAD
0.00
0.00
1.00
2.00
3.00
Point load 1
STRAND PATTERN
Area of tendons each row (mm2)
3
35
ROW 1 ROW 2
No. of tendons in each row
Cover to tendons (mm)
12
30
624 279
Bearing length
Ratio of initial prestress 12.5
Breadth of core
Area of concretePOINT LOADS
0.00
1.5 Strand 1000 hour relaxation 2.0
Ratio of initial prestress top 0.40
195000100 N/mm2
1770
0.700
Ratio of initial prestress 9.3 0.700
135 Steel yield strength for strandmm
COMPANY HEADERS
mm
mm
CLASS 3 TO BS8110
60
Diameter of tendons (mm) 9.3 12.5 9.3 7.0
mm2
mm4
mm
ROW 3 TOP
SPAN AND LOADS
10.000
3.77
1.50
m
kN/m2
kN/m2Self weight of screed
K S ELLIOTT
8/12/2006
8/12/2006
0
25
0
0
kN/m2
0.00
0.50
0.00
5.00
kN/m2
kN/m2
kN/m2
Fire resistance Point load 2
0.3N/mm2 Imposed l ive load factor for long term
Young's modulus of strand
TANDARD DESIGN CALCULATION FOR PRESTRESSE
Depth of unit
Breadth at top
Breadth at bottom
N/mm2
N/mm2
N/mm2
Effective span
Self weight of precast unit plus infill in1154
1197
35
32000
SECTION PROPERTIES MATERIAL PROPERTIES
Second moment of area (10^6)
Height to centroid from bottom
1365.00
175000
123.0
Concrete cube strength
Concrete transfer cube strength
Concrete Young's modulus
Concrete transfer modulus
250
No. of cores
Total breadth of webs
Depth of top flange
Depth of bottom flange
mm
mm
mm
6
CONCRETE HOLLOW CORE FLOOR UNIT
mm
40
35 Concrete creep coefficient
27000
0.0003
1.40
N/mm2 Finishes UDL298
Services UDL
Partitions UDL
Imposed live load UDLDesign tensile stress for Class N/mm2-6.24
Concrete shrinkage strain
LOGO
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TRANSFER STRESS CHECK
Transfer force after initial losses = 0.9049 x 1,118,817 = 1,012,406 N
Allowable stress = 0.5 x 35 = 17.5 N/mm2 PASS
Transfer stress at top = (1,012,406 / 175000) - (1,012,406 x 86.3 / 10,748,031) = -2.34 N/mm2 Allowable stress (Class 3) = -0.45 x 35^0.5 = -2.66 N/mm2 PASS
where Z bottom = 1365000000 / 123 = 11,097,561 mm3, and Z top = 1365000000 / 127 = 10,748,031 mm3
Further long time losses:
Creep loss = elastic shortening x creep factor = 0.0711 x 1.40 = 0.0901
Shrinkage loss based on 300 micro strain = 0.0003 x 195000 / 1,239.0 = 0.0472
Total losses = 0.0240 + 0.0711 + 0.0901 + 0.0472 = 23.2 %
Residual loss factor after final losses Rwk = 0.7676
Final force after final losses = 0.7676 x 1,118,817 = 858,791 N
FINAL PRESTRESS
Prestress at bottom = (858,791 / 175000) + (858,791 x 86.3 / 11,097,561) = 11.59 N/mm2 Allowable stress = 0.33 x 60 = 19.8 N/mm2 PASSPrestress at top = (858,791 / 175000) - (858,791 x 86.3 / 10,748,031) = -1.99 N/mm2 Allowable stress including depth factor of 1.075 (Class 3) = -6.235 N/mm2 PAS
SERVICEABILITY MOMENT OF RESISTANCE
Service moment based on top stress = (19.8 - -1.99) x 10,748,031 = 234,189,311 Nmm
Service moment based on bottom stress = (11.59 - -6.24) x 11,097,561 = 197,776,121 Nmm Stress fpb (N/mm2)
Critical service moment of resistance = 197.8 kNm Ultimate stress = 0.95 x 1770
ULTIMATE MOMENT OF RESISTANCE
Area of strands in tension zone (exclude top wires) = 903 mm2
Height to centroid of these strands = (624 x 34.7 + 279 x 41.3 + 0 x 4.7) / 903 = 36.7 mm Secant E = 50.01 kN/mm2Effective depth to strands in tension zone = 213.3 mm
Constitutive equations for stress v strain:
If final strain < 0.013623, then fpb = 1,000 + 50,010 x strain
If final strain > 0.013623, then fpb = 0.95 x 1770
X 0.005 + 0.95 x 1770 / 195000 = 0.013623
Prestrain = 1,239.0 x 0.7676 / 195000 = 0.004877 E = 195 kN/mm2
Ultimate strain = 0.0035 x (213.3 - X) / X
Strain
Page 3 of 10
Ultimate force in concrete Fc = 0.45 x 60 x 1154 x 0.9 X = 28,042X 1154 mm
d - X
Transfer stress at bottom = (1,012,406 / 175000) + (1,012,406 x 86.3 / 11,097,561) = 13.66 N/mm2
1,682
1,345
Total strain = 0.001377 + 0.747 / X Eq. 1 Stress v strain curve for strands
0.0035
1,000
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Ultimate force in tendons Fs = fpb x 903
Then for equilibrium: X / fpb = 903 / 28,042 = 0.0322
Sub. Eq. 2 into eq. 1; strain = 0.001377 + 23.185 / fpb Compression zone
Sub Eq. 3 into the above constitutive equation: total strain = 0.014727 > 0.013623, then fpb = 1,682 N/mm2
Sub. Into Eq. 2: X = 0.0322 x 1,682 = 54.1 mm
But 0.9X is greater than depth of top flange of 40 mm, therefore compression block considered as 'T section' comprising top flange and webs (see diagram)
Then final X = 82.0 mm
Depth to centroid of compression block = 26.6 mm
Lever arm = 213.3 - 26.6 = 186.7 mm
Transmission length
ULTIMATE SHEAR CAPACITY Vco - FLEXURALLY UNCRACKED
Distance to critical point from end of unit 'x' = 100 + 123.0 = 223.0 mm
Mean diameter of all strands = (12 x 9.3 + 3 x 12.5 x 0 x 9.3) / (12 + 3 + 0) = 9.9 mm
Transmission length Lt = 240 x 9.9 / 5.92 = 403.2 mm
Shear plane inside transmission zone; x / Lt = 223.0 / 403.2 = 0.553
Axial prestress at centroid level fcp = 858,791 / 175000 = 4.91 N/mm2
45 deg. shear plane
Prestress at shear plane fcpx = 4.91 x 0.553 x (2 - 0.553) = 3.927 N/mm2
Flexurally uncracked shear capacity Vco = 0.67 x 298.3 x 250 0.8 x 3.927 x 1.86 + 3.46 = 152.3 kN
ULTIMATE SHEAR CAPACITY Vcr - FLEXURALLY CRACKED
Vcr varies along the span of the unit depending on design moment Mu and shear force Vu (see table at end of report); Vcr = (1 - 0.55 R) vc bw d + Mo Vu / Mu
where R = residual loss factor = 0.7676
Concrete shear stress vc = 0.972 N/mm2
Breadth of webs bw = 298.3 mm
Effective depth d = 213.3 mm
Decompression moment Mo = 0.8 x 11.59 x 11,097,561 = 102.87 kNm
Page 4 of 10
BEARING CAPACITY
Ultimate bearing stress = 24 N/mm2
403 mm
100 123.0
Ultimate moment of resistance = 1,682 x 903 x 186.7 = 283.5 kNm 223 mm
Web breadth 298.3 mm
Top flange = 40 mm
XEq. 2
Eq. 3
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Ineffective bearing allowances = 35 mm
Effective bearing width = 600 mm
Bearing capacity = 504 kN
SERVICEABILITY DEFLECTION (are calculated for basic section only, i.e ignores holes)
Deflection at transfer.According to factory measurements, increase theoretical camber by 50%.Upward camber = 1.5 x 1,012,406 x 86.3 x 10000^2 / (8 x 27000 x 1365000000) = -44.5 mm
Due to self weight = 5 x 4.29 x 10000^4 / (384 x 27000 x 1365000000) = 15.1 mm
Net deflection at transfer = -29.3 mm
Deflection at installation. Creep factor at 28 days = 0.4 x 1.4 x 27000 / [0.5 x (27000 + 32000)] = 0.51
Camber = (1 + 0.51) x 1,012,406 x 86.3 x 10000^2 / (8 x 27000 x 1365000000) = -44.8 mm
Due to self weight = (1 + 0.51) x 15.1 = 22.9 mm
Net deflection at installation = -21.9 mm
Long-term deflections (calculated at midspan, even though the aggregate deflections for all UDL, line and point loads may not occur there)Creep factor from 28 days to final = 1.4 - 0.51 = 0.89
Camber = -44.8 -0.89 x 858,791 x 86.3 x 10000^2 / (8 x 32000 x 1365000000) = -63.7 mm
Due to visco self weight plus dead and live UDL = 22.9 + 5 x 1.2 x [3.77 x 0.89 + 2.00 x (1 + 0.89) + 1.50 x (1 + 1.4)] x 10000^4 / (384 x 32000 x 1365000000) = 61.3 mm
Long-term deflections due to point and line loads at mid-span
No point load 1
No point load 2
No point load 3
No point load 4
No line load 1
No line load 2
No line load 3
No line load 4
Net maximum deflection due to all loads = -4.4 mm Limiting deflection = span/250 = 40.0 mm PASS
Deflection due to imposed loads, camber and creep after installation = 10.1 mm Limiting deflection = span/350 or 20 mm = 20.0 mm PASS
Overall ratio of service moment / capacity ratio = 161.5 / 197.8 = 0.82 Overall ratio of ultimate shear / uncracked shear capacity ratio = 93.1 / 152.3 = 0.61
Overall ratio of ultimate moment / capacity ratio = 241.1 / 283.5 = 0.85 Overall maximum ratio of ultimate shear / cracked shear capacity ratio = 0.91Page 5 of 10
Dynamic, Acoustic and Thermal Properties
Maximum deflection due to imposed UDL dead and 10% live loads = (5 x 1.2 x 6.27 x 10000^4) / (384 x 1.2 x 32000 x 1365000000) = 19 mm
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Partitions not present and therefore dynamic damping factor = 0.02
Number of units side-by-side in slab field = 7, i.e. 8.4 m actual width
Width of slab field contributing to dynamic dispersion (least of span or actual width) = 8.40 m
Peak acceleration 'a/g' = 100 x 300 x e^ -(0.35 x 4.1) / (0.02 x 10.77 x 1200 x 8.40) = 0.67% making the slab field OK for shops, dining, dancing
Sound attenuation (standard reduction) = 37.5 x Log 10 [102 x (3.77 + 1.50 + 0.00)] - 44 = 58 dB
Thermal resistance = 0.35 x [150 + 102 x (3.77 + 1.50 + 0.00)] = 0.24 m2 degC / W
Notched Ends on Shelf Angles
x
x
No shelf angles present
=
Page 6 of 10
Section Properties and Resistances at Holes and Notches
1. Hole 1
Length of hole 1 (along span) = 300 mm Distance to start of hole 1 (from left end) = 2,850 mm
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Effective breadth of top flange = 1154 - 300 = 854 mm
Effective breadth of webs = 298.3 - 90 = 208.3 mm
Section properties at hole 1 are based on average top and bottom width, i.e. 0.5 x (1154 + 1197) = 1175.5 mm
Effective concrete area is pro-rata gross concrete area = 175000 x (1 - 300 / 1175.5) = 130,338 mm2
Effective 2nd moment of area is pro-rata gross concrete area = 1365000000 x (1 - 300 / 1175.5) = 1,016,637,601 mm4
Loss of tendons at the hole 1 (is determined by user as): 9.3 mm strands lost = 2; and 12.5 mm strands lost = 0
Area of strands remaining = 799 mm2
Height to centroid of strand = 37.0 mm
Eccentricity = 86.0 mm
SERVICE STRESS AT HOLE 1 ULTIMATE MOMENT OF RESISTANCE AT HOLE 1
Initial force in strands = 989,961 N Area of strands in tension zone (exclude top wires) = 799 mm2
Immediate relaxation and elastic shortening losses = 0.024 + 0.0842 Effective depth to strands in tension zone = 213.0 mm
Transfer force after initial losses = 882,820 N Total strain = 0.012951 < 0.013623, then fpb = 1,000 + 50,010 x 0.012951 = 1,648 N/mm2Check: Transfer stress at bottom = 15.96 N/mm2 PASS X = 122.3 mm
Check: Transfer stress at top = -2.72 N/mm2 FAIL Lever arm = 176.6 mm
Creep and shrinkage losses = 0.1052 + 0.0472 Ultimate moment of resistance = 1,648 x 799 x 176.6 = 232.5 kNm
Total residual losses Rwk = 0.7394
Final force after final losses = 731,978 N
Final prestress at bottom = 13.24 N/mm2 PASS ULTIMATE SHEAR CAPACITY Vco - FLEXURALLY UNCRACKED
Final prestress at top = -2.25 N/mm2 PASS Distance to shear plane from start of hole 1 = transmission length = 407 mm
Critical service moment of resistance = 160.9 kNm Prestress at shear plane fcpx = 5.62 N/mm2
Vco = 0.67 x 208.3 x 250 x 0.8 x 5.616 x 1.86 + 3.46 = 119.9 kN
ULTIMATE SHEAR CAPACITY Vcr - FLEXURALLY CRACKED
vc = 1.052 N/mm2
Mo = 0.8 x 13.24 x 8,265,346 = 87.5 kNm
Varies along span; see table below
Page 7 of 10
Section Properties and Resistances at Holes and Notches
2. Hole 2
Length of hole 2 (along span) = 300 mm Distance to start of hole 2 (from left end) = 6,850 mm
Width of hole 2 (perpendicular to span) = 100 mm Distance to end of hole 2 (from left end) = 7,150 mm
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Effective breadth of top flange = 1154 - 100 = 1054 mm
Effective breadth of webs = 298.3 - 45 = 253.3 mm
Section properties at hole 2 are based on average top and bottom width, i.e. 0.5 x (1154 + 1197) = 1175.5 mm
Effective concrete area is pro-rata gross concrete area = 175000 x (1 - 100 / 1175.5) = 160,113 mm2
Effective 2nd moment of area is pro-rata gross concrete area = 1365000000 x (1 - 100 / 1175.5) = 1,248,879,200 mm4
Loss of tendons at the hole 2 (is determined by user as): 9.3 mm strands lost = 1; and 12.5 mm strands lost = 0
Area of strands remaining = 851 mm2
Height to centroid of strand = 36.8 mm
Eccentricity = 86.2 mm
SERVICE STRESS AT HOLE 2 ULTIMATE MOMENT OF RESISTANCE AT HOLE 2
Initial force in strands = 1,054,389 N Area of strands in tension zone (exclude top wires) = 851 mm2
Immediate relaxation and elastic shortening losses = 0.024 + 0.0731 Effective depth to strands in tension zone = 213.2 mm
Transfer force after initial losses = 951,962 N Total strain = 0.014402 > 0.013623, then fpb = 1,682 N/mm2
Check: Transfer stress at bottom = 14.03 N/mm2 PASS X = 92.0 mmCheck: Transfer stress at top = -2.40 N/mm2 PASS Lever arm = 184.7 mm
Creep and shrinkage losses = 0.0925 + 0.0472 Ultimate moment of resistance = 1,682 x 851 x 184.7 = 264.3 kNm
Total residual losses Rwk = 0.7632
Final force after final losses = 804,697 N
Final prestress at bottom = 11.86 N/mm2 PASS ULTIMATE SHEAR CAPACITY Vco - FLEXURALLY UNCRACKED
Final prestress at top = -2.03 N/mm2 PASS Distance to shear plane from start of hole 2 = transmission length = 405 mm
Critical service moment of resistance = 183.7 kNm Prestress at shear plane fcpx = 5.03 N/mm2
Vco = 0.67 x 253.3 x 250 x 0.8 x 5.026 x 1.86 + 3.46 = 140.3 kN
ULTIMATE SHEAR CAPACITY Vcr - FLEXURALLY CRACKEDvc = 1.007 N/mm2
Mo = 0.8 x 11.86 x 10,153,489 = 87.5 kNm
Varies along span; see table below
Page 8 of 10
3. Notch at left end 4. Notch at right end
Length of notch along span = 200 mm Length of notch along span = 100 mm
Width of notch (perpendicular to span) = 200 mm Width of notch (perpendicular to span) = 100 mm
Effective breadth of top flange = 1154 - 200 = 954 mm Effective breadth of top flange = 1154 - 100 = 1054 mm
Effective breadth of webs = 298.3 - 90 = 208.3 mm Effective breadth of webs = 298.3 - 45 = 253.3 mm
Effective concrete area = 175000 x (1 - 200 / 1175.5) = 145,225 mm2 Effective concrete area = 175000 x (1 - 100 / 1175.5) = 160,113 mm2
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Effective 2nd moment of area = 1365000000 x (1 - 200 / 1175.5) = 1,132,758,401 mm4 Effective 2nd moment of area = 1365000000 x (1 - 100 / 1175.5) = 1,248,879,200 mm4
Loss of tendons: 9.3 mm strands lost = 1; and 12.5 mm strands lost = 0 Loss of tendons: 9.3 mm strands lost = 1; and 12.5 mm strands lost = 0
Area of strands = 851 mm2 Area of strands = 851 mm2
Height to centroid of strand = 36.8 mm Height to centroid of strand = 36.8 mm
Eccentricity = 86.2 mm Eccentricity = 86.2 mm
SERVICE STRESS AT LEFT NOTCH SERVICE STRESS AT RIGHT NOTCH
Initial force in strands = 1,054,389 N Initial force in strands = 1,054,389 N
Immediate relaxation and elastic shortening losses = 0.024 + 0.0806 Immediate relaxation and elastic shortening losses = 0.024 + 0.0731
Transfer force after initial losses = 944,056 N Transfer force after initial losses = 951,962 N
Check: Transfer stress at bottom = 15.34 N/mm2 PASS Check: Transfer stress at bottom = 14.03 N/mm2 PASS
Check: Transfer stress at top = -2.62 N/mm2 PASS Check: Transfer stress at top = -2.40 N/mm2 PASS
Creep and shrinkage losses = 0.1011 + 0.0472 Creep and shrinkage losses = 0.0925 + 0.0472
Total residual losses Rwk = 0.7471 Total residual losses Rwk = 0.7632
Final force after final losses = 787,691 N Final force after final losses = 804,697 N
Final prestress at bottom = 12.80 N/mm2 PASS Final prestress at bottom = 11.86 N/mm2 PASSFinal prestress at top = -2.19 N/mm2 PASS Final prestress at top = -2.03 N/mm2 PASS
Critical service moment of resistance = 175.3 kNm Critical service moment of resistance = 183.7 kNm
ULTIMATE MOMENT OF RESISTANCE AT LEFT NOTCH ULTIMATE MOMENT OF RESISTANCE AT RIGHT NOTCH
Area of strands in tension = 851 mm2 Area of strands in tension = 851 mm2
Effective depth = 213.2 mm Effective depth = 213.2 mm
Strain = 0.013411 < 0.013623, then fpb = 1,000 + 50,010 x 0.013411 = 1,671 N/mm2 Strain = 0.014402 > 0.013623, then fpb = 1,682 N/mm2
X = 121.8 mm Lever arm = 178.1 mm X = 92.0 mm Lever arm = 184.7 mm
Ultimate moment of resistance = 1,671 x 851 x 178.1 = 253.2 kNm Ultimate moment of resistance = 1,682 x 851 x 184.7 = 264.3 kNm
ULTIMATE SHEAR CAPACITY Vco - FLEXURALLY UNCRACKED ULTIMATE SHEAR CAPACITY Vco - FLEXURALLY UNCRACKED
Distance to shear plane = 223 mm Distance to shear plane = 223 mm
Prestress at shear plane fcpx = 4.33 N/mm2 Prestress at shear plane fcpx = 4.01 N/mm2
Vco = 0.67 x 208.3 x 250 x 0.8 x 4.328 x 1.86 + 3.46 = 109.7 kN Vco = 0.67 x 253.3 x 250 x 0.8 x 4.010 x 1.86 + 3.46 = 130.2 kN
Page 9 of 10
(includes holes, notches and shelf angles)
Service Serv moment Ultimate Ult moment Ultimate shear Ultimate shear Deflection at Deflection at Deflection after Final
moment of resistance moment of resistance force Vco or Vcr transfer installation installation deflection
Distance
DESIGN MOMENTS, SHEAR FORCES AND DEFLECTIONS, AND MOMENT AND SHEAR CAPACITY AT 50 POINTS ALONG THE SPAN
253.2 96.4 109.7
from left
0.00 0.0 175.3 0.0 0.0 0.0 0.0 0.0
0 20 12 7 175 3 18 9 253 2 92 6 109 7 -2 5 -2 0 0 6 -1 1
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65.1
2.60
2.80
0.60 36.4 175.3 54.4 253.2
0.40 24.8 175.3 37.0 253.2 88.7
84.9 152.3 -7.1 -5.7 1.9 -2.7
152.3 -4.9 -4.0 1.3 -2.0
1.00 58.1 197.8 86.8 283.5
0.80 47.6 197.8 71.0 283.5
77.2 152.3 -11.2 -8.9 3.2 -3.7
152.3 -9.3 -7.4 2.6 -3.381.0
1.40 77.8 197.8 116.1 283.5
1.20 68.2 197.8 101.8 283.5
69.4 152.3 -14.9 -11.7 4.4 -4.2
152.3 -13.1 -10.4 3.8 -4.073.3
1.80 95.4 197.8 142.4 283.5
1.60 86.8 197.8 129.6 283.5
61.7 152.3 -18.0 -14.0 5.5 -4.4
152.3 -16.5 -12.9 4.9 -4.365.6
2.20 110.9 197.8 165.5 283.5
2.00 103.4 197.8 154.3 283.5
54.0 69.3 -20.8 -16.0 6.5 -4.3
74.3 -19.5 -15.1 6.0 -4.457.9
3.20
3.403.60
3.80
4.00
4.20
-22.0 -16.9 7.02.40
3.00
232.5 46.3 61.4 -23.1
5.60
5.80
6.00
6.20
6.40
6.60
4.40
4.60
4.80
5.00
5.20
5.40
8.00
8.20
6.80
7.00
7.20
7.407.60
7.80
117.8 197.8 175.9 283.5 50.2
124.3 160.9 185.6
-4.2
-17.7 7.4 -4.0
130.2 160.9 194.4 232.5 42.4 46.8 -24.1 -18.4 7.9 -3.8
135.7 160.9 202.5 232.5 38.6 44.4 -25.0 -19.0 8.2 -3.7
140.6 160.9 209.9 232.5 34.7 42.2 -25.9 -19.6 8.6 -3.5
145.0 160.9 216.4 232.5 30.9 50.4 -26.6 -20.1 8.9 -3.3148.9 197.8 222.2 283.5 27.0 48.2 -27.2 -20.5 9.2 -3.1
152.2 197.8 227.2 283.5 23.1 46.2 -27.8 -20.9 9.4 -2.9
155.1 197.8 231.5 283.5 19.3 44.3 -28.3 -21.2 9.6 -2.8
157.4 197.8 234.9 283.5 15.4 42.5 -28.6 -21.5 9.8 -2.6
159.2 197.8 237.6 283.5 11.6 40.7 -28.9 -21.7 10.0 -2.5
160.5 197.8 239.6 283.5 7.7 39.0 -29.1 -21.8 10.0 -2.5
161.3 197.8 240.7 283.5 3.9 37.4 -29.3 -21.9 10.1 -2.4
161.5 197.8 241.1 283.5 0.0 35.7 -29.3 -21.9 10.1 -2.4
161.3 197.8 240.7 283.5 -3.9 37.4 -29.3 -21.9 10.1 -2.4
160.5 197.8 239.6 283.5 -7.7 39.0 -29.1 -21.8 10.0 -2.5159.2 197.8 237.6 283.5 -11.6 40.7 -28.9 -21.7 10.0 -2.5
157.4 197.8 234.9 283.5 -15.4 42.5 -28.6 -21.5 9.8 -2.6
155.1 197.8 231.5 283.5 -19.3 44.3 -28.3 -21.2 9.6 -2.8
152.2 197.8 227.2 283.5 -23.1 46.2 -27.8 -20.9 9.4 -2.9
148.9 197.8 222.2 283.5 -27.0 48.2 -27.2 -20.5 9.2 -3.1
145.0 183.7 216.4 264.3 -30.9 50.4 -26.6 -20.1 8.9 -3.3
140.6 183.7 209.9 264.3 -34.7 47.5 -25.9 -19.6 8.6 -3.5
135.7 183.7 202.5 264.3 -38.6 49.9 -25.0 -19.0 8.2 -3.7
130.2 183.7 194.4 264.3 -42.4 52.6 -24.1 -18.4 7.9 -3.8
124.3 183.7 185.6 264.3 -46.3 61.4 -23.1 -17.7 7.4 -4.0117.8 197.8 175.9 283.5 -50.2 65.1 -22.0 -16.9 7.0 -4.2
110.9 197.8 165.5 283.5 -54.0 69.3 -20.8 -16.0 6.5 -4.3
103.4 197.8 154.3 283.5 -57.9 74.3 -19.5 -15.1 6.0 -4.4
95.4 197.8 142.4 283.5 -61.7 152.3 -18.0 -14.0 5.5 -4.4
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Maxima =
Service Serv moment Ultimate Ult moment Ultimate shear Ultimate shear Deflection at Deflection at Deflection after Final
moment of resistance moment of resistance force Vco or Vcr transfer installation installation deflection
End of document
Program by K S Elliott, Nottingham University Consultants Ltd. 2006
8.60
8.80
9.00
from left
-29.3
-96.4 130.2 0.0
-21.9
9.20
9.40
9.60
9.80
10.00
Distance
10.1 -4.4
77.8 197.8 116.1 283.5 -69.4 152.3 -14.9 -11.7 4.4 -4.2
68.2 197.8 101.8 283.5 -73.3 152.3 -13.1 -10.4 3.8 -4.0
58.1 197.8 86.8 283.5 -77.2 152.3 -11.2 -8.9 3.2 -3.7
47.6 197.8 71.0 283.5 -81.0 152.3 -9.3 -7.4 2.6 -3.3
36.4 197.8 54.4 283.5 -84.9 152.3 -7.1 -5.7 1.9 -2.7
24.8 183.7 37.0 264.3 -88.7 152.3 -4.9 -4.0 1.3 -2.0
12.7 183.7 18.9 264.3 -92.6 130.2 -2.5
0.0 0.0
0.6 -1.1-2.0
0.00.0 183.7 0.0 264.3
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UNIT INPUT DATA 250 6 MOMENT & SHEAR RESISTANCES
Depth of unit 250 mm Basic unit At hole 1 At
Breadth at top 1154 mm Service moment of resistance Msr 197.8 160.9
Breadth at bottom 1197 mm Ultimate moment of resistance Mur 283.5 232.5
Total breadth of webs 298 mm Ult uncracked shear resistance Vco 152.3 119.9
Depth of top flange 40 mm Ult cracked shear resistance Vcr (kN)
Depth of bottom flange 35 mm
No. of cores 6 HOLLOW PRESTRESS CHECK Transfer
Breadth of core 135 mm Stress at bottom (N/mm2) 13.66
Area of concrete 175000 mm2 Stress at top (N/mm2) -2.34
Second moment of area (10^6) 1365.00 mm4
Height to centroid from bottom 123.0 mm INPUT LOADS & SPANS
Concrete cube strength 60 N/mm2 Effective span
Concrete transfer cube strength 35 N/mm2 Self weight of precast unit plus infill in
Concrete Young's modulus 32000 N/mm2 Self weight of screed
Concrete transfer Young's modulus 27000 N/mm2 Finishes UDL
Concrete shrinkage strain 0.0003 Services UDL
1.40 Partitions UDL
3 (0.2) Imposed live load UDL
-6.24 N/mm2 Imposed live load factor for long term
Steel yield strength for strand 1770 N/mm2
0.700 POINT LOADS Po
0.700
Ratio of initial prestress in top wires 0.400 Point load 1
Young's modulus of strand 195000 N/mm2 Point load 2Strand 1000 hour relaxation 2.0 % Point load 3
Strand transmission length 240 Point load 4
Bearing length 100 mm
Fire resistance 1.5 hour LINE LOADS PARALLEL WITH SPAN Line load Di
7 (kN/m) left
Minimum required sound density of 0 kg/m2 Line load 1 0.00
STRAND PATTERN Row 1 Row 2 Row 3 Top Line load 2 0.00
No. of tendons in each row 12 3 0 0 Line load 3 0.00
Cover to tendons in each row (mm) 30 35 0 25 Line load 4 0.00
Diameter of tendons in each row 9.3 12.5 9.3 7.0OUTPUT DESIGN MOMENTS &
OUTPUT DATA FOR UNIT Basic unit At hole 1 At hole 2 Left notch Right notch Basic unit At hole 1 At
Self weight of unit (exclude infill) Service moment Ms 161.5 145.0
Section modulus at bottom (mm3) 1 110E+07 8 265E+06 1 015E+07 9 209E+06 1 015E+07 Ultimate moment M 241 1 216 4
Varies see graph
Distance is from centre of bearing
Distance is from centre of bearing
4.29
Concrete creep coefficient for long - term (28 day = 40%)
Depth & no. cores
PRESTRESSED CONCRETE SOLID & HOLLOW CORE FLOORING DESIGNED TO BS8110 (TO BE CUSTOMISED TO YOUR REQUIREMENTS)
Serviceability tensile stress Class (and crack width)
Number of units side-by-side in slab field (for dynamic
Ratio of initial prestress in bottom strands of 12.5 mm dia. or
Ratio of initial prestress in bottom strands of 9.3 or 10.9 mm
Design hypothetical flexural tensile stress for
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HOLES IN UNIT
Distance* Length Width
Dimensions of hole 1 (mm) 3000 300 300 Deflection at installation of precast unit
Dimensions of hole 2 (mm) 7000 300 100
9.3 mm 12.5 mm
Number of bottom strands lost due 2 0Number of bottom strands lost due 1 0
Breadth of webs after deduction for 208
Breadth of webs after deduction for 253 Natural frequency
Dynamic damping factorMaximum width x length of hole = 400 x 1200
Peak acceleration and suitability
NOTCHES IN ENDS OF UNIT
Length Width
Dimensions of notch at left end 200 200Dimensions of notch at right end 100 100
9.3 mm 12.5 mm
1 0
1 0
208
253
SHELF ANGLE NOTCH NO
20075
Thermal resistance, including topping and finishes
Sound attenuation, including topping and finishes
DEFLECTIONS (to be corrected according to customer's data)
Camber at transfer (mm) = span / 341
Movement after installation, creep & losses (limit 20 mm,
OK for shops,
Elastic maximum deflection due to UDL (Ec = 1.2 x static)
DYNAMIC, ACOUSTIC & THERMAL PROPERTIES
Final long term deflection (limit span/250) (mm)
Width of slab field contributing to dynamic dispersion
Number of bottom strands lost due to notch at left end
Breadth of webs after deduction for notch at right end (mm)
Breadth of webs after deduction for notch at left end (mm)
Max width x length = 400 x 1200. If two notches are side by side in SAME unit, enter total width as one notch.
Do not use if less than 135 mm wide when it is cut through hollow core
Number of bottom strands lost due to notch at right end
If two holes are side by side, enter total width as one hole.
*Distance to centre of holes from LEFT end centre of bearing.
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D
# # # # # # # # # # # # # # # C
# # # # # # # # # # # # # # # D
D # D
B # BB # B
b # b
h # h
h # h
N # N
b # b
A # A
I # I
y # y
A # A
Section
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S U Incl A
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x V
x V x V V V x V V V V D a
P P p p d S D Cs T D s i a P P p p d S i i x V BS L T S L V
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # ## # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # ## # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #M # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # ##
# # # # # # # # ## # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
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# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # #
V #
# # # # # # # # # # # # # # # # # # #
V
# #
#
Ms Mu
x/L end left notch # # # # x/L end left notchx/L end right notch # # # # x/L end right notch
B A
A
L
# # # # #
# # # # #
V # # # # #V # # # # #
# # # # #
P P P P P
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1.00
1.20
- 1.000 2.000
Span (m)
0.000.200.400.600.801.001.201.401.601.80
2.002.202.402.602.803.003.203.403.603.80.
- 2.000
Tens
ilestrength(N/m
Span (m)
1.00
1.20
- 1.000 2.000
Span (m)
0.000.200.400.600.801.001.201.401.601.80
2.002.202.402.602.803.003.203.403.603.80.
- 2.000
Tens
ilestrength(N/m
Span (m)
1.00
1.20
- 1.000 2.000
Span (m)
0.000.200.400.600.801.001.201.401.601.80
2.002.202.402.602.803.003.203.403.603.80.
- 2.000
Tens
ilestrength(N/m
Span (m)
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PowerfunctionX
Variation in span with X for 225 mm slabBottom steel 4T14. Top steel 2T12.
Imposed load = 1.5 kN/m2
1.60
1.80
2.00
2.20
2.40
Creepfactor
Variation in span with creep factor for225 mm deep slab
Bottom steel 4T14. Top steel 2T12.Imposed load = 1.5 kN/m2Variation
in spanwith
tensilestrengthfor 225
mmdeepslab
BottomPowerfunctionX
Variation in span with X for 225 mm slabBottom steel 4T14. Top steel 2T12.
Imposed load = 1.5 kN/m2
1.60
1.80
2.00
2.20
2.40
Creepfactor
Variation in span with creep factor for225 mm deep slab
Bottom steel 4T14. Top steel 2T12.Imposed load = 1.5 kN/m2Variation
in spanwith
tensilestrengthfor 225
mmdeepslab
BottomPowerfunctionX
Variation in span with X for 225 mm slabBottom steel 4T14. Top steel 2T12.
Imposed load = 1.5 kN/m2
1.60
1.80
2.00
2.20
2.40
Creepfactor
Variation in span with creep factor for225 mm deep slab
Bottom steel 4T14. Top steel 2T12.Imposed load = 1.5 kN/m2Variation
in spanwith
tensilestrengthfor 225
mmdeepslab
BottomPowerfunctionX
Variation in span with X for 225 mm slabBottom steel 4T14. Top steel 2T12.
Imposed load = 1.5 kN/m2
1.60
1.80
2.00
2.20
2.40
Creepfactor
Variation in span with creep factor for225 mm deep slab
Bottom steel 4T14. Top steel 2T12.Imposed load = 1.5 kN/m2Variation
in spanwith
tensilestrengthfor 225
mmdeepslab
Bottom
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0.00
- 1.000 2.000
PowerfunctionX
Span (m)
1.00
1.20
1.40
1.60
1.80
2.00
- 1.000 2.000
Creepfactor
Span (m)
0.000.200.400.600.801.001.201.401.601.802.00
2.202.402.602.803.003.203.403.603.804.00
- 2.000
Tensilestrength(N/mm2)
Span (m)
deepslab
Bottom
0.00- 1.000 2.000
Powe
rfunctionX
1.00
1.20
1.40
1.60
1.80
2.00
- 1.000 2.000
Cr
eepfactor
S ( )
0.000.200.400.600.801.001.201.401.601.802.002.202.402.602.803.003.203.403.603.804.00
- 2.000
Tensilestrength
(N/mm2)
Span (m)
mmdeepslab
Bottom
0.00- 1.000 2.000
Powe
rfunctionX
1.00
1.20
1.40
1.60
1.80
2.00
- 1.000 2.000
Cr
eepfactor
S ( )
0.000.200.400.600.801.001.201.401.601.802.002.202.402.602.803.003.203.403.603.804.00
- 2.000
Tensilestrength
(N/mm2)
Span (m)
mmdeepslab
Bottom
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