M_IMP_Prestressed Hollow Core Design to Bs8110

7/27/2019 M_IMP_Prestressed Hollow Core Design to Bs8110

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-180

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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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Moment(kNm)


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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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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Servicebendingstress(N/mm2)


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



1.60

1.80

2.00

2.20

2.40

Creepfactor



in spanwith


mmdeepslab




1.60

1.80

2.00

2.20

2.40

Creepfactor



in spanwith


mmdeepslab




1.60

1.80

2.00

2.20

2.40

Creepfactor



in spanwith


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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Documents

M_IMP_Prestressed Hollow Core Design to Bs8110