member design - prestressed concrete beam and slab bs8110

Job No. Sheet No. Rev.

1

Job Title Gamuda Biz Suites

Prestressed Concrete Design SR 4/17/2023

Introduction


Calc Title Prestressed Concrete Design

Job No. GPSS / j102

By SR

Date 4/17/2023

Convention

SD Structure Design

MD Member Design

CD Connection Design

Indicates that cell is referenced by a macro, hence do not change its position.

Unless of course, the macro code is changed.

Indicates that cell is referenced by a macro through a link cell, hence its position

can be changed, but it should not be altered, added to or deleted.

G & P E N G I N E E

R S

G&P Special Structures Sdn Bhd Consulting Engineers GPSS /

j102

Unless explicitly designated in the sheet name as a subset to another sheet, all sheets are independent of each other (i.e. no cell links between them). However, data can be transferred between sheets when required.

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2



Worksheet Company Signature

Company

G & P E N G I N E E

R S


j102

G & P E N G I N E E

R S

G&P Special Structures Sdn Bhd Consulting Engineers

A R U P E N G I N E E

R S

Ove Arup and Partners Consulting Engineers

whitbybird E N G I N

E E R S

whitbybird Consulting Engineers

Bovis Lend Lease

Bovis Lend Lease Principal Contractors

Ramboll Whitbybird E

N G I N E E R S

Ramboll Whitbybird Consulting Engineers

G & P E N G I N E E

R S

G&P Professionals Sdn Bhd Consulting Engineers

G & P E N G I N E E

R S

G&P Special Structures Sdn Bhd Consulting Engineers

H S S ENGINEERING

HSS Integrated Sdn Bhd Consulting Engineers

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3



Member Design - PT Beam and PT Slab

Item Verification

1 Min beam elastic section modulus MOSLEY

2 Magnel diagram at design section MOSLEY

3 Max economic prestress force at transfer MOSLEY

4 TLS and SLS top and bottom stresses at design section MOSLEY

5 Prestress forces at design section MOSLEY

6 Tendon profile at all sections MOSLEY

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1



BS8110

Material Properties

50 OK

40 OK

460

460

24

30.0 GPa

15.0 GPa

7.5 GPa

28.0 GPa

14.0 GPa

7.0 GPa

Prestressing Characteristics and Criteria

40.0 OK

Pre-tension or post-tension ?

Pre-Tension

Post-Tension

Prestressing tendons bonded or unbonded ?

Bonded Increased fire and corrosion protection, greater ultimate flexural strength, safer demolition;

Unbonded No need for grouting, tendons can be replaced, less friction loss, quicker, cheaper;

Serviceability classification cl.4.1.3

Class 1 No flexural tensile stresses (eg. precast segments);

Class 2 Flexural tensile stresses, uncracked (no visible cracking) (generally employed);

Class 3 Flexural tensile stresses, cracked;

(crack widths ≤ 0.2mm normal, ≤ 0.1mm severe) (partial prestressing);

16.0 cl.4.3.5.1

-2.3 cl.4.3.5.2

Class 1 -1.0

Class 2 -2.3

Class 3 -4.6

16.5 cl.4.3.4.2

-2.5 cl.4.3.4.3

Class 1 0.0

Class 2 -2.5

Class 3 -4.6

Note by convention, positive stress is compressive and negative stress is tensile;

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Characteristic strength of concrete (prestressed beam and slab), fcu N/mm2

Note require fcu ≥ 35N/mm2 cl.4.1.8.1, usually 50N/mm2, ≤ 105N/mm2 HSC;

Characteristic strength of concrete (column), fcu (≤ 105N/mm2; HSC) N/mm2

Yield strength of longitudinal steel, fy N/mm2

Yield strength of shear link steel, fyv N/mm2

Type of concrete and density, rc kN/m3

Uncracked elastic modulus (prestressed beam and slab), Euncracked,28

Cracked elastic modulus (prestressed beam and slab), Eck = Euncracked,28 / 2

Cracked long term (creep) elastic modulus (prestressed beam and slab), Eck,cp = Eck / 2

Uncracked elastic modulus (column), Euncracked,28

Cracked elastic modulus (column), Eck = Euncracked,28 / 2

Cracked long term (creep) elastic modulus (column), Eck,cp = Eck / 2

Note Ec,28 = K0 + 0.2fcu,28 (cl.7.2 BS8110-2);

Note Euncracked,28,cp = Eck; Note Eck,cp has been calculated for normal loads, for storage loads use Eck / 3;

Characteristic strength of concrete at transfer, fci (≥ 25N/mm2 cl.4.1.8.1, usually 40N/mm2)N/mm2

TLS permissible compressive stress, f'max = 0.40fci N/mm2

TLS permissible tensile stress, f'min N/mm2

f'min = -1.0 N/mm2

f'min = -0.45Ö fci (pre-tension), -0.36Ö fci (post-tension) N/mm2

f'min = user defined N/mm2

SLS permissible compressive stress, fmax = 0.33fcu N/mm2

SLS permissible tensile stress, fmin N/mm2

fmin = -0.0 N/mm2

fmin = -0.45Ö fcu (pre-tension), -0.36Ö fcu (post-tension) N/mm2

fmin = -f (T.4.2, T.4.3) N/mm2

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BS8110

Section Dimensions

Span, L (usually ≥ 7m) 9.000 m OK

Available beam spacing 5.000 m

(for effective width calcs; usual spacing for interior beams; half for edge beams)

Section type and support condition

(support conditions are for effective width, action effects and kinematic effects calcs)

Design section hogging or sagging moment ?

(for incorporation of the relevant action effects into the Magnel Diagram)

Overall depth, h (includes insitu slab thickness) 650 mm

non-prestressed member;

0 mm OK

250 mm

Cover to all reinforcement, cover (usually 35 (C35) or 30 (C40) internal; 40 ext 40 mm T.4.8

Increased fire and corrosion protection, greater ultimate flexural strength, safer demolition;

N/A mm

Beam area, A 1625

1625

T-section YET

L-section YET

Beam second moment of area, I 572135

572135

T-section YET

L-section YET

17604

17604

T-section YET

L-section YET

14444 OK

-18081 OK

17604

17604

T-section YET

L-section YET

18081 NOT OK

-14444 OK

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Note usually h » L/25+100mm (L £ 36m), h » L/20 (L > 36m) or h » 70% of equivalent

Depth of flange, hf (0mm if not applicable)

Width (rectangular) or web width (flanged), bw

Effective width, b = MIN(bw + function (span, section, structure), beam spacing)

cm2

Rectangular section, I = bw.h cm2

cm2

cm2

cm4

Rectangular section, I = bw.h3/12 cm4

cm4

cm4

Beam top elastic section modulus, Zt cm3

Rectangular section, Zt = I / (h/2) cm3

cm3

cm3

Min beam top elastic section modulus, Zt ≥ (Mmax-K.Mmin)/(fmax-K.f'min) cm3

Min beam top elastic section modulus, Zt ≥ (K.Mmin-Mmax)/(K.f'max-fmin) cm3

Beam bottom elastic section modulus, Zb cm3

Rectangular section, Zb = I / (h/2) cm3

cm3

cm3

Min beam bottom elastic section modulus, Zb ≥ (Mmax-K.Mmin)/(K.f'max-fmin) cm3

Min beam bottom elastic section modulus, Zb ≥ (K.Mmin-Mmax)/(fmax-K.f'min) cm3

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BS8110

Material Stress-Strain Curves

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BS8110

Prestressing Reinforcement

10

Note prestressing strands usually [ASTM A416] Grade 270 d = 12.7mm or [BS5896] 7-wire super d = 12.9mm;

12.70 mm

98.71

YET GPa

1860

1670

183.7 kN

165.3 kN

Longitudinal Reinforcement Details

10 mm

3

236

Shear Reinforcement Details

8 mm

2

101

Pitch of links, S 200 mm

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Total number of prestressing strands, Ns

Prestressing strands code, grade and fs

Prestressing strands nominal diameter, fs

Prestressing strands nominal area, As mm2

Elastic modulus of prestressing strand, Ep

Ultimate (characteristic) tensile strength of prestressing strand, fpk N/mm2

Proof (0.1%) strength of prestressing strand, fp,0.1 N/mm2

Ultimate (characteristic) tensile load of prestressing strand, Fpk

Proof (0.1%) load of prestressing strand, Fp,0.1

Tension steel reinforcement diameter, ft

Tension steel reinforcement number, nt

Tension steel area provided, As,prov = nt.p.ft2/4 mm2

Shear link diameter, flink

Number of links in a cross section, i.e. number of legs, nleg

Area provided by all links in a cross-section, Asv,prov = p.flink2/4.nleg mm2

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Tendon = Duct + Strands

Wires ® Strands ® Tendons


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BS8110

External Loading

2.000 m

0.00 kPa OK

0.00 kPa

0.00 kPa

In service live load, LL 10.00 kPa

2.50 kPa

0.0 kN/m

3.9 kN/m

0.0 kN/m

20.0 kN/m

3.9 kN/m

28.9 kN/m

44.5 kN/m

Note for udl loads (DL, SDL and LL) uniform loading considered, no patch loading considered;

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Tributary width, tw

Dead load of beam flange, DLf = hf.rc

At transfer live load, LLT

At transfer superimposed dead load, SDLplan,T

In service superimposed dead load, SDLplan

Superimposed dead load on beam, SDLelev,beam

Dead load of beam web, DLw = (h-hf).bw.rc

At transfer LL beam loading, wLL,T = [LLT].tw

In service LL beam loading, wLL = [LL].tw

TLS beam loading, wTLS = [DLf+SDLplan,T+LLT].tw+DLw

SLS beam loading, wSLS = [DLf+SDLplan+LL].tw+DLw+SDLelev,beam

ULS beam loading, wULS = [1.4(DLf+SDLplan)+1.6LL].tw+1.4(DLw+SDLelev,beam)

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BS8110

Prestress Loading (Including Restraint to Member Shortening)

1286kN = 917 kN

369 kN

650

100

250 TR.43

300 TR.43

Colu

mn R

est

rain

t i

1 10.000 0.0072 14.0 4.000 123

2 5.000 0.0072 14.0 4.000 61

3 5.000 0.0072 14.0 4.000 61

4 10.000 0.0072 14.0 4.000 123

5 0.000 0.0000 14.0 0.000 0

6 0.000 0.0000 14.0 0.000 0

Prestress force loss factor, K (usually 0.70 i.e. 30% to 0.80 i.e. 20%) 0.75

Note short term prestress losses are due to friction losses in the tendon, wedge set or draw-in TR.43

and elastic shortening of concrete, whilst long term prestress losses are due to concrete shrinkage,

concrete creep under sustained compression and relaxation of prestressing tendons under sustained tension;

The bulk of the losses occur in the first two years, initially 10% at transfer and 20% thereafter;

-310 mm OK

310 mm OK

917 <= 1378 kN cl.4.7.1

Prestress force at transfer utilisation 67% OK

150 mm OK

Note by convention e is positive downwards;

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Prestress force at transfer, P0 - SHi

Total restraint force, SHi

Total long term strain, eLT = eE + eC + eS x10-6

Elastic strain, eE x10-6

Creep strain, eC = 2.5eE x10-6

Shrinkage strain, eS (usually 100 - 300 x 10-6) x10-6

li (m) Ii (m4) Ec (GPa) hcol (m) Hi (kN)

Top limit of (negative) eccentricity of prestress tendon, emin,t

Bottom limit of (positive) eccentricity of prestress tendon, emax,b

Prestress force at transfer, P0 £ 75%.(Ns.Fpk)

Eccentricity of prestress tendon, e (emin,t £ e £ emax,b)

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BD27

Note Ec taken as Euncracked,28,cp;


7



BS8110

Utilisation Summary

Checks UT Status Overall

N/A OK

999%

N/A NOT OK

67% OK

N/A OK

N/A OK

N/A OK

N/A OK

N/A NOT OK

1512 kN

110 mm

1279 917 1243 kN

15.00 m cl.3.4.1.6

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Min beam top elastic section modulus, Zt

Min beam bottom elastic section modulus, Zb

Prestress force at transfer, P0

Eccentricity of prestress tendon, e

TLS stress at bottom, f'b

TLS stress at top, f't

SLS stress at top, ft

SLS stress at bottom, fb

Max economic prestress force at transfer, P0,ecomax

Eccentricity of prestress tendon at P0,ecomax, eecomax

Allowable P0 range

Max LTB stability (compression flange) restraints spacing, LLTB

Note simply supported / continuous LLTB = MIN (60(bw or b), 250(bw or b)2/h)

and cantilever LLTB = MIN (25bw, 100bw2/h);

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≤≤


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BS8110

Action Effects From Structural Analysis

Note that moment redistribution to cl.4.2.3 BS8110 is not performed herein;

Cantilever

TLS-158 kNm

35 kN

SLS-1170 kNm

260 kN

ULS-1801 kNm

400 kN

Simply Supported

TLS39 kNm

18 kN

SLS293 kNm

130 kN

ULS450 kNm

200 kN

Encastre / Continuous Infinitely

TLS

100% -26 kNm

100% 13 kNm

100% 18 kN

SLS

100% -195 kNm

100% 98 kNm

100% 130 kN

ULS

100% -300 kNm

100% 150 kNm

100% 200 kN

Design section hogging or sagging moment ? Sagging moment

39 kNm

293 kNm

450 kNm

Dist, x 0.000 0.692 1.385 2.077 2.769 3.462 4.154 m

0 11 21 28 34 37 39 kNm

0 83 152 208 249 277 291 kNm

0 128 234 320 384 426 447 kNm

Dist, x 4.846 5.538 6.231 6.923 7.615 8.308 9.000 m

39 37 34 28 21 11 0 kNm

291 277 249 208 152 83 0 kNm

447 426 384 320 234 128 0 kNm

Note by convention, a negative moment indicates hogging moment;

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MHOG=-[0.500(wTLS)]L2

V=[(wTLS)]L

MHOG=-[0.500(wSLS)]L2

V=[(wSLS)]L

MHOG=-[0.500(wULS)]L2

V=[(wULS)]L

MSAG=[0.125(wTLS)]L2

V=[0.500(wTLS)]L

MSAG=[0.125(wSLS)]L2

V=[0.500(wSLS)]L

MSAG=[0.125(wULS)]L2

V=[0.500(wULS)]L

MHOG=-[0.083(wTLS)]L2

MSAG=[0.042(wTLS)]L2

V=[0.500(wTLS)]L

MHOG=-[0.083(wSLS)]L2

MSAG=[0.042(wSLS)]L2

V=[0.500(wSLS)]L

MHOG=-[0.083(wULS)]L2

MSAG=[0.042(wULS)]L2

V=[0.500(wULS)]L

TLS minimum bending moment, Mmin

SLS maximum bending moment, Mmax

ULS maximum bending moment, Mmax,uls

Mmin

Mmax

Mmax,uls

Mmin

Mmax

Mmax,uls

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0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.000

050

100150200250300350400450500


Mmin Mmax Mmax,ulsDistance, x (m)

Ben

din

g M

om

en

t (k

Nm

)

BY28

Note percentage (%) to allow for user defined action effects.

BY29


BY30


BY31


BY32


BY33


BY34


BY35


BY36



9



BS8110

Kinematic Effects From Structural Analysis

Note that the following deflection calculations assume an uncracked section for serviceability

classes 1 and 2 and cracked section for serviceability class 3 (cl.4.3.6.2 BS8110);

Cantilever

191.1 mm

276.2 mm

Simply Supported

19.9 mm

28.8 mm

Encastre / Continuous Infinitely

100% 4.0 mm

100% 5.8 mm

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dLL=wLLL4/(8EI)

dSLS=wSLSL4/(8EI)

dLL=5wLLL4/(384EI)

dSLS=5wSLSL4/(384EI)

dLL=wLLL4/(384EI)

dSLS=wSLSL4/(384EI)

Note that E in the above equations is Euncracked,28,cp (classes 1 and 2) and Eck,cp (class 3);

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CI21


CI22



10



BS8110

Magnel Diagram at Design Section

Drawing limits

Equation

Equation 1, EQ1 108 200 mm

Equation 2, EQ2 108 200 mm

Equation 3, EQ3 -108 200 mm

Equation 4, EQ4 -108 200 mm


1512 kN

110 mm

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emin,t,magnel emax,b,magnel

Max economic prestress force at transfer, P0,ecomax

Eccentricity of prestress tendon at P0,ecomax, eecomax

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-150 -100 -50 0 50 100 150 200 2500

5000

10000

15000

20000

25000

30000

35000

Magnel Diagram

EQ1 EQ2 EQ3 EQ4 e P0

Eccentricity, e (mm)

106/

P0(

kN)

- - -

t l0 max max t max min t

1 11/ A e/ Z .

P MIN f M / Z /K, f M / Z

£ - - -

t l0 min min t min max t

1 11/ A e/ Z .

P MAX f M / Z , f M / Z /K

£

b l0 min max b min min b

1 11/ A e/ Z .

P MAX f M / Z /K, f M / Z

b l0 max min b max max b

1 11/ A e/ Z .

P MIN f M / Z , f M / Z /K


11



BS8110

TLS and SLS Top and Bottom Stresses at Design Section

917 kN

150 mm

-2.3 11.2 16.0 OK

5.6 7.8 2.2

-2.3 0.1 16.0 OK

5.6 7.8 2.2

-2.5 15.0 16.5 OK

4.2 5.9 16.6

-2.5 -6.5 16.5 NOT OK

4.2 5.9 16.6

Secondary Effects 5.6

Secondary Effects 4.2

Note by convention, positive stress is compressive and negative stress is tensile;

TR.43

TR.43

TR.43

restraint to slab shortening by supports become important, otherwise they may be ignored; TR.43

Secondary effects may also be ignored in the case of statically determinate structures; TR.43

TR.43

Prestress Forces at Design Section

917 kN

150 mm

MIN 69 kN OK

MAX 1910 kN OK

MIN 1279 kN NOT OK

MAX 1243 kN OK

Note in the first two inequalities, should the denominator be negative, the inequality is flipped;

1279 917 1243 kN

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Chosen prestress force at transfer, P0

Chosen eccentricity of prestress tendon, e

TLS stress at bottom, f'b N/mm2

N/mm2

TLS stress at top, f't N/mm2

N/mm2

SLS stress at top, ft N/mm2

N/mm2

SLS stress at bottom, fb N/mm2

N/mm2

TLS average stress, (f'b+f't)/2 N/mm2

SLS average stress, (ft+fb)/2 N/mm2

Average prestress levels usually vary from 0.7N/mm2 to 2.5N/mm2 for solid slabs;

Average prestress levels occasionally vary up to 6.0N/mm2 for ribbed or waffle slabs;

When the average prestress exceeds 2.0N/mm2 or the floor is long, the secondary effects of

Past experience shows that for precompression to be effective it should be at least 0.7N/mm2;

Chosen prestress force at transfer, P0

Chosen eccentricity of prestress tendon, e

Allowable P0 range

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+ -

- +

+

+

-

-

≤

≤

≤≤

≤≤

≤

≤

≤

≤

£ - £

l l l0 0 minmin b max

b b

P Pe Mf f f

A Z Z

£ - £

l l l0 0 minmin t max

t t

P Pe Mf f f

A Z Z

£ - £

0 0 maxmin t max

t t

KP KPe Mf f f

A Z Z

£ - £

0 0 maxmin b max

b b

KP KPe Mf f f

A Z Z


12



BS8110

Tendon Profile at All Sections

Dist, x 0.000 0.692 1.385 2.077 2.769 3.462 4.154 m

152 164 174 183 189 193 195 mm

-173 -53 48 129 189 229 249 mm

Dist, x 4.846 5.538 6.231 6.923 7.615 8.308 9.000 m

195 193 189 183 174 164 152 mm

249 229 189 129 48 -53 -173 mm


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emax

emin

emax

emin

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0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.000

-200

-150

-100

-50

0

50

100

150

200

250

300

Tendon Profile

emax eminDistance, x (m)

Ec

ce

ntr

icit

y,

e (

mm

)


13



BS8110

Design Flow Chart

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BS8110

Flat Slab Tendon Arrangement Options

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Two way spanning flat slab: tendons banded in both orthogonal directions employed for regular column grids in both perpendicular directions.

One way spanning flat slab: tendons banded in one direction employed for regular column grids in one direction.

Figure :

Figure :


15



BS8110

Equivalent Frame Analysis

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BS8110

Scheme Design: PT One Way Spanning Solid Slab

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BS8110

Scheme Design: PT One Way Spanning Ribbed Slab

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BS8110

Scheme Design: PT Flat Slab With Edge Beams

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BS8110

Scheme Design: PT Beam and PT Slab

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Table X

7

73 4

5

6

Table X


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BS8110

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Table X


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BS8110

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BS8110

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BS8110

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BS8110

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BS8110

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26



BS8110

Typical Initial Span / Effective Depth Ratios

G & P E N G I N E E

R S


j102

Made by Date Chd.

Drg. Ref.

Member/Location

0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.000

050

100150200250300350400450500


Mmin Mmax Mmax,ulsDistance, x (m)

Ben

din

g M

om

en

t (k

Nm

)


1



Standard Design Concepts (Basic Prestressing Principle)

G & P E N G I N E E

R S


j102

Made by Date Chd.

Drg. Ref.

Member/Location


2



G & P E N G I N E E

R S


j102

Made by Date Chd.

Drg. Ref.

Member/Location


3



Standard Design Concepts (Pre- and Post-Tensioning)

G & P E N G I N E E

R S


j102

Made by Date Chd.

Drg. Ref.

Member/Location


4



Standard Design Concepts (Bonded or Unbonded)

G & P E N G I N E E

R S


j102

Made by Date Chd.

Drg. Ref.

Member/Location


5



G & P E N G I N E E

R S


j102

Made by Date Chd.

Drg. Ref.

Member/Location


6



Standard Design Concepts (Restraint to Elastic and Creep Shortening due to Prestressing)

G & P E N G I N E E

R S


j102

Made by Date Chd.

Drg. Ref.

Member/Location


7



Standard Design Concepts (Disproportionate Collapse Requirements)

G & P E N G I N E E

R S


j102

Made by Date Chd.

Drg. Ref.

Member/Location


8



Standard Design Concepts (Accommodation of Service Openings)

G & P E N G I N E E

R S


j102

Made by Date Chd.

Drg. Ref.

Member/Location


9



Standard Design Concepts (Construction Joints and Pour Size)

G & P E N G I N E E

R S


j102

Made by Date Chd.

Drg. Ref.

Member/Location


10



Standard Design Concepts (Stressing)

G & P E N G I N E E

R S


j102

Made by Date Chd.

Drg. Ref.

Member/Location


11



Standard Design Concepts (Slab Soffit Marking)

G & P E N G I N E E

R S


j102

Made by Date Chd.

Drg. Ref.

Member/Location


12



Standard Design Concepts (Demolition and Alterations)

G & P E N G I N E E

R S


j102

Made by Date Chd.

Drg. Ref.

Member/Location


13



G & P E N G I N E E

R S


j102

Made by Date Chd.

Drg. Ref.

Member/Location


14



G & P E N G I N E E

R S


j102

Made by Date Chd.

Drg. Ref.

Member/Location


15



G & P E N G I N E E

R S


j102

Made by Date Chd.

Drg. Ref.

Member/Location


16



G & P E N G I N E E

R S


j102

Made by Date Chd.

Drg. Ref.

Member/Location


17



G & P E N G I N E E

R S


j102

Made by Date Chd.

Drg. Ref.

Member/Location


18



G & P E N G I N E E

R S


j102

Made by Date Chd.

Drg. Ref.

Member/Location


19



G & P E N G I N E E

R S


j102

Made by Date Chd.

Drg. Ref.

Member/Location


20



G & P E N G I N E E

R S


j102

Made by Date Chd.

Drg. Ref.

Member/Location


21



G & P E N G I N E E

R S


j102

Made by Date Chd.

Drg. Ref.

Member/Location


22



G & P E N G I N E E

R S


j102

Made by Date Chd.

Drg. Ref.

Member/Location


23



G & P E N G I N E E

R S


j102

Made by Date Chd.

Drg. Ref.

Member/Location


24



G & P E N G I N E E

R S


j102

Made by Date Chd.

Drg. Ref.

Member/Location


25



G & P E N G I N E E

R S


j102

Made by Date Chd.

Drg. Ref.

Member/Location

member design - prestressed concrete beam and slab bs8110

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