A030 BCA detailed design of composite concrete bridge superstructures

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DETAILED DESIGN OF COMPOSITE CONCRETE BRIDGE SqdPERSTRQCTdRES A Kumar BE, PhD, CEng, MICE, MIStructE -_-Ê abe Tứ +} f= E x1) | 3% * 28 (Tại * Teo where

[= bending inertia of the top slab; I = bending inertia of the bottom slab; I, = bending inertia of the equivalent |

length of longitudinal beam about

the Z axis;

a = spacing of the longitudinal beams b = distance between the neutral

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Acknowledgements

lam most grateful to Mr E M Jones of Cleveland County Council (formerly of Staffordshire County Council) and Mr J F White of Staffordshire County Council for checking the design calculations and making many constructive criticisms

I would like to thank many former colleagues at the Cement and Concrete Association* who have contributed indirectly through their discussions with me, notably Mr Tony Threlfall | am also grateful to Dr Tom Harrison and Dr Bill Cranston for their interest and provision of the necessary facilities at the Cement and Concrete Association to carry out this work Finally | would like to thank Mr A E Brooks for his editorial contribution to the text

Arvind Kumar * Now called the

Kumar Associates British Cement Association

Beaconsfield

46.506 Published by

First published 1988 British Cement Association

ISBN 0 7210 1362 7 Wexham Springs, Slough SL3 6PL

Price Group L Telephone Fulmer (028 16) 2727

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DETAILED DESIGN OF COMPOSITE

CONCRETE BRIDGE SũPERSTRäCTRES A Kumar BE, PhD, CEng, MICE, MiStructE

Contents

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Introduction

The purpose of this publication is to extend the broad design intentions and considerations discussed in

reference 1 in order to obtain the detailed design of various parts and components of composite concrete

bridge superstructures For obvious reasons, it is not possible to cover the detailed design of all types of

beam and their possible applications However, two

examples, representative of practical bridging situations and utilizing the most popular of the beam types, have been chosen for detailed design here and are discussed on this page

Since the various types of precast beam and various

requirements of the Code'**) have many structural

similarities, only the essential ways in which other

types of superstructure differ from M-beam superstructure design are outlined on pages 4 to 7 Full details

about the standardized sections, manufacture of

beams and preliminary superstructure design are con- tained in reference 1

Extent of design effort

Since the initial publication of the limit state Code in 1978‘, many engineers have expressed the view that the five new load combinations and the two basic limit states would considerably increase the analysis and design work required for bridge design Experience has not, however, supported this view Combination 1 remains essentially the same as in the previous approach, i.e only permanent forces and live loads need be considered in the design Combinations 2 to 5 in the new Code”? clearly define how the various transient forces are to be combined This contrasts with the previous Combination 2, in which all compatible forces had to be considered, and yet no guidance was given on how this was to be done, thus engendering inconsisten- cies in bridge design practice

Additionally, separate calculations were previously required for reinforced concrete and prestressed concrete, to check against the permissible overstresses®°) in the materials of up to 30% of the basic values when HB load was present on the bridge deck In the new Code! this is no longer the case, although some com- plication is caused by the requirement to check crack- ing in reinforced concrete and tensile stresses in prestressed concrete under serviceability Combination 1 for 25 units of HB, compared with 45 or 37.5 units of HB (depending upon the class of the road) forthe rest of the design

The two detailed design examples included in this publication are intended to illustrate that an adequate design complying with the Code can be obtained with-

out either an excessive amount of computer analysis of

the superstructure or lengthy hand design calculations If more precision is desired or the behaviour of the

superstructure is not well known, additional loading

cases for the computer analysis are recommended In time, with the accumulation of experience with the new 2

Code, engineers will be able to discern the critical

loading conditions more readily and take short cuts, as they have done in the past, to arrive at satisfactory designs Simply supported and continuous T-beam superstructures using M beams

To illustrate the design procedure and compliance with

the Code, two representative examples of the cesign of a composite concrete superstructure have been in-

cluded at the end of this publication Both examples utilize M beams in the form of a T-beam superstructure construction (there is no bottom-flange in situ concrete) Example A deals with the design of a single- span simply supported superstructure using (a) fully bonded, (b) part debonded or (c) part deflected tendon configurations in the precast beams Example B deals with the design of a two-span live load continuity-type superstructure (as described in reference 1) using part deflected tendons in the precast beams

Example B has been extended to deal with the design of the continuity moments over the middle support in the design of the middle diaphragm The end diaphragms, the links in the precast beams and the top slab are also designed for this second case (design for the simply supported case will be broadly similar) References to various parts of BS 5400 and clause numbers are indicated in the left-hand margin of the examples for the benefit of the reader

For both these examples, substantial diaphragm members exist at the support positions which are shown to possess sufficient strength for separate bear- ings to be provided under alternate beams only During the construction period, each beam will obviously be provided with a separate temporary bearing until the diaphragms are cast

The Department of Transport have issued imple- mentation documents for the Code"®) and these have also been taken into account in the detailed design cal-

culations of Examples A and B Table 1 indicates the

values of Y, to be used in the calculations for these examples The section properties for the precast M beams are given in references 1 and 9 The section properties for the composite section using M beams

with 160 mm top slab are given in Table 2

In the context of live load continuity in composite

construction, the Code gives some guidance (Part 4,

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Table 1 Loads to be taken in each combination with appropriate Y,,

QLS: ultimate limit state Reproduced with slight amendments from BS 5400 with permission from B S| SLS: serviceability limit state

Clause No Load Limit Y,, to be considered in in BS 5400 state combination 1 2 3 4 5 5.1 Dead: steel : tLS* 1.05 105 1.05 105 1.05 SLS 1.00 1.00 1.00 1.00 1,00 concrete ULS* 115 1.15 115 1.15 1.15 SLS 1.00 1.00 1.00 1.00 1.00 3.2 Superimposed dead: deck surfacing (LS† 17500 061.75 1/75 -175 1.75 SI.ST 1.20 1.20 1.20 120 1.20 other loads aLs 1.20 1.20 1.20 1.20 1.20 SLS 1.00 1.00 1.00 1.00 1.00 5.1.2.2 & Reduced load factor for dead and superimposed qLS 1.00 1.000 1.00 1.00 1.00 5.2.2.2 dead load where this has a more severe total effect

5.3 Wind: during erection acs 1.10

SLS 1.00

with dead plus superimposed dead load only qLS 1.40

SLS 1.00

with dead plus superimposed dead plus other qLS 1.10 appropriate Combination 2 test loads SLS 1,00

relieving effect of wind qLS 1.00 SLS 1.00 5.4 Temperature: restraint due to range ais 1.30 SLS 1.00 frictional bearing restraint äLS 1.30 SLS 1.00 effect of temperature difference dLs 1.00 SLS 0.80 5.6 Differential settlement qLS 1.20 1.20 1.20 1.20 1.20

(Part IV) Shrinkage and creep SLS 100 1.00 1.00 100 1.00

5.8 Earth pressure: retained fill and/or live load surcharge aLs 1.50 1.50 1.50 1.50 1.50 SLS 1.00 1.00 1.00 1.00 1.00

relieving effect aLs 1.00 1.00 1.00 1.00 1.00

2.9 Erection: temporary loads Ls 1.15 4.15 SLS 1.00 1.00 6.2 Highway bridges live loading: HA alone äLS 1.50 1.25 1.25 SLS 1.20 1.00 1.00 6.3 HA with HB or HB alone qLS 1.30 1.10 1.10 : SLS 1.10 1.00 1.00 6.5 Centrifugal load and associated primary live load aLS 1.50 SLS š 1.00 6.6 Longitudinal load: HÀ and associated primary live load GLS # 5 1.25 SLS Bê 1.00 HB and associated primary live load qLS 1$ 1.10 SLS 3$ 1.00 6.7 Accidental skidding load and associated primary live load qLS ce 1.25 SLS 8 ễ 1.00

6.8.1 Vehicle collision load with bridge parapets and associated Sẽ

primary live load: for local effects (LS oe 1.50

SLS | 36 1.20

6.8.2 for global effects with containment parapets: se

HA only aLS >o 1.25 | SLS | B= 1.00 HA with HB or HB alone ULS os 1.10 SLS as 1.00 6.9 Vehicle collision load with highway and foot/cycle track §Š bridge supports { Mi 5 1.50 SLS 7 Foot/cycle track bridges: live load and effects due to parapet load ULS ~ 1.50 1.25 1.25 SLS- 1.00 1.00 1.00 8 Railway bridges:type RU and RL primary and secondary live : - L5 1.40 1.20 1.20 loading SLS 110 1.00 1.00 (Part [V) Prestress: shear & torsion ULS S——————]1.15/0.B7——————® secondary effects dqLŠS « 1.00 >

all purposes Sis ~ 1.00 >

* 1, shall be increased to at least 1.10 and 1.20 for steel and concrete respectively to compensate for inaccuracies when dead loads are not accurately assessed

+ T, may be reduced to 1.2 and 1.0 for the ULS and SLS respectively subject to approval of the appropriate authority (see Clause 5.2.2.1 of BS 5400 : Part 2) t This is the only secondary live load to be considered for foot/cycle track bridges

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Table 2 Section properties of composite M beams, beam spacing 1 m, modular ratio = 1.0

Height of Section moduli (mm3x10%)

centroid Second Top fibre of — Top fibre Bottom Bottom fibre Total above moment composite of precast fibre of of precast Precast depth Area bottom of area section section top slab section section (mm) (mm?) (mm) (mm^x10°) 2 2 4 Z, M2 850 467 650 429.3 42.98 102.16 147.84 164.86 100.11 M3 930 499 650 474.37 54.49 119.59 167.33 184.31 114.86 M4 1010 531 650 517.98 67.69 137.57 186.98 203.87 120.68 M5 1090 506 050 553.00 81.82 152.37 201.04 217.04 147.96 M6 1170 538 050 601.21 98.80 173.70 225.16 241.69 164.34 M7 1250 570 050 649.10 135.79 225.97 288.36 307.98 209.20 M8 1330 544 450 675.84 135.31 206.84 258.14 273.81 260.20 M9 1410 576 450 727.29 158.56 232.25 286.87 303.34 218.01 M10 1490 608 450 777.92 183.41 257.57 315.09 332.22 235.77 1000 S m 1 _‡Ê © -

Restraint moments due to prestress and its profile,

and dead load, both modified by creep, should also be

calculated (no expressions are given in the Code) The

creep modification factor for these latter effects sug-

gested in the Code is given by equation 35 but assumes

that continuity is established at the time of prestressing the beams This could result in seriously overestimat- ing the support sagging moments, since much of the prestress and dead-load creep would have taken place prior to the establishment of continuity For this reason,

the approach used in Example B is based on ‘first

principles’ and only involves the residual creep due to prestress and dead load at the time of establishing continuity Some information on the background of the Code equations can be found in reference 10

Inverted T-beam, solid

infill superstructures

The live loading on an inverted T-beam superstructure with solid infill concrete will be resisted by the rectangu- lar composite section and this should be reflected both in the analysis and in the design of the superstructure The design of diaphragms and top slab will be replaced by the design of transverse reinforcement through the web holes for the whole length of the span If no longitudinal bars (parallel to the beams) are placed at

the bottom of the in situ concrete between the beams,

the crack width for the transverse bars only needs to be 4

checked at a nominal cover away from the surface of these bars Longitudinal steel, if required at this posi-

tion, should be placed on either side of, not directly

above, the gap between the bottom flanges This will avoid contravening the crack-width limitations of the Code for these bars (see Figure 1)

As indicated elsewhere"), lightweight-aggregate concrete is sometimes used as an in situ infill medium with this form of construction in order to reduce the dead load of the structure The Code does not ceal with

the use of such concrete as prestressed members in

highway structures However, as an in situ infill me-

dium, this concrete is only reinforced in the transverse

direction and can be dealt with under the provisions of the Code In the longitudinal direction, the lightweight-

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For stress analysis of the composite section for the serviceability limit state, the lightweight part of the section can be transformed on the basis of the modular ratio of the two concretes According to the Code, the modulus of elasticity of lightweight-aggregate concrete is related to that of normal-weight concrete of the same grade by the square of the ratio of their dry densities For the flexural strength of the composite section at the ultimate limit state, the modular ratio will not be appli- cable, and the grades of two concretes will determine their contribution to the compressive force in the section Shear strength of composite sections can be determined as for normal concrete superstructures, albeit that the reduced Code values apply for the lightweight component Alternatively, as for all forms of composite construction, the precast units them-

selves can be designed to resist the entire shear force

on the composite sections, as indicated in the Code

For the analysis of the superstructure, the stiffness values calculated for the individual members should be based on the transformed concrete section in both directions, to reflect the lower modulus of elasticity of the lightweight-aggregate concrete

Pseudo-box

superstructures with M beams

For pseudo-box superstructures with M beams, the live load on the deck will be resisted by the pseudo-box section, the properties of which should be considered in the grillage analysis and may be calculated as follows

The longitudinal flexural inertia of the composite section may include full contribution from the in situ concrete on the bottom flanges, as shownin Figure 2"), The transverse flexural inertia of each strip equal to the spacing of the web holes may be calculated by replac- ing the whole of the bottom in situ concrete and the reinforcement by an area of concrete which is 4D horizon- tally and 2.5D vertically, where D is the diameter of a single equivalent bar equal in area to that of the transverse reinforcing bars through the hole This is indicated in Figure 3"),

The longitudinal torsional inertia for a single cell should be calculated using the thin-wall formula by Transverse section of top slab Transverse section of equivalent bottom slab in situ top slab In situ bottom slab

Figure 3 Section for transverse stiffness evaluation

considering half the thickness of the beam webs in con- junction with the top slab and the bottom in situ

concrete taken uniform of its maximum thickness,

which occurs mid-way between the bottom flanges as shown in Figure 42): 4A2 ý ds t area inside the median line of the concrete; and

sum of the lengths of the sides around the median line each divided by the appropriate wall thickness

Torsional inertia, C = where A

g§ ds/t

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equivalent closed box section and then applying the

thin wall formula

The thickness ¡ of the equivalent continuous side

wall for the idealization shown in Figure 5 is given by the formulat1?):

where I = bending inertia of the top slab; s ° bending inertia of the bottom slab; I,, = bending inertia of the equivalent

length of longitudinal beam about

the Z axis;

a = spacing of the longitudinal beams b = distance between the neutral

axes of the top and bottom slabs

The method of calculating torsional inertias in the two

directions for a pseudo-box, M -beam superstructure is

illustrated with the help of a numerical example in

Appendix 1 of reference 12

The superstructure is acting both ways simultane-

ously and the longitudinal torsional inertia calculation is more likely to be an accurate assessment of the total torsion stiffness of the superstructure The longitudinal value should therefore be split into longitudinal and transverse components in proportion to originally cal-

culated values in the two directions, for in-putting into a

grillage analysis program This procedure is discussed by West in reference 12 The contribution to transverse

stiffness from the diaphragms should be included in the

support edge members of the grillage

The presence of the bottom in situ concrete is usually ~ Spacing of transverse grillage members wah ety (a) actual (b) idealized Figure 5 Transverse torsion in a pseudo-box 6

ignored in any design calculations of longitudinal flexural stresses and strength provision Transverse rein-

forcement passing through the bottom web holes should be appropriately considered to be acting with the top slab in resisting the transverse bencling mo-

ments Crack control forthis bottom flange steel can be handled in the same way as for the inverted T-beam

superstructures, except that the simplified equation for

flange in over all tension, given in the Code, should be

utilized

d-beam

Superstructures

As discussed elsewhere (see page 39 of reference 1), each U beam should be represented by a longitudinal grillage member and the properties of the transverse grillage members should reflect the fact that the slab length between the beams is shorter than the centre-to- centre spacing of the beams The torsional stiffness of the G beams, when acting compositely with the top

slab, will be very substantial Also, unlike the T-beam

superstructure using M beams, the torsional liriks in the

webs can be spaced further apart because of “he good

proportions of the sides of these sections and the Code

requirements in this respect

The section properties forthe composite section with

CU beams and 160 mm top slab are givenin Table 3 The

unsupported webs of these beams are vulnerable to mishandling and shock loads; therefore, during the manufacture, lifting and transport of these beams, some temporary bracing of the webs is often necessary to avoid overstressing the junction of the webs with the bottom flange

Box-beam

superstructures

Box-beam superstructures are only provided with a

nominal thickness of levelling screed with mesh rein-

forcement; their transverse distribution properties emanate from post-tensioning through transverse dia-

phragms The precast box beams therefore carry the

entire longitudinal effects themselves, while in situ infill concrete (between the beams) combined with post- tensioning, handles the load distribution and the result- ing transverse effects Thus, any structural contribu-

tion from the screed or topping which may be provided

is ignored, both in the analysis and in the design of this

type of superstructure Vertical shear due to live loads

and longitudinal shear due to a component of transverse prestress in skew bridges (if prestress is applied parallel to the supported edges) should be checked at the vertical interface of the precast and the in situ

concretes

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Table 3 Section properties of composite C beams; beam spacing 2 m, modular ratio = 1.0

Height of Section moduli (mmx 10°)

centroid Second Top fibre of Top ñbre of Bottom Bottom Total above moment composite precast fibre of fibre of Precast depth Area bottom of area section section top slab precast section section (mm) (mm?) (mm) (mm*x10°) Z 2.0 48 % dl 960 786 450 568.62 82.87 211,75 358.17 145.75 q5 1060 819450 627.71 107.40 248.45 394.44 171.10 q5 1160 852 450 685.87 136.31 287.49 433.01 198.73 ũ7 1260 885 450 743.83 169.29 327.98 475.32 227.59 dé 1360 918 450 800.43 206.42 368.89 516.61 Tp, 257.89 a9 1460 951 450 857.03 248.12 411.49 560.11 289.51 (10 1560 984 450 913.72 294.22 455.25 605.04 322.00 q11 1660 1017 450 969.23 345.59 500.29 651.10 356.56 q12 1760 1050450 1024.62 401.49 545.95 697.77 391.84 x 2000 1 | J 8 |

| - be a m 5 DEPARTMENT OF TRANSPORT Reinforced concrete

2 for highuuau structures London, 1973 BS 1/73

su p erstructures 6 DEPARTMENT OF TRANSPORT Prestressed concrete

for highway structures London, 1973 BS 2/73 This type of superstructure is essentially similar to the ;

T-beam construction using M beams, except that there @, DEPARTMENT OF TRANSPORT Loads for highway are in situ transverse diaphragms acting compositely bridges: use of BS 5400: Part 2: 1978 London with the top slab, which must be considered both in the BD 14/82: 1982 and its Amendment No 1 :

analysis and in the design of this type of superstructure 1983

8 DEPARTMENT OF TRANSPORT Design of concrete bridges: use of BS 5400: Part4: 1984 London

9 PRESTRESSED CONCRETE ASSOCIATION,

1 KUMAR, A Composite concrete bridge _ Prestressed concrete bridge beams Second

superstructures Wexham Springs, British edition Leicester, 1984 7 pp + folder Cement Association, 1988 46 pp Publication

46.505 10 CLARK,L.A Concrete bridge design to BS 5400 London, Construction Press, 1983 186 pp

2, BRITISHSTANDARDS INSTITUTION Steel, concrete

and composite bridges Part 2: Specification for 11 MANTON, B.H and WILSON, C.B MoT/C&ECA

loads London 46 pp BS 5400 : Part 2:1978 standard bridge bears: prestressed inverted T beams for spans from 15m to29m London, 3 BRITISH STANDARDS INSTITUTION Steel, concrete Cement and Concrete Association, 1975 20 pp

and composite bridges Part 4: Code of practice for Publication 46.012 design of concrete bridges London 68 pp

BS 5400: Part 4: 1984 12 WEST,R CGCA/CIRIA Recommendations on the 4 BRITISH STANDARDS INSTITUTION Steel, concrete

and composite bridges Part 4 : Code of practice for design of concrete bridges London 48 pp BS 5400: Part 4: 1978

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EXAMPLE A: Simply supported composite concrete superstructure

Basic data 2 ee ee eee ee es 1

End support and điaphragm section .- eee ee tte teen ene 2 Deck section and grillage idealization .- -.- ee eee ete 3 Stiffnesses for grillage analysis - Examples A andB 2 et eee 5 Live load patterns 2.00 ee ee nee ee eee eee eee 7 Basic load cases for grillage analysis 2.0.0 cc eee eee eee ete hà ki mi ng 10 Longitudinal moments in precast beams 2.0 ee eee ee eee 11 Section properties .0 0.0 ee eee ee ee eee eee eens 14

Allowable stresses in precast concrete 1.2 0 cee ce ee ee ee eee eee ene 15

Stresses due to dead load and live load 1 2 Lee ee nee teen eens 16 Temperature difference stresses (PTD and NTD) ee eee nee 17 Differential shrinkage stresses (DSH) Q HQ HQ HH hy hy hà 20 (A) Precast beams with straight fully bonded tendons Ặ ẶQ Q HS 21 Differential creep stresses (DC) Q Q Q LH Q HQ HQ Q H ng HH n HH gà H ĐH nà kà kh kh va 25 Final stress checks Q Q Q HQ HQ HQ HH HH HH Ho gu Hy ng kg Hy kg k KV Hy kg eens 28 (B) Precast beams with straight part debonded tendons 29 (C) Precast beams with straight part deflected tendons -.-ẶVẶẶ VỤ 38 ULS checkS 2 ee ee ee ee ee ee ee ee 40

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Project SIM F LY W PPORTED COM PosiTE Job ref E A CONCRETE S/PERSTRUCTVURE XAMPLE Part of structure ABASIC DATA, Calc sheet no rev 11 As Drawing ref Calc by Date Check by Date AK Ref Calculations Output

Spare 18:1 we Sify snppeortiol

Width, «1B mo cannapeniay befrren kinks Alert

Ấy» foofhattsonr both sides

Peek, M2 Seamé rv [bo mm Wp Hab ancl

SD wm nde chia plriatrns sahishying the web hole clearances, Cost whew the beand

were 3 do tt mentee old

C(AsfoVC k4 n/f Orn cas.Á (vxvÀ⁄«na(2

Ge of abrtmenti , sue Fi 1/A

dc 17 M3 beams af (wm conics wit

O-3m x 2:3 panopel bint cash write

the deck , see Fig 2/A

Gril Nine lonpitrGralty at cevbus of

alkramak M beams representinp (T/y x

single been shiffrts Nine transversely vepreserhing /8-‡/2= 2-4 alors the Yaar,

spacer ak- 781/8 = 2-2625 Diadehang més

and fasrafect plinths wers treludd with

the edlpe mermbers , See hy 3f/A -

Based or Weak recommentahions (

prbbeakon 46017) amd ab ivdircatiol on

fapes S and C/A

i

Soy dens oye od od FR we ete 5 ray, eR RTE PRK EE ey

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Project Job ref

Part of structure £A/ b> SUPPORT AND Calc sheet no rev

DIAPHRAGM SECT On! 2/ A!

Drawing ref Calc by Date Check by Da-e

Ref Calculations Output ne 850 — Ỉ | — _ẮÏ—ừ-p ae — — eee —— Ƒ— > — — — — pe——— 390 7-150 — Fig 1/4 End Su ke anol 26x ve» 905m —=~ £ a * x ety ag Baader sae et eet SR ww ee ee A

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Project Job ref Part of structure Calc sheet no rev 4 14A ¡ Drawing ref Calc by Date Check by Date Ref Calculations Output &5 5480 R 2:/9B Bo '4yfg2 IK Amend, ES 5896 4 é-7-h Abljene.£ es Letolir § v4 Car cree

The CAR Epler hey ca, J Ibm wrtl

be iwiced afro Lno 3'25munde mithiernel loo Sec ha 3/A

HA YP = 9123 kM/m`

HÀ kế = 120 EA /inre width

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+ US waits 1 8 + Ahm” on fot pats

xe cv CC S50] am

Inti, Coretta HOM nn

fy : H4EO Nome y = 5 = 200 kn] mon”

IS*2 mm Twine shandenel stone

Be = 195 kA/ÌmuÈ

Sp = 6†o N fm

Thao fot procticah kvubrav2 He

the poll tendon frre 10 mutable

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Project Job ref Part of structure ST/FFVESS ES Fe GRIULLAGE Calc sheet no rev AN Btysis — EXAMPLES A MB 5 | AY

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Ref 12

Ref (2

hLongitrGinehL JT Reeastond rss conerde

for infer emote Long: lnelinal C fet Tt me i OL grille bears “đẻ Longa br fined I (rg rg '&@ua£ ¿ (sự rte S4 oh fpr T onby

10 NG vase theredere Here i6 no

nacol or teen Êaee2

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leomm wp stleb,

T= 17% 0054S'/9=0:103 m4

See Fig yj for idecdisrdl acction Using Slam Verd St Vernal

cochicent and “ae, top stato corGrbrher , C= 2* (25 4033x016 + 0-206 2 3 x0'U + 02382016 x 0335 % O25 + 0'291x 0°185°% 0-95 )= 0:0076 mat

[ecco pet ““2 2> conaictti2ad fe

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Project Job ref Part of structure Calc sheet no rev

&¿ LẠ ¡

Drawing ref Calc by Date Check by Date Ref Calculations Output = ‘ 1 / _ - # # - 4 C(=0:2065+ 0 00+ 1% £)z 0-01 Cøẹe= 9-21 = “An+2ex.9)z fo Jin Cid Hh of top Sob Y= 000072 wt 3 C= OS 033% 0-16« Zhe 0 00148 mF Framsreaase I fot 19 term Siete Trey —xytxwC“ fo mere Gs pilose dro—t L La]

“Freaminae L Lf m OBS wm LOT] m ý

ceri eT 1 conaidosd to act with he Top tab (proving ob pth bute T= 0:0465 mt 3 7/N&¬-£vtx2c € C= OIG XO-8S * O77 4 OSX 0:33 erry x:2øx Ô-l@”= 0:0606 wm? Ty, = 0:00072m? Ch 0:00 1122 wt Ty ge 0-045 me ¥ te STIFFNESSES FOR £XAMPLE B ONLY - Framsvoce I Ø//0140 / lSmx O77 d riddle ds " s ⁄ cac achvg with the +p sab 7= OO6#S mĩ 3 /W#x~4ytveC Ê fel Ê=0-22Øz⁄ 5x07? + 0-:6v 0233 ma Alle haphreprr 3 i rs XOBKCIG = GIShS mw y= Ờ: 0645 wm! Che O1SES xà" tị OUT-PUT INTERPRETATION

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Project Job ref

Part of structure /,/V/£ LOAD PATTERNS Calc sheet no rev 7 IAL Drawing ref Cale by Date Check by Date Ref Calculations Output

UB spacins Em betiieen Ae egg et wi lf

frduer Tha wed” “fect:

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Fig, #4 Maxi minrn long hGined "9 reement

a mie - San proition

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Project Job ref

Part of structure Calc sheet no rev

Š LA ¡

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Ref Calculations Output

camse the worst offeet- IF

Vier urene no feotpatts ý ức

been 0m2, be meek”

An Leech UPL tena ty

v» nti ta kiol by te cliwaihy ⁄ hating, Moa? tremsercse At Node #1, fr loool pattern of Fs © 5 a GIA —— oe w eee 7 ——2°ø— D3 by), Meximmurn Gansverse +29 moment +

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PAH EOUY SOO CUPPA Mey y

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Project Job ref

Part of structure Cale sheet no rev

Q 1A I

Ref Calculations Qutput vw xí o Io ˆ Max teomamae At Alede #1, fo ad pattion op Mig T/p epg mgm tol ene + ƒ 2 odwe f 1 es PTTL LTT -— 6-05-+|

Fig 7) Maxi mano Am nsvevte Aepgi ng ae

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Project Job ref Part of structure BA S/c LOA CASES FOR Calc sheet no rev GRILLAGE ANALYSIS lo | A |

Drawing ref Calc by Date Check by Date Ref Calculations Output 1 2 SDL of 24 kN/m setieen herbs anol 364N},t /0, 4

The briotre otek t2 anny 502

fot he fe Lenstrng foc ad ca ws, PL vf prwat Aianis ef § 23 EN / ne an >

msit, conerele >⁄ 3 Sy kN fon Re sisted by

ANE precant btanes And caleLs biol by hen),

over The 44 A-rtas

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Ca rvza2-tvt sš#rt +22 fet a romwhrnahens (as xe of 72 ) “o be Len thar the atlersale ,

Tatle 1 mrdceates brild- op ef moments alm

Node 39, SH wao ebeenvtel from the tombal

art pot- tral” seme repetive momen erenrcol

mm te enck Hie of the sam These mamenti af

the fare of the daaphregr (Team 2) were abort to) of the mid shaw valnes (Tate 1) Mee the mum ots

at tre ymarter spam (TeAte 3) rere abenl- bof of tre

rid- shaw valves, fev SA 200052 the dedeorhs of

fll brihd-np of values at these brahions have

beer Omitted Unkss additonal Lad cess art denis, the mements ot thease (tan bald be

comseriahicly estimated The variahen of mam enti Aas been arsnmeel + be Anes atthe erds ard furebolic

nv the nnd shaw reg ones , ek “2 ?/A

Project Job ref

Part of structure LOWG/TUDINAL MOMENTS Calc sheet no rev

IN PRECAST BEAMS fof AT]

Botk fet ULE anol AS Nocte 39 Is the mat ential

fr tre hal fatteins of Fig Ff:

4] ure Ter vile strug foc Comms (25 wwsts 4 #6) +

de Lim tet dy Chie I ana fet Gowt.3 (4s

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Project Job ref Part of structure Calc sheet no rev 12 | | Drawing ref Calc by Date Check by Date Ref Calculations IS Yy, Max moment et Mole 249 k Ala [m Po SLE s 5 | —_- ULS

Nominel lambs Comp) |Gome.t(tens)| Comb, 3 | Comb.? | Come 3

Moment Foedorcd Fac+oxc3 Factovc Fectover | Feetored

po Ye Moment} ft Mom ent] "Pe planet T° Moment FFL Moment Case! : : DL (Recast) 1337-0 | 0 ' 337-0 [1-0 | 337-0] ko (3370| !2 0| L2 bom DL (Insita) 157-3 | FO) 1573 | bo | 157-3 | 1-0 | 1873 | 2 fee | 2 eRe Case 2 | : SDL* U26 |I2./35 |2 03521 | l2 | Sy [PIS 1471 | t7 1471 Case 3 FPL (1) (44 | ro lew | bo lạng fF bo led LS 2G | h25 lo lfase 9 | | HB (605,375) {6873 | Ii 756-0 Luật 420-0 | 10 1687-3 | là 892-2 | fei 7560 lose HA Ubt (2) 20-0 | be 1324) fy 03221 |0 1202) |3 1562 | bị 1321 Case, 5 (hamaded) HA UBL (3) 8:3 ht Bt by %7 bo | &3 L2 log | bl 44 Case 7 (handed) , , | | HA KE 9-05 (3) {2-7 /¡ 3-0 Ip | 3-0 0 2T 3 3.5 | lì 36 _— Total S44 1208 1462 1376 1709 lái #2 lô td fy sign moment (S44 1208 jf 462 20 63 , (880 Table 2), Fst mated moments at the fare of the ae aphrag mui het DL) -Ø‹1 x 7A4 1 Í-/Z2#|_ |2 4G -!P -/7 Ys 1Ð 1-0 ro hy hf

Design moment -iS5A —/2} ~lựé -201 - /#§

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Project Job ref Part of structure Calc sheet no rev 13) AY Drawing ref Calc by Date Check by Date Ref Calculations Output 500-3, 631 Soo Lị › 239%4 1: 9050 * 3394 {JJ ToT +146 fate of the mm ví \ parabolic /462

Hogeing moments due to LL only

Sagging moments ane to DL +LL,

Fig Y Bending moments envelope fer SLS L¢e3

Mihengt m thu “6 the Maxi mum

momerk values enerreel 2» Yhe Have

pillage Bean hina > gorrak re

VBLLONS maxima may Otows ir 2x

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Project Job ref

Part of structure SECT/ON PROPERTIES Calc sheet no rev

/ 1A |

Drawing ref Calc by Date Check by Date

Fibves fancl 2 refer bo the preeail bears soffit

avd tof and frres 3 ancl 4 vi» fo ne

Sept and tp af the ania wreck shed

Subroripts onde olenete fpreeacl and

cư kệ section wopectirey

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Project Job ref Partofstructure ALLOWABLE STRESSES IN PRECAST CONCRETE Calc sheet no rev 5 | Â | Đrawing ref Calc by Date Check by Date Ref Calculations Output 2z ay 32 blesery T24 2⁄43‹2-2 4+ 23 #⁄4-3:2:„ Feu = 50 Non vo fei = 4O MT SLE

lompreaarvre shun at fibre ! #02 tứ 20 09 rom Loproeve shia ot fae 2B 128x04F 00 ee 25 NT won|

Xe sec 0 te Charl fot Gwb.t (herr)

L-32Y inne bt Claas I for low-b 3

ru

(amjvvzưưv€ sheva 0-5fe, Ott ¿.e 20 | ron”

Tenwile stess fi! Nm for Comes f

+- 0-45 fon Ue =2-Ệ§ Ms Tai Comb.3

This hrak /^wxcE AHiauis — NES Nn re do cưng

Lith, any ky or Aan dein SWtv2x⁄2

whieh the preceat- nits vn AZ be subjected + y

—F Maw being otrerely pri” from Hrnmeger

por im the Cole for he rtehen fpevied ,

Her ve nid fratew novia gated “`, ¬ 5 = ey

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Project Job ref

Partofstructure STRESSES Duc TO DEAP | Cale sheetno rev

LOAD AND LIVE LOAD fo, A |

Drawing ref Cale by Date Check by Date Ref Calculations

Output

Ter site stress Oimids at team shen tonal sowrcendn 6 gerrcll, cortuk te dean Comfrrcasive sheised

deters tan obro bur (ác, (122/72 «4.504

ne ức,

NI, dernoks momends rensead fy precast beams only

My clmolea mements wiisted by combs silt section

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Project Job ref Part of structure FEM PERATURE DIFFERENCE STRESSES (PTD AND NTD) Calc sheet no rev 17 1A] Drawing ref Calc by Date Check by Date

E = 33 KN | me (Sex fot bork conevekes )

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Project Job ref

J8 | 8 J

Ref Calculations Output Rez Mont mement- ebert eentreteal axis = 0-396) ons xã (456-75) 4 O15 x 5:25 (456-50) # 0.01% 2-95 (USB - SS) + 0-4 x O-24x!°45(45b- 160-80) - 0-45 x0-/86 X!-2S (41% -:£6/2)) = 175 kAlx Keshoaends ave new relenced to itd skesses QA? showm m Fg I /A Negetive tems differences ( NTD) Reshinivt fore = - 0-396} 160 (2454+7-85)/2 tO4X26 (2-454 155)/2 + 0-4 x 200% 25/2 + 045% 185 (6241'S) [2 + O16 x200x 0-75} =-637 KN Restart moment abent untiodelh axir = - 0-396} O-1ex2H5 (456-80) + O16 (785-2-45)/2 X(#Sá~ 160/3) + Or4x 0-026 1:55 (456 - (áo -/3) +#'*X0-026(2:u5— 155) /2 x (456- 160- 26/3) + OK XO2KIS5/2 x(S&~ 18-100) ~ 0-†5x2:1§5x “5 (474 - 1285/2) - 095% 0-185 (6-2- M5) /2 x(b74- 185/,\) - 0:16 x0-2x0-75 (4p- 185-200/s)} = - 24 kN mn

Reshornss are new relerard & per

SÁt2222 Aa? Shen in fog r2 ‡ oar Ệ yey : Nự SUK Ra) ‘ £8 # ry ÔNG Ệ ays 3 LỚN ¬ Morey 3 oye ees

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Project Job ref Part of structure Calc sheet no 19 | A | rev Drawing ref Cale by Date Check by Date Ref Calculations Output S35 =j'2 1-99 320

Freq, [2 Ssse4 dine +o megatie remnp differen ceS.INTD }

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Project Job ref Part of structure DIFFERENTIAL SHRINKAGE STRESSES ( DSH) Calc sheet no rev 40/ A | Drawing ref Calc by Date Check by Date Ref Calculations Output ZHau 472% -2-84 0:36 136 0-62

Assuwe Yoo- tirds vf Cota potential

2Chôn ke s⁄ 39oxoÊ 4x2 aber y lohet

pleee pr the Arccaalhramd Wher ingthe

slab > cart Thougere 200x160"

Aaffran bok Z2 eke/< of tre slab cyÊ set

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Project Job ref

Part of structure (A) FRE CAST REAMS WITH

STRAIGHT FULLY BONDED TENDONS Calc sheet no 2! 1A | rev Drawing ref Calc by Date Check by Date Ref Calculations Output

Assunieé 2o? le20 ef prCrrw drbsernend do 6 xxx,

71A^§t#@kt tr bolleriy fibre at wn d- share LC1 (tension): 28(£ + 2)_ 1296-086 >o =p, “ Bete, DSH C3; 0-8 (2 xổ ~ 15-07 = 0°56 -O-8x bY B32 2 BF DB it DSH (C3 is move cruitcal there fot z Fe 5 47 Eo, 1/4 A” % = ?!/ /2m.§1#8^L tr fibre at the srfpert Fravsfr Fe 2b M - ae =) 24) +183 2 0 Li, t¿+ 163: 08(F - Re) 20264 183 - oan >- 3-2 A Zp, 2t,tc - JĐếh UA Prb

SBiv2209 oltre te otiffferenbal c^+zZ are net brown ok thar Stage brit art enpecteol to be of ruhevirg

> -~Í

natant Thin in olemansHalerl tater

Tran sfr conciter is heart ne mort riheal, F_ Fe ` > -] Eq 2/A + 2 Muthply £4 !/A by Dh anol Egy, 2 /A by ipe and add P > A ( 17 Zp - 222 ) “pr + Ba '7* 743) — 46°96 = 3 = ZZ 49 ( Spe 3l a 4646 3500 kN

Assume a lo 2 hewn tf free pret to And anAvg

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Project Job ref Part of structure Calc sheet no rev 22 / A |

Use 23 [15:2 tam Mindared shrrwdls wit an

bon fal fore of OFS fe proving

Fy = O75 xZ23Bx 232 = 4ooz ka/ anil P= hoo2 x 0-9 = Z3Lo2 LW Fre nr Eq V/A e > 17 Z2: - Zp! Ye 138 mm e A From Z2 2/A ex ape + 242 ie 14.8 mm - P A | | Oo 6 eS J 1 i, / ® e ® [

Fig lt /A Strand pattern

2x6o + 6X llO + x!éO+ 2x 430 + 2x S550 € - 37D - _— ,

23

= 810 — Ííơ = /42 mm

e - v

Mowing fol 11) Aakoratien lira in steel befiere

Trang 33

K 4696

inital stemig due do dead ford and ÂytA #22

ef ma- pan are at Sharm om fg 1S /A 337 7-48 6-60 | - N \ N + — \ N N / i LH !1-7o NV / 743! ~ 454 | Ot (Beam: only ) | f6 13:06 < ƒ⁄L/> Freshress

Fig IS/ Stresses a transfer art mid shan

Project Job ref

22/1 A I

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Project dob ref

Part of structure Calc sheet no rev 2¿! A} Drawing ref Calc by Date Check by Date -£ * = (v0 X 48x10 x 42 )x MTOR IFS » 23n139 = 350 kM 4o Brat force af Gy hl blezee-y fo = 3685 — 802-187-3502 3068 LN " Ye /P z 3068 2:832£ 3686 Final shizz elne vo prcbve clone will “ưv/m fe el titel tè G8225 x 17:6 = !⁄#'É£Z NT een

fib 2 = ~O8325x OSB 2 -O-4E ad

du vz.tẾ ¿22 /w - lena TH wt

Lea of f etl Ar Fhe (eng (Fone:

t/6-722 Cu» va we fost x 0:02 (Say) ¥ 4002 = 8OkN

724 — Shninkare lots ( Eos Es Abs)

= 300x10 195%23%/39= IRTEN

Yenrs| Gap bors (6 foo ks ops)

+ z4 obmg “fo the Dt meme , te to

faas revll vary along Me bean, Wre fol trké t2 thea tere buen daa ew -2/4A—

Mew conchbin xx Ac memder, “test Frese

be brad ew cv, sÊxae alan whe, Cops fe beau,

‘ ae oy ean owe § - awe a ae oe SR RY

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Project Job ref

Partof structure D/FFERENTIAL CREEP Calc sheet no rev STRESSES (DC) 25/ Af Drawing ref Cale by Date Check by Date Ref Calculations Output Ref lo % Tạ 10

Basis af tale lation (See comments on Faae 3)

Asse YLat Aso - Wk As “f up ont +o

pr lirse ancl enon self magi Hake 7 pee frieg +o The coctimp of fp Hab( sory

ak 180 dogs ) powdfere the Aciiaduval eed

for bees = x GE The Lame neers

factor can fe Adcumed fer the slab ⁄

reagan whieh ¢ a Small pre fodion of ý

he flal clad Lond ord us afphcd

ot “ 160 Mays whew the beam conn i

cen aiclr.ably mre mats han al Rewmsfr

Assume tet tyo-tivels ef the total di

od preatres ag ti Coop vi k2 plac “ee

«4/46 n cook, tharspere Fey= Fat t(P-Fe)

Fesheus, C force dp rear nt xen ial ‹ ~ee/

Are Ýo kh‹Z +2 F p= — fe;.Poah

Eecenti city of prtcael- earn cerlisad to

the NI nước centrerd “¿¿= 7Ø - 3!0= 164 mm

Nlom wn abart Preceat tram tentreiad to Pustornr bnrvadirr clre Có Afperentiol reef

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Project Job ref Part of structure Calc sheet no rev

26 / A ¡

Kelhinze re amd memint on the Compote

seetrer, witt therefore be — Fran of - BT tư c4 Án, Fey = 3068 + 3 (36ÊE~3068)= 3274 kM Pees £ (1 x 4? x 16°) x 23 x10” = 2:52a8 Fp > - 3274< 0526 % O43 - -73 kK Fp Che = -723X O64 = — 122 kNm At med- span _ P9 lof Ts M, = (3274 xo2- 494 )¥ 0-528 x04 3=— 7 kim - + Kb = F - 722 = -fit kn At ohn aphragm fore See Frq.f7 “9 WA Tú Mp = (3274 x0-142- 53:0) x 0-528% 0-43= 73 Wm Ni Ta wr Cre = -93 -122 = —-2/5 knw

Ay mid — spam a con fartooive strez of

O-4Y Nim” exists ot feel At the fcr of Yh Hi fbn open Oo 26 42s‹-C st23> of G-04 AF ne exists at fibre 2 | These ANL tố 004 s6%22+2 of he crithenk fbres sy ey 3 HƯỚNG a -

È atsows ear et among com NT NỆ

TARR EAL EY AO OSE COVEY LEAS EE No Qt ONAN AEDES AE URE NONE ES

wea

|

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Project Job ref

a7 iA |

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Project Job ref

Partofstructure Fyng/ Stress Checks Calc sheet no rev

29 ! 4 ¡

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Project Job ref

Part of structure ( 6 ) PRECAST BEAMS WITH

STEM GHT PRET PEBENPtbD TENDONS

Calc sheet no rev 22] A ¡ Drawing ref Catc by Date Check by Date Ref Caiculations Output p2i/A

Assume 207, Lew of prusburr subacg nent fo

effective okt gm ante Le “mm Self a

3, 337 _ s z

A ergy = 337 Nim at fins 1 and 2 ropectirely ak grantor, Sion powtens Tare fare

SES LES Mid-spaw Fibre } P Re > f7 Eq 3/4 Hho Z af £ Fe b- — — ` > - 34 Ea 4/4 A Zp $-4/ Mult ply F4.3/p by Zhy amel Es Ala oy Zp 2 and Adlol 2 74-31 + HE |

Allowing 107 Loss of preshrss Cefore amd during |

Tams fer ; ®e</me respec d Be 2980 LM

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Project Job ref

30, A |

to oblav~ Stine peri bilirs in hitondhing ) | fo = 20K O75 * 232 = 2480 kN P = O'-9x348o = 3132 kN From ky Bi @ >7 ot „ 7X74 31 _ 7431 >> ————— - _— 3/22 0349 = 190 we Frm £4.4) ye © < “pe, 6:35 eP2 SM 2 x 4696 , 639 26% 034% 2132 SS 280 wwe

Fry the skand petierar of Fig 1e/A

Fig 18) SMa ol pettan with de bonded t-dons |

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