BME Department of Mechanics, Materials and Structures Design of Reinforced Concrete Structures Introduction 1

BME Department of Mechanics, Materials and Structures

Lecture 1:

INTRODUCTION

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CONTENT

1. Some executed examples of reinforced concrete (rc) structures of the latest period of time 2. What is rc? 3. Problems, possibilities, requirements 4. Phases of design 5. Mechanical behaviour of simple supported rc beams

6. Mechanical design

Cross-section design in ultimate limit state (ULS) of linear and planar members Check of the serviceability limit states (SLS)

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7. Some historic concrete and reinforced concrete buildings 8. Developments in theory and construction 9. Requirements of the present

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1. Some executed examples of the latest period of time

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Bio architecture Stefano Boeri, Milan

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Museum on the Strom, Antwerp, Belgium, Riedijk Arckitekten

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Communal bath Makó, Hungary by Imre Makovecz

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Department store, Budapest XIth district

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World Trade Centre, Bahrain, 2007

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Budapest, Metro line 4, Fő vám square station

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2. What is rc?

Composit material:

Concrete resists well to compression aggregate + cement + water

gravel or ground stone hydraulic bound of particles (fresh concrete should be kept wet!)

Reinforcement: to resist tension

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3. Problems, possibilities, requirements Problems Rc is heavy (γrc= 25 kN/m3) The concrete cracks under service conditions (fctd≈ 0,1 fcd) Wrong thermal and noise insulation capacity Formwork is necessary Design problems: Geometry, dimensions of concrete?

Quantity, diameter and arrangement of the reinforcement?

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Possibilities unlimited form design possibilities (!) simple jointing by monolithic technology: pour concrete and ready! same coefficient of thermal expansion of concrete and steel

concrete protects steel from corrosion and from heating up in fire

use of light aggregates (lightweight concrete) use of high strength concrete and steel

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Requirements Adequate safety against rupture, loss of stability, excessive deformations and cracking when loaded Durability (protection of steel against corrosion and of concrete against chemical corrosion, resistance to fatigue failure) Adequate safety in fire (adequate concrete cover) To fulfil the above requirements, it is very important:

Good bound connection to assure safe anchorage of steel bars by both static and dynamic loading Leave enough space for proper placing and compacting of the concrete (use of fluid and self compacting concrete)

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4. Phases of design

-conceptual design → decision about the structural material and the static model -detailed design mechanical design

- loads and effects, mechanical analysis, - cross-sectional design of concrete - dimensions and of steel bars -detailing of the structural members and connections → reinforcement projects

fire safety design durability design technological design (use of additives) construction design (methods of execution) aesthetical design (architectural design, details)

energetic design (way of improving the thermal insulation capacity)

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5. Mechanical behaviour of simple supported rc beams

The tied-arch model of reinforced concrete beams

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Principal stress trajectories in uncracked and cracked state

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The truss model of shear behaviour

Simple and double grading system Prefabricated reinforced concrete truss designed according to the truss

model

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Early failure polygon of reinforced concrete beam designed with vertical links

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Research test of rc beam

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6. Mechanical design

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Cross-section design and check – of the reinforcement - of linear and planar members in ultimate limit state (ULS)

1 Bending cross-section static model and load cross-section

(simplified)

Stress-strain diagrams of concrete and steel deformations stresses

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Equilibrium equations

Check: Nc=Ns: fcdxcb = Asfyd 1233,13250

435942xc

mm ≤ xco

0Mc : MRd = Nsz = Asfyd z 61066,102251435942 Nmm

= 102,66 kNm > MEd = 88,36 kNm OK! Design: 0Ms → xc≤ xco 0Mc → As

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2 Shear Shear capacity of the concrete section: dctwcRd dfcbV ,,

Values of c for calculation of VRd,c = c bw d fctd , concrete: C20/25

ρl=Asw /(bws) %]

d [mm]

≤ 200 300 400 500 600 700 800 900 1000

C20/25 0,00 0,429 0,371 0,338 0,316 0,301 0,288 0,279 0,271 0,264

fctd =1,0 0,25 0,429 0,371 0,340 0,325 0,314 0,305 0,298 0,293 0,288

0,50 0,501 0,455 0,428 0,409 0,395 0,385 0,376 0,369 0,363

1,00 0,632 0,574 0,539 0,515 0,498 0,485 0,474 0,465 0,457

2,00 0,796 0,723 0,679 0,649 0,628 0,611 0,597 0,585 0,576

Shear supported by the shear reinforcement (vertical links):

ywdswsRd fAs

zV ,

The shear capacity of the rc section:

Max. shear capacity limited by fcd Ed

bs,Rds,Rds,Rd

c,Rd

max,Rd

Rd V

VVV

Vmax

V

minV

cdwRd fzbV 5,0max,

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3 Axial compression NRd ≥ NEd

uRd NN where

400

fminAfAN

ydscdcu

Values of the reduction coeff. in function of the concrete strength grade and of α=l0/h

Concrete

Rectangular cross-section, reinforcement arranged in 2

rows (Figure a)

Rectangular cross-section, reinforcement arranged in 3

rows (Figure b)

Circular cross-section (Figure f )

α=l0/h α=l0/h α=l0/h

≤12 14 16 18 20 22 ≤10 12 14 16 18 20 22 ≤12 14 16 18 20 22

C20/25 0,86 0,81 0,75 0,68 0,56 0,39 0,88 0,83 0,77 0,68 0,54 0,41 0,33 0,87 0,82 0,75 0,55 0,38 0,30

C50/60 0,85 0,79 0,71 0,51 0,38 0,30 0,88 0,83 0,75 0,58 0,40 0,32 0,24 0,86 0,79 0,58 0,39 0,31 0,24

Supposition: the cross-section contains the quantity of reinf. corresponding to the minimum steel ratio.

Axis of buckling

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4 Eccentric compression

2i

Ed

EdEd2ieEdEdEd ee

N

MN)eee(N)N(M ≥MRd(NEd)

sscdu AbhfN

400;fmin yds [N/mm2]

sis AA

syds1s zfAM

cocdbal bxfN

2

x

2

hNM co

bal , MMM smaxRd,

Specific values of additional eccentricities

lo /d1

0 8 12 16 20 24 28 32 36 40 46 50

(ei + e2 )/d1 0,00 0,08 0,15 0,23 0,32 0,42 0,50 0,61 0,76 0,92 1,20 1,41

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The (MRz, MRy, NR) capacity body Check of the given force combination

Check by use of the simplified diagram:

1NM

M

NM

M

EdzRd,

zEd,

EdyRd,

yEd,

Safe!

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Check of the serviceability limit states (SLS)

SLS of deformations (limitation of deflections)

wmax l /250

Simplified check of the deflection by limiting the slenderness ratio ℓ/d:

allowable)d/( d

K/

where: ℓ/K distance between 0-moment

points,

K: tabulated, (ℓ/d)allowable tabulated, qp

Ed

p

p

2

1

ykEd

Rd

f

500

M

M

ykrequ,s

prov,s

f

500

A

A pqp= gk + ψ2qk quasi perm.load

ψ2qk long term part of the variable load

ℓ

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Basic values of the allowable slenderness ratio (l/d)allowable for rectangular

sections in function of:

Concrete strength grade

Load intensity b

pEd [kN/m2]

(by beams b is the width of the beam in m, by slabs b=1,0 m)

300 250 200 150 100 50 25 20 15 10 5

≥C40/50 13 14 14 15 17 20 25 27 30 35 47

C35/45 13 14 14 15 16 19 24 26 29 34 45

C30/37 13 13 14 15 16 19 23 25 28 33 43

C25/30 13 14 14 16 18 22 24 27 31 41

C20/25 14 14 15 18 21 23 25 29 39

C16/20 14 15 17 21 22 24 28 37

――„beam” ―――――――→ ←――――――„slab” ―――――

For T-sections and flanged beams use another table of the design aids (DA) In case of applying pre-camber of the extent l/500, we can add Δ(l/d)allow =4 to the values of the previous table, whereas in case of a pre-camber by l/250, Δ(l/d)allow =8 can be added to the tabulated values

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SLS of cracking (crack width limitation)

Limits of the crack width

Aesthetical problems 0,4 mm Corrosion in ambient variably dry and wet (XC2 to XC4) or by exposure to chlorides (XD1….XD3) 0,3 mm

In wet ambient 0,2 mm In aggressive ambient, in soil 0,1 mm

Characteristic crack patterns

BME Department of Mechanics, Materials and Structures Design of Reinforced Concrete Structures Introduction 36 provs,

reqs,

Ed

qpyds

A

A

p

pf

Simplified check of the crack width by limiting the bar diameter

Ste

el str

ess

s (

N/m

m2)

Maximum diameter max (mm) of the reinforcement in function of the steel ratio and steel stress

to fulfil the crack width limitation condition wk≤ wk,allow , if mm 20min,dur c .

wk,allow = 0,4 mm wk,allow = 0,3 mm wk,allow = 0,2 mm

Steel ratio (ρ=As/bd, %) Steel ratio (ρ =As/bd, %) Steel ratio (ρ =As/bd, %)

0,15 0,2 0,5 1,0 1,5 2,0 0,15 0,2 0,5 1,0 1,5 2,0 0,15 0,2 0,5 1,0 1,5 2,0

160 16 21 40 40 40 40 12 16 34 40 40 40 7 10 23 30 35 38

200 13 17 34 40 40 40 9 12 26 34 39 40 5 7 16 21 26 30

240 10 14 26 36 40 40 7 10 19 27 33 37 - 6 10 14 18 21

280 9 11 21 31 37 40 6 8 14 21 27 31 - 4 7 10 12 14

320 7 10 17 25 32 36 - 7 11 16 21 26 - - 4 6 8 9

360 6 8 14 21 28 32 - 6 8 13 17 20 - - - - 4 4

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7. Some historic concrete and reinforced concrete buildings

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Dome of the Pantheon, Rome

27 BC, D=43 m

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Basic

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Examples

The famous boat of Lambot, 1848

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Monnier vault and slab

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Wilkinson, 1854

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Reinforced concrete floor system of Hennebique (France, 1930-ies)

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Jahrhunderthalle, Breslau 1913.

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Freyssinet: Orly hangar, 1920

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The first concrete and reinforced concrete structures in Hungary

Concrete foundation slab of the Chain bridge, Budapest, cca. 1846

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3 m thick foundation slab under the Hungarian Parliment, end of 19th cent.

Roman cement weighing 100.000 kN made in Lábatlan (Hungary) was used

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Hungarian Music Academy 1907

Structure designed by Sigismund Jemnitz

Longitudinal section

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Cross-section

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4,85 m cantilever and column

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Reinforcement project of the viaduct Sinka, 1908. Gút (Zielinski bureau)

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Water tower on Margarete island, Budapest Zielinski 1911

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8. Developments in theory and construction

Concrete Hydraulic bound

Lime, trass (puzzolana), cement roman cement – Parker England, 1796

portland cement – Vicat (France), Aspdin (England) cca. 1820 (burning and grinding of mixture of clay and chalk)

Reinforced concrete

Common application of concrete and iron Lambot, Monnier, Cognet (France, cca 1850), Hyatt (lawyer!, USA)

Prestressing (France, Freyssinet, beg. of 20th cent.) Use of high strength steel

Post-tensioning, prefabrication Standard-based design (national and international)

Technological developments of concrete and steel production, supply, mounting

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9. Requirements of the present

Beside traditional requirements formulated for the ULS and SLS, development in

-design philosophy and structural analysis -production technology of concrete and steel

-realization technology of structures result in new, more and more detailed requirements to be fulfilled by

design, like for example:

-durability requirements

-verification of safety against accidental loads, like fire, earthquake, blasting

-fulfilment - by loadbearing structural members – of traditional requirements of building constructions, like:

-watertight behaviour, heat insulation, acoustic insulation, reduction of the self-weight, frost-resistance, workability

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Way of checking and/or fulfilling these requirements will be treated during the course

END OF LECTURE 1