dr andrás draskóczy lecture 5: design of rc beams … courses/design_of_reinforced... ·...

Design of Reinforced Concrete Structures 1 BEAMS, FLOORS, BRACING

BME Department of Mechanics, Materials and Structures

Dr András Draskóczy

Lecture 5:

DESIGN OF RC BEAMS AND FLOORS, BRACING


CONTENT:

BEAMS

Examples

General characteristics

Approximate design of beam dimensions Constructional rules

R.c. cantilevers used as architectural motifs.

FLOORS

Characteristic span ranges of reinforced concrete structures

Advantages of different floor systems

Design of variable height and variable thickness RC floor systems

1 Monolithic solid slabs

2 Partially prefabricated floors

3 Cobiax (or bubble deck) floor slabs

4 Steel-concrete composite floors


5 Post-tensioned floors (lecture of Máté Borbás Pannon Freyssinet Kft.)

BRACING

Ways of bracing Bracing systems of reinforced concrete load bearing structures.

Connection of tilting and bracing


BEAMS

Examples


Series of continuous arched diaphragm beams of Nervi, Orvieto airplane

hangars


Monolithic rc cantilever of the Flaminio stadium, Rome by Nervi


Variable section arched continuous rc beams of Calatrava,Lyon railway

station


Variable section rc frame beam of Calatrava, Lyon railway station


Metro line 4 Budapest, Fővám square, slurry wall supporting beams


General characteristics of beams

DEFINITION, INTERNAL FORCES Beams are linear members generally supporting vertical loads, with their axis running

horizontally and mainly being subjected to moments and shear forces along their axis

(M+V), but axial force (in frame beams) can not be excluded either. Try to avoid torsion!

TYPES

-Geometry -Axis: straight, curved or eventu-

ally poligonal

-Cross-section: constant, variable, haunched near supports, flanged

(when cast integral with the floor slab)

The way of variation is mainly in connection with the variation

of moments, which can also be

exploited for rainwater canalisation -Static models:


-single span and continuous with or without cantilever

-beams can also be part of frames, joining to other members by hinged or rigid joint.

Principal beams and secundary beams, joist floors


Ribs

Column

Principal beam


Approximate design of beam dimensions

1 Estimation of the width (b, bw) and height (h):

b, bw is generally determined by technological requirement: b= wall thickness or column width

h estimate by approximate value of the slenderness ratio: l/d≈l/(h-5 cm):

-heavily loaded simple supported beam: l/d≈10 to 12

-simple supported beam with low load intensity: l/d≈14 to 16 -continuous beam, flanged beam: l/d≈ 16 to 18

-prefabricated prestressed beam: l/d≈ 18 to 22

2 Rigidity check in SLS of deformations (limitation of deflections)

wmax l /250

ℓ


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 (see below!), 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


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

Concrete

strength

grade

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


Constructional rules of beams (for information only) 1. Reinforcement designed for bending

Minimum quantity of tensile reinforcement

As,min=ρminbtd

ρmin = max 0,26 fctm/fyk ; 0,0015 see table below

bt medium width of the tension zone

Minimum steel ratio min (%o)

fyk

concrete

C12 C16 C20 C25 C30 C35 C40 C45 C50

500 1,5 1,5 1,5 1,5 1,51 1,66 1,82 1,98 2,13

400 1,5 1,5 1,5 1,69 1,89 2,08 2,28 2,47 2,67

240 1,73 2,06 2,38 2,82 3,14 3,47 3,79 4,12 4,44

The allowable maximum quantity of the total steel cross-section:

As,max=0,04Ac , where Ac is the area of the total concrete cross-section.

At overlaps the double of this quantity is allowed.


Partial restraint at beam ends:

Partially restrained ends of monolithic beams must be designed for the calculated restrain moment. The respected restrain moment can not be smaller than 15% of

maximum moment in the span. The section design for 15% of the span moment

should be made even if the beam was considered simply supported. The rule concerning the minimum reinforcement must be respected.

Anchorage of bent-up bars with straight end

The anchorage length in the tension zone must be at least 1,3lbd, in the compression zone at least 0,7 lbd , which should be measured from the intersection point with the

longitudinal reinforcement.


Anchorage of the bottom longitudinal reinforcement above support

At least 1/3 of the span reinforcement must be continued beyond the theoretical support point.

At extreme support reinforcement must be anchored for the tensile force FEd given in

point 6.5.1. , and the anchorage should be measured from the internal face of the support.

At intermediate supports one of the solutions indicated below can be applied.

The mostly recommended solution is (d). The figures do not indicate the top reinforcement. Values of db= Dmin are given in section 8.2.


2. Shear reinforcement

In case of designed shear reinforcement at least half of the shear force should be

equilibrated by links.

The shear steel ratio: w=Asw/(s . bw

. sin) , where α is the angle between axis

of the beam and axis of elements of the shear reinforcement

The minimum shear steel ratio: w,min=max

001,0;f

f08,0

yk

ck , which can be taken from

the table below.

Values of the minimum shear steel ratio: w,min (%o)

fyk

Concrete

C12/16

C16/20

C20/25

C25/30

C30/37

C35/45

C40/50

C45/55

C50/67

500 1,00 1,00 1,00 1,00 1,00 1,00 1,01 1,07 1,13

400 1,00 1,00 1,00 1,00 1,10 1,18 1,26 1,34 1,41

240 1,15 1,33 1,48 1,67 1,81 1,95 2,05 2,21 2,33


If bw>h: w,min=

ww

yk

ckb/h0003,00007,0

001,0

b/h0003,00007,0

f

f08,0,

The greatest allowable spacing of elements of the shear reinforcement

Maximum spacing of links

in general sl,max=0,75d )cot1( mm300;b5,1min w

in case of designed compression steel sl 15 [13], [15]*

is the smallest diameter of the compression steel perpendicular to the beam axis sl,max=0,75d 1000 mm.

Maximum spacing of 45 bent-up bars sb,max=1,5d

Detailing of links

a) b) c) d) e) f) g)

* The Eurocode does not give a rule for beams, the given proposal is the same as the similar one to be applied by compression bars of

columns (see chapter 8.7).

.


Open links can only be applied in flanged beams, if there is transverse reinforcement

in the slab. Links cages can also be bent using spot-welded meshes. Related constructional rules

see in point 8.2.

At junction of principal and secondary beam the links of the principal beam must go through, at column-beam junctions links of the column must go through.

3. Torsion reinforcement Links must be anchored with overlap.

Spacing of links can not be greater than a) 1/8 of the concrete perimeter

b) the smaller side length Distance between elements of the longitudinal reinforcement uniformly distributed

along the link perimeter must be smaller than 350 mm.

(In the cross-section indicated on the figure elements of flexural and torsion reinforcement can also be seen.)


R.c. cantilevers used as architectural motifs


Some design principles

(Beams)

5

h cc

(Deep beams, walls)

15 to

12h cc

c

(Slabs)

Smaller Fc better:

Greater compression zone better


Pile foundation or heavy mass foundation may be necessary to anchor Ft!

Downloading by G better ( tF2

G )


Greater restrain length better:

< restrain length >

Symmetric arrangement better:


Storey-high cantilever (deep beam cantilever) better:


FLOORS Characteristic span ranges of reinforced concrete structures Advantages of different floor systems

Design problems of variable height and variable thickness

RC floor systems 1 Monolithic solid slabs

2 Partially prefabricated floors

3 Cobiax (or bubble deck) floor slabs 4 Steel-concrete composite floors

5 Post-tensioned floors


CHARACTERISTIC SPAN RANGES OF RC FLOOR STRUCTURAL SYSTEMS

Construction

type

one-way

two-way

Char.

slender

ness l/d

Approximate maximum span l(m) 5 7,5 10 12,5 15 17,5 20 25 30 35 >35

monolithic rc

solid slab

one-way 25-30

30-35

two-way

prefab.

prestressed

hollow core

floor panels

one-way 35-40

monolithic rc

beams

one-way 10-15

solid flat slab two-way 25-35

prestressed

solid slab

one-way 30-35

prestressed

solid flat slab

two-way 35-40

hollow core

(flat) slab

two-way 30-40

prestressed h.

core flat slab

two-way 35-40


CHARACTERISTIC SPAN RANGES OF RC FLOOR STRUCTURAL SYSTEMS (cont.)

Construction

type

one-way,

two way

Char.

slender

ness l/d

Approximate maximum span (m) 5 7,5 10 12,5 15 17,5 20 25 30 35 >35

prestressed rc

beams (used

in building

construction)

one-way 18-22

prestressed rc

beams (used

in bridge

construction)

one-way 18-22

deep beams one-way 5

prefabricated

box-culvert

construction

with post-

tensioning

one-way


ADVANTAGES OF DIFFERENT FLOOR SYSTEMS

monolithic or prefabricated floors?

Cheaper, mainly if manpower is cheaper More rapid construction Increases safety through better structural integrity

Better possibilities for individual design Higher level of weather independency

No problem in jointing members Partial pre-fabrication can integrate well all advantages!

one-way or two-way floors?

Mass production by application of hollow Load intensity and moment reduction

core pre-stressed floor panels Deflection reduction

→ structural height reduction

normal or pre-stressed floor structures?

Cheaper Deflection reduction

Better possibilities for individual design → structural height reduction


DESIGN OF VARIABLE HEIGHT AND VARIABLE THICKNESS

Beams

Variable beam height for rainwater

canalization (cca 5% fall) from flat

roof of an industrial hall

Favourable effect: shear capacity increase a)

variation on side of the compression zone

tan,cEdEd NVV

b) variation on side of the tension zone ssEdEd NVV tan,


Slabs

Favourable effects of the self weight reduction of cantilever slabs achieved by 50% reduction of the thickness at the free extremity

The 33% moment and deflection reduction can also be exploited by cca 10 to 13% reduction of the slab thickness itself.

The floor slab becoming thin looks lighter, having also a positive aesthetical effect.


RC STRUCTURAL FLOOR SYSTEMS 1 MONOLITHIC SOLID SLABS


2 PARTIALLY

PREFABRICATED

FLOORS

Omnia floors 5 to 6 cm thick prefab

formwork panels strength-

ened by lattice-like reinforcement, provisory

supported at 1,5 to 2 m axis

distances


Stadium Debrecen


Details of Omnia floors


Slim-floor construction details

Hollow core rc floor panels supported by flanged steel beams to reduce the overall

structural height of the floor. In situ concreting constitutes the compression zone and impreves fire resistance. With use of bent-up bars F90 fire resistance can be achieved


3 COBIAX (OR BUBBLE DECK) FLOOR SLABS


Installation guide

Post-tensioning

Mainova · Frankfort, Germany


SPAN RANGE – SPHERE DIAMETER – LOAD INTENSITY DIAGRAM

OF COBIAX FLOORS

Spans [m] with the same slab thickness 22 C

20

18

Loads [kN/m22] 16 B

14

12

10 A

8

6

4

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

d = deck thickness dia. = sphere diameter

A d 23.0 cm / dia. 18.0 cm

B d 40.0 cm / dia. 31.5 cm

C d 58.0 cm / dia. 45.0 cm


Omnia products incorporate

the triangular Omnia lattice girder that is attached to a

lower layer of reinforcement

before wet concrete is poured to create the Omnia panel


The wet-method The dry-method THREE ALTERNATIVES OF PARTIAL PREFABRICATION AND MOUNTING

The in situ-method


Lifting of the ready-assambled floor panel by application of the dry construction

method .


Mayor advantages of COBIAX (Bubble-deck) floors:

- up to 18 m span without beams

- biaxial load-bearing, reduced deflections

- up to 30% selfweight reduction - unification of the advantages of prefabrication and monolithic technology

STEEL-CONCRETE COMPOSITE FLOORS


4 STEEL – CONCRETE COMPOSITE FLOORS

Flexural resistance of encased steel beam

Alternative solutions


5 PRESETRESSED RC SLABS WITH BOUNDED AND UNBOUNDED TENDONS

50 cm thick transition slab with unbounded post-tensioned cables, Jerusalem


The manual pre-stressing jack


BRACING

Ways of bracing

Beside solid sheared-walls, bracing of buildings can be assured by use of

diagonals rigid frames frame filling walls

(Andrew-crosses, characteristic for

steel constructions)


EXAMPLE: ORVIETO AIRPLANE HANGAR BY NERVI


Bracing systems of reinforced concrete loadbearing structures


Connection of tilting and bracing


END

dr andrás draskóczy lecture 5: design of rc beams … courses/design_of_reinforced... ·...

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