Detailing reiforcement concrete bendingbeam (tài liệu neo thép ACI)

9.9.1.1 which is a potential plastic hinge zone as discussed in Section 2.4 and illustrated in Figure 3.11 the compression reinforcement ≥ one-half of the tension reinforcement in the sa

500(D)  400(W), f cu 35MPa with a symmetrical flange width = 2160mm and flange depth = 150mm carrying a total factored uniformly distributed load of 62.5kN/m So the maximum moment is

500 8

5 62 8

By Cl 5.2.1.2 of the Code, as b eff,1 b eff,2 2160400/2880mm

> 8000.1l pi  mm, shear stress between the flange and the web should

be checked

EC2 Cl 6.2.4 requires x to be half distance between the section where the moment is 0 and the section where the moment is maximum,

x = 0.542m

The next step is to calculate Fd The greatest value should be that

between the support where F d = 0 (zero moment) and the section at 2m from support having 0.75 of the maximum moment which is

375 500 75

Assuming the compression zone does not fall below the flange at

35 440 2160

10 375

2

6











1 427 9

0 25 0 5















9

 880 2160375106 418880 2160365497



150

2000365497 







f

d sf

xh

F v

∆

∆

f

sf f sf f

sf y

s

A h v s

A f

Use T12@250c/c, or 0.3% > 0.15% (required by Table 9.1 of the Code)

The followings should be observed in placing of longitudinal steel bars for bending Re Cl 9.2.1 and 9.9.1 of the Code The requirements arising from

“ductility” requirements are marked with “D”:

generally (Table 9.1 of the Code) and 0.3% in accordance with Cl 9.9.1 of the Code for ductility requirements (D); except for beams subject to pure tension which requires 0.45% as in Table 9.1;

9.9.1.2(a)) (D) Maximum tension steel percentage : 4% at location outside critical section (Cl 9.2.1.3 of the Code);

required for ultimate design, Table 9.1 of the Code should be followed

by providing 0.2% for rectangular beam and different percentages for others In addition, at any section of a beam within a critical zone (a zone extending from the column face to twice the beam depth for beam contributing in the lateral resisting system as described in Cl 9.9.1.1 which is a potential plastic hinge zone as discussed in Section 2.4 and illustrated in Figure 3.11) the compression reinforcement ≥ one-half of the tension reinforcement in the same region (Cl 9.9.1.2(a) of the Code) (D) The reason of limiting tension steel in (ii) and at the same time requiring compression steel not less than half of that of tension steel in “critical regions” is because tensile steel decreases ductility while compression steel increases ductility as discussed by Law (2011) The requirements thus ensure certain level of ductility in the beam;

percentages of tension and compression steel required in various parts

of flanged beams (Table 9.1 of the Code);

eff

b

h

f

h

w b

Longitudinal bars in web:

h b

A st  0 0018 w if b w/b eff  0 4

h b

A st  0 0013 w if b w/b eff  0 4

h b

A sc  0 002 w

Longitudinal bars in flange

h b

A st  0 0026 w (T-beam)

h b

A st  0 002 w (L-beam)

f eff

A  0 004

Transverse bars in flange

1000 0015

.

unit metre of flange length

Heavy Moment Easily Lead

to Plastic Hinge Formation

Critical zones in Beam contributing in the Lateral Load Resisting System

2h

h

2h

Figure 3.11 – Location of “Critical Zone” in Beam

Bending Moment Diagram

Figure 3.12 – Minimum Steel Percentages in Various Parts of Flanged Beams

(v) For calculation of anchorage lengths of longitudinal bars anchored into

ductility requirement according to Cl 9.9.1.2(c) of the Code That is, stresses in the steel should be f instead of y 0.87f y in the assessment of anchorage length As such, the anchorage length as indicated in Table 8.4 of the Code should be increased by 15% as per (Ceqn 8.4) of the Code in which

bu

y b f

f l

4



increasing stress in steel from 0.87f y to f ) where y f bu  f cu

anchorage for ribbed steel reinforcing bars in accordance with Table 8.3 of the Code (D) An illustration is shown in Figure 3.20, as in addition to the restriction on the start of the anchorage;

portion of the splice shall be located within the beam/column joint region or within one effective depth of the beam from the column/wall face as per Cl 9.9.1.2(d) (D) and illustrated in Figure 3.13;

(vii) Type 2 couplers, can however, be used anywhere in the beam as per Cl

9.9.1.2(e) of the Code (D) The reason is that the Type 2 couplers are stronger and are tested to be able to resist cyclic tension and compression loads which are simulating seismic actions;

(viii) By Cl 9.9.1.2(f) of the Code, a general requirement is stated that

distribution and curtailment of longitudinal bar shall be such that the flexural overstrength will be within the critical section (D)

(ix) At laps in general, the sum of reinforcement sizes in a particular layer

should not exceed 40% of the beam width as illustrated by a numerical example in Figure 3.14 (Cl 8.7.2 and Cl 9.2.1.3 of the Code);

no lap / mechanical coupler Type 1 zone

potential plastic hinge section

d

d

Figure 3.13 – Location of No Lap / Mechanical Coupler Type 1 Zone in Beam

(x) Minimum clear spacing of bars should be the greatest of bar diameter,

20 mm and aggregate size + 5 mm (Cl 8.2 of the Code);

redistribution (ratio of moment after redistribution to moment before

b prov s

req s y s A

A f f



1 3

2 ,

redistribution), the maximum clear spacing is 140mm (Cl 8.7.2 and 9.2.1.4 of the Code) as illustrated in Figure 3.15;

(xii) By Cl 9.2.1.9 of the Code, requirements for containment of

compression steel bars in beam is identical to that of column as described in Cl 9.5.2 of the Code :

(1) Every corner bar and each alternate bar (and bundle) in an outer layer should be supported by a link passing around the bar and having an included angle  135o;

(2) Links should be adequately anchored by means of hook through a bent angle ≥ 135o;

(3) No bar within a compression zone be more than 150 mm from a restrained bar supported / anchored by links as stated in (1) or (2)

as illustrated in Figure 3.15

In addition, in accordance with Cl 9.5.2 of the Code, spacing of links along the beam should not exceed the least of :

(1) 12 times smallest longitudinal bar diameter;

(2) The lesser beam dimension; and (3) 400mm;

(xiii) No tension bars should be more than 150 mm from a vertical leg (link)

as illustrated in Figure 3.15 (Cl 6.1.2.5(d) and Cl 9.2.2 of the Code);

bar diameter

d = 40

beam width b = 900

Sum of reinforcement sizes = 40  8 = 320

< 0.4  900 = 360

So O.K

Figure 3.14 – Illustration of Sum of Reinforcement Sizes at Laps < 0.4 of

Beam Width

(xiv) At an intermediate support of a continuous member, at least 30% of the

calculated mid-span bottom reinforcement should be continuous over the support as illustrated in Figure 3.16 (Cl 9.2.1.8 of the Code);

(xv) In monolithic construction, simple supports top reinforcements should

be designed for 15% of the maximum moment in span as illustrated in Figure 3.17 (Cl 9.2.1.5 of the Code) to allow for partial fixity;

1 3

0 A s

2 3

0 A s



Figure 3.16 – At least 30% of the Calculated Mid-span Bottom Bars be

Continuous over Intermediate Support

Calculated

mid-span steel

area A s2

Calculated mid-span steel area A s1

 250 and 20 times dia of link in critical zone (D)

 250 and 20 times dia of link in critical zone (D)

 250 and 20 times dia of link in critical zone (D)

Spacing of tension bar 150 from

a vertical leg  140 (clear bar spacing under no

moment redistribution)

 150

 150

 150

 150

 150

135 o

 150

 150

compression zone

bar in compression  150 from a restrained bar

Links bent through

angle ≥ 135 o for

anchorage in concrete

Figure 3.15 – Anchorage of Longitudinal Bar in Beam Section

Alternate bar in an outer layer restrained by link of included angle 135 o

 150

(xvi) For flanged beam over intermediate supports, the total tension

reinforcements may be spread over the effective width of the flange with at least 85% inside the web as shown in Figure 3.18 reproduced from Figure 9.1 of the Code;

(xvii) For beam with depths > 750 mm, provision of sides bars of size (in

mm) ≥ s b b/ f y where s is the side bar spacing (in mm) and b b

is the lesser of the beam (in mm) breadth under consideration and 500

mm f is in N/mm y 2 In addition, it is required that s b 250mm and side bars be distributed over two-thirds of the beam’s overall depth measured from its tension face Figure 3.19 illustrate a numerical example (Cl 9.2.1.2 of the Code);

Section top steel designed for 0.15 M max

maximum bending moment M max

Bending moment diagram Simple support by

beam or wall

Figure 3.17 – Simple Support be Designed for 15% of the Maximum Span

Moment

b

eff

b

at least 85% of reinforcements inside the web

at most 15% of reinforcements outside the web

Figure 3.18 – Distribution of Tension Reinforcement Bars of Flanged Beam

over Support

(xviii) When longitudinal beam bars are anchored in cores of exterior

columns or beam studs, the anchorage for tension shall be deemed to commence at the lesser of 1/2 of the relevant depth of the column or 8 times the bar diameter as indicated in Figure 3.20 In addition, notwithstanding the adequacy of the anchorage of a beam bar in a column core or a beam stud, no bar shall be terminated without a vertical 90o standard hook or equivalent anchorage device as near as practically possible to the far side of the column core, or the end of the beam stud where appropriate, and not closer than 3/4 of the relevant depth of the column to the face of entry Top beam bars shall be bent down and bottom bars must be bent up also indicated in Figure 3.20 (Cl 9.9.1.2(c) of the Code) (D);

(xix) Beam should have a minimum support width by a supporting beam,

wall, column as shown in Figure 3.21 as per Cl 8.4.8 of the Code The requirement stems from the practice that bend of bar not to begin

anchorage

length

based on f y

Not permitted

X

≥ 500mm or h

D

5 0



or 8Ø

D

75 0



D

anchorage commences at this section generally

anchorage can commence at this section

if the plastic hinge (discussed in Section 2.4) of the beam is beyond X

Figure 3.20 – Anchorage of Reinforcing Bars at Support

Bar of diameter Ø

T16

1000

600

1500

b is the lesser of 600 and 500, so

500



b

s chosen to be 200 mm  250mm,

So size of side bar is

74 14

460 / 500 200 /







y

b b f s

Use T16

The side bars be distributed over

1000 1500 3

2   from bottom which is the tension side tension side

Figure 3.19 – Example of Determination of Side Bars in Beam

before the centre of support as specified in Cl 9.2.1.7(a) As such, the requirement should be that in Figure 3.20 which does not quite agree with Cl 8.4.8 of the Code which has omitted for the case Ø  12

(xx) Curtailment of flexural reinforcements except at end supports should

be in accordance with Figure 3.22 (Cl 9.2.1.6(a) to (c) of the Code)

Worked Example 3.12

Worked example 3.12 is used to illustrate the arrangement of longitudinal bars and the anchorages on thin support for the corridor slab beam of a typical housing block which functions as coupling beam between the shear walls on both sides Plan, section and dimensions are shown in Figure 3.23 Concrete grade is C35 The design ultimate moment at support due to combined gravity and wind load is 352kNm

Section beyond which the bar is no longer required

≥12Ø and d at least;

if the bar is inside tension zone, ≥ 1.0 bond length as per Cl 9.2.1.6(c)

d

Bar of diameter Ø

Figure 3.22 – Curtailment of Reinforcement Bars

c

≥0

Figure 3.21 – Support Width Requirement

2(3Ø+c) if Ø  12; Ø=10,12

2(4Ø+c) if Ø < 20; Ø=16

2(5Ø+c) if Ø  20; Ø=20,25,32,40,50

2Ø if Ø  12;

3Ø if Ø < 20;

4Ø if Ø  20

bar of diameter Ø

The designed moment is mainly due to wind load which has resulted in required longitudinal steel area of 3763 mm2 (each at top and bottom) The

200 mm thick wall can accommodate at most T16 bars as

3819 mm2 Centre to centre bar spacing is 140025216/1874mm

factor 38 is taken from Table 8.4 of the Code which is used in assessing anchorage length Anchorage details of the longitudinal bars at support are shown in Figure 3.24;

3.7.1 Checking of Shear Stress and Provision of Shear Reinforcements

Checking of shear in beam is based on the averaged shear stress calculated from (Ceqn 6.19)

d b

V

v

200

300

1400

Slab beam

Plan

Section Figure 3.23 – Layout of the slab beam in Worked Example 3.12

T16

cross bar

T10 – 10 legs – 200 c/c

608

11

64

25

200

Anchorage commences at centre line of wall as 200/2=100<168=128

19T16

19T16

Figure 3.24 – Anchorage Details at Support for Worked Example 3.12

where v is the average shear stress, V is the ultimate shear, d is the effective depth of the beam and b is beam width v b should be taken as the v

averaged width of the beam below flange in case of flanged beam)

If v is greater than the values of v , termed “design concrete shear stress” in c

Table 6.3 of the Code which is determined by the formula

m v

s cu

c

d d

b

A f

v



1 400 100

25 79

1 3

1 3

1





































the following limitations :

(i) m 1.25;

(ii)

d b

A

v s

100

should not be taken as greater than 3;

1 400













reinforcements and should not be taken as less than 1 for members with links;

yv

r v yv

c v v

sv

f

v b f

v v b s

A

87 0 87

6.2 of the Code) where v r 0.4 for f cu 40MPa and 0.4(f cu/40)2/3 for

40

80 f cu  Alternatively, less than half of the shear resistance can be taken

b yv

sb b

s

d d f

A V

cot sin cos

87 0 5

per Ceqn 6.20 and Cl 6.1.2.5(e) of the Code and the rest by vertical links Maximum shear stress should not exceed v tu 0.8 f cu or 7 MPa, whichever

is the lesser by Cl 6.1.2.5(a)

3.7.2 Minimum Shear Reinforcements (Table 6.2 of the Code)

If v0.5v c throughout the beam, no shear reinforcement is required in beams of minor structural importance while minimum shear links be in other beams;

If 0.5v c vv cv r, minimum shear links of

yv

r v v

sv

f

v b s

A

87 0

whole length of the beam be provided where v r 0.4 for f cu 40 and

40 / 4

3.7.3 Enhanced Shear Strength close to Support (Cl 6.1.2.5(g))

At sections of a beam at distance a v 2d from a support, the shear strength can be increased by a factor

v a

d

2 , bounded by the absolute maximum of v tu

which is the lesser of 0.8 f cu and 7 MPa as illustrated by Figure 3.25

3.7.4 Where load is applied to the bottom of a section, sufficient vertical

reinforcement to carry the load should be provided in addition to any reinforcements required to carry shear as per Cl 6.1.2.5(j) and shown in Figure 3.26;

3.7.5 Worked Examples for Shears

(i) Worked Example 3.13 – Shear design without shear enhancement in concrete

644 16 40



bd

A st

; 35f cu  MPa;

700



81 0 1 400 100

25 79

1 3

1 3

1









































m v

s cu

c

d d

b

A f

v

1 400











Vertical rebars to resist beam bottom loads which may increase required provisions of links Hanging Load at Beam Bottom

Figure 3.26 – Vertical Rebars to Resist Hanging Load at Beam Bottom

(e.g Inverted Beam)

d

v

a

Figure 3.25 – Shear enhancement near support

section under consideration, shear strength enhanced to c

v

v a d

2