05-Ch5-Analytical Study and Comparison Between Codes Requirements

7/30/2019 05-Ch5-Analytical Study and Comparison Between Codes Requirements

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CH. 5: ANALYTICAL STUDY AND COMPARISON BETWEEN CODES REQUIREMENTS 73

Table 5-2: Partial safety factors considered in codes

Loading Material

Dead Live Concrete (shear) Steel

ECP 1.4 1.6 1.5 1.15ACI 1.2 1.6 1/0.75=1.33 1/0.9=1.11

BS 1.4 1.6 1.25 1.05

CSA 1.25 1.5 1/0.65=1.54 1/0.85=1.18

EC 2 1.35 1.5 1.5 1.15

Table 5-3: The main provisions in ACI, BS, and ECP Codes

Parameter

Co

de

Commentary

Locationofcriticalshearsection

ACI,ECP

bo=2(C1+C2) +4d for Interior Columns

BS

bo=2( C1+C2) +12d for Interior Columns

C

olumnsnearunsupported

ed

es

ACI

Considered as Edge column Considered as interior column

punching perimeter of columns near edges[16]


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Openingseffect

ACI

Effect of opening shall be considered if it located within column strip, orwithin [10.ts] from Col. Face

[1].

BS

Effect of opening shall be considered if it located within column strip, or

within [6.ts] from Col. Face[2]

, Single hole can be ignored if its largest

width is less than the smaller of: One quarter of the side of the loaded

area , or Half the slab depth.

BS

Where a concentrated load is

located close to a free edge, the

effective length of a perimeter

should be taken as the lesser of the

two illustrated in Figure. The sameprinciple may be adopted for corner

Columns[2]

.


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Punchingstressconsideringunbalancedm

oment

ACI,ECP

. . . .

.

fx qx CB fy qy AB

o cx cy

M C M CV uu

b d J J

Where :

Vu : Column Load.

bo : Punching Shear Perimeter at d/2 from Col. Face.

b1,b2 :Shear Perimeter Side Length Parallel and Perpendicular to

Axis of Bending Respectively.

d : Effective Depth of Slab.

Mf : Moment Transferred to Columns.

J /c : Section Properties.

Moment Transferred to Columns due to Load Cases or Lateral Loads[1]

BS

1

1

,. .o

eff eff u u

o

V V

b d b d

,

,

1.5( )

..

1.5( )

.

t x

eff

t y

mV f

V YV Max

mV f

V X

Where :bo : Punching Shear Perimeter at Col. Face.

b1 : Punching Shear Perimeter at 1.5d from Col. Face.

V : Column Load.

Mt : The design moments transmitted from the slab to the column at

the connection.

X, Y: Length of perimeter side considered parallel to the axis of

bending.

f : Equal to 1 for interior columns and 1.25 for edge and

corner columns.


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Punchingstress

intheabsenceofunbala

ncedmomentcalculation

ACI

- It is permitted to adjust thelevel of moment transferred by shearwithout revising membersizes. Tests indicate that some flexibility in

distribution ofunbalanced moments transferred by shear and flexure

at bothexterior and interior supports is possible.

-

it shall be permitted to increase the value of f : For edge columns with unbalanced moments about an axis parallelto the edge, f = 1.0 provided that Vu at an edge support does notexceed 0.75.Vc, or at a corner support does not exceed 0.5.Vc.

For interior supports, and for edge columns with unbalancedmoments about an axis perpendicular to the edge, increase f to asmuch as 1.25 times the value f=1/(1+2/3 cr) but not more than f= 1.0, provided that Vu at the support does not exceed 0.4.Vc.

ECP

- It is permitted to exclude the moment transfer calculations only in the

following cases:

1. for interior columns with span variations not more than 20% and live

load not more than 400 Kg/m2.

2. for exterior that have either rigid spandrel beam (tb 3ts) orcantilever slab of span 0.25 interior span (under the same liveload).

3. The smallest column dimension should not less than 30 cm.

.

.

u

u

o

Vv

b d

[]: factor depends on the eccentricity of the punching shear force Isequal to [1.15, 1.3, and 1.5] for internal, edge, and corner columns

respectively.

BS

In the absence of calculation, it will be satisfactory to take a value of {

Veff = [1.15, 1.40, and 1.25] x Vt } for internal, edge, and corner

columns respectively in braced structures with approximately equal

spans; where Vt is calculated on the assumption that the maximum

design load is applied to all panels adjacent to the column considered.


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Calculationsof

unbalancedmomentfo

rgravityloads

Notes

- The unbalanced negative moments in column strip(Mf) aretransferred to supporting columns by flexure and torsional moments

and divided between above and below columns according to their

stiffness as follows: for external columns, all the negative moments

are transferred to columns, while in internal columns the difference

of negative moments are transferred[3]

.

ACI

- For an interior support, supporting elementsabove and below the slabshall resist the factored

moment specified by the following Eq. in

direct proportion totheir stiffness unless a general analysis is made.

Where: qDu, L2, and Ln refer to shorter span, This Eq. refers to twoadjoining spans, with one span longer than the other, and with full

dead load plus one-half live load applied on the longer span and

only dead load applied on the shorter span.

ECP

- Moments Transferred to Internal and External Columns Should betaken equal to 50%, 90% of ve Moment in Column StripRespectively, and Divided between above and below Columns

according to their stiffness.

- For internal column, the direct load on the can be reducedconsidering that only one side of the panel is loaded with live loads.

- For external column carry part of Slab as cantilevers, bendingmoment in these columns can be reduced by the value of bending

moment due to dead load of cantilever.

BS

- The design moments transmitted from the slab to the column at theconnection above and below the slab can be taken equal to:

(Mfmax = 0.15. be.d2.fcu), where be is the effective width.

- Mfmax shouldn`t be taken smaller than 70% of the moment obtainedby finite element analysis.


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Allowa

blepunchingstresses

ACI

The Smallest Of: (Units in Kg, Cm)

*0.53[1 2* ]. `

.

*0.27*[ 2]. `

* ` W ` 27

c c

c c

o

c c c

aF

b

d

Fb

F here F

ECP

The Smallest Of: (Units in Kg, Cm)

.2.5 *[ 0.2]. /

[0.5 ]. /

/ 16

p

p

p

cu cu c

o

cu cu c

cu cu c

dq F

b

aq F

bq F

BS

at 1.50 d: (Units in N, mm)

1/3 1/ 4 1/3100*0.79 400[ ] [ ] *[ ] (Mpa)

. 25

s cu

c

m

A f

b d d

at Column Face:

vc = 0.8(fcu)1/2 5.0 Mpa

*Refer to chapter 4 for detailed equations and parameter definitions


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5-2 Comparative study on the influence of various parameters on

punching shear for internal columns5-2-1 Concrete compressive strength

Generally the punching shear strength values specified in different codes vary

with concrete compressive strength fc or fcu and are usually expressed in terms of

fcn. In the Egyptian, and the British standards; the equations are applicable to

normal strength concrete up to a grade of 40 MPa. While in American Codes the

value of fc0.5

shall not exceed 8.3 MPa, this implies that the equations are

available to concrete strength not greater than 70MPa. These limits are required

due to the lack of experience and limited test data on the two-way shear strength

of high strength concrete slabs[1]

.The relation between the ultimate punching force and the concrete

compressive strength has been plotted in figure 5-1, 5-2. It can be noticed that:

Figure 5-1: Concrete compressive strength Vs. ultimate punching shear strength

Dimensions

d =20cm,

Col. = 30x30cm

bo d =10 Constant


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Figure 5-2: Concrete compressive strength Vs. Ultimate punching shear force

According to ECP, as the concrete compressive strength increases from 200 to400 Kg/cm

2, the failure load increases from 46 to 64 ton (1.39% increase).

But in ACI, as the concrete compressive strength increases from 200 to 400Kg/cm

2

, the failure load increases from 38 to 53 ton (1.39% increase). In BS when the tension steel ratio equal to 1%, as the concrete compressive

strength increases from 200 to 400 Kg/cm2, the failure load increases from 50

to 63 ton (1.26% increase).

ACI code results are more conservative, and significant differences betweenfailure load in ACI, BSI, and ECP can be observed.

The results of ECP code, Which neglecting the effect of the flexure steel areconvergent with BS code results when taking the flexure steel intoconsideration (=1%).

5-2-2 Effective depth

It is well established in ACI, ECP that the ultimate punching shear strength is

constant with varying depth if the ratio ofbo /d is less than 20, 15, or 10 for internal,

edge, or corner columns respectively. While in BS when, increasing depth, the

ultimate punching shear stress decreases if other parameters are kept constant.

Dimensions

d =20cm,

Col. = 30x30cm

bo /d =10 (Constant)


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Figure 5-3 shows values of (vu/Ac (fcu. 100As/b.d)1/3

) from the CIRIA[28]

tests

plotted against (d). A reasonable overall correlation is obtained with the forth root

relationship.

Figure 5-3: influence of slab depth on punching resistance[28]

Birkle suggested the following equation proposed for the nominal shear

stress resistance of concrete in slabs without shear reinforcement to take the size

effect into account[23]

.

From the test results[8]

, size factors suggested in CSA, BS and EC

underestimate the influence of the effective depth on the punching shear capacity.

The predicted ultimate punching shear forces according to codes equations are

plotted with depth to show the effect of depth variation on results, the calculations

have been done on slabs with concrete compressive strength equal to 250 kg/cm2,

the perimeter to depth ratio is less than 20, the column is 30x30 cm. It can benoticed that:

- ACI code results are more conservative, it shows the least value for ultimatefailure load (ACI/ECP=0.82%, ACI/BS

=1%=0.79%).

- There are significant differences between failure load in BS, and ECP canbe observed (1.05% difference), when the tension steel ratio equal to 1.00%.


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Table 5-4: The Relation between ultimate punching shear force and depth for internal

column in various codes

d

cm

PU (Ton) PU.ACI.

/

PU.ECP

%

PU.BS.(=.34%)

/PU.ECP

%

PU.BS.(=1%)

/PU.ECP

%

PU.BS.(=2%)

/PU.ECP

%

ECP ACI BS=0.34%

BS=1%

BS=2%

15 34.86 28.64 25.32 36.26 41.50 0.82 0.73 1.04 1.19

20 51.64 42.43 37.70 53.99 61.80 0.82 0.73 1.05 1.20

25 71.00 58.34 51.99 74.47 85.23 0.82 0.73 1.05 1.20

30 92.95 76.37 68.13 97.57 111.68 0.82 0.73 1.05 1.20

35 117.48 96.52 86.03 123.22 141.04 0.82 0.73 1.05 1.20

40 144.59 118.79 105.66 151.34 173.22 0.82 0.73 1.05 1.20

45 174.28 143.19 126.96 181.85 208.14 0.82 0.73 1.04 1.19

50 206.56 169.71 149.90 214.69 245.73 0.82 0.73 1.04 1.19

55 241.42 198.34 174.42 249.81 285.94 0.82 0.72 1.03 1.18

60 278.85 229.10 200.50 287.17 328.70 0.82 0.72 1.03 1.18

65 318.88 261.98 228.12 326.72 373.96 0.82 0.72 1.02 1.17

70 361.48 296.98 257.23 368.42 421.69 0.82 0.71 1.02 1.17Notes:

fcu =250kg/cm2, bo/d


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5-2-3 Column aspect ratio

Figure 5-5: Column aspect ratio Vs. ultimate punching shear force

Figure 5-6: Column aspect ratio Vs. ultimate punching shear strength (ECP, ACI)


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5-2-4 Perimeter to depth ratio bo /d

Figure 5-7: bo /d Vs. ultimate punching shear force

Figure 5-8: bo /d Vs. ultimate punching shear force


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5-2-5 Flexure steel ratio

Mentrey 2002 list that by varying the percentage of flexural reinforcing the

following can be shown; Firstly, all the slabs show a similar cracking pattern,

regardless of the percentage of longitudinal flexural reinforcing. Secondly, all the

slabs show similar initial elastic behavior. Lastly, it is shown that the post-elastic

behaviors vary considerably with varying percentages of reinforcing. The higher

the reinforcing ratio is, the higher is the failure load, and with increasing

reinforcing percentages the ductility of the connection decreases. This is in

agreement with the experimentally observed transition from flexural, tough failure

to high capacity brittle punching failure.

Figure 5-9: Influence of the percentage of flexural reinforcing on response curves

(Mentrey 2002)

By plotting the relation between the ultimate punching shear force and the

tension reinforcement ratio as shown in figure 5-10, it is clear that increasing

causes increasing the punching failure load as in British code of practice which

uses as an effective parameter in its equations, while Egyptian, and Americancodes neglects the effect of the flexure reinforcement.

- According to BS, for slab effective depth equal to 200,400 mm, byincreasing the percentage of main steel ratio from 1% to 3%, the punching

failure load increased about 40% (from 54 ton to 76 ton). This indicates the

efficiency of dowel action of tension steel in increasing the punching shear

resistance of flat slabs.


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05-Ch5-Analytical Study and Comparison Between Codes Requirements