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8/9/2019 Failure Analysis ... Flat Slab - Column Connections With Shear Reinforcement
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Proceedings fib Symposium PRAGUE 2011
ISBN 978-80-87158-29-6 Session 1-4: New Model Code
1
FAILURE ANALYSIS OF SYMMETRIC FLAT-SLAB COLUMN
CONNECTIONS WITH SHEAR REINFORCEMENT
Dan Vasile
Bompa
Traian
One
Abstract
Flat slab structural systems have a large applicability due to their functional and economicaladvantages. Form engineering point of view, these structures develop a complex behavior at flatslab – column connection. Close to ultimate states flat slabs are susceptible to punching. Underextensive loading, stress distribution lead to a concentration of stresses near the column. Stress boosting is followed by a loss of shear strength across the connection. Existing minute and flexuralflaws influence the behavior of the flat slab column connection zone by diminishing the stresstransfer capacity. Punching of flat slabs occurs without any warning and as a consequence of load
boost showing extensive cracking and large deflections.The paper presents a failure analysis on five large-scale reinforced concrete slabs. Four of
the slabs are fitted with two shear reinforcement configurations having the same reinforcement
ratio: double headed stud rails and closed stirrups. The fifth slab, used as control slab, has no shearreinforcement inserted. The tests are focused in analyzing flat slab rotation near column, maximum punching capacity and behavior of the two shear reinforcement configurations up to the failure.A yield line analysis was made in order to justify the behaviour at failure.
Keywords: punching shear, shear reinforcement, stud rails, stirrups, failure analysis
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fib Symposium PRAGUE 2011 Proceedings
Session 1-4: New Model Code ISBN 978-80-87158-29-6
2
1 Introduction
It is well known that concrete has a contrastable behaviour in extremes, strong in compression and
weak in tension. Since most of the analysis upon concrete are defined by these characteristics,(i.e. crushing and cracking), behaviour of the flat slab column connection under monotonic loadcan be marked out through them. At a coarse view it can be divided in four stages: the elastic stagewhen both constitutive materials behave can sustain reversible strains; flexural stage starts whenthe first bending crack occurs and ends when the first tangential crack cannot transfer stressesthrough its interface. During this stage cracks propagate in radial direction from most critical point
to the bearings. If the slab is fitted with adequate flexural reinforcement, shear transfer mechanismscan be activated and the connection has the capacity to pass to the next stage, which is called shearstrength stage. As mentioned, dowel action and concrete-to-concrete friction mechanisms aredeveloped. The capacity to resist concentrated loads can be enhanced by providing transversal barswithin the critical perimeter. Shear reinforcement share is consumed in this stage. Final stage is
reached when the diagonal crack forms a cone around the column and perforates the slab above.
In an ideal circular slab-column connection column force V u is transferred to the slab in radialdirection. Considering that the shear crack has reached the neutral axis due to radial bending, theforces have to pass under the crack. Since all the stress transfer capacity through crack is cut, (i.e.
stress free crack), the entire bearing capacity lies on the strength of the compression strut. Failureoccurs when punching ultimate strain or maximum compressive strength is reached in the strut.
Due to the high concentration of stresses in the critical perimeter the expected failure takes place in a non-ductile, brittle manner. When this happens, it means that the slab is lacking in post- punching rotational capacity and ductility. Structural design has to overcome this problem providing adequate rotational capacity to the members. A higher ductility can be reached by placing transversal reinforcement in the zones where the stresses are high, and a flexural failure can be initiated. Anyhow, since the behaviour is complex, even an expected flexural failure can lead to
a punching failure due to development of large displacements and rotations.
Vu2
Vy
Vu1 Vshear < Vflex
Vshear > Vflex
Ductile
failureBrittle
failure
w
V
Fig. 1 Failure modes for a flat slab column connection
A flexural failure corresponds to the moment when tension reinforcement reaches the yielding
limit. In order to find the flexural punching value of a flat slab column connection the plasticity based yield line theory has to be used. The theory uses the same behaviour stages as presented
earlier. Plastification occurs following incrementally the envelope of maximum bending moments.The sections where the reinforcement reaches the yielding limit increasing the strains anddevloping plastic rotations. Plastification follows the strips where the highest concentration ofcracks is found. The boundry condition influence in a very important way how these yielding linesare developed. Failure occurs when a mechanism is formed.Several research studies have been
made upon this issue and the conclusion regarding the ranges of the ratio between test and flexuralfailure force. Some of them consider value of 1 to be the point of balance. A more complex
approach which diviedes in three main failure types, considering an intermediate punching failurewould be [2]:
V test /V u,flex > 1.15 – flexural failure (F), (1a)
0.95< V test /V u,flex <1.15 - flexural punching failure (FP), and (1b)
V test /V u,flex ≤ 0.95 - brittle punching (P). (1c)
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Proceedings fib Symposium PRAGUE 2011
ISBN 978-80-87158-29-6 Session 1-4: New Model Code
3
2 Shear reinforcement
A large discussion about the share of the transversal reinforcement has been made in many papers.
The common agreement is that the failure can be divided in four large categories: flexural failure by yielding of tension reinforcement, maximum shear capacity, failure inside the shear reinforcedarea and failure outside the shear reinforced area.
Failure mechanism in case of transversal reinforced flat slabs is activated due to existence ofmicrocracks and development of flexural cracks. After first diagonal crack is opened the entireshear capacity is taken by the transversal bars that cross the interface. In order to account their
share on the maximum punching capacity the bars have to conform to the anchorage and bondregulations. A discussion can be made upon the topic of the capacity of transversal reinforcementto transfer stresses when the shear crack has opened.
It has been showed, both experimentally and numerically that the concrete found at the rootof the punching crack is in a triaxial compressive state and the bar is confined. On the other side the
part of the dowel situated above the plane parallel with the face of the slab that intersects the root
of the punching crack, the stress transfer between the two sides of the neutral axis is restrained. Inconclusion the punching capacity is highly influenced. Consequently, the effectiveness of the shearreinforcement depends on the angle and the length of the punching crack. Coarsely considering the
CEB-FIB 2010 regulations regarding the confinement level and bond conditions a correction factorfor stud-rails of 0.625 can be applied (table 6.11 in [1]).
When stirrups, hooks or bent-up bars are provided with enough anchorage length the bars arenot highly influenced by the stress state and can reach yield strength. ACI design code obliges thestructural designer to enclose the two layers of flexural reinforcement by stirrups.In order to find a closest share of the shear reinforcement a stress-strain computation can be made by means of fracture energy, considering the strain in the bar due to the opening of the crack.
a) b)
Fig. 2 Shear reinforcement used in tests
It can be noticed that effectiveness of the shear reinforcement is not only influenced by their position, yielding strength and quantity, but also the anchoring conditions and bond characteristics.The four shear reinforced slabs were fitted with the reinforcement in the Fig. 2. Two of the slabshave been provided with stirrup beams and the other two with double headed stud-rails.Transversal reinforcement has been positioned after normal and diagonal directions after all fourcolumn faces and edges. It has to be mentioned that the stirrup beams have been placed between
the two layers of flexural reinforcement.First type of reinforcement, Fig. 2a, was made of Ø10 stirrups forming a beam of 500 mm.
Longitudinal bars used to connect stirrups were 4Ø10. Ø10 hooks connected on 2Ø10 at the edgeswere used for the diagonal shear reinforcement. The entire “stirrup beam” was position in between
the two faces of flexural reinforcement. Double headed stud-rails, reinforcement type II, werewelded on a rectangular plate of 20 mm x 3 mm cross-section. The head of the studs was Ø24 andthe welded plate was placed on the tensioned face of the slab.
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fib Symposium PRAGUE 2011 Proceedings
Session 1-4: New Model Code ISBN 978-80-87158-29-6
4
3 Geometrical configuration of the slabs and test set-up
Fig. 3 Geometrical configuration and reinforcement positioning in tested slabs
Tests were carried out in the Central Laboratories of Technical University of Cluj-Napoca. Therewere performed six punching tests upon large scale symmetric flat slab column connections. Thegeometrical configuration of the slab was chosen in order to fit the essay stand requirements.
Square shaped flat slabs had the dimensions ( L ×l ) of 1500 mm × 1500 mm. The nominalheight of the slab was 170 mm and the average effective depth 155 mm. Column part had the cross
section of 300 mm × 300 mm and a height of 600 mm. Slabs were reinforced on both faces withØ10/100mm bars for tension and integrity. Columns had 8 bars Ø14 at each corner and middle point of the four faces and were transversally reinforced with Ø8 stirrups posed at 100mm. Allconnections were uniformly supported on rubber bearings along the four sides at an averagedistance of 30 mm from the edges. It is important to mention that this way the corners of the slabswere able to lift from the bearing stand and the flexural analysis sketch has to account this fact.Positioning of the shear reinforcement in the critical perimeter is plotted in Fig. 3. Both
configurations of shear reinforcement contained 5 rows of Ø10 bars at 100 mm spacing. The firstrow of shear reinforcement was placed at 50 mm from column faces which would mean 0.32d and
the last one at 3.54d , where d represents the effective depth of the slab.Compressive strength of concrete f cm, tested on 150 mm cubes, varied from 22.79 MPa to
43.89 MPa at 74 days after cast-in, representing the week of essays, as presented in Tab. 1.Uniaxial tensile strength of specimens, tested by means of splitting and flexure tests reached anaverage of f ctm=1.50 MPa. Both flexural and shear reinforcement were from the same sample groupand had average yielding strength f y,s = 475.60 MPa and an ultimate uniaxial strength f u,s = 638.58MPa Essay stand was compound of modular steel elements. Force was recorded during the entireload process through a force transducer HDM C6A, deflection at the middle point of thecompressed face of slab was read using an inductive standard displacement transducer HBMW200. Strains at faces of the slab were recorded using microcomparators. Deflection at midpoint
on the tension face and displacement at the supports were read using fleximeters. Load was applied
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fib Symposium PRAGUE 2011 Proceedings
Session 1-4: New Model Code ISBN 978-80-87158-29-6
6
have an area of A2=129 mm2 and a lever of 156 mm. Without accounting the bond conditions, ratio
between the products of these values is 1.576, giving an advantage to the DHSR transversalreinforced slabs.
Tab. 1
Results of the tested slabs
S p e c i m e n
S h e a r
r e i n f o r c e m e n t
f c m
M P a ]
D i s p l a c e m e n t
I S D T
[ m m ]
E f f e c t i v e
d i s p l a c e m e n t
[ m m ]
U l t i m a t e
r o t a t i o n [ o / o
o ]
L o a d a t f i r s t
c r a c k [ k N ]
V u , t e s t
[ k N ]
V u , f l e x
[ k N ]
V u , t e s t /
V u , f l e x
F a i l u r e M o d e
DB01 DHSR 31.37 25.28 19.08 32.9 110.00 517.20 487.01 1.062 FP
DB02 ST-B 43.62 18.66 13.16 22.69 100.00 557.40 493.57 1.129 FP
DB03 ST-B 22.79 18.63 11.35 19.57 140.00 561.30 478.25 1.174 F
DB04 DHSR 30.48 23.74 17.64 30.41 120.00 527.40 486.33 1.084 FP
DB05 N/A 43.89 12.40 4.55 7.84 90.00 495.00 493.75 1.002 (F)P
*DHSR – Double headed stud-rails, ST-B – Stirrup beam, N/A – Without shear reinforcement
4.2 Concrete strengths and strains
Distribution of concrete strains after radial and tangential direction was made using a total of 15analogue deformeters on the both tensioned and compressed faces of the slab. On the compressed
face results have been recorded at every load increment until ULS was reached and on thetensioned face over the SLS limit was passed.
It has been noticed that all shear reinforced connections reached ultimate strain ε cu of 3.5 at the faceof the column, point MC1, Fig. 5 b. Fig. 5a presents the strain on slab faces at a 2d distance fromthe column edge. DHSR group specimens were able do develop larger strains at the ultimate stage,showing larger rotational capacity. Concrete strain on the compressive face for ST-B specimengroup was 25% lower than the aforementioned. Strains read on the tensioned faces were highly
influenced by crack openings and propagation.As can be seen on Tab. 1 concrete designed strength was crossed for four of the five specimens. Itis showed that the type of shear reinforcement has more influence on final failure value than theconcrete strength. The fact that maximum failure load being was reached by DB03 makes thesupposition stronger (V u=561.30kN, f cm=22.79MPa).
Fig. 5 Concrete strain curves on compressed and tensioned face of the slab
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Proceedings fib Symposium PRAGUE 2011
ISBN 978-80-87158-29-6 Session 1-4: New Model Code
7
r
r 0
r q
s
V
r
m m
A
A
x
yield lines
bearing conditions
column
18 3 2 2
1 flexV m r
L
= − + −
20.5
1 s
ys
ck
f m f d
f
ρ ρ
= −
Fig. 6 Yield line paths
4.3 Failure modes.
Comparing the ultimate value of failure of the DB05 connection, which had no shearreinforcement, with other connections, their failure values were only with 4 - 13% higher. It isknown that for a flat slab to reach the maximum punching capacity it was to be fitted adequate bending stiffness in order to pass the flexural stage. Expected punching values predicted by ModelCode 2010, considering a maximum yielding strength of shear reinforcement less than 250+0.25d ,was 774.57 kN. As can be noticed none of the connections reached the maximum predicted punching shear capacity. It has been showed that for small flexural reinforcement rations (i.e. ρl =0.5% in this case) and V Test /V MC ratio of 0.5-1.0 the main recorded failures were flexural [fib bulletin 12]. Accounting this, a flexural failure analysis based on yield line theory was made. Inorder to find the exact flexural failure value Elstener and Hognestad (1956) specifications wereapplied. Slabs were considered simply supported and corners free to lift as plotted in Fig. 6.
Considering the range of V test /V flex ratios from (1), as presented in Tab. 1, it can be seen that
slabs DB01, DB02 and DB04 can be placed in flexural punching failure category and DB03 inflexural failure. If we consider the V test /V flex =1.00 the border point between flexural and punchingfailure, one can say that all connections failed in flexure. After failure was reached another chargewas applied to the column in order to get the main crack patterns. Specimens DB02 and DB03showed a post-punching behaviour creating a possible punching cone. As can be seen on the crack pattern map, of Fig. 7, the limit of the shear crack developed close to the supports with an averageslope of 21.45
ofor DB02 and 17.57
o for DB03. In this case the diagonal crack crossed three
perimeters of shear reinforcement. Having this value of the angle for DB03, one can sustain theentire shear force was transferred to the supports, failure occurring through shear reinforcement. Inopposition to his speciment DB01 and DB04 showed a strong flexural pattern.
Since the main purpose of this research was to find which of the two reinforcement types provide a higher rotational capacity, one can say that DHSR specimens showed a more ductile
mode of failure reaching an ultimate rotation over 30o/oo. ST-B specimen group showed an averagerotation capacity smaller with 33.25% than DHSR, but 2.69 times higher than the specimen without
shear reinforcement. (Tab. 1).
0302 01 04
Fig. 7 Crack patterns for tested slabs
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fib Symposium PRAGUE 2011 Proceedings
Session 1-4: New Model Code ISBN 978-80-87158-29-6
8
5 Conclusions
This paper presents a failure analysis upon four shear reinforced flat slab column connections with
thin plates. Both tension and integrity reinforcement ratio was 0.5%. Five perimeters of shearreinforcement, Ø10/100mm, under star dirrection were fitted in the critical perimeter. Averageeffective depth of the slab was 155 mm and designed concrete strength was C20/25. Accountingthis few conclusions can be drawn:
• Flat slab column connections with thin slabs having tension reinforcement of 0.5(i.e. d=155mm) and and high shear reinfoced ratio develop strong flexural behaviour failing inflexure. None of the shear reinforced connections reached the maximum punching capacity predicted by any design codes.
• For thin flat plates with medium reinforcement shear force is dirrected main to the supports,
angle of post-punching crack reaching values around 20oshowing a tendency of transferring the
entire shear force to the supports.
• As showed earlier concrete uniaxial compressive strength does not influence the final failure
values. Load-deflection behaviour was mainly influenced by the type of shear reinfocement thanthe concrete strength.
• As discussed in chapter 2 of the paper, bond conditions and anchorange length highly influencethe effectiveness of double headed stud-rails reinforcement. In situations when the state ofstresses crossed the SLS stage, perfect bond cannot be adopted.
• DHSR specimen group showed a better behaviour regarding rotational capacity reaching valuesabove 30o/oo. Specimens reinforced with stirrup beams showed rotations 50% smaller that thecompared ones, stud-rails showing better ductility behaviour.
References
[1] ***, fib Bulletin 55, 56 – Model Code 2010, First complete draft, 2010,[2] ***, fib Bulletin 12, Punching of Structural Concrete Slabs, Technical Report, August 2001
[3] A. Muttoni – Punching Shear Strength of Reinforced Concrete Slabs without TransverseReinforcement, ACI Structural Journal, V. 105, No. 4, July-August 2008.
[4] Ph. Menetrey, Numerical Analysis of Punching Failure in Reinforced Concrete Structures,Doctoral Thesis, EPFL, 1994
[5] C.E.Broms, Concrete Flat Slab and Footing Design Method for Punching and Detailing for
Ductility, Doctoral Thesis, KTH, 2005
[6] Min-Yuan Cheng, Punching Shear Strength and Deformation Capacity of Fiber ReinforcedConcrete Slab-Column Connections Under Earthquake-Type Loading, Annex 1, DoctorateThesis, The University of Michigan 2009,
Dan-Vasile Bompa, TS., C.Eng. Technical University of Cluj-Napoca
Faculty of Civil EngineeringDepartment of Concrete and SteelStructuresBarițiu 2540027 Cluj-Napoca, Romania
+40 265 401 513 +40 723 283 704☺ dan.bompa[at]bmt.utcluj.ro
URL http://dbproiect.ro/danbompa/
Prof. Dr. Ing. Traian One, C.Eng. Technical University of Cluj-Napoca
Faculty of Civil EngineeringDepartment of Concrete and SteelStructuresBarițiu 2540027 Cluj-Napoca, Romania
+40 265 401 513 +40☺ traianonet[at]gmail.comURL