Evaluation of punching shear in flat slabs

IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
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IC-RICE Conference Issue | Nov-2013, Available @ http://www.ijret.org 102
EVALUATION OF PUNCHING SHEAR IN FLAT SLABS
Alkarani1
, Ravindra. R2
1
Mtech student, 2
Assistant Professor, Department of Civil Engineering, R.V College of Engineering, Bangalore
alkakathare@gmail.com, ravimurd@gmail.com
Abstract
Flat-slab construction has been widely used in construction today because of many advantages that it offers. The basic philosophy in
the design of flat slab is to consider only gravity forces; this method ignores the effect of punching shear due to unbalanced moments
at the slab column junction which is critical. An attempt has been made to generate generalized design sheets which accounts both
punching shear due to gravity loads and unbalanced moments for cases (a) interior column; (b) edge column (bending perpendicular
to shorter edge); (c) edge column (bending parallel to shorter edge); (d) corner column. These design sheets are prepared as per
codal provisions of IS 456-2000. These design sheets will be helpful in calculating the shear reinforcement to be provided at the
critical section which is ignored in many design offices. Apart from its usefulness in evaluating punching shear and the necessary
shear reinforcement, the design sheets developed will enable the designer to fix the depth of flat slab during the initial phase of the
design.
Keywords: Flat slabs, punching shear, unbalanced moment.
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1. INTRODUCTION
Reinforced concrete slabs supported on columns were initially
developed in the United States of America and Europe in the
beginning of the 20th century [1].Their designs typically
included large mushroom-shaped column capitals to facilitate
the local introduction of forces from the slab to the column. In
the 1950s, flat slabs without capitals started to become
prevalent. Because of their simplicity, both for construction
and for use (simple formwork and reinforcement, flat soffit
allowing an easy placement of equipment, and installation
underneath the slab); they have become very common for
medium height residential and office buildings as well as for
parking garages. The design of flat slabs is mostly governed
by serviceability conditions on the one side (with relatively
large deflections in service) and by the ultimate limits state of
punching shear (also called two-way shear) on the other side.
These two criteria typically lead to the selection of the
appropriate slab thickness.
Punching shear failure is caused by the vertical shear and
unbalanced moment borne by the slab-column connection,
which makes the flat-slab connections a weak link in the
whole flat-slab structure, and then leading to serious damage
or even collapse. Unbalanced moments commonly occur in
buildings with flat slabs, caused by unequal spans or loading
on either side of the column. Differences of temperature or
differential creep between two adjacent floors results in
differential displacements of the top and bottom of the
columns, which induce moments in the slab-column
connection, even if the columns, as is assumed for this study,
do not participate in the horizontal load resisting system. In
the presence of such moments, the phenomenon of punching
becomes unsymmetrical, and the punching strength of the slab
decreases. This phenomenon has been described by
researchers [2].
1.1 Punching Shear Due To Unbalanced Moment
The analysis for punching shear in flat slabs is assumed that
the shear force, Vu was resisted by shearing stresses uniformly
distributed around the perimeter bo of the critical section, a
distance d/2 from the face of the supporting column. If
significant moments are to be transferred from the slab to the
columns, as would result from unbalanced gravity loads on
either side of a column or from horizontal loading due to
wind or seismic effects, the shear stress on the critical section
is no longer uniformly distributed.
The situation can be modeled as shown in Fig. 1. Here, Vu
represents the total vertical reaction to be transferred to the
column, and Mu represents the unbalanced moment to be
transferred. The vertical force Vu causes shear stress
distributed more or less uniformly around the perimeter of the
critical section as assumed earlier, represented by the inner
pair of vertical arrows, acting downward. The unbalanced
moment Mu causes additional loading on the joint,
represented by the outer pair of vertical arrows, which is
added to the shear stress caused by Vu.

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Fig.1 Combined action of shear and shear due to moment transfer at interior column
According to IS 456-2000, Clause 31.3.3, the moment
considered to be transferred by flexure is
... (1)
Where
Where
For Interior column
For Edge column
For Corner column
The fraction of moment transferred by the variation of shear
stress about bending axis ( ) is given in terms of the total
moment ( ) transferred by eccentricity of shear about the
centroid of the critical section for shear.
(2)
Where
According to the IS 456-2000, the shear stress may be taken
linearly varying about the centroid of the section (Fig.1c). The
shear stress at any point in the periphery arises from two
effects, namely, that due to the shear force Vu and that arising
from transfer of unbalanced moment to column. Combining
these two, the maximum shear stress τ is given by,
(3)
The value of J is computed from SP: 24-1983 Explanatory
hand book to IS 456-2000.
For a structure to be safe, the punching shear stress should be
less than the safe value. The ultimate safe value of the
punching shear of concrete is given by the least value of the
following two equations (IS 456 Clause 31.6.3)
(4)
(5)
Eqn.(4) is the initial value suggested for a square column but
research has shown that its magnitude is affected by the shape
of the column so that it can be expressed for a rectangle by
Eqn.(5), where ratio of short side to long side of column
capital. The code requires that the shear stresses should be
investigated at successive sections away from the support, but
does not indicate suitable intervals. It is suggested that these
successive sections may be taken at intervals of 0.75 d (SP:
24-1983 Explanatory hand book to IS 456-2000).

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If the shear stress exceeds 1.5 , the flat slab shall be
redesigned.
2. ALGORITHM
STEP 1:- Input- slab thickness (D), size of column ( ),
factored design load (V), unbalanced moment ( , ),
characteristic strength ( , ), section (s), length of opening
(c), diameter of steel bars (d*), diameter of stirrups(d’)
STEP 2:- Compute effective depth
d= D-clear cover-d*/2
STEP 3:- Compute perimeter of shear zone
;
STEP 4:- Compute net length of shear zone
STEP 5:- Compute coefficients
;
STEP 6:- Compute bending moment and torsion moment
;
;
STEP 7:- Compute centriodal distance
X=a/2; y=b/2
STEP 8:- Compute moment of inertia
(As per the code IS 456-2000)
STEP 9:- Compute punching shear
;
STEP 10:- Compute β=ratio of shorter side to longer side of
the column
STEP 11:- Compute allowable shear stress
STEP 12:- Check for safety, depth and shear links
If max ( , < , “safe”, “unsafe”
If max ( , “revise the (go to step
1), “depth ok”
If max ( , and max
( , > , “provide shear links”,
“no shear links is required”
STEP 13:- Terminate
STEP 13:- If shear link is to be provide, compute shear force
at the distance d/2
STEP 14:- Compute area of steel required
STEP 15:- Compute area of steel required at each face of the
column Asve
STEP 16:- Compute area of single stirrup
STEP 17:- Compute spacing of bars
STEP 18:- Check for minimum spacing as per the code IS 456
.
STEP 19:- Terminate

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2.1 Parametric Study of Punching Shear for Different
Aspect Ratio of Slab
A parametric study is performed to evaluate the magnitude of
punching shear due to unbalanced moments. The main
parameter of the study is the aspect ratio of the slab and the
corresponding variation of punching shear for the four types of
column as described earlier. Table 1 summarizes the
geometrical parameters used in the study and the results
obtained. The loading on the slab and the unbalanced
moments considered are the same for all the cases.
Table1. Variation of punching shear with respect to aspect ratio
Panel dimensions
L2 / L1 Aspect ratio
Punching shear(N/mm2
)
Internal
column
Corner
column
Edge column (bending
parallel to shorter edge)
Edge column (bending
perpendicular to shorter edge)
7/7 1 2.79 18.21 4.29 9.70
8/7 1.14 3.42 22.4 5.39 11.09
9/7 1.29 4.09 26.98 6.61 12.49
10/7 1.43 4.82 31.96 7.95 13.88
11/7 1.57 5.60 37.34 9.41 15.27
12/7 1.71 6.44 43.11 10.99 16.76
13/7 1.86 7.34 49.28 12.70 19.54
14/7 2 8.28 55.84 14.52 22.53
It can be concluded from Table 1 that as the aspect ratio
increases, the punching shear in the slab also increases.
Punching shear is found to be more critical at corner columns
and least at interior columns.
CONCLUSIONS
Design sheets developed will help the designer to check for
punching shear and calculate the shear reinforcement as per IS
456-2000 for different conditions of column locations. The
program is validated by manual calculations and the results are
found to be comparable. The design sheets developed will
enable the designer to fix the depth of flat slab during the
initial phase of the design in a simple manner.
REFERENCES
[1] Aurelio Muttoni; “Punching Shear Strength of
Reinforced Concrete Slabs without Transverse
Reinforcement”, ACI Structural Journal, Title no. 105-
S42, pp. 440-450, July-August 2008.
[2] Gaston Kruger, Olivier Burdet, Renaud Favre;
“Punching strength of R.C. Flat slabs with moment
transfer”, 2nd Intern. Ph.D. Symposium in Civil
Engineering, Budapest 1998, pp. 1-8, Budapest,
Hungary, 1998.
[3] Vikunj K.Tilva, B. A. Vyas, Parth Thaker;
“Enhancing the punching shear resistance of flat plates
using shear heads, shear stud rails and shear stirrups: a
comparative study”, Volume 04, No 06 SPL, pp. 596-
599, October 2011.
[4] IS 456:2000, “Indian standard code of practice for plain
and reinforced concrete”, Fourth Revision, Bureau of
Indian Standards, New Delhi, July 2000.

Evaluation of punching shear in flat slabs

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