Page 11 - Open-Access-Mar-2020

TECHNICAL PAPER

2way BSF Mechanism (Figure 5): R = 1.80, m x = 8.32 kNm/m, m y (2way BSF) mode. In design practice, the slab reinforcement
= 19.52 kNm/m, μ = 2.35, r = 2.39, n = 4, ηc = 42.16, M x = 496.3 is first fixed (starting with the minimum code-specified
kNm. Using Equation 5, the ultimate load, w = 18.73 kN/m 2 requirement), and based on the values of m x and m y, the design
moment capacities in the beams can be appropriately arrived at,
The ultimate load capacities, corresponding to the three assuming 2way BSF mode. However, after actual detailing of the
possible collapse mechanisms, are summarised in Table beam reinforcement (actual steel area will exceed the required
3a (in the range 18.73 to 29.93 kN/m ), and are all found to area), it is possible that an alternative BSF collapse mechanism
2
exceed, by large margins, the factored design load of 14.25 may prevail, although the beam design remains valid. In some
kN/m , suggesting that the slab has been over-designed. The cases, where the slab aspect ratio exceeds 2.0, it is possible that,
2
corresponding load factors (over the service load, w service = 9.5 as per calculations, the SAF collapse mechanism may govern,
kN/m ), are in the range, 1.97 to 3.15. The most likely collapse requiring the beams to appropriately redesigned. In the interest
2
mechanism, corresponding to the lowest load factor of 1.97, is of rational and economical design, it is necessary to predict
the combined 2way-BSF collapse mechanism (Figure 5), and not correctly the most likely collapse mechanism and corresponding
the expected one-way slab failure of either the end span or the load factor and also estimate the total consumption of steel (in
interior span. slabs and beams) in order to arrive at the optimal solution. This
is demonstrated in the current study.
In summary, these two design examples show that the prevailing
design basis (one-way slab behaviour along the short span) is 8 IsOLAteD BeAM-sLAB sYsteM
neither rational nor economical. With a proper understanding
of the behaviour at the limit state of collapse, aided by yield line Option 1
analysis that also includes plastic hinge formation in the beams, As shown earlier, the steel provided in the conventional design
the beam-slab system can be more rationally and economically in the short span direction (8Y @ 90 mm c/c) is excessive,
designed, satisfying all the code requirements.
and can be reduced significantly. We begin by exploring the
possibility of providing the same minimum reinforcement (8Y
7. pROpOseD eCONOMICAL AND RAtIONAL @ 250 mm c/c) in the short span direction as in the long span
DesIGN direction, giving design moment capacities, m x = 8.90 kNm/m

In the two examples shown, the proportioning of the beams and m y = 8.32 kNm/m.
and slabs have been based on satisfying adequately limiting The required beam-slab relative strengths, and hence the design
deflection criteria, and in the proposed design, the same slab
thickness and beam sizes are adopted, with a focus on reducing moment capacities for the long span and short span beams can
reinforcing steel, and yet satisfying the strength requirements at now be derived, assuming 2way BSF, using Equations 2 and 3
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the limit state of collapse. This essentially implies that the load respectively, as follows, considered w u = 14.25 kN/m , q u = 6.75
factor should be not less than 1.5 and the mode of failure should kN/m, l x = 3.526 m, r = 2.30, μ = 0.93:
be ductile. M 2 2
u
by w 2 q rl x 788 M 247 3 . kNm
.
The most structurally efficient design is one that utilises the y ml u l x 16 m x 2 by
xx
flexural capacities of the slab (in both directions) and beams
(long span and short span) to the fullest extent possible. This M bx w 2 q rl x 2 r 205 M 6433kNm
u
.
.
ideally corresponds to the combined two-way beam-slab failure x ml u rl x 16 m x 2 bx
xx
table 3: Ultimate loads of continuous beam-slab system for the possible collapse mechanisms
COllApSE (A) CONVENTIONAl DESIGN (B) pROpOSED DESIGN
MEChANISM ulTIMATE lOAD ACTuAl lOAD FACTOR = ulTIMATE lOAD ACTuAl lOAD FACTOR =
INTENSITY (w) w INTENSITY (w) w
(kN/M ) w service (kN/M ) w service
2
2
SAF-end span > 29.20* > 3.07* > 17.88* >1.88*
SAF-interior span > 29.93* > 3.15* >21.74* >2.29*

2way BSF 18.73 1.97 16.62 1.75

* Values are likely to be higher in reality on account of tensile membrane action (which is ignored in the present study)

The IndIan ConCreTe Journal | MarCh 2020 19