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TECHNICAL PAPER

SAF collapse mechanism, a one-way BSF long span collapse
2QUKVKXG [KGNF
NKPGU mechanism can occur, as shown in Figure 4. Similarly, the one-way
continuous slab behaviour expected for the system in Figure 2 at
service loads (due to the presence of stiff beams) can transform
OO into a two-way large slab panel behaviour at collapse, with the

OO
predominant bending occurring in the orthogonal direction,
with yield lines forming in the slab (as would be expected in the
0GICVKXG
[KGNF NKPGU absence of the supporting beams), along with plastic hinges
developing at the midpoints of the beams – a two-way BSF
collapse mechanism, as shown in Figure 5. The SAF collapse
OO OO
mechanism will govern only if the beams are so heavily reinforced
Figure 3: Possible SAF mechanism at the limit state of collapse. as to prevent the formation of plastic hinges in the beams.

After the slabs have been designed and detailed, the next step #
in conventional design practice is to design the beams. The #
gravity loads from the slabs are assumed to be transmitted to
the supporting beams, using the ‘tributary area’ concept, and 2NCUVKE 2NCUVKE /CUQPT[ RKNNCT
JKPIGU
the beams are designed as simply supported beams . For JKPIGU /CUQPT[ RKNNCT
[1]
 Þ OO
example, in the design of the long span beams in Figure 1,  Þ OO
half of the total slab load can be assumed to be transmitted

as uniformly distributed loading on each long span beam. OO OO

The beam section is commonly assumed to be rectangular, 2QUKVKXG [KGNF NKPG
although it would be more accurate and economical to consider 2QUKVKXG [KGNF NKPG 5GEVKQP # #
# 5GEVKQP # #
a flanged section (L-beam in Figure 1 and T-beam in Figure #  Ý OO
2). Additional loads, such as those from walls above, may also  Ý OO
have to be considered in the beam design, if applicable. It Figure 4: 1way BSF-long collapse mechanism in an isolated system.
is tacitly assumed in the design that if the long span beams
 Ý OO  Ý OO
(with ‘under-reinforced’ sections) were to collapse at the limit  Ý OO  Ý OO
state, they would do so with ‘plastic hinges’ forming at their
mid-span locations. It is not realised that this mode of collapse
2NCUVKE
of the long span beams is kinematically incompatible with JKPIGU
the expected mode of collapse of the slab (Figure 3a); both 2NCUVKE
JKPIGU

cannot occur simultaneously. The yield line formations shown in Ý  Þ OO

Ý  Þ OO
Figure 3 tacitly assume that the supporting beams do not have 2QUKVKXG
plastic hinges forming in them (i.e., they remain elastic, with 2QUKVKXG [KGNF NKPG
no significant deflections); such collapse mechanisms may be [KGNF NKPG
referred to as ‘slab-alone failure’ (SAF). Þ OO
Þ OO
If the collapse of the long span beams were to occur (with plastic
hinges at their midpoints), they will bring down the slabs along Figure 5: 2way BSF collapse mechanism in continuous system.
with them, with yield lines in the slab intersecting with the plastic
hinge locations in the beams. The likely collapse mechanism A recent paper published by the authors in the ACI Structural
[3]
would be as shown in Figure 4 for the isolated system (Figure 1), Journal on isolated two-way beam-slab systems establishes
and as shown in Figure 5 for the continuous system (Figure 2). that while the relative beam-slab stiffness governs the behaviour
Such combined ‘beam-slab failure’ (BSF) mechanisms are rarely up to service loads, the subsequent load-deflection behaviour
anticipated by the designer, except in rare situations where the and final collapse mechanism are governed by the relative
long span beams are very shallow. This paper shows that such beam-slab flexural strength. This has been established both
‘unexpected’ BSF collapse mechanisms are not only possible, experimentally and theoretically (using yield line theory). In most
but are very likely, even in the case of conventionally designed cases of conventionally designed isolated beam-slab systems,
systems with stiff beams. The one-way slab behaviour (along the the combined BSF collapse mechanism (Figure 4) is more likely
short span direction) expected for the isolated system in Figure to occur. Of the seven beam-slab specimens tested, five failed
1 is valid at service loads, but can transform into a completely by the combined mechanism (Figure 4), as shown in Figure 6a,
different behaviour at the limit state of collapse. Instead of a and only two specimens, which were deliberately designed

The IndIan ConCreTe Journal | MarCh 2020 15