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TECHNICAL PAPER

3. YIeLD LINe ANALYsIs FOR BeAM-sLAB 3.1.3 Combined BSF collapse mechanism
FAILURe (BSF) (2way BSF)
The expression for the collapse load per unit area, w, for the
3.1 Isolated Beam-slab system
2way BSF collapse mechanism shown in Figure 7b, is given
3.1.1 BSF collapse mechanism along long span below [3, 7] :
(1way BSF-long) m 2 q
w 4 x y x u l
l
r 2
y
x
The expression for the collapse load per unit area, w, for the rl x r r rl x 2 (4)
2
1way BSF-long collapse mechanism shown in Figure 4, is given
below [3, 7, 8] : 4. CONtINUOUs BeAM-sLAB sYsteM
w 8 m x 2 y 2 q 4.1 Two way Beam-Slab Collapse Mechanism
rl x 2 l x (2) (2way BSF)
2
where q is the total line load acting on the beam (including The expression for the collapse load per unit area, w, is given
self-weight) and α y is the beam-slab relative strength parameter, below, in terms of the aspect ratio R (L y/L x) and number of slab
defined as the ratio of the sagging moment capacity M y of the panels along short span n for the 2way BSF collapse mechanism
[7]
long span beam and the total short span moment capacity of shown in Figure 5 is given below :
the slab, m xl x : mR
2
w 6 x (5)
M nL y 2 c
ml y
y
xx
where
3.1.2 BSF collapse mechanism along short span 1 r 1 r 2
3
4 (5a)

c
(1way BSF-short) R R

The expression for the collapse load per unit area, w, for the n n 1
1way BSF-short collapse mechanism shown in Figure 7a, is given x
below [3, 7] :
and α x is the beam-slab relative strength parameter defined as
w 8 m x r 2 x 2 q the ratio of sagging moment capacity M x of the beams and the
rl x 2 l y (3) total long span moment capacity of the slab [7, 9] :

M
where α x is the beam-slab relative strength parameter defined as x (5b)
x
yx
the ratio of the sagging moment capacity M x of the short span ml
beam and the total short span moment capacity of the slab [3, 4] :
5. CONveNtIONAL DesIGN – LIKeLY
M
ml x COLLApse MeCHANIsM
x
xx
5.1 Isolated Beam-slab system
According to conventional design practice, the slab in the
isolated system in Figure 1 is designed as a one-way slab,
spanning in the short span direction. The effective span l x works
2QUKVKXG out to 3526 mm, considering the effective depth of the slab to
[KGNF NKPGU
OO be 160 – 30 – 8/2 = 126 mm (assuming 30 mm clear cover and 8
OO
mm dia. bars). Considering the imposed loads as indicated in
Figure 1, and a load factor of 1.5 (as per IS 456 ), the total
[2]
design factored load w u works out to 14.25 kN/m , whereby the
2
wl 2
design bending moment is obtained as m ux = ux = 22.15 kNm/m.
8
Assuming M25 concrete and Fe 415 steel, the required area of
OO OO steel works out to 525.4 mm /m . Hence, it suffices to provide
2
[1]
C D
8Y @ 90 mm c/c (558.5 mm /m) in the short span direction and
2
Figure 7: Alternate collapse mechanisms (a) 1way BSF-short (b) 2way BSF. distribution steel, 8Y @ 250 mm c/c in the long span direction of
The IndIan ConCreTe Journal | MarCh 2020 17