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TECHNICAL PAPER

the slab, with nominal steel at the beam-slab interface at the corresponds to the 1way BSF-long mode, which has a load
top, as shown in Figure 1. factor of 1.96. There is scope for a more economical design,
where the load factor is close to 1.5. The proposed design, with
The long span beam is typically designed as a simply supported this objective, is described later.
beam, having an effective span of 8300 mm. The gravity load
effects from the slab are assumed to be transmitted to each of 6. CONtINUOUs BeAM-sLAB sYsteM
the two long span and short span beams with trapezoidal and
triangular distributions respectively. Including the self weight of The slabs in the continuous beam-slab system shown in Figure
the beam, the design bending moment at mid-span is obtained 2 with relatively stiff beams and number of slab panels, n = 4,
as 271 kNm and the maximum shear force as 114 kN. Commonly, are typically designed in practice as a one-way continuous slab
the beam is designed as a rectangular section. Assuming a clear system. This is a textbook problem and the design calculations,
cover of 30 mm, M 25 concrete and Fe 415 steel, it suffices to complying with the code requirements, assuming M25 concrete
[1]
provide 2 – 28Y plus 1 – 25Y at the bottom (A st = 1722.4 mm ), and Fe 415 steel, are explained in detail in the book . The
2
and nominal 2-12Y at top, with nominal stirrups 8Y @ 300 mm rebars provided in the end span and interior spans of the slab
c/c, as shown in Figure 1. It is possible to reduce the bottom in the short span direction are summarised in Table 2, along
steel slightly (to 3-25Y) by considering the section to act as a with the corresponding moment capacities, m x. In the long span
flanged L-section, although this is not commonly practised. direction, distribution steel of 8Y @ 250 mm c/c (with m y = 8.32
Carrying out a similar analysis for the short span beams, it can be kNm/m) is provided.
shown that it is adequate to provide 2 – 16Y at the bottom and
nominal 2 – 12Y at top, with nominal stirrups 8Y @ 300 mm c/c. table 2: Reinforcement details in continuous slab
system [1]
The ultimate load capacities for various possible collapse lOCATION END SpAN INTERIOR SpAN
mechanisms can now be estimated using yield line analysis
(Equations 1, 2, 3 and 4). Considering the parameters, r = 2.30, end mid- first int. mid- int.
m x = 23.53 kNm/m, m y = 8.32 kNm/m, μ = 0.35; i x = i y = 0.5, M y support span support span support
= 291.9 kNm, M x = 77.2 kNm, q = 4.5 kN/m, α x = 0.93, α y = 3.52, Spacing of (top) (bottom) (top) (bottom) (top)
the results obtained are summarised in Table 1. bars provided
8Y 220 110 110 150 110
The ultimate load capacities in Table 1 (in the range 18.60 to m x (kNm/m) 10.08 19.52 19.52 14.56 19.52
30.55 kN/m ) are all found to exceed the factored design load of
2
14.25 kN/m . Although the code requirement is for a load factor As similar to the isolated system, the design bending moment in
2
2
of 1.5 (over the service load, w service = 9.5 kN/m ), the actual load the beam is obtained as 470 kNm and maximum shear force as
factor, corresponding to the various collapse mechanisms, are as 194 kN, having an effective span of 8230 mm. Considering the
shown in Table 1. beam as having a rectangular cross-section and assuming a clear
cover of 40 mm, M 25 concrete and Fe 415 steel, it suffices to
2
table 1: Ultimate loads of conventionally designed provide 2–32Y and 2–25Y at the bottom (A st = 2590.2 mm ), and
nominal 2-12Y at top, with nominal stirrups 8Y @ 300 mm c/c,
isolated beam-slab system
as shown in Figure 2. It is possible to reduce the bottom steel
COllApSE ulTIMATE lOAD ACTuAl lOAD w slightly (to 2-32Y and 1–25Y) by considering the section to act as
MEChANISM INTENSITY (w) (kN/m ) FACTOR = w service a flanged T-section.
2
SAF > 30.55* > 3.22*
Three possible collapse mechanisms, as shown in Figure 3b
1way BSF-long 18.60 1.96
and Figure 5, need to be investigated, using yield line analysis
1way BSF-short 26.28 2.77 (Equations 1 and 5). The relevant parameters and the ultimate
2way BSF 22.44 2.36 load intensity, for each mechanism, are summarised below.
* Values are likely to be higher in reality on account of tensile membrane
action (which is ignored in the present study). SAF collapse mechanism in the end span (Figure 3b): r = 2.34,
m x = 19.52 kNm/m, m y = 8.32 kNm/m, μ = 0.43, i x1 = 0.52, i x2 = 1,
Although the slab has been designed assuming that it will i y1 =i y2 = 0 and η = 2.99. Using Equation 1, the ultimate load, w =
undergo SAF mode, this mode of collapse is most unlikely, 29.20 kN/m 2
having the highest load factor of 3.22 (or even higher, if the
effect of tensile membrane action is included). The slab has SAF collapse mechanism in the interior span (Figure 3b):
been over-designed; i.e., excessive steel has been provided in r = 2.39, m x = 14.56 kNm/m, m y = 8.32 kNm/m, μ = 0.57, i x1 = i x2
the short span direction, assuming one-way slab behaviour in = 1.34 and η = 3.96. Using Equation 1, the ultimate load,
the short span direction. The most likely collapse mechanism w = 29.93 kN/m 2

18 The IndIan ConCreTe Journal | MarCh 2020