Annex D(Clauses 23.4 and 36.1.2) SLABS SPANNING IN TWO DIRECTIONS

NBC 2016 (SP 7:2016) Volume 1

2016 · PDF page 875

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D-1 Restrained Slabs

D-1.0 When the corners of a slab are prevented from lifting, the slab may be designed as specified in D-1.1 to D-1.11.

D-1.1 The maximum bending moments per unit width in a slab are given by the following equations:

M _ {\mathrm{x}} = \alpha_ {\mathrm{x}} w l _ {\mathrm{x}} ^ {2}

M _ {\mathrm{y}} = \alpha_ {\mathrm{y}} w l _ {\mathrm{x}} ^ {2}

where

$\alpha_{x}$ and $\alpha_{y}$ are coefficients given in Table 30;

$w =$ total design load per unit area;

$M_{\mathrm{x}}, M_{\mathrm{y}} =$ moments on strips of unit width spanning $l_{\mathrm{x}}$ and , respectively; and

$l_{x}$ and $l_{y}$ = lengths of the shorter span and longer span respectively.

D-1.2 Slabs are considered as divided in each direction into middle strips and edge strips as shown in Fig. 31, the middle strip being three-quarters of the width and each edge strip one-eighth of the width.

D-1.3 The maximum moments calculated as in D-1.1 apply only to the middle strips and no redistribution shall be made.

D-1.4 Tension reinforcement provided at mid-span in the middle strip shall extend in the lower part of the slab to within 0.25l of a continuous edge, or 0.15l of a discontinuous edge.

D-1.5 Over the continuous edges of a middle strip, the tension reinforcement shall extend in the upper part of the slab a distance of 0.15l from the support, and at least 50 percent shall extend a distance of 0.3l.

D-1.6 At a discontinuous edge, negative moments may arise. They depend on the degree of fixity at the edge of the slab but, in general, tension reinforcement equal to 50 percent of that provided at mid-span extending 0.1l into the span will be sufficient.

D-1.7 Reinforcement in edge strip, parallel to that edge, shall comply with the minimum given in Section 5A(C) and the requirements for torsion given in D-1.8 to D-1.10.

D-1.8 Torsion reinforcement shall be provided at any corner where the slab is simply supported on both edges meeting at that corner. It shall consist of top and bottom reinforcement, each with layers of bars placed parallel to the sides of the slab and extending from the edges a minimum distance of one-fifth of the shorter span. The area of reinforcement in each of these four layers shall be three-quarters of the area required for the maximum mid-span moment in the slab.

D-1.9 Torsion reinforcement equal to half that described in D-1.8 shall be provided at a corner contained by edges over only one of which the slab is continuous.

D-1.10 Torsion reinforcements need not be provided at any corner contained by edges over both of which the slab is continuous.

D-1.11 Where $l_{\mathrm{y}} / l_{\mathrm{x}}$ is greater than 2, the slabs shall be designed as spanning one way.

D-2 Simply Supported Slabs

D-2.1 When simply supported slabs do not have adequate provision to resist torsion at corners and to prevent the corners from lifting, the maximum moments per unit width are given by the following equation:

M _ {\mathrm{x}} = \alpha_ {\mathrm{x}} w l _ {\mathrm{x}} ^ {2}

l_{y}

2

Table 30Bending Moment Coefficients for Rectangular Panels Supported on Four Sides with Provision for Torsion at Corners (Clauses D-1.1 and 23.4.1)

Sl No.	Case No.	Type of Panel and Moments Considered	Short Span Coefficients $\alpha_x (Values of l_y/l_x)$								Long Span Coefficients $\alpha_y for All Values of l_y/l_x$
Sl No.	Case No.	Type of Panel and Moments Considered	1.0(4)	1.1(5)	1.2(6)	1.3(7)	1.4(8)	1.5(9)	1.75(10)	2.0(11)	Long Span Coefficients $\alpha_y for All Values of l_y/l_x$
(1)	(2)	(3)
i)	1	Interior panels:
		Negative moment at continuous edge	0.032	0.037	0.043	0.047	0.051	0.053	0.060	0.065	0.032
		Positive moment at mid-span	0.024	0.028	0.032	0.036	0.039	0.041	0.045	0.049	0.024
ii)	2	One short edge discontinuous:
		Negative moment at continuous edge	0.037	0.043	0.048	0.051	0.055	0.057	0.064	0.068	0.037
		Positive moment at mid-span	0.028	0.032	0.036	0.039	0.041	0.044	0.048	0.052	0.028
iii)	3	One long edge discontinuous:
		Negative moment at continuous edge	0.037	0.044	0.052	0.057	0.063	0.067	0.077	0.085	0.037
		Positive moment at mid-span	0.028	0.033	0.039	0.044	0.047	0.051	0.059	0.065	0.028
iv)	4	Two adjacent edges discontinuous:
		Negative moment at continuous edge	0.047	0.053	0.060	0.065	0.071	0.075	0.084	0.091	0.047
		Positive moment at mid-span	0.035	0.040	0.045	0.049	0.053	0.056	0.063	0.069	0.035
v)	5	Two short edges discontinuous:
		Negative moment at continuous edge	0.045	0.049	0.052	0.056	0.059	0.060	0.065	0.069	-
		Positive moment at mid-span	0.035	0.037	0.040	0.043	0.044	0.045	0.049	0.052	0.035
vi)	6	Two long edges discontinuous:
		Negative moment at continuous edge	-	-	-	-	-	-	-	-	0.045
		Positive moment at mid-span	0.035	0.043	0.051	0.057	0.063	0.068	0.080	0.088	0.035
vii)	7	Three edges discontinuous (One long edge continuous):
		Negative moment at continuous edge	0.057	0.064	0.071	0.076	0.080	0.084	0.091	0.097	-
		Positive moment at mid-span	0.043	0.048	0.053	0.057	0.060	0.064	0.069	0.073	0.043
viii)	8	Three edges discontinuous (One short edge continuous):
		Negative moment at continuous edge	-	-	-	-	-	-	-	-	0.057
		Positive moment at mid-span	0.043	0.051	0.059	0.065	0.071	0.076	0.087	0.096	0.043
ix)	9	Four edges discontinuous:
ix)	9	Positive moment at mid-span	0.056	0.064	0.072	0.079	0.085	0.089	0.100	0.107	0.056

Chart

FIG. 31 DIVISION OF SLAB INTO MIDDLE AND EDGE STRIPS

PART 6 STRUCTURAL DESIGN — SECTION 5 CONCRETE: 5A PLAIN AND REINFORCED CONCRETE

M _ {\mathrm{y}} = \alpha_ {\mathrm{y}} w l _ {\mathrm{x}} ^ {2}

where

$M_{\mathrm{x}}, M_{\mathrm{y}}, l_{\mathrm{x}}, l_{\mathrm{y}}$ are same as those in D-1.1, and $\alpha_{\mathrm{x}}$ and $\alpha_{\mathrm{y}}$ are moment coefficients given in

Table 31.

D-2.1.1 At least 50 percent of the tension reinforcement provided at mid-span should extend to the supports. The remaining 50 percent should extend to within $0.1l_{x}$ or $0.1l_{y}$ of the support, as appropriate.

Table 31Bending Moment Coefficients for Slabs Spanning in Two Directions at Right Angles, Simply Supported on Four Sides

(Clause D-2.1)
$l_y/l_x$	1.0	1.1	1.2	1.3	1.4	1.5	1.75	2.0	2.5	3.0
$\alpha_x$	0.062	0.074	0.084	0.093	0.099	0.104	0.113	0.118	0.122	0.124
$\alpha_y$	0.062	0.061	0.059	0.055	0.051	0.046	0.037	0.029	0.020	0.014