optimum dimensions of waffle slab for medium size …€¦ · slab, ribs and band beams. 2.3...

ASIAN JOURNAL OF CIVIL ENGINEERING (BUILDING AND HOUSING) VOL. 6, NO. 3 (2005) PAGES 183-197

OPTIMUM DIMENSIONS OF WAFFLE SLAB FOR MEDIUM SIZE FLOORS

J. Prasad∗, S. Chander and A.K. Ahuja Department of Civil Engineering, I.I.T.R., Roorkee, India

ABSTRACT

Waffle slab has had its genesis in a rather thick solid-slab floor from which the bottom layer concrete in tension is partially replaced by their ribs along orthogonal directions. The ribs are reinforced with steel to resist flexural tensile stresses. The dimensions and spacing of ribs are decided in a manner so as to achieve better load distribution without requiring the shear reinforcement. The present paper elaborates the results obtained from the analytical study carried out on waffle slab medium size floor system with a view to achieve the optimum dimensions of rib spacing, its depth and width. The waffle slab has been considered as monolithically connected to band beams. Feasibility of structural design of members has been ensured under the provision of IS: 456-2000.

Keywords: waffle slab, medium size floor, R.C.C. slab, optimization

1. INTRODUCTION

1.1 R.C. Floors Structural floor systems made of Reinforced Cement Concrete are required to efficiently transmit the floor loads to the vertical systems through Shear, Bending and Torsion resisting capacities. In addition to these strength requirements, they are required to satisfy the deformation criteria also, in terms of low deflection and crack width. This entails into the study of the role of various structural elements specially provided to meet one or more of the requirements in the domain of strength or deformation. In case of medium span (6 to 12 m) floor plans, the structural elements playing specific roles are (i) Column Capital and Drop Panel in Flat Slab Floor System (Figure 1), (ii) Rib stiffness, Rib spacing and Band Beams in Waffle Slab floor system (Figure 2), (iii) RC Column shape and size, (iv) relative stiffness of the horizontal system to that of the vertical system and (v) connectivity of the horizontal system with the vertical systems.

1.2 Waffle slab As mentioned above, waffle slab floor system is quite suitable for medium size floors. These ∗ Email-address of the corresponding author: [email protected]

J. Prasad, S. Chander and A.K. Ahuja 184

may be rested on a system of vertical supports e.g. walls, in which case the floor moment and deflection get concentrated near the mid-span. The floor, on the other hand, can be framed into the vertical structural system such that there is lateral shifting of moment and deflection from the mid-span zone towards the supports. Thus, floor framing with the help of wide band-beams rigidly connected to a system of columns becomes an obvious choice.

Figure 1. Flat slab floor

2. PARAMETRIC STUDY

2.1 Structural dimensions In order to carry out parametric investigation to arrive at optimum values of rib number and dimensions for a given floor size, the waffle slabs with square floor plans of size 6×6 m, 7×7 m and 8×8 m have been considered keeping the residential and office floors in mind. Larger spans would need much higher floor thickness, which would be suitable for Grid floor structural system.

Top slab of the waffle slab floors may be kept at its minimum thickness from construction point of view. It has been kept as 65 mm for all the floors studied herein. Width of the ribs has been taken as 100 mm (Figure 3). The shape of ribs is considered as rectangular during analysis, although in actual practice it may be slightly tapered. The rib depth has been varied in the range from 130 mm to 260 mm with a regular increment of 10 or 20 mm. The overall floor depth, thus, varies from 195 mm to 325 mm.

OPTIMUM DIMENSIONS OF WAFFLE SLAB FOR MEDIUM SIZE FLOORS...

185

(a) (b)

Figure 2. Waffle slab floors: (a) without band beams and (b) with band beams

Figure 3. Detailed view of a waffle slab floor with band beams


The number of ribs has been taken as five at the minimum with an increment of two until all the structural requirements are adequately satisfied for the particular floor plan. It may be considered prudent to increase the rib depth after a certain number of rather closely spaced ribs are found to be inadequate in meeting a particular structural requirement. The maximum number of ribs for the largest span is, therefore, taken to be nine. Waffle slabs are assumed to have band beams along all four edges. Width of the band beams is taken as 1000 mm extending 500 mm from the center of the columns on both sides and depth as equal to total thickness of floor. Table 1 summarizes the structural dimensions of the floors studied herein.

Table 1. Dimensions of structural elements

Floor size (m) No. of ribs Sl.

No. Lx Ly Nx Ny

Rib spacing (bc)

(mm)

Effective flange width

(bf) (mm)

Rib depth (Dr)

(mm)

1 6 6 5 5 850 850 130, 140, 150, 160

2 6 6 7 7 638 638 130, 140, 150, 160

3 6 6 9 9 510 510 130, 140, 150, 160

4 7 7 5 5 1017 880 160, 180, 200, 220

5 7 7 7 7 763 763 160, 180, 200, 220

6 7 7 9 9 610 610 160, 180, 200, 220

7 8 8 5 5 1183 880 200, 220, 240, 260

8 8 8 7 7 888 880 200, 220, 240, 260

9 8 8 9 9 710 710 200, 220, 240, 260

2.2 Floor loading Only gravity loading on the floor has been considered. The influence of lateral load (wind or earthquake) has not been considered with a view to ascertain the influence of the predominant (gravity) loading on the size and configuration of the floor structural members. The live load values adopted are 3 kN/m2 and 5 kN/m2. Floor finish load has been taken as 1.5 kN/m2 and unit-weight of R.C.C. as 25 kN/m3 in order to evaluate dead loads due to top slab, ribs and band beams.

2.3 Materials of construction The present study has been carried out using M-20 grade concrete and Fe-415 grade steel as the materials of construction. However, behavior of 8×8 m size waffle floor has been studied using M-40 grade concrete also.

3. METHOD OF ANALYSIS


187

3.1 Analytical procedure For the analysis of waffle slabs, orthotropic plate theory [1-5], finite element method [6] and grid or grillage analysis [7-8] are generally used. In the present study, waffle slab is considered as made of grid or grillage of beams. The loads are distributed between longitudinal beams by bending and twisting of transverse beams. The stiffness matrix is developed on the basis of writing joint equilibrium in terms of stiffness co-efficient and unknown joint displacements. Straight members of constant cross-section have been considered. The deformations considered are two orthogonal rotations in the horizontal plane and a vertical deflection at each of the node. Nodal displacements in the horizontal plane and rotations along the vertical axis are not considered keeping in view that they do not significantly contribute to the structural behavior and hence are ignored.

3.2 Computer program The computer program for grid analysis, written in FORTRAN 77, has been used for the present study. It results in moment, shear force and torsion for each of the elements and deflection and rotation about the two orthogonal axes at each of the nodes. 3.3 Acceptance criteria For the purpose of accepting a set of number and dimensions of ribs satisfying structural requirements, codal-provisions given by Bureau of Indian Standards [9-11] have been adopted in general. It recommends that final deflection due to all loads including the effects of temperature, creep and shrinkage, and measured from the as-cast level of the supports of floors, roofs and all other horizontal members should not normally exceed span/250. However, final deflections after creation of partitions and the applications of finishes should not normally exceed span/350 or 20 mm whichever is less. Codal-provisions of American Concrete Institute [12-14] have also been referred to with a view to highlighting certain advantages and some special features.

In the present study, floor deflections have been computed separately as elastic deflection (short-term) (∆e) and creep deflection (long-term) (∆c). There would be additional long-term deflection due to shrinkage and temperature fluctuations. This component has not been computed separately, but assumed to be within 10% of the maximum permissible deflection, i.e. span/250. Therefore, floor deflection requirement (∆max) has been taken as 90% of span/250 value.

Taking 30% live load as permanent and creep coefficient as 1.6, creep deflection is obtained from the values of elastic deflection for dead loads [(∆e)DL]and those for live loads [(∆e)LL] as

∆c = 1.6 [(∆e)DL + 0.3 (∆e)LL] (1)

Total deflection (∆t) is, then, obtained as

∆t = ∆e + ∆c (2)

4. RESULTS AND DISCUSSIONS


4.1 Floor plan: 6×6 m Results of the analytical study on 6×6 m square waffle slab under a live load intensity of 3 kN/m2 are presented in Tables 2-4. Whereas, Table 2 shows the results of the slab provided with 5 ribs along each of the two spans, Table 3 gives results for slab with 7 ribs. Results for slab with 9 ribs in each direction are given in Table 4.

Maximum allowable deflection (∆max) including elastic and creep deflections in case of 6 m span slab is (0.9× span / 250 =) 21.6 mm. A close study of the deflection values in Table 2 and Figure 4 reveals that a rib depth of 130 mm exceeds the maximum permissible deflection (∆max) by 13% and hence needs to be stiffened by increasing the rib depth. Rib depth of 140 mm marginally increases the dead load percentage from 60.3 to 60.8 but brings down the deflection by 15% from 113% to 98%. This configuration of ribs is found suitable for shear capacity and bending moment resistance point of view also. It is interesting to note that a rib depth of 130 mm does not satisfy the deflection requirement even when the number of ribs is increased from 5 to 7 and finally to 9 as shown in Tables 3-4. However, increasing number of ribs does result in increase in dead load percentage from 60.3 to 61.1 and to 61.8 respectively. It is, therefore, inferred that increasing the rib depth is more advantageous to reducing the rib spacing.

Consumption and distribution of reinforcement may be effected by having a better dispersion of moment along the span, from negative to positive moment. For this, attention is drawn to the moment values in Tables 2-4 and Figure 5. It is seen that moment values per rib deceases with the increase in the number of ribs and steel requirement per rib decreases. This would be advantageous if accommodating the bars in the thin (100 mm) rib becomes difficult. The amount of steel consumption would, however, be more for the entire floor since the number of ribs would be more.

Table 2. Deflection, bending moment and shear force values for waffle slab floor of size 6×6 m with no. of ribs Nx = 5 and Ny = 5 and live load of 3 kN/m2

Maximum Deflection (mm)

Maximum Bending Moment (kN-m)

Value as Percentage of

Balanced Capacity

Rib Depth (Dr)

(mm)

Dead Load as

Percentage of Total

Load ∆e ∆c ∆t

Deflection as % of

Maximum Permissible Deflection

(∆max) -ve +ve

Maximum Shear Force (kN)

-ve BM Shear

130 60.3 11.3 13.1 24.4 113 86.6 9.4

49.3 10.9

68.6 10.3

115 118

68 99

140 60.8 9.8 11.4 21.2 98 87.9 9.6

50.0 10.9

69.7 10.4

104 108

65 95

150 61.4 8.6 10.1 18.7 87 89.1 9.8

50.7 11.0

70.7 10.5

95 99

63 90

160 61.9 7.5 8.8 16.3 76 90.4 10.0

51.4 11.0

71.8 10.5

86 91

60 86

Note : First row values are for band beams and second row values are for ribs.

Table 3. Deflection, bending moment and shear force values for waffle slab floor of size 6×6 m


189

with no. of ribs Nx = 7 and Ny = 7 and live load of 3 kN/m2




Balanced Capacity

Rib Depth (Dr)

(mm)

Dead Load as

Percentage of Total

Load ∆e ∆c ∆t

Deflection as % of


(∆max) -ve +ve


-ve BM Shear

130 61.1 10.6 12.4

23.0 107

84.7 8.6

45.8 8.9

69.8 9.5

113 108

69 92

140 61.7 9.2 10.8 20.0 93 86.1 8.8

46.5 10.0

71.0 9.6

102 99

66 87

150 62.3 8.0 9.4 17.4 81 87.4 9.0

47.2 10.0

72.2 9.7

93 90

64 83

160 62.9 6.9 8.1 15.0 70 88.8 9.2

47.9 10.1

73.4 9.8

85 83

62 80

Note : First row values are for band beams and second row values are for ribs. Rib depth of 140 mm satisfies the deflection and shear requirements but bending moment

value marginally exceeds the capacity (8%) for the floor having 5 ribs. At this stage, a choice becomes available from among the following.

(i) making the ribs doubly reinforced, (ii) going in for higher rib depth (say 150 mm), (iii) increase the rib number (say 7).





Balanced Capacity

Rib Depth (Dr)

(mm)

Dead Load as

Percentage of Total

Load ∆e ∆c ∆t

Deflection as % of


(∆max) -ve +ve


-ve BM Shear

130 61.8 10.5 12.3 22.8 106 84.5 8.2

44.5 8.1

70.5 9.0

113 103

70 87

140 62.5 9.1 10.8 19.9 92 86.0 8.4

45.2 8.2

71.8 9.1

102 94

67 83

150 63.1 7.9 9.4 17.3 80 87.4 8.6

45.9 8.3

73.1 9.2

93 86

65 80

160 63.8 6.8 8.1 14.9 69 88.0 8.8

46.6 8.4

74.4 9.3

84 80

63 76



048

1216202428

120 130 140 150 160 170Rib depth (mm)

Max

. def

lect

ion

(mm

) TotaldeflectionCreepdeflectionElasticdeflection

8586878889909192

120 130 140 150 160 170Rib depth (mm)

Max

. - v

e B

.M. i

n ba

nd

beam

s (k

N-m

)

Bandbeams

Figure 4. Variation of maximum deflection with depth of rib

Figure 5. Variation of maximum –ve B.M. with depth of rib

Amongst these choices, the first one is advantageous in the sense that it needs marginal

increase in steel requirement from the balanced design to doubly reinforced design. It would meet all the requirements at the lowest percentage of dead load. Thus, it may be concluded that 5 ribs of 140 mm depth would be structurally most advantageous for the 3 kN/m2 live load category.

Behavior of 6×6 m waffle floor under 5 kN/m2 live load can be understood by studying the results presented in Tables 5-7 . For this loading, the ribs are required, to be made deeper as well as increased in number. It is seen that 5 ribs are unsuitable. A choice of 150 mm depth with 9 ribs or 160 mm depth with 7 ribs appears to be working.

4.2 Floor plan: 7×7 m Analytical results of 7×7 m size waffle floor are given in Tables 8-10 for live load intensity of 3 kN/m2. It is observed that rib depths have to be substantially increased from those suitable for 6×6 m floor. This implies that floor spans are very significant factors in comparison with others. For 7×7 m floor, the range of ridge depth considered lie between 160 mm and 220 mm. The percentage of dead load increases from around 61% for 6 m span to around 63% for 7 m span. It is also important to note that this 2% increase in material has to be located approximately by increasing the rib depth and / or number of ribs so as to achieve the maximum advantage. It is this aspect, which is brought out clearly through the study of values presented in Tables 8-10.


191





Balanced Capacity

Rib Depth (Dr)

(mm)

Dead Load as

Percentage of Total

Load ∆e ∆c ∆t

Deflection as % of


(∆max) -ve +ve

Maximum Shear

Force (kN) -ve BM Shea

r

130 47.6 14.5 14.7 29.2 135 109.3 12.1

62.3 14.1

86.6 13.2

146 152

86 127

140 48.2 12.6 12.9 25.5 118 110.6 12.2

63.0 14.1

87.6 13.3

131 137

82 121

150 48.8 10.9 11.2 22.1 102 111.8 12.4

63.7 14.1

88.7 13.4

119 125

79 116

160 49.3 9.6 9.9 19.5 90 113.0 12.6

64.3 14.2

89.7 13.4

108 114

75 110






Balanced Capacity

Rib Depth (Dr)

(mm)

Dead Load as

Percentage of Total

Load ∆e ∆c ∆t

Deflection as % of


(∆max) -ve +ve


-ve BM Shear

130 48.5 13.5 13.8 27.3 126 106.4 10.9

57.6 11.4

87.6 12.0

142 137

87 116

140 49.1 11.7 12.0 23.7 110 107.7 11.1

58.3 11.4

88.8 12.1

128 124

83 110

150 49.8 10.2 10.6 20.8 96 109.1 11.3

59.0 11.5

90.0 12.2

116 114

80 105

160 50.4 9.0 9.4 18.4 85 110.6 11.5

59.7 11.5

91.2 12.3

106 96

77 101

Note : First row values are for band beams and second row values are for ribs. It is clear from the values shown in Table 8 that slab with 5 ribs of 200 mm depth is

slightly deficient in both shear as well as bending moment capacity. Rib depth of 220 mm makes it safe but becomes a little too stiff and thereby floor deflection is reduced to as low as about 71% of the maximum permissible. It is seen from Table 9 that 7 ribs of 200 mm depth appear to be quite suitable with about 64% dead load. However, 9 ribs of 180 mm (Table 10) depth can easily be managed by marginally making the ribs doubly reinforced. Doubly reinforced section is generally preferred because of its improved ductility. Based on these observations, it is concluded that for 3 kN/m2 live load, 9 ribs of 180 mm depth is structurally most efficient for 7×7 m floor plan.






Balanced Capacity

Rib Depth (Dr)

(mm)

Dead Load as

Percentage of Total

Load ∆e ∆c ∆t

Deflection as % of


(∆max) -ve +ve


-ve BM Shear

130 49.3 13.3 13.7 27.0 125 105.7 10.3

55.7 10.2

88.2 11.3

141 129

88 109

140 50.0 11.5 12.0 23.5 109 107.2 10.5

56.4 10.3

89.5 11.4

127 118

84 104

150 50.6 10.0 10.5 20.5 95 108.6 10.7

57.1 10.4

90.7 11.5

115 108

80 99

160 51.3 8.8 9.3 18.1 84 110.1 10.9

57.8 10.5

91.9 11.6

105 99

77 95






Balanced Capacity

Rib Depth (Dr)

(mm)

Dead Load as

Percentage of Total

Load ∆e ∆c ∆t

Deflection as % of


(∆max) -ve +ve


-ve BM Shear

160 60.8 16.0 18.6 34.6 137 138.1 15.8

78.0 17.7

94.7 14.5

132 144

80 119

180 61.7 12.5 14.7 27.2 108 141.6 16.4

79.8 17.7

97.3 14.8

111 123

74 110

200 62.7 10.0 11.8 21.8 87 145.1 16.9

81.7 17.8

99.8 15.0

95 106

70 103

220 63.7 8.1 9.7 17.8 71 148.6 17.3

83.6 17.9

102.3 15.3

83 93

66 97


Results presented in Tables 11-13 explain the behavior of 7×7 m waffle floor under 5 kN/m2 live load. It is seen that 5 ribs of any depth adopted therein does not satisfy all the requirements. Increasing the number of ribs to 7 with a rib depth of 220 mm does not provide a solution. However, 9 ribs of depth 200 mm can be managed since the shear capacity along with bending capacity can be increased, by making the section doubly reinforced. It is, therefore, concluded that for 5 kN/m2 live load, 9 ribs of 200 mm depth may be considered as structurally most efficient.

4.3 Floor plan: 8×8 m Response of waffle floor of size 8×8 m has also been obtained under live load intensities of


193

3 kN/m2 and 5 kN/m2. It is seen from the values listed in Table 14 that 5 ribs are unsuitable for 8×8 m floor plan with live load intensity of 3 kN/m2. Further 7 ribs of 240 mm depth are deficient in both shear as well as bending moment carrying capacity. Increasing rib depth to 260 mm also does not provide a solution. However, 9 ribs of 240 mm depth can be managed by making the section doubly reinforced since shear capacity is also increased along with bending moment capacity. (Results of 7 ribs and 9 ribs are not included in this paper due to paucity of space). It is, therefore, concluded that for 3 kN/m2 live load, 9 ribs of 240 mm depth may be considered as the structurally most efficient for 8×8 m floor plan.





Balanced Capacity

Rib Depth (Dr)

(mm)

Dead Load as

Percentage of Total

Load ∆e ∆c ∆t

Deflection as % of


(∆max) -ve +ve

Maximum Shear Force (kN) -ve

BM Shea

r

160 61.7 14.9 17.5 32.4 129 136.1 14.5

73.1 14.8

96.4 13.4

130 132

81 110

180 62.7 11.7 13.8 25.5 100 139.9 15.1

75.0 15.0

99.2 13.7

110 113

76 102

200 63.7 9.3 11.1 20.4 81 143.7 15.6

77.0 15.2

102.1 14.0

94 98

71 96

220 64.7 7.6 9.2 16.8 67 147.5 16.1

78.9 15.5

104.9 14.3

82 86

68 90

Note : First row values are for band beams and second row values are for ribs. Table 10. Deflection, bending moment and shear force values for waffle slab floor of size 7×7 m

with no. of ribs Nx = 9 and Ny = 9 and live load of 3 kN/m2




Balanced Capacity

Rib Depth (Dr)

(mm)

Dead Load as

Percentage of Total

Load ∆e ∆c ∆t

Deflection as % of


(∆max) -ve +ve


-ve BM Shear

160 62.5 14.3 16.9 31.2 124 134.2 13.8

69.9 13.1

97.4 12.7

128 125

82 104

180 63.6 11.2 13.4 24.6 98 138.2 14.4

71.8 13.4

100.4 13.0

108 108

77 97

200 64.6 9.0 10.8 19.8 79 142.2 14.9

73.8 13.7

103.5 13.3

93 94

72 91

220 65.6 7.3 8.9 16.2 65 146.2 15.5

75.9 14.0

106.6 13.7

81 83

69 86

Note : First row values are for band beams and second row values are for ribs. Results of the analysis of 8×8 m size waffle floor under live load intensity of 5 kN/m2


show that even 9 ribs of any depth adopted therein do not satisfy all the requirements. Increasing the number of ribs to 11 also will not provide a solution since reduction in maximum shear force and bending moments and ribs will be marginal. To make the floor satisfy all the requirements especially to avoid the shear requirements in ribs, the rib depth is required to be increased by a large amount resulting in very stiff floor with reduced deflection and very high dead load percentage. Higher rib depth also reduces the available headroom, which also may not be desirable. Results for live load intensity of 5 kN/m2 are not shown here due to paucity of space.





Balanced Capacity

Rib Depth (Dr)

(mm)

Dead Load as

Percentage of Total

Load ∆e ∆c ∆t

Deflection as % of


(∆max) -ve +ve


-ve BM Shear

160 48.2 20.5 20.9 41.4 164 173.7 20.2

98.2 22.8

119.1 18.6

166 184

100 153

180 49.2 15.9 16.4 32.3 128 177.1 20.8

100.0 22.9

121.6 18.8

139 156

93 141

200 50.2 12.7 13.2 25.9 103 180.6 21.3

101.8 22.9

124.1 19.1

119 134

87 131

220 51.2 10.2 10.8 21.0 83 184.1 21.9

103.7 23.0

126.6 19.3

103 117

82 122






Balanced Capacity

Rib Depth (Dr)

(mm)

Dead Load as

Percentage of Total

Load ∆e ∆c ∆t

Deflection as % of


(∆max) -ve +ve


-ve BM Shear

160 49.2 18.9 19.5 38.4 153 170.2 18.3

91.5 18.9

120.4 17.0

162 166

101 139

180 50.2 14.8 15.4 30.2 120 173.9 18.9

93.4 19.0

123.3 17.2

136 142

94 129

200 51.2 11.7 12.3 24.0 95 177.6 19.5

95.3 19.2

126.1 17.5

117 123

88 120

220 52.2 9.5 10.1 19.6 78 181.4 20.1

97.2 19.4

128.9 17.8

101 108

83 112


Another alternative can be the use of higher strength concrete, such as M-40, in lieu of


195

M-20 grade. Since the modulus of elasticity of concrete is directly proportional to square root of characteristic compressive strength of concrete (fck), the deflections will be reduced to about 71% by the use of M-40 grade concrete. Further rib depth of 220 mm will satisfy the deflection criteria. However, there will be no significant change in bending moment and shear force values. Since design shear strength of concrete will also be higher for M-40 grade concrete, it is noticed that 9 ribs of 220 mm depth can be managed by slightly increasing the flexure reinforcement in ribs such that their shear capacity is increased up to desired level. Based on these observations, it is concluded that by using M-40 grade concrete, 9 ribs of 220 mm depth may be considered as the structurally most efficient for 8×8 m floor plan with live load intensity of 5 kN/m2.





Balanced Capacity

Rib Depth (Dr)

(mm)

Dead Load as

Percentage of Total

Load ∆e ∆c ∆t

Deflection as % of


(∆max) -ve +ve


-ve BM Shear

160 50.1 18.0 18.7 36.7 146 167.0 17.3

87.1 16.5

121.1 16.0

159 157

102 131

180 51.2 14.1 14.9 29.0 115 171.0 17.9

89.0 16.7

124.2 16.3

134 134

95 122

200 52.2 11.2 11.9 23.1 92 175.0 18.5

91.0 17.0

127.3 16.6

115 116

89 114

220 53.2 9.1 9.8 18.9 75 179.0 19.1

93.0 17.3

130.3 16.9

100 103

84 107






Balanced Capacity

Rib Depth (Dr)

(mm)

Dead Load as

Percentage of Total

Load ∆e ∆c ∆t

Deflection as % of


(∆max) -ve +ve


-ve BM Shear

200 61.7 19.1 22.4 41.5 144 208.5 25.0

116.9 26.7

126.3 19.7

137 157

88 135

220 62.5 15.5 18.3 33.8 117 213.2 25.7

119.4 26.8

129.3 19.9

119 138

83 126

240 63.3 12.8 15.2 28.0 97 217.8 26.3

121.9 26.9

132.2 20.2

104 122

79 118

260 64.1 10.7 12.8 23.5 82 222.5 27.0

124.4 27.0

135.2 20.6

93 109

75 113


Note : First row values are for band beams and second row values are for ribs. 5. CONCLUSIONS

Following conclusions are drawn from the study presented in this paper.

1. For 6×6 m square floor plan, 5 ribs of 140 mm depth (overall depth 205 mm) is

found to be structurally most efficient for 3 kN/m2 live load intensity. 2. For 5 kN/m2 live load intensity on a 6×6 m square floor plan, a choice between 9

ribs of 150 mm depth and 7 ribs of 160 mm depth becomes available. Percentage of dead load is about 50 in both the cases.

3. For square floor plan of 7 × 7 m, the most efficient structural system is 9 ribs of 180 mm depth for a live load intensity of 3 kN/m2.

4. For a live load intensity of 5 kN/m2, the most efficient structural system is 9 ribs of 200 mm depth for 7 × 7 m square floor plan.

5. For square floor plan of 8 × 8 m, the most efficient structural system is 9 ribs of 240 mm depth for a live load intensity of 3 kN/m2.

6. For square floor plan of 8 × 8 m, the most efficient structural system is 9 ribs of 220 mm depth using M-40 grade concrete for a live load intensity of 5 kN/m2.

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Book Co., New York, 1959. 2. Wang, C.K. and Salman, C.G., Reinforced Concrete Design, Harper and Row

Publishers, New York, 1985. 3. McCormac, J.C., Design of Reinforced Concrete, Harper and Row Publishers, New

York, 1986. 4. Nawy, E.G., Reinforced Concrete : A Fundamental Approach, Prentice Hall, Engle

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optimum dimensions of waffle slab for medium size …€¦ · slab, ribs and band beams. 2.3...

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