CHAPTER XI

COST ANALYSIS OF MULTIPLE FUNICULAR SHELL AND CONVENTIONAL

REINFORCED CEMENT CONCRETE FOUNDATIONS

11.1 Comparison of Costs between Multiple Funicular Shell

Footings and Conventional Reinforced Concrete Footings

11.1.1 Necessity of the study

The structural efficiency alone may not

result in the new foundation methods being adopted by

engineers. Ease of construction and reduced cost only will

enable the conventional type to be replaced by a new one.

Therefore, a study was undertaken to determine the relative

costs of multiple funicular shell footing and conventional

plain reinforced concrete footing at the usual ranges of

allowable bearing capacity. Since the dimensions of the

funicular shell footings consisting of 4 shells were fixed

in this study, the conventional footings of same dimensions

out the relative costs. For

4.1t/m 2 (40kH/m 2 ) to 9.2t/m 2

were considered for working

various soil pressures from

(90kn/m 2 ) the dimensions and reinforcements for the

connecting beams and edge beams of the multiple funicular

shell footings and thickness and reinforcements for th~

plain footing were worked out for arriving at their costs as

given in Tables 11.land 11.2

147

11.1.2 Design details

11.1.2.1 Multiple funicular shell footing

The central connecting beams were designed as

cantilevers acted upon by a uniform soil reaction acting on

the triangular areas ABC, and EFG and on the rectangle

EABF. The edge beams of the footings were designed as

cantilevered from the ends of the central connecting beams,

the design bending moments being that due to the uniform

soil reaction acting on the area DEC (Fig.8.1). The

structural designs were carried out as per 1.5.456-1978.

The grade of concrete used for design is 1'115

and HYSD steel

bars (grade Fe 415). The width of the connecting beams was

30cm and that of the beams along the edges, 15cm. A cover

of 6cm was provided at the bottom of all the beams. The

connecting

portion, and

beams were of constant depth for the central

then of sloping section to be compatible with

the top of the edge beams at their ends. The columns of

the structure Ivere assumed to have a cross section of 30cm

x 30cm and to start at the junction between the central

connecting beams. The edge beams vie r e sloping from the

junction bet I-lee n them and the connecting beams to the

corners of the unit, the slope being 1 : 10. The details of

the dimensions of the beams and the reinforcements \>/ere as

given in To~le 11.1.

11.1.2.2 Plain reinforced concrete footing

The design of the plain concrete footings were

also done as per I.S.456-1978.

148

The concrete of grade 1,1 15

and HYSD bars (grade Fe 415) were adopted for design

purposes. The design dimensions of the footings have been

obtai ned based on considerations of flexural and perimeter

shear failure. A cover of 6cm 'rIa s given at the bottom of

tile footings. The details of the footings and the

reinforcements for the various a11 O~I ab 1 e pressures on the

soil "/ere as given in Table 11. 2.

11.1.3 Cost estimates

For the connecting beams and the edge beams of

multiple funicular shell footings, shuttering work of mild

steel sheets of suitable thicknesses can be fabricated and

used wi th great economy and ease. Since the shuttering can

be used a number of t i [,leS for a 1 arge housing complex, the

cost per unit of footing \'i i 11 be reduced to a minimum. The

heigl1t of the shuttering can be uniform, commensurate 'vI i th

the total depth of the connecting beams of the most heavily

loaded footing of the proposed structre. Thus, the form

work of the same dimensions can be used for all the

footings.

For the plain footings, no shuttering work is

required.

The cost of MIS grade concrete prepared, placed in

position, compacted, and cured properly was worked out to be

Rs 633/m 3 and that of lkg of HYSD bars (grade Fe 415) bent

and tied as per designs in place as Rs 7.12 as per Kerala

Stat e Pub 1 i c \10 r ks De par men t rat e s as 0 n 1. 10 • 1986 \'Ii t h

all 0'11 a11 ce for can veyan ceo f mat eria1 s for 20 kill. The serat e s

149

were taken for arriving at the total cost of multiple

funicular shell footings and plain footings.

11.1.4 Comparsion of costs and savings in materials between

the two types of footings

The details of the costs of and the quantities for

plain footings and mUltiple funicular shell footings were as

given in Table 11.3. The savings in the quantity of

concrete required for the latter progressively increased

2from 34 to 49% for contact pressures varying from 4.1t/m to29.2t/m. There iJere savings in the quantity of steel for

multiple funicular shell footing for low pressures. But the

requirments of steel for the foundations with larger contact

pressures iJere higher than that for the conventional

footings. However, as far as the costs were concerned,

the rei sal Vi ay s areduct ion inc 0 s t s for the she 11 f 0 0 tin gs

over the plain reinforced concrete footings at the

corresponding contact pressures. It was observed that the

maxmimum savings in cost of 23% was obtained for the shell

2footing for a contact pressure of 5.1t/m •

11.2 Comparison of Costs between Multiple Funicular Shell

Rafts and Conventional Reinforced Concrete Raft

The functions of the multiple funicular shell raft

and the conventional reinforced concrete raft are the same.

Suitably connected funicular shells replace the slab of the

latter. For comparison of costs between the two t;pes of

rafts, tile structural designs \'Jere carried out as per 1.S

456- 1978, assuming uniform contact pressures acting on

150

them. grade of concrete used for designs is M and15HYSD bars (grade Fe 415) as tension and shear

reinforcements. The esimates of costs of the rafts for

various pressures have been made based on the Kerala State

Public Works Department rates as on 1.10.1986.

11.2.1 Design of multiple funicular shell rafts

For the design of the connecting beams of the

raft, the design moments and shear forces were determined

using the theory of Salvadori (1967) for a rectangular grid.

With reference to fig.11.1

k = q{j.k) . . (11.l)

Taking the first term of the Furier Series

expansion for uniform contact pressure qo'

16 rrx 7r.yq = -;2- qo Sin---- Sin---- • • (11.2)

a b

Assuming the follo\'Jing solution of equation 11.1

1\x 7\yz =

aSin

b

equation 11.1 is solved to give

Za1

-------------------------a 4 k I

1 + (---) (---) ( __l_)b j I x

151

• • (1 1.4)

ilzMx = -Eel x -~;~- =

7rx 7\Yq a2k 5in---- 5in---­o a b

-----------------------~a 4 k I

1 + (--_) ( ) ( __ l_)b j Ix

•• (11.5)

16 ~Q~~ cos-~~- sin-~~-

;"3 a 4 k I a b1 + (---) (---) ( __ l_)

b j I x

•• (11.6)

---izN = -E Iy c y ox 2

= 16 ~Q~~~ cos-~~--47r b 4 k I a

1 + (---) (---) (--~-)a j Iy

• •

lfY5in----

b

(11.7)

03 Z 16 ~Q~~ cos-~:- ITYVy = -Eel y ~y-3 = -3 5in----

o 7f b 4 j Ix a b1 + (---) (---) (----)

a k Iy

• • (1 1.8)

For multiple funicular shell rafts consisting of 4

shells (Fig 11.2) the maximum bending moments and shear.

forces acting on the connecting beams were calcutated for

uniform contact pressures from 4.1tlm2 to 9.2tlm 2 using a

computer programme from equations 11.5 and 11.6. Here,

j=k I =1 =1 since the raft panels were squares. The, x y

design bending moments and shear forces obtained were as

given in Table 11.4. The cover adopted for all the beams

was 6cms at bottom, 2cm each on sides and at top. Two, 8mm

152

di aIi1 e t er HYSDba r s \', ere

each connecting beam.

legged stirrups of 6mm

provided as stirrup holders for

iIi i ni mu111 she ar rei nfor cem en t s oftW0

diameter HYSD bars at 19.5cm

intervals were provided for each connecting beam. The

details of dimensions of the beams and the reinforcements

were as given in Table 11.5.

11.2.2 Design of conventional reinforced concrete rafts

The raft slabs were designed for maximum bending

moments of 0.032 q o12 where qo' is the corresponding uniform

contact pressure and 1, the span. A cover of 6CM was given

for the raft slabs at their bottom. The same area of

reinforcements was provided in both the directions in the

slab. The details of dimensions and reinforcements of the

rafts were as given in Table 11.6.

11.2.3 Estimation of costs

For the purposes of estimation, the actual areas

of tensile reinforcements obtained as per design were taken

into account. The cost of the four funicular shells and the

connecting ~eams were compared with the cost of the slab

portion of the conventional reinforced concrete raft that

was replaced by the former. The details of comparison of

costs were as given in Table 11.7.

11.2.4 Comparison of cost and of materials used for the

shell rafts and the conventional reinforced concrete

rafts

In th the increase in contact pressures from

4.1t/m 2 to 9.2 t/m 2 , the percentage savings in cost of the

153

mUltiple funicular sllell raft also increased progressively

from 12.68 to 20.88 (Table 11.7). The percentage savings in

concrete were around 24 and in steel reinforcement varied

between 36 and 55 for the above range of contact pressures.

Therefore, as in the case of footings the adoption of

multiple funicular shell rafts can result in considerable

savings in cost and in the conservation of scarce

construction materials like cement and steel.

154

NN ___ N_NN ___ N _____________________ • ___________ N _________ N ___________________N_~______________________

Applied Effective depth Effective Volume of Area of Volume Weightpressure in metres depth footing reinforcement of steel of steel

--------------------------- adopted (bothfrom from 3 directions) cm3 kg

t/m2 perimeter bending m m 2shear moment em(ktllri) consideration consideration----------------------------------------------------------------------------------------------------

I-'4.1 (40) 0.1340 0.183 0.1840 1.4065 27.7882 6669.1860 52.353

U'1

+>- 5.1 (50) 0.2151 0.204 0.2151 1.5845 29.7132 7131.1580 55.979Cl

6.1 (60) 0.2430 0.224 0.2430 1.7478 31.5049 7561.1870 59.365

7.1 (70) 0.2690 0.242 0.2690 1.8982 33.1952 7966.7712 62.539

8.2 (80) 0.2940 0.258 0.2940 2.0384 34.7952 8350.8532 65.554

9.2 (90) 0.3170 0.274 0.3170 2.1698 36.3201 8716.8312 68.427______________________________________________________ ______________________________________ N _

Table 11.1 Details of Thicknesses and Reinforcements of ConventionalPlain Reinforced Concrete Footings of Size 2.4 m Square

_________ H ~ N _

Central connecting beams of the footing

......(.rrlJl

Contactpressure

2tim(kN/m 2 )

4.1 (40)

5.1 (50)

6.1 (60)

7.1 (70)

8.2 (80)

9. 2 ('90)

Bendingmomentat thejunction

kNm

37.485

46.856

56.223

65.599

74.970

84.340

Effectivedepth ofbeam

cm

43.57

48.72

53.37

57.65

61. 62

65.36

t·1a inreinfo­rcementin beam

2em

8.312

9.292

10.179

10.994

11.754

12.468

Area ofstirrupholders

cm 2

2.0

2.0

2.0

2.0

2.0

2.0

Totalvolumeofreinfo­rcement

crn 3

2475

2710

2923

3119

3301

3472

Volumeofstirrups

3cm

518

858

1354

1747

2357

2758

Volumeofconcrete

m3

0.5265

0.5796

0.6270

0.6717

0.7126

0.7512

----------------------------------------------------------------------------------Table 11.2 Details of Dimensions and Reinforcements of Connecting Beams and Edge

Beams of Multiple Funicular Shell Footings of Size 2.4 m square

Contd .••

Contactpres·sure

4.1 (40) 6.0506 24.76

5.1 (50) 7.5633 27.68

6.1 (60) 9.0763 30.32

7.1 (70) 10.5890 32.75

8.2 (80) 12.1020 35.02

9.2 (90) 13.6140 37.14

Edge beams of. the footing

2.2624 2092.10 445.60 2537.70 0.4282

0.8768

0.9533

Totalvolume ofconcreterequiredfor connect­ing beams &edge beams

3m

1.0552

1.1378

1.2118

1.2818

53.49

40.77

46.62

kg

59.32

66.65

72.20

Total'deight ofsteel forcon:'~cting

beams andedge beams

3m

Totalvolumeofconcrete

Totalvolumeofsteel

3em

Volumeofstirrups

em3

Volumeof mainreinfo­rcementandstirrupholders

Area ofstirrupholders

em2

2.2G24 1815.90 385.00 2200.90 0.3503

2.2624 1961.00 409.70 2370.70 0.3737

2.2624 2212.70 478.60 2691.30 0.4661

2.2624 2323.98 509.14 2833.12 0.4992

2.2624 2429.80 538.18 2967.98 0.5306

Hainreinfo­rcementin beams

2em

4.722

5.280

5.784

6.248

7.083

6.676

kNm em

Bending Effectivemoment depth of

beam

2tim 2

(klUm ).....{Jl

0-,

----------------------------------------------------------------------------------------------------------------Table 11.2 Details of Dimensions and Reinforcements of Connecting Beams and Edge Beams of

Funicular Shell Footings of Size 2.4 m square

.......V-,-.....I

-------- -------------------------------- ---------------------------------_N_______

-------------------------------------- -------Volure of concrete, m3 Height of HYSD steel bars, kg Total cost of funicular shell footing

Total PercentageContact For For Percentage For For Percentage cost of Cost of Cost of Total cost savings inpressure plain funi cu1ar increase plain funicular increase or plain concrete casting cost for

footings shell of vdlurre footings shell decrease in footings and shells and fil.1ltiple

2 footings of concrete steel for steel shuttering funiculart/r'l 2 for plain plain shell

(kN/m ) footings footings Rs Rs Rs Rs footings

4.1(40) 1.4065 1.0506 33.88 52.353 40.77 28.41 1263 955 90 1045 20.86

5.1(50) 1.5045 1.1270 40.53 55.979 46.62 20.07 1401 1045 90 1135 23.44

6.1(60) 1.7478 1.2260 42.56 59.390 53.49 11.03 1529 1157 90 1247 22.61

7.1(70) 1.8982 1.3116 44.70 62.539 59.32 5.43 1647 1253 90 1343 22.63

8.2(30) 2.0384 1.3356 47.11 65.554 66.65 -1.64 1757 1352 90 1442 21.84

9.2(90) 2.1697 1.4557 49.04 68.427 72.20 -5.22 1360 1436 90 1526 21.39

------------------------------------------ --------------------------------- --------- --------------------------------- __ 'v ...____

Table 11.3 Garparison of QJantities of Concrete and Steel and Costs for Conventional Reinforced Concrete Footings andt'ultiple Funicular Shell Footings of Size 2.4 msqJare

Contactpressure

t / m2

"2(kN/m )

4.1 (40)

5.1 (50)

6.1 (60)

7.1 (70)

8.2 (80)

9.2 (90)

t-iaximumbending momentat the centre

of beam

t m (k i~ m)

2.939 (28.823)

3.673 (36.029)

4.408 (43.230)

5.140 (50.440)

5.880 (57.640)

6.613 (64.852)

t·iax i mumshear force

at the supports

t (k to

3.553 (34.840)

4.440 (43.551)

5.328 (52.260)

6.220 (6.217)

7.100 (69.680)

7.990 (78.392)

Table 11.4 Bending Moments and Shear Force for theDesign of the Connecting Beams of the MultipleFunicular Shell Rafts of size 2.6 m Square.

158

___ W~ _________ ~ _____ H ____ ~ ___ ~ _____________________ ~ __ ________ ~ _________________

Contact t-ia:dmum bending Effective Total Volume of Weight of Volume ofpressure moment acting depth area of reinforce- reinforce- concrete

on the slab reinforce- ment ment

2 menttIm 2 3 3(kN/m 2) t-m (kll-m) em kgem em m_______ N ~ ~ _

...... 4.1 (40) 0.8823 (8.6528) 11. 46 18.9672 4931.47 38.71 0.9236tn<.0

5. 1 ( 50) 1.1029 (10.816) 12.82 21.1938 5510.39 43.26 0.9955

6.1 (60) 1.3234 (12.979) 13.95 23.3726 6076.88 47.70 1.0553

7.1 (70) 1.5440 (J5.142) 15.17 25.0752 6519.55 51.18 1.1198

8.2 (80) 1.7640 (17.306) 16.21 26.3180 6972.68 54.74 1.1749

9.2 (90) 1.9850 (19.469) 17.20 28.4340 7392.84 58.03 1.2273

---~----------------~---------------------------------------------------.------

Table 11.5 Details of Thicknesses and Reinforcements in Conventional ReinforcedCement Concrete Rafts of Size 2.6 m. square

___~_N__ ~ ~ ~ N __ N N _

Contactpressure

2tim 2(kN/m }

Maximum bending Depth ofmoment connecting

bea~s

t-m (k~-m} cm

j'lai nreinf.inbeams

2em

Area of Total Volumestirrup of main reinf.holders & stirrup

holders2 3em e~

Volume Totalof weightstirrups of

steel

cm3kg

Total volumeof concretefor connect­ing beams

3rnI-'

0'c

4.1 (40) 2.939 (28.8231) 38.21

5.1 (50) 3.674 (36.0289) 42.72

6.1 (60) 4.409 (43.2347) 46.79

7.1 (70) 5.130 (50.4405) 50.55

8.2 (30) 5.878 (57.6463) 54.04

9.2 (90) 6.613 (64.8520) 57.32

7.288 2

3.149 2

8.928 2

9.640 2

10.310 2

10.930 2

2414.38

2638.70

2841.18

3026.66

3199.72

3362.16

726.20 24.66 0.5703

775.85 26.80 0.6285

823.24 28.77 0.6810

865.75 30.56 0.7294

905.23 32.22 0.7745

942.33 33.79 0.8168___________ N ~ -- _

Table 11.6 Details of Connecting Beams for Multiple Funicular Shell Rafts of Size 2.6 m. square

____N _________~________________________________________________________________________________________________________

Contact Voltr.'E of % increase l':eight of %increase Total Cost of multiple %savingpressure con~rete in caa::nt HYSD bars in steel cost of funicular shell in cost

r:1'" for reinf- kg for rein- plain forarced forced footings nllltiple

For re- For concrete For re- For CEriEnt Cost of Cost of Total funicular

2 infol"Ced wltiple raft inforced multiple concrete concrete casting cost shellt/Iil concrete funicular slab concrete funicular raft .& steel shells& footings

(kl~/rihraft shelll raft shell shutt-slab raft slab raft Rs • ering Rs.

......c.I-' 4.1 (40) 0.9236 0.7441 24.12 38.708 28.430 36.15 860.24 673.44 90.00 763.44 12.68

5.1 (50) 0.9955 0.8023 24.08 43.256 30.577 41.46 933.13 725.56 90.00 815.56 15.02

6.1 (600 1.0553 0.8548 23.45 47.703 32.539 46.60 1007.65 772.77 90.00 862.77 16.79

7.1 (70) 1.1198 0.S'.Q32 23.89 51.178 34.328 49.08 1073.22 816.14- 9O.W ~'16.14 18.44

8.2 (80) 1.1749 0.9483 23.89 54.735 35.993 52.07 1133.42 856.54 90.00 946.54 19.74

9.2 (90) 1.2273 0.9906 23.89 58.033 37.563 54.49 1190.08 894.50 90.00 984.50 20.38

---- ..._-----,.,. ......---".---~---_ • _ 111_____________ III"

... _.. "._...--------------------------------

Table 11.7 Cooparison of Quantities of Concrete and Steel Required for and Costs bebo.een Conventional ReinforcedConcrete Rafts and r1Jltiple Funicular Shell Rafts of Sizes 2.6 msquare

y

x

joint:q(jxk)

~. Iy

Load at/~

I-

W ~

,j'/

~t/~~01~

- I-

Ix

• .~ J , J 1_

a

..0

(0< b)q:Uniform loading intensity

o

FIG.11.1 ANALYSIS OF A GRrO PANEL

162a

.. .... '....

Connecting beams 30cm wide

, 'F~'nic'ul~r' ~h~ils' .', .._ELEVATIQtL .

2.6m

Connecting bea ms

Ec..qN r. - -- ---

Raft beams------,

L.:: _ _ _ _ _

--~

IIIIIIIIII

L.-..-,..~__....J._--l I__ _________ -4

Funicular shell 110cmxl10cm sizePLAN

FIG.11.2 TYPICAL SETUP OF A MULTIPLE FUNICULARSHELL RAFT 2·6mx2·6mWITH FOUR SHELLS

162 b