Analysis Between a Beam Supported Structure and a Flat Plate Structure (Part 3)

COMPARATIVE STUDY:

 General:

The buildings are analyzed for determine the best condition which can be constructed economically. The behavior of each condition is observed carefully. Then suitable condition is selected and suitable dimensions as well as steel area are also determined. The chapter gives a comparative of the material, dimensions etc required for both the options I building and potion II building. It is obvious that the amount of material required for option I building will be higher than the option II building. But the option I building got beam free floor height. Due to this beam free space, looks nice and the floor will be heavily reinforced and it will be durable.

 Comparison Between the Two Types of Structure:

The comparison is made in terms of element dimension, volume of concrete and steel

 requirement, their cost and economic view.

 Dimension of different parts of beam supported structure and flat pate structure:

 Table 4.1: Dimension of different portion of the flat plate structure and beam-supported structure.

Element

Option I building

(Beam supported structure)

Option II building

(Flat plate structure)

Column noThere are 16 columns at each floor. So the total nos of columns of this six storied building is 16.There are 16 columns at each floor. So the total nos of columns of this six storied building is 16.
   

Table 4.1: Dimension of different portion of the flat plate structure and beam-supported structure (continued…).        

Element

Option I building

(Beam supported structure)

Option II building

(Flat plate structure)

Column size          All the columns are:

  1. C1,C4,C10,C16:

Size = 18” * 10”

  1. C2,C3,C5,C8,C9,C12,C14,C15

Size = 24” * 12”

  1. C6,C7,C11,C13:

Size = 26” * 18”

 

         All the columns are:

  1. C1,C4,C10,C16:

Size = 15” * 15”

  1. C2,C3,C5,C8,C9,C12,C14,C15

Size = 24” * 12”

  1. C6,C7,C11,C13:

Size = 30” * 22”

 

Column height

All floor columns height are 10 ft

All floor columns height are 10 ft

Beams

Slab with beams

Slab without beams

Slab thickness

All floor slab thickness are 6″

All floor slab thickness are 7.5″

Required concrete volume for beam supported structure and flat plate structure:

Table 4.2: Comparative concrete volumes.

Element

Option I building

(Beam supported structure)

Option II building

(Flat plate structure)

ColumnColumn: C1, C4, C10, C16= 4 * 6 * 0’- 10” * 1’- 6” * 10’- 0” = 333.12 cft.Column: C2, C3, C5, C8, C9, C12, C14, C15= 8 * 6 * 1’- 0” * 2’- 0 * 10’- 0” = 960.00 cft

Column: C6, C7, C11, C13

= 4 * 6 * 1’- 6” * 2’- 2” * 10’- 0” = 779.76 cft

Total R.C.C = 2072.88 cft.

Column: C1, C4, C10, C16= 4 * 6 * 1’- 3” * 1’- 3” * 10’- 0” = 375.00 cftColumn: C2, C3, C5, C8, C9, C12, C14, C15= 8 * 6 * 1’- 0” * 2’- 0 * 10’- 0” = 960.00 cft

Column: C6, C7, C11, C13

= 4 * 6 * 1’- 10” * 2’- 6” * 10’- 0” = 1099.80 cft

Total R.C.C = 2434.80 cft

  Table 4.2: Comparative concrete volumes (continued…)

Element

Option I building

(Beam supported structure)

Option II building

(Flat plate structure)

 

BeamsBeam: B1, B3, B4, B6, B7, B9, B10, B11= 1 * 10” * 10” * 13’ – 7” * 8= 75.46 cftBeam: B2, B5, B8, B12

= 1 * 15” * 10” * 18’ – 0” * 4

= 75.00 cft

Beam: B14, B17, B20, B23

= (1 * 18” * 10” * 17’-10” * 2) + (1 * 18”10” * 18’-5” * 2)

= 90.83 cft

Beam: B13, B15, B16, B18, B19, B21, B22, B24

= 1 * 12” * 10” * 13’-5” * 8

= 89.46 cft

Total R.C.C = 75.46 + 75.00 + 90.83 + 89.46 = 330.75 cft

None

  Table 4.2: Comparative concrete volumes (continued…).

Element

Option I building

(Beam supported structure)

Option II building

(Flat plate structure)

 

Beams

(5th + 6th) Floor R.C.C= 2 * 330.75 = 661.50 cftR.C.C Beam at 4th Story:Beam: B1, B3, B4, B6, B7, B9, B10, B11

= 1 * 15” * 10” * 13’ – 7” * 8

= 113.17 cft

Beam: B2, B5, B8, B12

=1 * 15” * 10” * 18’ – 0” * 4

= 75.00 cft

Beam: B14, B17, B20, B23

= (1 * 18” * 10” * 17’- 10” * 2) + (1 * 18” *10” * 18’- 5” * 2)

= 90.83 cft

Beam: B13, B15, B16, B18, B19, B21, B22, B24

= 1 * 15” * 10” * 13’-5” * 8

= 113.17 cft

Total R.C.C = 113.17 + 75.00 + 90.83 + 113.17 = 392.17 cft

(3rd + 4TH) Floor R.C.C = 2 * 392.17 = 784.34 cft

R.C.C Beam at 2nd Story:

Beam: B1, B3, B4, B6, B7, B9, B10, B11

= 1 * 15” * 12” * 13’- 7” * 8

= 135.80 cft

Beam: B2, B5, B8, B12

= 1 * 15” * 10” * 18’- 0” * 4

= 75.00 cft

Beam: B14, B17, B20, B23

None

 Table 4.2: Comparative concrete volumes (continued..).

Element

Option I building

(Beam supported structure)

Option II building

(Flat plate structure)

Beam

= (1 * 18” * 12”*17’- 10” * 2) + (1 * 18” * 12” * 18’-5” * 2)= 108.99 cftBeam: B13, B15, B16, B18, B19, B21, B22, B24= 1 * 15” * 10” * 13’-5” * 8

= 113.17 cft

Total R.C.C = 135.80 + 75.00 + 108.99 + 113.17 = 432.96 cft

(1st + 2nd) Floor R.C.C = 2 * 432.96 = 865.92 cft

Total R.C.C = 135.80 + 75.00 + 108.99 + 113.17 = 432.96 cft

(1st + 2nd) Floor R.C.C = 2 * 432.96 = 865.92 cft

Total R.C.C of beam: 661.50 + 784.34 + 865.92 = 2311.76 cft.

 

None

Slab

Concrete in slab for one story:1 *  50.83 * 50.83 * (6 / 12)= 1292 cftConcrete in slab for six stories:

1 * 1292*6 = 7752 cft

 

Concrete in slab for one story:1 * 51.33 * 51.33 * 7.5 / 12= 1647 cft.Concrete in slab for six stories:

1 * 1647 * 6 = 9882 cft

Required steel volume for beam supported structure and flat plate structure.

 Table 4.3: Comparative steel volumes.

Element

Option I building

(Beam supported structure)

Option II building

(Flat plate structure)

Column

Column: C1, C4, C10, C164 # 9 bars = 4 * 4 * 65’- 6”= 1048 rft# 3 bars @ 15” c/c

= 49 * 4 * 4’- 4”= 849.26 rft

Column: C2, C3, C5, C8, C9, C12, C14, C15

4 # 8 bars = 4 * 8 * 65’- 0”

= 2080 rft

2 # 6 bars = 2 * 8 * 64’ – 0”

= 1024 rft

# 3 bars @ 12” c/c = 61 * 8 * (5’- 4” + 1’- 1”) = 3131 rft

Column: C6, C7, C11, C13

4 # 10 Bars = 4 * 4 * 66’- 4”

= 1061.28 rft

12 # 9 bars = 12 * 4 * 65’- 6”

= 3144 rft

# 3 bars @ 18” c/c = 41 * 4 * (8’- 0”+ 5’- 10”+ 4’- 5”) = 2992.84 rft

# 8 Bars = 2080 rft = 2444 kg

# 6 bars = 4608 rft = 3464 kg

# 9 Bars = 4192 rft = 6180.64 kg

 

Column: C1, C4, C10, C164 # 8Bars = 4 * 4 * 65’- 0”= 1040 rft2 # 6 Bars = 2 * 4 * 64’- 0”

= 512 rft

# 3 bars @ 10” c/c

= 4 * (73 * 4’- 0” + 73 * 0’- 11”)

= 1435.48 rft

Column: C2, C3, C5, C8, C9, C12, C14, c15

4 # 8 Bars = 4 * 8 * 65’- 0”

= 2080 rft

8 # 6 Bars = 8 * 8 * 64’- 0”

= 512 rft

= 4096 rft

# 3 Bars @ 12” c/c

= 61 * 8 * (5’- 4”+3’- 3”+1’- 11”) = 5123.67 rft

 

Table 4.3: Comparative steel volumes (continued..).

Element

Option I building

(Beam supported structure)

Option II building

(Flat plate structure)

Column# 10 Bars = 1061.28 Rft= 2043 kg# 3 Bars = 6973.10 Rft = 1309.58 kgTotal M.S Rod      = 11977.00 kgTotal M.S Rod =11977.00 kg

= 11.98 ton

Column: C6, C7, C11, C134 # 10 Bars= 4 * 4 * 66’- 4” = 1061.28 rft6 # 9 bars

= 6 * 4 * 65’- 6”= 1572 rft

# 3 bars @ 18” c/c

= 41* 4 * (6’- 8”+2’- 3”+ 4’- 2”) = 2145.55 rft

# 8 bars = 3120 rft = 3666 kg

# 6 bars = 4608 rft = 3464 kg

# 9 Bars = 1572 rft = 2318 kg

# 10 bars = 1061.28 rft = 2043 kg

# 3 bars = 8704.22 rft = 1635 kg

Total M.S Rod = 13126.00 kg

Total R.C.C = 2072.88 cft

Total M.S Rod =13126 kg

=13.126 ton

 

Beam

M.S Rod of beam at 6th Story:Beam: B1, B2, B3, B4, B5, B6, B7, B8, B9, B10, B11, B12Top Bars: 2 # 5

=1 * 51.17’ * 2 * 2 = 204.68 ft * 0.481 = 98.45 kg

 

Bottom Bars: 3# 5

= 1 * 51.17’ * 3 * 4 = 614.04 ft * 0.481 = 295.35 kg

 

Mid = 1 * 10’ * 2 * 4 = 80.00 ft * 0.481 = 38.48 kg

None

Table 4.3: Comparative steel volumes (continued…).

Element

Option I building

(Beam supported structure)

Option II building

(Flat plate structure)

Beam

Extra top End: 2 # 7= 1 * 5.92’ * 2 * 8 = 94.72ft * 0.911 = 86.29 kgExtra top mid: 2 # 7 & 1 # 5= 1 * 9.5’ * 2 * 8 = 152.00 ft * 0.911 = 138.47 kg

= 1* 9.5’ * 8 = 76.00 ft * 0.481

= 36.56 kg

Stirrups #3Bars@ 6.50” C/C

= 85 * 3.75 * 4 = 1275 ft * 0.188 = 239.70 kg

Total Rod = 933.30 kg

Beam: B13, B14, B15, B16, B17, B18

Top Bars: 2#5

= 1 * 51.17’ * 2 * 2 = 204.68 ft * 0.481 = 98.45 kg

Bottom Bars: 2 # 6 &2 # 5

= 1 * 51.17’ * 2 * 2 = 204.68 ft * 0.752 = 153.92 kg

= 1* 51.17’ * 2 * 2 = 204.68 ft * 0.481 = 98.45 kg

Extra top End: 2 # 7

= 5.92’ * 2 * 2 * 2 = 47.36 ft * 0.911 = 43.14 kg

Extra top mid: 2 # 8

= 1 * 9.5’ * 2 * 2 * 2 = 760.00 ft * 1.176 = 89.34 kg

 

None

Table 4.3: Comparative steel volumes (continued..).

Element

Option I building

(Beam supported structure)

Option II building

(Flat plate structure)

Beam

Total = 483.30 * 2 = 966.60 kgStirrups # 3 bars @ 6.50” C / C= 85 * 3.75 * 4 = 1275 ft * 0.188 = 239.70 kgTotal = 1206.30 kg

Total Rod at 6th Floor = 933.30 + 1206.30 = 2139.60 kg

M.S Rod of Beam at 1st floor:

Beam: B1, B2, B3, B4, B5, B6, B7, B8, B9, B10, B11

Top Bars: 2 # 5

= 2 * 51.17’ * 4 = 409.36 ft * 0.481 = 196.90 kg

Bottom bars: 3 # 5

= 1 * 51.17’ * 3 * 4 = 614.04 ft * 0.481 = 295.35 kg

Extra top end: 4 # 6

= 1 * 5.92’ * 4 * 8 = 189.44 ft * 0.75 = 142.46 kg

Extra top mid: 2 # 9

= 1 * 9.5’ * 2 * 8 = 152.00 ft * 1.536 = 233.47 kg

Stirrups # 3 bars @ 6.50” C/C

= 85 * 3.75 * 4 = 1275 ft * 0.188 = 239.70 kg

Beam: B13, B14, B15, B16, B17, B18, B19, B20, B21, B22, B23, B24

Top bars: 2 # 5

None

Table 4.3: Comparative steel volumes (continued..).

Element

Option I building

(Beam supported structure)

Option II building

(Flat plate structure)

Beam

= 2 * 51.17’ * 4 = 409.36 ft * 0.481 = 196.90 kgBottom bars: 2 # 7 & 2 # 5= 2 * 20’ * 8 = 320.00 ft * 0.911 = 291.52 kg= 2 * 51.17’ * 8 = 818.72 ft * 0.481 = 393.80 kg

Extra top end: 2 # 8 & 2 # 6

= 2 * 5.92’ * 2 * 2 * 2 = 94.72 ft * 1.176 = 111.39 kg

= 2 * 5.92’ * 8 = 94.72 = 0.752

= 71.22 kg

Extra top mid: 2 # 9, 2 # 6 & 1 # 5

= 2 * 9.5’ * 2 * 2 * 2 = 152.00 ft * 1.536 = 233.47 kg

= 2 * 9.5’ * 8 = 152.00 ft * 0.752 = 114.30 kg

= 1*15’* 8= 120.00 ft *0.481

= 57.72

Stirrups # 3 bars @ 6.50” C/C

= 85 * 3.75 * 8 = 2550.00 ft * 0.188 = 479.40 kg

Total = 3077.43 kg

6th Story = 2139.60 kg

1st Story = 3077.43 kg

Total = 5217.03 kg

 

None

 Table 4.3: Comparative steel volumes (continued..).

Element

Option I building

(Beam supported structure)

Option II building

(Flat plate structure)

Beam

5th to 2nd story = 5217.03/2= 2608.51 kgTotal Rod = 2139.60+2608.51 * 4+3077.43 = 15651.07 kg

None

Slab

15 ft*15 ft slab:4.375 * (6+9+5) = 87.5 ft15.42 * (6+9+5) = 308 ft5.14 * (6+10+5) = 108 ft

4.375 * (6+9+5) = 87.5 ft

15.42 * (6+9+5) = 308 ft

5.14 * (6+11+5) = 113 ft

= 1012 ft

15 ft*20 ft slab:

4.16 * (8+15) = 96 ft

5.14 * (8+15) = 118 ft

15.42 * (8+15) = 355 ft

5 * (6+13+5) * 2 = 240 ft

20 * (6+9+5) = 400 ft

= 1209 ft

20 ft*20 ft slab:

6.81 * (12+12) = 327 ft

20 * (12+12) = 480 ft

6.81 * (12+13) * 2 = 341 ft

20*(12+12) = 480 ft

= 1628 ft

 

1S:  6 * 15.7’ = 94 ft (+ve)5 * (4.1’+ 16/12)= 27.2 ft (Ex. – ve)11 * (4.1’+ 8/12)

= 52.43 ft (In. – ve)

= 94 + 27.2 + 52.43 = 173.63 ft.

1L:  7 * 15.7’ = 109.9 ft (+ve)

6 * (4.1’+ 16 / 12)

= 32.6 ft (Ex. – ve)

12 * (4.1’+ 8 / 12)

= 57.2 ft (In. – ve)

= 109.9 + 32.6 + 57.2

= 199.7 ft.

2S:  7 * 15.7’ = 109.9 ft (+ve)

7 * (3’+ 16/12)

= 30.33 ft (Ex. – ve)

7 * (3’+ 8/12)

= 25.6 ft (In. – ve)

= 109.9 + 30.33 + 25.6

= 165.83 ft.

 

 Table 4.3: Comparative steel volumes (continued..).

Element

Option I building

(Beam supported structure)

Option II building

(Flat plate structure)

Slab

Total steel in slab = 1012 + 1209 + 1628 = 3849 ft = 3849 * (0.11 / 144)= 2.94 cft= 1440.6 lb= 653 kg. = 0.653 tonTotal steel in slab for six stories: 1 * 0.653 * 6 = 3.92 ton 2L:  165.83 ft.For panel 1: 173.63 * 2 + 199.70 * 2 + 165.83 * 2 = 1078.32 ft.3:   9 * 20’ = 180 ft (+ve)11 * 2 * (5.6’ + 8/12)

= 137.87 ft (-ve)

11 * 2 * (3.74’+ 8/12)

= 96.82

= 180 + 137.87 + 96.82

= 414.69 ft.

4:   7 * 20’ = 140 ft (+ve)

= 206.73 ft.

5:   9 * 15.7 = 141.3 ft (+ve)

7 * (5.6’+ 16/12)

= 48.53 ft (Ex. – ve)

8 * (5.6’+ 8/12)

= 50.13 ft (In. – ve)

7 * (3.74’+ 8/12)

= 30.85 ft (In. – ve)

=141.3+48.53 +50.13 + 30.85

= 270.81 ft.

6:   11 * 15.7 = 172.7 ft (+ve)

11 * (4.1’+ 16/12)

= 59.77 ft (Ex. – ve)

= 172.7 + 59.77 = 284.9 ft.

For Panel 2: 414.69 * 2 + 206.73 + 270.81 * 2 + 284.9 = 1862.63 ft.

 

 Table 4.3: Comparative steel volumes (continued..).

Element

Option I building

(Beam supported structure)

Option II building

(Flat plate structure)

Slab

7S: 11 * 20 = 220 ft (+ve)14 * 2 * (5.6’+8/12)= 175.5 ft (-ve)13 * 2 * (3.74’+ 8/12)

= 114.57 ft (-ve)

= 175.5 + 114.57 = 510.1 ft.

7L: 12 * 20 = 240 ft (+ve)

14 * 2 * (5.6’+ 8/12)

= 175.5 ft (-ve)

13 * 2 * (3.74’+ 8/12)

= 114.57 ft (-ve)

= 240 +175.5 +114.57= 530.1 ft.

8S: 9 * 20 = 180 ft (+ve)

9 * 2 * (4.1’+ 8 / 12)

= 85.8 ft (-ve)

= 180 + 85.80 = 265.8 ft.

8L: 265.8 ft.

For panel 3:  510.10 * 2 + 265.8 + 530.10 * 2 + 265.8 = 2612 ft

Total steel: 1078.32 * 4 + 1862.63 * 4 + 2612 = 14376 ft

= 19.67 cft = 4.38 ton.

Total steel in slab for six stories

= 1 * 4.38 * 6 = 26.28 ton

 

 Summary of the Comparative Study:

This cost analyses, shown in Table 4.4, are completed according to “schedule of rate for civil works”, 12th edition, PWD and as per considerations made in Chapter IV, Art 4.3.

Table 4.4: Cost analysis for volume of concrete of beam supported structure.

Sl. no.

Short description

Unit

Total

Rate  (Tk.)

Amount (Tk.)

Option I:

Beam supported structure

        i. Ground Floor

 

 

201

406576.77

cft

2022.77

ii.  1st Floor

cft

2022.77

205

414667.85

iii.  2nd Floor

cft

2022.77

209

422758.93

iv.  3rd Floor

cft

2022.77

213

430850.01

v.   4th  Floor

cft

2022.77

217

438941.09

vi)  5th Floor

cft

2022.77

221

447032.17

Total costing for concrete works  =

Tk.25,60,826.82

Table 4.5: Cost analysis for volume of concrete of flat plate structure.

Sl. no.

Short description

Unit

Total

Rate  (Tk.)

Amount (Tk.)

Option II: Flat plate structure

i.  Ground Floor

cft

2052.80

201

412612.80

ii.  1st Floor

cft

2052.80

205

420824.00

iii.  2nd Floor

cft

2052.80

209

429035.20

iv.  3rd Floor

cft

2052.80

213

437246.40

v.   4th  Floor

cft

2052.80

217

445457.60

vi)  5th Floor

cft

2052.80

221

453668.80

Total costing for concrete works =

Tk.25,98,844.80

 

 

 

 

The cost analyses of the both structures are summarized in table  below.

Table 4.6: Cost analysis for volume of 60 grade deformed bar (steel) of beam supported

                  structure.

Sl. no.

Short description

Unit

Total

Rate  (Tk.)

Amount (Tk.)

Option I: Beam supported structure

i.  Ground Floor

Kg

5450

86.99

474095.50

ii. 1st Floor

Kg

5450

87.23

475403.50

iii. 2nd Floor

Kg

5450

87.47

476711.50

iv. 3rd Floor

Kg

5450

87.71

478019.50

v.  4th Floor

Kg

5450

87.95

479327.50

vi. 5th Floor

Kg

5450

88.19

480635.50

Total costing for concrete works =

Tk.28,64,193.00

 

Table 4.7: Cost analysis for volume of 60 grade deformed bar (steel) for flat plate

                   structure.

Sl. no.

Short description

Unit

Total

Rate  (Tk.)

Amount (Tk.)

Option II: Flat plate structure

i.  Ground Floor

Kg

6050

86.99

526289.50

ii. 1st Floor

Kg

6050

87.23

527741.50

iii. 2nd Floor

Kg

6050

87.47

529193.50

iv. 3rd Floor

Kg

6050

87.71

530645.50

v.  4th Floor

Kg

6050

87.95

532097.50

vi. 5th Floor

Kg

6050

88.19

533549.50

Total costing for concrete works =

Tk.31,79,517.00

Grand Total (I+II) =

 Tk.11,203,381.62

The table below is showing total concrete requirement, steel requirement and cost difference for flat plate structure and beam-supported structure.

Table 4.8: Summary of cost analyses for both structures

Type of structure

Total volume of concrete works

(cft)

Total volume of steel works

 

(kg)

Total costing of concrete works

(Tk)

Total costing of steel works

 

(Tk)

Remarks

Beam supported structure

12136.64

32700.00

25,60,826.82

28,64,193.00

About 6.5 %  more cost required for flat plate  structure

Flat plate structure

12316.80

36300.00

25,98,844.80

31,79,517.00

CONCLUSION AND RECOMMENDATION

 Recommendations for Further Study:

For further study in this field, the following recommendations are put forward:

i) The study needed use of conventional finite element software and manual calculation for both analysis and design of whole structures to give a comprehensive conclusion.

ii) Instead of one residential square building of about 3.5 katahs it requires other geometrically shaped and larger areas residential building for accurate comparison.

Conclusions:

From the comparative study of beam supported structure and flat plate structure, we gathered knowledge that:

a)      From the Finite Element Analysis result it can be said that the internal forces in the flat plate structure is higher than that of beam supported structure.

b)      The construction of flat plate structure requires more construction material which results in more cost. Such as, concrete requirement increased in flat plate structure about 1.5% and steel requirement about 11% and finally increased cost of 6.5% than beam supported structure.

c)      In case of flat plate structure interior space of building looks nice, due to absence of beams offset. Flat plate slab is thicker and more heavily reinforced than slabs with beams and girders.

d)     It is apparent from the cost comparison that the difference between two estimates is very insignificant and moreover this difference is for only frame of the building. The cost per unit area for finishing items will remain same for all cases. In compare to the enormous benefit that can be gained for aesthetic view and also for light provision, the cost increase in this case is very insignificant.

References:

  1. ACI Code, 1995, USA
  2. ETABS -Version 8.2.7
  3. BNBC (1993), “Bangladesh National Building Code” 1st  edition, city Art Press,

      Bangladesh.

4.   “Design of concrete structure”- 13th edition by Arthur H. Nilson, David Darwin,  Charles W. Dolan.

  1. “Schedule of Rate for Civil works”, 11th edition, Public works department,

Government of the Peoples Republic of Bangladesh, 21st November. 2008.

Flat Plate

Some are parts:

Analysis Between a Beam Supported Structure and a Flat Plate Structure (Part 1)

Analysis Between a Beam Supported Structure and a Flat Plate Structure (Part 2)

Analysis Between a Beam Supported Structure and a Flat Plate Structure (Part 3)