Architecture

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 no There 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: C1,C4,C10,C16: Size = 18” * 10” C2,C3,C5,C8,C9,C12,C14,C15 Size = 24” * 12” C6,C7,C11,C13: Size = 26” * 18” All the columns are: C1,C4,C10,C16: Size = 15” * 15” C2,C3,C5,C8,C9,C12,C14,C15 Size = 24” * 12” 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) Column Column: 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) Beams Beam: 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,

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.

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)

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