DESIGN REINFORCED AREAS OF CONCRETE BEAM DEPEND ON THE CONCRETE TABLE

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1 International Journal of Civil Engineering and Tehnology (IJCIET) Volume 10, Issue 04, April 019, pp Artile ID: IJCIET_10_04_15 Available online at ISSN Print: and ISSN Online: IAEME Publiation Sopus Indexed DESIGN REINFORCED AREAS OF CONCRETE BEAM DEPEND ON THE CONCRETE TABLE Leturer of Civil Engineering Department Universitas Kristen Indonesia Paulus, Makassar, Indonesia ABSTRACT The traditional method of reinfored onrete beam design that using the table depend on the onrete and strength of the steel. There are many strenght steel in market and onrete, so many tables are also needed. A simpler method namely the new method where is using table depend on the onrete is needed. All the equilibrium equation variable hange into ξ=/d, so only one type table is needed. In this study, only onrete table should be provided. Priniple alulation in the traditonal method and the new method is samed. The strenght of steel is used later. From the example an be onluded that the new method an be used as a method of designing reinfored onrete beam. Keywords: variable ξ=/d and onrete table Cite this Artile:, Design Reinfored Areas of Conrete Beam Depend on the Conrete Table, International Journal of Civil Engineering and Tehnology, 10(4), 019, pp INTRODUCTION 1.1. The traditional method Singly reinforement Compression of onrete Tension of steel C = 0.85f ab (1) T s = A s = ρbd () editor@iaeme.om

2 Design Reinfored Areas of Conrete Beam Depend on the Conrete Table Fores equilibrium Moment equilibrium Figure 1 Singly reinforement setion F = f ab A s = f ab = A s a = ρd 0.85f (3) M = 0 M A s (d 1 a) = 0 M = ρbd (d 1 a) (4) If :n M = 0.9ρbd (1 ρ 1.7f ) (5) M bd = 0.9ρ (1 ρ 1.7f ) R u = M bd (6) = 0.9 (redution fator) (7) 0.9 f y 1.7 f ρ 0.9 ρ + R u = 0 (8) ρ = 0.85 f R u ( f ) (9) So, in the traditional method ρ diretly alulated from Ru, strength of steel and behavior of onrete namely β 1 and f and A s = ρbd (10) editor@iaeme.om

3 Control ρ min < ρ < ρ max for singly reinforement. Where : Or : ρ max is taken : ρ min = f 4 (11) ρ min = 1.4 (1) d = ε u = = ε u +ε y Es (13) = (14) d + = + d (15) H = 0 C T s = f ab A s = f β 1 b ρ b bd = f β 1 ρ b d = f β 1 + d ρ b d = f β 1 + ρ b = 0 ρ b = 0.85 f For struture under reinfored, ratio maximum is taken: ρ max = 0.75ρ b = f β 1 + (16) β 1 = f + β f 1 (17) y +. DOUBLY REINFORCEMENT If more slender beam is needed in design for aestheti, so maybe ξ > ξ max. In this ase ompression steel is needed Figure 3 Doubly reinforement sestion editor@iaeme.om

4 Design Reinfored Areas of Conrete Beam Depend on the Conrete Table All the formula assumed f s =. So M is needed to devide two segment M u1 dan M u Where : M u1 is a bending moment related ρ max and Tensile steel is : z = (d 1 a) (18) A s1 = ρ max bd (19) M u1 = ρ max bd (d 1 a) M u1 = 0.9ρ max bd (1 ρ 1.7f ) (0) M u is the remaining moment against by the same tensile steel and ompresssion steel. The arm bending moment is z = d d The total added steel A s = A s : Total A s :. METHODOLOGY.1. The New method A s = A s = M u M u1 (d d) A s = A s1 + A s = ρ max bd + M u M u1 (d d) (1) ().1.1. Singly reinforement In this study all the equilibrium equation, is onverted to ξ = ( ) as variable : d Moment equilibrium : M = 0 M A s (d 1 a) = 0 M = f ab(d 1 a) M = f bd { a d 1 (a d ) } M bd = 0.765β 1f { d 1 β 1 ( d ) } R u = M bd ξ = ( d ) (3) 0.385β 1 f ξ 0.765β 1 f ξ + R u = 0 (4) editor@iaeme.om

5 ξ = 1 β 1 (1 1 R u f ) (5) From of this equation, ξ diretly alulated, only depend on Ru and behavior of onrete namely β 1 andf, so it beome easier. And As = A s = 0.85 f The strenght of steel is used later F = 0 C T s = f ab A s = 0 ab = 0.85 ( a d ) f bd = 0.85β f 1 ( y d ) f bd A s = 0,85 β 1 ξ f ρ = 0.85β 1 ξ f ρ b = 0.85β 1 ξ b f ρ max = 0.75 ρ b = β 1 ξ b f 3. DOUBLY REINFORCEMENT Where : M u1 is the bending moment related ξ max. Tensile steel is bd (6) (7) ξ max = ) f A s1 = ρ max bd = β 1 ξ f b bd = 0.85β f 1 ξ max bd (9) y M u1 = 0.9ρ max bd (1 ρ 1.7f ) M u1 = 0.765β 1 f bd ξ max {1 1 β 1ξ max } (30) M u is the remaining momen against by the same tensile steel and ompresssion steel. The arm bending moment is The total added steel A s = A s : z = d d (31) Total A s : A s = A s = M u M u1 (d d) A s = A s1 + A s = 0.85β 1 ξ max f bd + M u M u1 (d d) (3) editor@iaeme.om

6 Design Reinfored Areas of Conrete Beam Depend on the Conrete Table 4. BORDER FOR TABLE 4.1. R u border : 4.. ξ border For simpliation : D 0 (33) (0.765 β 1 f ) β 1 f R u 0 R u 0.385f (34) ξ max = Where : min = 80 MPa (35) For simpliation : So : ξ max = (36) ξ min = 1.4 Where : max = 550 MPa (37) Or : So : ξ min = (38) ξ min = β 1 f = β 1 f f 1 = 4 3.4β 1 f (39) Table 1 ξ min f' 1 min min 17 0,850 0,006 0, ,850 0,006 0, ,850 0,006 0, ,836 0,006 0, ,800 0,006 0, ,764 0,006 0, CASE STUDY 5.1. The traditional method. b = 0.4 d = 0.5 m f = 35 MPa = 400 MPa M u = 850 knm R u = M u bd = 8500 kn/m = 8.5 MPa editor@iaeme.om

7 ρ = 0.85 f (1 1 R u 0.385f ) = 0.09 > Doubly reinforement Atually the traditional method provides the table for alulation but here used hand alulation. ρ max = f β 1 + = ρ min = f 4 = ρ min = 1.4 = M u1 = 0.9ρ max bd (1 ρ max 1.7f ) = ,4 0, (1 ) = knm A s1 = ρ max bd = = m A s = A s1 + A s = ρ max bd + M u M u = = (d d) (50 5) = m 5.. The new method. From the table(attahement), founded : R u = M u = 8500 MPa = 8.5 MPa < Ru = = 13,3875 bd ξ max = 0.75 = 0.45 < ξ = Doubly reinforement +400 A s1 = 0.85β 1 ξ max f bd = = m M u1 = 0.765β 1 f bd ξ max {1 1 β 1ξ max } = (1 Total A s : = 0.85β 1 ξ max f 1 bd + M u M u1 (d d) ) = knm A s = A s1 + A s = = = m (50 5) 6. CONCLUSION From the ase study obtained the new method is same with the result from the traditional method, namely As = 53,554 m m. This indiates that the new method an be used as method of designing reinfored onrete beam editor@iaeme.om

8 Design Reinfored Areas of Conrete Beam Depend on the Conrete Table REFERENCES [1] Badan Standarisasi Nasional (BSN) SNI , Persyaratan beton struktural untuk bangunan gedung, Jakarta, 013. (Indonesian onrete ode same as ACI) [] Ma Gregor, James G., Reinfored onrete (Mehanis and design), Third edition, Prentie-Hall International, In,1988. [3] Park, R,. and T. Paulay, Reinfored Conrete Strutures, Department of Civil Engineering University of Canterbury New Zealand, John Wiley & Sons, New York. [4] Vis, W. C. dan Kusuma, Gideon, 1993, Grafik dan tabel perhitungan beton bertulang (Seri beton 4), Penerbit Erlangga, Jakarta. (Vis, W. C. (Duthman) and Kusuma, Gideon, 1993 Graph and table for reinfored onrete alulation (Conrete series 4), Erlangga Publisher, Jakarta). ATTACHEMENT f' 17 f' 0 f' 5 1 0, , ,850 M u/bd M u/bd M u/bd 4,4 0,511 5,0 0,511 6,50 0,511 4,40 0,507 5,10 0,497 6,40 0,500 4,30 0,49 5,00 0,484 6,30 0,489 4,0 0,476 4,90 0,471 6,0 0,479 4,0 0,476 4,80 0,458 6,10 0,469 4,10 0,461 4,70 0,446 6,00 0,458 4,00 0,447 4,60 0,434 5,90 0,448 3,90 0,43 4,50 0,4 5,80 0,439 3,80 0,418 4,40 0,410 5,70 0,49 3,70 0,404 4,30 0,398 5,60 0,419 3,60 0,390 4,0 0,386 5,50 0,410 3,50 0,377 4,10 0,375 5,40 0,400 3,40 0,364 4,00 0,364 5,30 0,391 3,30 0,351 3,90 0,353 5,0 0,38 3,0 0,338 3,80 0,34 5,10 0,373 3,10 0,35 3,70 0,331 5,00 0,364 3,00 0,313 3,60 0,30 4,90 0,355,90 0,301 3,50 0,310 4,80 0,346,80 0,89 3,40 0,300 4,70 0,338,70 0,77 3,30 0,89 4,60 0,39,60 0,65 3,0 0,79 4,50 0,30,50 0,53 3,10 0,69 4,40 0,31,40 0,4 3,00 0,59 4,30 0,304,30 0,31,90 0,49 4,0 0,95,0 0,19,80 0,40 4,10 0,87,10 0,08,70 0,30 4,00 0,79,00 0,198,60 0,1 3,90 0,71 1,90 0,187,50 0,11 3,80 0,63 1,80 0,176,40 0,0 3,70 0, editor@iaeme.om

9 f' 17 f' 0 f' 5 1 0, , ,850 M u/bd M u/bd M u/bd 1,70 0,165,30 0,193 3,60 0,47 1,60 0,155,0 0,183 3,50 0,40 1,50 0,145,10 0,174 3,40 0,3 1,40 0,134,00 0,165 3,30 0,4 1,30 0,14 1,90 0,157 3,0 0,17 1,0 0,114 1,80 0,148 3,10 0,09 1,10 0,104 1,70 0,139 3,00 0,0 1,00 0,094 1,60 0,130,90 0,194 0,90 0,084 1,50 0,1,80 0,187 1,40 0,113,70 0,180 1,30 0,105,60 0,173 1,0 0,096,50 0,165 1,10 0,088,40 0,158 1,00 0,080,30 0,151,0 0,144,10 0,137,00 0,130 1,90 0,13 1,80 0,116 1,70 0,110 1,60 0,103 1,50 0,096 1,40 0,090 1,30 0,083 1,0 0,076 1,10 0,070 f' 30 f' 35 f' , , ,764 M u/bd M u/bd M u/bd 7,70 0,510 8,70 0,510 9,60 0,510 7,60 0,501 8,60 0,50 9,50 0,503 7,50 0,49 8,50 0,495 9,40 0,496 7,40 0,483 8,40 0,487 9,30 0,489 7,30 0,475 8,30 0,479 9,0 0,48 7,0 0,466 8,0 0,47 9,10 0,476 7,10 0,458 8,10 0,464 9,00 0,469 7,00 0,449 8,00 0,457 8,90 0,46 6,90 0,441 7,90 0,450 8,80 0,456 6,80 0,433 7,80 0,44 8,70 0, editor@iaeme.om

10 Design Reinfored Areas of Conrete Beam Depend on the Conrete Table f' 30 f' 35 f' , , ,764 M u/bd M u/bd M u/bd 6,70 0,45 7,70 0,435 8,60 0,443 6,60 0,417 7,60 0,48 8,50 0,436 6,50 0,409 7,50 0,41 8,40 0,430 6,40 0,401 7,40 0,414 8,30 0,44 6,30 0,393 7,30 0,407 8,0 0,417 6,0 0,385 7,0 0,400 8,10 0,411 6,10 0,378 7,10 0,393 8,00 0,405 6,00 0,370 7,00 0,387 7,90 0,399 5,90 0,36 6,90 0,380 7,80 0,39 5,80 0,355 6,80 0,373 7,70 0,386 5,70 0,348 6,70 0,367 7,60 0,380 5,60 0,340 6,60 0,360 7,50 0,374 5,50 0,333 6,50 0,353 7,40 0,368 5,40 0,36 6,40 0,347 7,30 0,36 5,30 0,319 6,30 0,340 7,0 0,357 5,0 0,31 6,0 0,334 7,10 0,351 5,10 0,305 6,10 0,38 7,00 0,345 5,00 0,98 6,00 0,31 6,90 0,339 4,90 0,91 5,90 0,315 6,80 0,333 4,80 0,84 5,80 0,309 6,70 0,38 4,70 0,77 5,70 0,303 6,60 0,3 4,60 0,70 5,60 0,97 6,50 0,316 4,50 0,64 5,50 0,91 6,40 0,311 4,40 0,57 5,40 0,84 6,30 0,305 4,30 0,50 5,30 0,78 6,0 0,99 4,0 0,44 5,0 0,7 6,10 0,94 4,10 0,37 5,10 0,67 6,00 0,88 4,00 0,31 5,00 0,61 5,90 0,83 3,90 0,4 4,90 0,55 5,80 0,78 3,80 0,18 4,80 0,49 5,70 0,7 3,70 0,1 4,70 0,43 5,60 0,67 3,60 0,05 4,60 0,37 5,50 0,61 3,50 0,199 4,50 0,3 5,40 0,56 3,40 0,193 4,40 0,6 5,30 0,51 3,30 0,187 4,30 0,0 5,0 0,45 3,0 0,180 4,0 0,14 5,10 0,40 3,10 0,174 4,10 0,09 5,00 0,35 3,00 0,168 4,00 0,03 4,90 0,30,90 0,16 3,90 0,198 4,80 0,5,80 0,156 3,80 0,19 4,70 0,19,70 0,150 3,70 0,187 4,60 0, editor@iaeme.om

11 f' 30 f' 35 f' , , ,764 M u/bd M u/bd M u/bd,60 0,144 3,60 0,181 4,50 0,09,50 0,138 3,50 0,176 4,40 0,04,40 0,13 3,40 0,170 4,30 0,199,30 0,17 3,30 0,165 4,0 0,194,0 0,11 3,0 0,160 4,10 0,189,10 0,115 3,10 0,154 4,00 0,184,00 0,109 3,00 0,149 3,90 0,179 1,90 0,104,90 0,144 3,80 0,174 1,80 0,098,80 0,138 3,70 0,169 1,70 0,09,70 0,133 3,60 0,164 1,60 0,087,60 0,18 3,50 0,159 1,50 0,081,50 0,13 3,40 0,155 1,40 0,075,40 0,118 3,30 0,150 1,30 0,070,30 0,11 3,0 0,145 1,0 0,064,0 0,107 3,10 0,140,10 0,10 3,00 0,135,00 0,097,90 0,131 1,90 0,09,80 0,16 1,80 0,087,70 0,11 1,70 0,08,60 0,116 1,60 0,077,50 0,11 1,50 0,07,40 0,107 1,40 0,067,30 0,10 1,30 0,06,0 0,098,10 0,093,00 0,089 1,90 0,084 1,80 0,079 1,70 0,075 1,60 0,070 1,50 0,066 1,40 0, editor@iaeme.om