Design Beam

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    02-Dec-2014

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I/ Design BeamGB9A effective span= m1 - Loading Slab Panel x m andmTHK (Slab on one side of the beam)Dead LoadSlab kN/m x m / = kN/mBeam kN/m x m / = kN/mOther kN/m x m = kN/mWall 10cm kN/m x m = kN/mWall 20cm kN/m x m = kN/mFloor Finished kN/m x m = kN/mTotal Dead Load kN/m (Trapezoidal Dead load per m lenghtLive Load or Imposed loadon one side of the beam)Floor LL kN/m x m / = kN/mTotal live Load kN/m (Trapezoidal Live load per m lenghtDesign Loadon one side of the beam)Design Load ( x )+( x ) = kN/m (Trapezoidal load= kN/m)Convert Trapezoidal load to uniformly distributed load Uniformly distributed Load ( x ) = kN/mLoad on the other side of the bem ( - ( x / )= kN/m (Reduce 30% for theload on the other side)Total Load on both side of the bem + = kN/m2 - Bending MomentMax moment at support Msup= = kN/mMax moment at mid spanMmid= = kN/mBS8110 REF. OUTPUT CALCULATION- ql/12 -255.897.7 3.410.12247.76.48ql/24 127.9425 1.052.2542.08 7.77.7 2.252.251.202.2502.702.25 m 918.21.5 2.25 3.3830 10091.6 #### 1.4 9.00 41.730.5 #### 51.841.721.341.73 0.73 30.530.5 ####2 xe xe xe l n M = | = xe | = xe M 2 x xm xm l n M = | kNm = xm M 2 x ye ye l n M = | = xm | = ye | = ye M kNm 2 x ym ym l n M = | = ym | = ym M kNm = = z f M A y xe req s 87 . 0 , = cu f 2 mm N = bar rolling y f , 2 mm N = y f 2 mm N m mm/ 2 = pro s A , 2 mm = = z f M A y xm req s 87 . 0 , m mm/ 2 m mm/ 2 m mm/ 2 = = z f M A y ye req s 87 . 0 , = = z f M A y ym req s 87 . 0 , 2 mm N 2 mm N = = x xe force l n V | m kN/ = = bd V V force stress / 2 mm N = |.| \| ||.| \| = 4 1 3 1 , 400 100 25 . 1 75 . 0 d bd A V pro s capacity 2 mm N m kN/ = = bd V V force stress / 2 mm N = |.| \| ||.| \| = 4 1 3 1 , 400 100 25 . 1 75 . 0 d bd A V pro s capacity 2 mm N = = x ye force l n V | = pro s A , 2 mm = pro s A , 2 mm = pro s A , 2 mm 2 xe xe xe l n M = | = xe | = xe MkNm2 x xm xm l n M = | kNm= xm M 2 x ye ye l n M = | = xm | = ye | = ye MkNm2 x ym ym l n M = | = ym | = ym MkNm= = z f M A y xe req s 87 . 0 , = cu f 2 mm N = bar rolling y f , 2 mm N= y f 2 mm N m mm/ 2 = pro s A , 2 mm= = z f M A y xm req s 87 . 0 , m mm/ 2 m mm/ 2 m mm/ 2 = = z f M A y ye req s 87 . 0 , = = z f M A y ym req s 87 . 0 , 2 mm N 2 mm N = = x xe force l n V | m kN/ = = bd V V force stress / 2 mm N = |.| \| ||.| \| = 4 1 3 1 , 400 100 25 . 1 75 . 0 d bd A V pro s capacity 2 mm N m kN/ = = bd V V force stress / 2 mm N = |.| \| ||.| \| = 4 1 3 1 , 400 100 25 . 1 75 . 0 d bd A V pro s capacity 2 mm N = = x ye force l n V | = pro s A , 2 mm= pro s A , 2 mm= pro s A , 2 mm2 mm2 mm2 mm2 mm kNm13 - Beam Sectionb= (0.4 to 0.5)h=(0.4 to 0.5) . b= mm b= mmCover: C= mm ;Assume Steel Bar DR= mm ; DT= mmd= h - C - DR/2 - DT/2 = = mm d'= mmii - Define Steel AreaAssume fcu= N/mm ; fy v= N/mm fy = N/mma - Define Steel Area at Support Mmax= kNmxx xz = = = mmthat zmm z = mm As = =As =mm2 T As=mm2 P=100(As,req / bd)= > < 4 b - Define Steel Area at Mid span Mmax= kNmxx xz = = = mmthat zmm z = mm As = =As =mm2 T As=mm2 P=100(As,req / bd)= > < 4 [(k'. fcu.b.d^2)/(0.87.fy.z)]+As'[(0.13x30x200x362^2) x10^6)/ (0.87x390x297)]+12562285.92 Assume 9 20 2826d.[0.5+(0.25-(k'/0.9))^(1/ 2)] .[0.5+(0.25-(0.132/ 0.9)^(1/ 2))] 297297 not exceed 0.95d= 344390k=M=160(Doubly Reinforced Section)bd2fcu 200 1310440.15635297344 so 344400 - 25 - 3 - 10106362mm 400(Doubly Reinforced Section)20h= to10Lk=bd2fcu=15=770010255.89h=400256 h= 550 mm2480.156to20060.95d=362.[0.5+(0.25-(0.132/ 0.9)^(1/ 2))] d.[0.5+(0.25-(k'/0.9))^(1/ 2)]LM30 2500.325 >30 131044 200not exceed3087.46 Assume 11 20 3454[(k'. fcu.b.d^2)/(0.87.fy.z)]+As'[(0.13x30x200x362^2)x10^6) / (0.87x390x343.9)]+219830106OKso1600.203 >OK15253.53 0.134.32 0.1377002c - Check Deflectionxx5 58 8- fs(0.9+(M / bd2))= ( table3.9 in Code BS8110 Part 1 1985) = x == lx / dx = / = = > = c - LinkMax Shear at Support= kN= / bd = / = N/mmVcapacity= (0.79/1.25) [(100As/bd)^(1/3)] [(400/d)^(1/4)] [(fcu/25)^(1/3)]= x== N/mm > N/mm (Case 3 in table3.7 in Code BS8110)Asv(bv Sv(vs-vc))/0.87fyAssume 6 mm Area of link mm2 Link SpacingSv(Asv x 0.87fy)/(bv(vs-vc)) = mm mmHence R6@80Shear at L/4 from the support= kN= N/mm= N/mm Assume 6 mm Area of link mm2 Link SpacingSv(Asv x 0.87fy)/(bv(vs-vc)) = mm mm 60.380180Vcap.1.0855Asv= 55Vl/4150Vstress2.07Asv=Vstress2.32 Vcapacity48.2+0.4= 1.48=bd26.10Mmax=160 106200 131044fs = fyAs,reqAs,pro= x 390 x2286= 197 (Service Stress)2826modification factor = 0.55 +477= 0.97120Bassic span/depth 26Allowable span/depth 26 0.97 25.37700OK362 21.3Allowable span/depth 25.3 Actual span/depth 21.31.08Actual span/depthVmax168VstressVmax200x362 2.32 168x(10^3)0.63 [((100x2826)/(200x362))^(1/3)]x (400/362)^(1/4)x (30/25)^(1/3)kNm 3 / 1 4 / 1 3 / 1 25 400 100 25 . 1 79 . 0 |.| \| |.| \| |.| \| cu f d bdAs3Hence R6@1804RE-Design Section of Ground BeamGB9A I/ Design BeamGB9Aeffective span= m1 - Loading Slab Panel x m andx m andmTHKDead LoadSlab kN/m x x = kN/m kN/m x x = kN/mBeam kN/m x x = kN/mOther kN/m x = kN/m kN/m x = kN/mWall 10cm kN/m x = kN/m kN/m x = kN/mWall 20cm kN/m x = kN/m kN/m x = kN/mFloor Finished kN/m x = kN/m kN/m x = kN/mTotal Dead Load kN/m kN/mLive Load or Imposed loadFloor LL kN/m x m = kN/m kN/m x m = kN/mTotal live Load kN/m kN/mTriangle or Trapezoidal Design Load= kN/m (1.4 x 16.11) + (1.6 x 3.75) = kN/mConvert Trapezoidal load to uniformly distributed loadfor bending momentUniformly distributed Loadx = kN/m x = kN/mTotal uniformly distributed load + = kN/m(1.4 x 17.79) + (1.6 x 3.75) 30.9 28.617.8 16.13.75 3.751.5 2.5 3.75 1.5 2.5OUTPUT53.751.5 3.3 4.95 1.5 3.30 2.54.950 0 0 0 0 01.2 3.3 3.96 1.2 3.3 3.960 0 2.5 024 0.35 0.2 1.6830.9 0.67 20.6Left Side of the beam Right Side of the beam24 0.12 2.5 7.2 24 0.12 2.5 7.2BS8110 REF.5 2.5 5 2.5 0.12CALCULATION28.620.6 18.8 39.430.66 18.852 - Bending MomentMax moment at support Msup= = kN/mMax moment at mid spanMmid= = kN/m3 - Beam Sectionb= (0.4 to 0.5)h=(0.4 to 0.5) . b= mm b= mmCover: C= mm ;Assume Steel Bar DR= mm ; DT= mmd= h - C - DR/2 - DT/2 = = mm d'= mm4 - Define Steel AreaAssume fcu= N/mm ; fy v= N/mm fy = N/mma - Define Steel Area at Support Mmax= kNmxx xz = = = mmthat zmm z = mmx = ( - )/ = Compression Steel Area Tension Steel Area As = =As =mm2 T As=mm2 P=100(As,req / bd)= > < 4 ql/2435030-82.14mm h=41.075000- ql/12to h=LtoL=5000350 mm10 15 10 15 h= 357161 20025 6 16350 - 25 - 3 - 8 314 33250 39082.14k=M=82.1 1060.139bd2fcu 200 98596 30298< 0.156(Singly Rienforced Section)d.[0.5+(0.25-(k/0.9))^(1/ 2)] 314.[0.5+(0.25-(0.139/ 0.9)^(1/ 2))] 254not exceed 0.95d= 298 soM /0.87 fy.z811.592 Assume 5 16 10051.44 0.13 OK[(82x10^6) / (0.87x390x298.3)]OUTPUT BS8110 REF. CALCULATION314 298 0.45 34.9No Steel Require6b - Define Steel Area at Mid span Mmax= kNmxx xz = = = mmthat zmm z = mmx = ( - )/ = Compression Steel Area Tension Steel Area As = =As =mm2 T As=mm2 P=100(As,req / bd)= > < 4 c - Check Deflectionxx5 58 8- fs(0.9+(M / bd2))= ( table3.9 in Code BS8110 Part 1 1985) = x == lx / dx = / = = > = 0.96 0.13 OKM /0.87 fy.z [(41x10^6) / (0.87x390x298.3)]405.796 Assume 3 16 6030 298 0.45 -663No Steel Requirek=M=41.1 106so41.07bd2fcu 200 98596 300.069298< 0.156(Singly Rienforced Section)not exceed 0.95d= 298d.[0.5+(0.25-(k/0.9))^(1/ 2)] .[0.5+(0.25-(0.069/ 0.9)^(1/ 2))] 288Mmax=41.1 106= 2.08=bd2200 98596fs = fyAs,req=164 (Service Stress)As,pro603= x 390 x406314Allowable span/depth 26 1.94 50.51.94120Bassic span/depth 26modification factorOK0.55 +477=Actual span/depth 15.9 5000Allowable span/depth 50.5 Actual span/depth 15.9BS8110 REF. CALCULATION OUTPUT7d - LinkConvert Trapezoidal load to uniformly distributed loadfor bending momentUniformly distributed Loadx = kN/m x = kN/mTotal uniformly distributed load + = kN/m Total load per m lenght forbending moment kN/mMax Shear at Support= = kN= / bd = N/mmVcapacity= (0.79/1.25) [(100As/bd)^(1/3)] [(400/d)^(1/4)] [(fcu/25)^(1/3)]= N/mm= N/mm > N/mmAssume 6 mm Area of link mm2 Link SpacingSv(Asv x 0.87fy)/(bv(vs-vc)) = mm mmHence R6@120Shear at L/4 from the support= = kN= N/mm= N/mm Assume 6 mm Area of link mm2 Link SpacingSv(Asv x 0.87fy)/(bv(vs-vc)) = mm mmHence R6@150(Case 3 in table3.7 in Code BS8110)OUTPUTVmaxql/215.5+0.4= 1.23 1.18 VcapacityVstressVmax74.31.184Asv= 551073 15055170 12055.74 q(l-0.25l)/229.715.5Asv=0.83Vstress14.3Vcap.0.83Vl/4Vstress0.89BS8110 REF. CALCULATION29.73Left Side of the beam Right Side of the beam30.9 0.5 28.6 0.5 14.38Check Existing Section of Ground Beam GB7 (Along Grid 4 from Grid E-G) I/ Check ExistingGB7 effective span= mA -Loading Slab Panel x m andx m andmTHKDead LoadSlab kN/m x x = kN/m kN/m x x = kN/mBeam kN/m x x = kN/mRoof Load kN/m x = kN/m kN/m x = kN/mWall 10cm kN/m x = kN/m kN/m x = kN/mWall 20cm kN/m x = kN/m kN/m x = kN/mFloor Finished kN/m x = kN/m kN/m x = kN/mTotal Dead Load kN/m kN/mLive Load or Imposed loadFloor LL kN/m x m = kN/m kN/m x m = kN/mRoof LL kN/m x m = kN/m kN/m x m = kN/mTotal live Load kN/m kN/mTriangle or Trapezoidal Design Load= kN/m = kN/mConvert Trapezoidal load to uniformly distributed load Uniformly distributed Loadx = kN/m x = kN/mTotal uniformly distributed load + = kN/m1 18.647.4 18.59 65.9647.4 1 47.4 18.64 3.313.2 4.4(1.4 x 18.75) + (1.6 x 13.2) 47.4 (1.4 x 8.25) + (1.6 x 4.4) 18.60 1.7 0 0 0.83 013.2 41.1 1.6518.8 8.31.1 4.41.5 3.3 4.95 1.53.3 3.960 0 0 0 0 01.2 3.3 3.96 1.20.83 024 0.20 1.7 0 0BS8110 REF. CALCULATION0.4 1.92Left Side of the beam Right Side of the beam24 0.1 24 0.1 1.1 2.64 3.3 7.92OUTPUT6.66.6 3.3 6.6 1.1 0.19B -Bending MomentMax moment at support Msup= = kN/mMax moment at mid spanMmid= = kN/mC -Beam Sectionb= (0.4 to 0.5)h=(0.4 to 0.5) . b= mm b= mmCover: C= mm ;Assume Steel Bar DR= mm ; DT= mmd= h - C - DR/2 - DT/2 = = mm d'= mmD- Define Steel AreaAssume fcu= N/mm ; fy v= N/mm fy = N/mma - Define Steel Area at Support Mmax= kNm Compression Steel AreaExisting Steel Area T As'=mm2 Tension Steel AreaExisting Steel Area T As=mm2T As'=mm2Total Steel Area mm P