BEAM 5007 DESIGN IS 456
Caption Calculation Symbol =ValueUnitReference OR Explanation
BEAM GEOMETRY
Design Parameters
0System of UnitsSys=SI
1Length Units LUnits=metre
2Force Units FUnits=Newton
3Concrete Strengthfck=20N/mm^2Cl: 5.2 of IS 13920
4Concrete safety factorγc=1.5Cl 36.4.1 of IS 456-2000
5Concrete Young's ModulusEc=22360.67977N/mm^2Cl 6.2.3.1 of IS 456-2000
6Steel Strengthfy=415N/mm^2Cl: 5.3 of IS 13920
7Steel safety factorγs=1.15Cl.36.4.1 of IS 456-2000
8Steel Young's ModulusEs=200000N/mm^2Cl 5.6.3 of IS 456-2000
9Member LengthL=2644mm
10Member BreadthB=230mm
11Member Gross DepthDg=250mm
12Clear Coverdc=25mm
13Max Tension Steelρt,max=4%
14Max Compr Steelρc,max=4%
15Min Tension Steel %ρt,min=0.12%
16Min Compr Steel %ρc,min=0.12%
17Weight of ConcreteWc=25kN/m^3
18Weight of SteelWs=785kN/m^3
19Load Safety Factorγl=1.5
20Main bar Diaφ=12mm
21Stirrup Steel Stressfys=250N/mm^2
22Stirrup bar Dias_bar=8mm
23Stirrup Spacingsv=450mm
24Min SpacingminSv=50mm
25Depth of FlangeDf=125mmFlange Depth
26Span/d ratio limitLim L=10m
27Creep Coefficientcft=1.6
28Continuous Both EndsbTy=2Beam Type
29Crack Width LimitWcrL=0.3mm
30Span LEFTLlt=2500mm
31Span RIGHTLrt=3000mm
STAAD BM FORCE ENVELOPE
Max +Ve Bending Moments
Section 0.00 Load Case: 29BM=26.65kN m26,650,000 N mm
Section 0.44 Load Case: 29BM=13.45kN m13,450,000 N mm
Section 0.88 Load Case: 8BM=4.64kN m4,640,000 N mm
Section 1.32 Load Case: 8BM=0.42kN m420,000 N mm
Section 1.76 Load Case: 7BM=3.80kN m3,800,000 N mm
Section 2.20 Load Case: 32BM=11.97kN m11,970,000 N mm
Section 2.64 Load Case: 28BM=24.98kN m24,980,000 N mm
Max -Ve Bending Moments
Section 0.00 Load Case: 32BM=-15.41kN m-15,410,000 N mm
Section 0.44 Load Case: 32BM=-13.20kN m-13,200,000 N mm
Section 0.88 Load Case: 28BM=-10.95kN m-10,950,000 N mm
Section 1.32 Load Case: 28BM=-6.04kN m-6,040,000 N mm
Section 1.76 Load Case: 29BM=-9.82kN m-9,820,000 N mm
Section 2.20 Load Case: 29BM=-12.14kN m-12,140,000 N mm
Section 2.64 Load Case: 33BM=-14.39kN m-14,390,000 N mm
STAAD SHEAR FORCE ENVELOPE
Max +Ve Shear Forces
Section 0.00 Load Case: 29SF=33.02kN26,650 N
Section 0.44 Load Case: 29SF=26.86kN13,450 N
Section 0.88 Load Case: 8SF=20.69kN4,640 N
Section 1.32 Load Case: 8SF=14.52kN420 N
Section 1.76 Load Case: 7SF=10.76kN3,800 N
Section 2.20 Load Case: 32SF=9.58kN11,970 N
Section 2.64 Load Case: 28SF=9.58kN24,980 N
Max -Ve Shear Forces
Section 0.00 Load Case: 32SF=-9.58kN-15,410 N
Section 0.44 Load Case: 32SF=-9.58kN-13,200 N
Section 0.88 Load Case: 28SF=-10.57kN-10,950 N
Section 1.32 Load Case: 28SF=-14.28kN-6,040 N
Section 1.76 Load Case: 29SF=-20.38kN-9,820 N
Section 2.20 Load Case: 29SF=-26.55kN-12,140 N
Section 2.64 Load Case: 33SF=-32.72kN-14,390 N
Sagging @0
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DESIGN FLEXURE
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Factored moment=26.65*10^6Mu=26,650,000N mm
Stress Block
Min Tensile Steel=(0.85 /415) *230*225ptt=0.205%26.5.1 IS 456 As = 0.85/fy *(b*d)
Eff depth=250-25-12/2d=225mmde = Dg - dc - barDia/2
Ultimate strain in steel=(415/1.15/200000/)+0.002esu=0.0038Constant((fy / gs / Es) + 0.002
Limiting depth of N-A=(0.0035 / (0.0035 +0.0038)) *225Xu=108mm(0.0035 / (0.0035 + esu)) * d OR 0.48d
Parabolic depth=0.002*108/ 0.0035Xp=62mm0.002 * Xu / 0.0035
Area Constant=(((2/3/1.5)*20*108*230)-((2/3/1.5)*20*62/3*230))/20/108/230k1=0.36Constant0.364 * fck * x * b ; == 0.36 cl 38.1 of IS 456-2000 {(((2 / 3 / gc) * fck * X * B) - ((2 / 3 / gc) * fck * X1 / 3 * B))}
Centroid Constant=(108 - (((2/3/1.5) * 20*108*230*(108/2) - ((2/3/1.5) *20*230*62^ 2 /12))/(0.36*20*108*230))) /108k2=0.417Constant0.416 OR say 0.42 as per IS 456 clause 37.1c ((X - (((2 / 3 / gc) * fck * X * B * (X / 2) - ((2 / 3 / gc) * fck * B * X1 ^ 2 / 12)) / (k1 * fck * X * B))) / X)
TEE Section
LEFT spanInput GeometryLlt=2500mm
RIGHT spanInput GeometryLrt=3000mm
Dist btw point of 0 Moments=0.7*2644Lrt=1851mm
Width of Flange TEE=1851/6+230+6*125bf=1288mm23.1.2a IS 456
Xu,lim < Df case
Moment of ResistanceT/L sectionMu,lim=180,007,979Nmm=0.7*2644
Steel Required
Steel Percentage %=0.765pt=0.765%By trials; pt = 0.745 produces lower Moment of Resistance than 26650000
MR with steel % 0.765= 230*(225^2) * ((415/1.15 ) * (0.765/100 ) * (1-(0.416 * (415/1.15) / (0.36*20) * (0.765/100))))MR=27,017,181N mmB * (d ^ 2) * ((fy / gs) * (pt / 100) * (1 - (k2 * (fy / gs) / (k1 * fck) * (pt / 100))))
Steel Area=0.765*230*225/100Ast=396mm^2Ast = pt * B * d / 100
Section 0=
Min Eff d REQD for under-reinforced
MR Coefft=180007979/(20*1288*225^ 2)k= 0.138Constant0.138 for fe 415 (= Mu/ fck * B * de^2)
Min Depth=Sqrt(26,650,000/ (0.138*20*230))dr=205mmUsing formula Mu = k * fck * B * d^2
Steel Provided
No of bars reqd 12mm dia=396/ (PI() *12^ 2 / 4)φ=4NrLimited to min 2
Area providedAst=452mm^2
No of bars reqd 12mm diaφ=2NrLimited to min 2
Area providedAsc=0mm^2
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DEFLECTION CHECKS ANNEX C IS 456
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Service MomentMs=26,650,000Nmm
bfbf=1,288mm
Area of Steel RequiredAsReq=396mm^2
ASC ReqAscReq=0mm^2
Depth of Neutral AxisXu=109mm
Area of Steel ProvidedAsProv=452mm^2
Service stress =0.58 * 415fs=241N/mm^258% of yield stress fy
Gross Moment of Inertia=230*(250)^ 3 / 12Igr=299,479,167mm^4ANNEX C IS 456
Moment Constant=-0.0073*(22360.67977*299479167)MCon=48,884,871,583constantreverse calculation from elastic deflection
Continuous both endsSpan/effDepth RatioL/d=26Cl: 42 &23.2.1 of IS 456
Tension Steel % modification factor=1 / (0.225 + 0.00322 * 210.88+ 0.625 * Log10(0.786))F1=1.192Limited to 2.0
Compression Steel % factor=1.6 *0/ (0 + 0.275)F2=1Range 1.0 to 1.5
Flange modification factor=0.8 + 2 / 7 * (230/1288- 0.3)F3=0.76
Calculated modification factor=26*1.192*1*0.765S/d=23.71Computed final span/eff d ratio
Span/Deff ratio in limits
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DESIGN SHEAR
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Max Shear ForceMax of +Ve & -VeVu=33020NFrom STAAD Analysis
Shear Force factored=33020Vu=33020cl 40 IS 456
Shear Stresstv=0.656
Given % of steelρ=0.12%Read τc from Table 19 of IS 456
beeta Constant= 0.8 * 20/ (6.89 * 0.12)beeta=19.352Constant8 * fck / (6.89 * pt)
Shear strength of concrete=(0.85 * Sqrt(0.8 *20)* (Sqrt(1 + 5 *19.352) - 1)) / (6 * 19.352)tc=0.26N/mm^20.85 * Sqrt(0.8 * fck * (Sqrt(1 + 5 * beeta) - 1)) / (6 * beeta)
Shear reinforcement required since0.26<0.656
Tie Legslegs=2nr
Stirrups Provided#8@150 mm c/c=
Hogging @0
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DESIGN FLEXURE
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Factored moment=-15.41*10^6Mu=15,410,000N mm
Stress Block
Eff depth=250-25-12/2d=225mmde = Dg - dc - barDia/2
Ultimate strain in steel=(415/1.15/200000/)+0.002esu=0.0038Constant((fy / gs / Es) + 0.002
Limiting depth of N-A=(0.0035 / (0.0035 +0.0038)) *225Xu=108mm(0.0035 / (0.0035 + esu)) * d OR 0.48d
Parabolic depth=0.002*108/ 0.0035Xp=62mm0.002 * Xu / 0.0035
Area Constant=(((2/3/1.5)*20*108*230)-((2/3/1.5)*20*62/3*230))/20/108/230k1=0.36Constant0.364 * fck * x * b ; == 0.36 cl 38.1 of IS 456-2000 {(((2 / 3 / gc) * fck * X * B) - ((2 / 3 / gc) * fck * X1 / 3 * B))}
Centroid Constant=(108 - (((2/3/1.5) * 20*108*230*(108/2) - ((2/3/1.5) *20*230*62^ 2 /12))/(0.36*20*108*230))) /108k2=0.417Constant0.416 OR say 0.42 as per IS 456 clause 37.1c ((X - (((2 / 3 / gc) * fck * X * B * (X / 2) - ((2 / 3 / gc) * fck * B * X1 ^ 2 / 12)) / (k1 * fck * X * B))) / X)
MR of Concrete=0.36*20*108*230*(225-(0.417*108))Mu,lim=32,144,282N-mm k1 * fck * xu * B * (d - (k2 * xu))
Steel Required
Steel Percentage %=0.405pt=0.405%By trials; pt = 0.385 produces lower Moment of Resistance than 15410000
MR with steel % 0.405= 230*(225^2) * ((415/1.15 ) * (0.405/100 ) * (1-(0.416 * (415/1.15) / (0.36*20) * (0.405/100))))MR=15,580,569N mmB * (d ^ 2) * ((fy / gs) * (pt / 100) * (1 - (k2 * (fy / gs) / (k1 * fck) * (pt / 100))))
Steel Area=0.405*230*225/100Ast=210mm^2Ast = pt * B * d / 100
Section 1=
Min Eff d REQD for under-reinforced
MR Coefft=32144282/(20*230*225^ 2)k= 0.138Constant0.138 for fe 415 (= Mu/ fck * B * de^2)
Min Depth=Sqrt(15,410,000/ (0.138*20*230))dr=156mmUsing formula Mu = k * fck * B * d^2
Steel Provided
No of bars reqd 12mm dia=210/ (PI() *12^ 2 / 4)φ=2NrLimited to min 2
Area providedAst=226mm^2
No of bars reqd 12mm diaφ=2NrLimited to min 2
Area providedAsc=0mm^2
Sagging @0.44
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DESIGN FLEXURE
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Factored moment=13.45*10^6Mu=13,450,000N mm
Stress Block
Eff depth=250-25-12/2d=225mmde = Dg - dc - barDia/2
Ultimate strain in steel=(415/1.15/200000/)+0.002esu=0.0038Constant((fy / gs / Es) + 0.002
Limiting depth of N-A=(0.0035 / (0.0035 +0.0038)) *225Xu=108mm(0.0035 / (0.0035 + esu)) * d OR 0.48d
Parabolic depth=0.002*108/ 0.0035Xp=62mm0.002 * Xu / 0.0035
Area Constant=(((2/3/1.5)*20*108*230)-((2/3/1.5)*20*62/3*230))/20/108/230k1=0.36Constant0.364 * fck * x * b ; == 0.36 cl 38.1 of IS 456-2000 {(((2 / 3 / gc) * fck * X * B) - ((2 / 3 / gc) * fck * X1 / 3 * B))}
Centroid Constant=(108 - (((2/3/1.5) * 20*108*230*(108/2) - ((2/3/1.5) *20*230*62^ 2 /12))/(0.36*20*108*230))) /108k2=0.417Constant0.416 OR say 0.42 as per IS 456 clause 37.1c ((X - (((2 / 3 / gc) * fck * X * B * (X / 2) - ((2 / 3 / gc) * fck * B * X1 ^ 2 / 12)) / (k1 * fck * X * B))) / X)
TEE Section
LEFT spanInput GeometryLlt=2500mm
RIGHT spanInput GeometryLrt=3000mm
Dist btw point of 0 Moments=0.7*2644Lrt=1851mm
Width of Flange TEE=1851/6+230+6*125bf=1288mm23.1.2a IS 456
Xu,lim < Df case
Moment of ResistanceT/L sectionMu,lim=180,007,979Nmm=0.7*2644
Steel Required
Steel Percentage %=0.345pt=0.345%By trials; pt = 0.325 produces lower Moment of Resistance than 13450000
MR with steel % 0.345= 230*(225^2) * ((415/1.15 ) * (0.345/100 ) * (1-(0.416 * (415/1.15) / (0.36*20) * (0.345/100))))MR=13,453,689N mmB * (d ^ 2) * ((fy / gs) * (pt / 100) * (1 - (k2 * (fy / gs) / (k1 * fck) * (pt / 100))))
Steel Area=0.345*230*225/100Ast=179mm^2Ast = pt * B * d / 100
Section 2=
Min Eff d REQD for under-reinforced
MR Coefft=180007979/(20*1288*225^ 2)k= 0.138Constant0.138 for fe 415 (= Mu/ fck * B * de^2)
Min Depth=Sqrt(13,450,000/ (0.138*20*230))dr=146mmUsing formula Mu = k * fck * B * d^2
Steel Provided
No of bars reqd 12mm dia=179/ (PI() *12^ 2 / 4)φ=2NrLimited to min 2
Area providedAst=226mm^2
No of bars reqd 12mm diaφ=2NrLimited to min 2
Area providedAsc=0mm^2
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DESIGN SHEAR
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Max Shear ForceMax of +Ve & -VeVu=33020NFrom STAAD Analysis
Shear Force factored=33020Vu=33020cl 40 IS 456
Shear Stresstv=0.656
Given % of steelρ=0.12%Read τc from Table 19 of IS 456
beeta Constant= 0.8 * 20/ (6.89 * 0.12)beeta=19.352Constant8 * fck / (6.89 * pt)
Shear strength of concrete=(0.85 * Sqrt(0.8 *20)* (Sqrt(1 + 5 *19.352) - 1)) / (6 * 19.352)tc=0.26N/mm^20.85 * Sqrt(0.8 * fck * (Sqrt(1 + 5 * beeta) - 1)) / (6 * beeta)
Shear reinforcement required since0.26<0.656
Tie Legslegs=2nr
Stirrups Provided#8@150 mm c/c=
Hogging @0.44
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DESIGN FLEXURE
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Factored moment=-13.2*10^6Mu=13,200,000N mm
Stress Block
Eff depth=250-25-12/2d=225mmde = Dg - dc - barDia/2
Ultimate strain in steel=(415/1.15/200000/)+0.002esu=0.0038Constant((fy / gs / Es) + 0.002
Limiting depth of N-A=(0.0035 / (0.0035 +0.0038)) *225Xu=108mm(0.0035 / (0.0035 + esu)) * d OR 0.48d
Parabolic depth=0.002*108/ 0.0035Xp=62mm0.002 * Xu / 0.0035
Area Constant=(((2/3/1.5)*20*108*230)-((2/3/1.5)*20*62/3*230))/20/108/230k1=0.36Constant0.364 * fck * x * b ; == 0.36 cl 38.1 of IS 456-2000 {(((2 / 3 / gc) * fck * X * B) - ((2 / 3 / gc) * fck * X1 / 3 * B))}
Centroid Constant=(108 - (((2/3/1.5) * 20*108*230*(108/2) - ((2/3/1.5) *20*230*62^ 2 /12))/(0.36*20*108*230))) /108k2=0.417Constant0.416 OR say 0.42 as per IS 456 clause 37.1c ((X - (((2 / 3 / gc) * fck * X * B * (X / 2) - ((2 / 3 / gc) * fck * B * X1 ^ 2 / 12)) / (k1 * fck * X * B))) / X)
MR of Concrete=0.36*20*108*230*(225-(0.417*108))Mu,lim=32,144,282N-mm k1 * fck * xu * B * (d - (k2 * xu))
Steel Required
Steel Percentage %=0.345pt=0.345%By trials; pt = 0.325 produces lower Moment of Resistance than 13200000
MR with steel % 0.345= 230*(225^2) * ((415/1.15 ) * (0.345/100 ) * (1-(0.416 * (415/1.15) / (0.36*20) * (0.345/100))))MR=13,453,689N mmB * (d ^ 2) * ((fy / gs) * (pt / 100) * (1 - (k2 * (fy / gs) / (k1 * fck) * (pt / 100))))
Steel Area=0.345*230*225/100Ast=179mm^2Ast = pt * B * d / 100
Section 3=
Min Eff d REQD for under-reinforced
MR Coefft=32144282/(20*230*225^ 2)k= 0.138Constant0.138 for fe 415 (= Mu/ fck * B * de^2)
Min Depth=Sqrt(13,200,000/ (0.138*20*230))dr=144mmUsing formula Mu = k * fck * B * d^2
Steel Provided
No of bars reqd 12mm dia=179/ (PI() *12^ 2 / 4)φ=2NrLimited to min 2
Area providedAst=226mm^2
No of bars reqd 12mm diaφ=2NrLimited to min 2
Area providedAsc=0mm^2
Sagging @0.88
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DESIGN FLEXURE
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Factored moment=4.64*10^6Mu=4,640,000N mm
Stress Block
Eff depth=250-25-12/2d=225mmde = Dg - dc - barDia/2
Ultimate strain in steel=(415/1.15/200000/)+0.002esu=0.0038Constant((fy / gs / Es) + 0.002
Limiting depth of N-A=(0.0035 / (0.0035 +0.0038)) *225Xu=108mm(0.0035 / (0.0035 + esu)) * d OR 0.48d
Parabolic depth=0.002*108/ 0.0035Xp=62mm0.002 * Xu / 0.0035
Area Constant=(((2/3/1.5)*20*108*230)-((2/3/1.5)*20*62/3*230))/20/108/230k1=0.36Constant0.364 * fck * x * b ; == 0.36 cl 38.1 of IS 456-2000 {(((2 / 3 / gc) * fck * X * B) - ((2 / 3 / gc) * fck * X1 / 3 * B))}
Centroid Constant=(108 - (((2/3/1.5) * 20*108*230*(108/2) - ((2/3/1.5) *20*230*62^ 2 /12))/(0.36*20*108*230))) /108k2=0.417Constant0.416 OR say 0.42 as per IS 456 clause 37.1c ((X - (((2 / 3 / gc) * fck * X * B * (X / 2) - ((2 / 3 / gc) * fck * B * X1 ^ 2 / 12)) / (k1 * fck * X * B))) / X)
TEE Section
LEFT spanInput GeometryLlt=2500mm
RIGHT spanInput GeometryLrt=3000mm
Dist btw point of 0 Moments=0.7*2644Lrt=1851mm
Width of Flange TEE=1851/6+230+6*125bf=1288mm23.1.2a IS 456
Xu,lim < Df case
Moment of ResistanceT/L sectionMu,lim=180,007,979Nmm=0.7*2644
Steel Required
Steel Percentage %=0.205pt=0.205%ptMin = 0.205 produces higher Moment of Resistance than 4640000
MR Produced > than Factored Moment= 230*(225^2) * ((415/1.15 ) * (0.205/100 ) * (1-(0.416 * (415/1.15) / (0.36*20) * (0.205/100))))MRs=8,245,662N mmB * (d ^ 2) * ((fy / gs) * (pt / 100) * (1 - (k2 * (fy / gs) / (k1 * fck) * (pt / 100))))
Section 4=
Min Eff d REQD for under-reinforced
MR Coefft=180007979/(20*1288*225^ 2)k= 0.138Constant0.138 for fe 415 (= Mu/ fck * B * de^2)
Min Depth=Sqrt(4,640,000/ (0.138*20*230))dr=85mmUsing formula Mu = k * fck * B * d^2
Steel Provided
No of bars reqd 12mm dia=106/ (PI() *12^ 2 / 4)φ=2NrLimited to min 2
Area providedAst=226mm^2
No of bars reqd 12mm diaφ=2NrLimited to min 2
Area providedAsc=0mm^2
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DESIGN SHEAR
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Max Shear ForceMax of +Ve & -VeVu=33020NFrom STAAD Analysis
Shear Force factored=33020Vu=33020cl 40 IS 456
Shear Stresstv=0.656
Given % of steelρ=0.12%Read τc from Table 19 of IS 456
beeta Constant= 0.8 * 20/ (6.89 * 0.12)beeta=19.352Constant8 * fck / (6.89 * pt)
Shear strength of concrete=(0.85 * Sqrt(0.8 *20)* (Sqrt(1 + 5 *19.352) - 1)) / (6 * 19.352)tc=0.26N/mm^20.85 * Sqrt(0.8 * fck * (Sqrt(1 + 5 * beeta) - 1)) / (6 * beeta)
Shear reinforcement required since0.26<0.656
Tie Legslegs=2nr
Stirrups Provided#8@150 mm c/c=
Hogging @0.88
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DESIGN FLEXURE
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Factored moment=-10.95*10^6Mu=10,950,000N mm
Stress Block
Eff depth=250-25-12/2d=225mmde = Dg - dc - barDia/2
Ultimate strain in steel=(415/1.15/200000/)+0.002esu=0.0038Constant((fy / gs / Es) + 0.002
Limiting depth of N-A=(0.0035 / (0.0035 +0.0038)) *225Xu=108mm(0.0035 / (0.0035 + esu)) * d OR 0.48d
Parabolic depth=0.002*108/ 0.0035Xp=62mm0.002 * Xu / 0.0035
Area Constant=(((2/3/1.5)*20*108*230)-((2/3/1.5)*20*62/3*230))/20/108/230k1=0.36Constant0.364 * fck * x * b ; == 0.36 cl 38.1 of IS 456-2000 {(((2 / 3 / gc) * fck * X * B) - ((2 / 3 / gc) * fck * X1 / 3 * B))}
Centroid Constant=(108 - (((2/3/1.5) * 20*108*230*(108/2) - ((2/3/1.5) *20*230*62^ 2 /12))/(0.36*20*108*230))) /108k2=0.417Constant0.416 OR say 0.42 as per IS 456 clause 37.1c ((X - (((2 / 3 / gc) * fck * X * B * (X / 2) - ((2 / 3 / gc) * fck * B * X1 ^ 2 / 12)) / (k1 * fck * X * B))) / X)
MR of Concrete=0.36*20*108*230*(225-(0.417*108))Mu,lim=32,144,282N-mm k1 * fck * xu * B * (d - (k2 * xu))
Steel Required
Steel Percentage %=0.285pt=0.285%By trials; pt = 0.265 produces lower Moment of Resistance than 10950000
MR with steel % 0.285= 230*(225^2) * ((415/1.15 ) * (0.285/100 ) * (1-(0.416 * (415/1.15) / (0.36*20) * (0.285/100))))MR=11,263,731N mmB * (d ^ 2) * ((fy / gs) * (pt / 100) * (1 - (k2 * (fy / gs) / (k1 * fck) * (pt / 100))))
Steel Area=0.285*230*225/100Ast=147mm^2Ast = pt * B * d / 100
Section 5=
Min Eff d REQD for under-reinforced
MR Coefft=32144282/(20*230*225^ 2)k= 0.138Constant0.138 for fe 415 (= Mu/ fck * B * de^2)
Min Depth=Sqrt(10,950,000/ (0.138*20*230))dr=131mmUsing formula Mu = k * fck * B * d^2
Steel Provided
No of bars reqd 12mm dia=147/ (PI() *12^ 2 / 4)φ=2NrLimited to min 2
Area providedAst=226mm^2
No of bars reqd 12mm diaφ=2NrLimited to min 2
Area providedAsc=0mm^2
Sagging @1.32
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DESIGN FLEXURE
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Factored moment=0.42*10^6Mu=420,000N mm
Stress Block
Eff depth=250-25-12/2d=225mmde = Dg - dc - barDia/2
Ultimate strain in steel=(415/1.15/200000/)+0.002esu=0.0038Constant((fy / gs / Es) + 0.002
Limiting depth of N-A=(0.0035 / (0.0035 +0.0038)) *225Xu=108mm(0.0035 / (0.0035 + esu)) * d OR 0.48d
Parabolic depth=0.002*108/ 0.0035Xp=62mm0.002 * Xu / 0.0035
Area Constant=(((2/3/1.5)*20*108*230)-((2/3/1.5)*20*62/3*230))/20/108/230k1=0.36Constant0.364 * fck * x * b ; == 0.36 cl 38.1 of IS 456-2000 {(((2 / 3 / gc) * fck * X * B) - ((2 / 3 / gc) * fck * X1 / 3 * B))}
Centroid Constant=(108 - (((2/3/1.5) * 20*108*230*(108/2) - ((2/3/1.5) *20*230*62^ 2 /12))/(0.36*20*108*230))) /108k2=0.417Constant0.416 OR say 0.42 as per IS 456 clause 37.1c ((X - (((2 / 3 / gc) * fck * X * B * (X / 2) - ((2 / 3 / gc) * fck * B * X1 ^ 2 / 12)) / (k1 * fck * X * B))) / X)
TEE Section
LEFT spanInput GeometryLlt=2500mm
RIGHT spanInput GeometryLrt=3000mm
Dist btw point of 0 Moments=0.7*2644Lrt=1851mm
Width of Flange TEE=1851/6+230+6*125bf=1288mm23.1.2a IS 456
Xu,lim < Df case
Moment of ResistanceT/L sectionMu,lim=180,007,979Nmm=0.7*2644
Steel Required
Steel Percentage %=0.205pt=0.205%ptMin = 0.205 produces higher Moment of Resistance than 420000
MR Produced > than Factored Moment= 230*(225^2) * ((415/1.15 ) * (0.205/100 ) * (1-(0.416 * (415/1.15) / (0.36*20) * (0.205/100))))MRs=8,245,662N mmB * (d ^ 2) * ((fy / gs) * (pt / 100) * (1 - (k2 * (fy / gs) / (k1 * fck) * (pt / 100))))
Section 6=
Min Eff d REQD for under-reinforced
MR Coefft=180007979/(20*1288*225^ 2)k= 0.138Constant0.138 for fe 415 (= Mu/ fck * B * de^2)
Min Depth=Sqrt(420,000/ (0.138*20*230))dr=26mmUsing formula Mu = k * fck * B * d^2
Steel Provided
No of bars reqd 12mm dia=106/ (PI() *12^ 2 / 4)φ=2NrLimited to min 2
Area providedAst=226mm^2
No of bars reqd 12mm diaφ=2NrLimited to min 2
Area providedAsc=0mm^2
***********************************************************=****************************
DESIGN SHEAR
***********************************************************=****************************
Max Shear ForceMax of +Ve & -VeVu=33020NFrom STAAD Analysis
Shear Force factored=33020Vu=33020cl 40 IS 456
Shear Stresstv=0.656
Given % of steelρ=0.12%Read τc from Table 19 of IS 456
beeta Constant= 0.8 * 20/ (6.89 * 0.12)beeta=19.352Constant8 * fck / (6.89 * pt)
Shear strength of concrete=(0.85 * Sqrt(0.8 *20)* (Sqrt(1 + 5 *19.352) - 1)) / (6 * 19.352)tc=0.26N/mm^20.85 * Sqrt(0.8 * fck * (Sqrt(1 + 5 * beeta) - 1)) / (6 * beeta)
Shear reinforcement required since0.26<0.656
Tie Legslegs=2nr
Stirrups Provided#8@150 mm c/c=
Hogging @1.32
***********************************************************=****************************
DESIGN FLEXURE
***********************************************************=****************************
Factored moment=-6.04*10^6Mu=6,040,000N mm
Stress Block
Eff depth=250-25-12/2d=225mmde = Dg - dc - barDia/2
Ultimate strain in steel=(415/1.15/200000/)+0.002esu=0.0038Constant((fy / gs / Es) + 0.002
Limiting depth of N-A=(0.0035 / (0.0035 +0.0038)) *225Xu=108mm(0.0035 / (0.0035 + esu)) * d OR 0.48d
Parabolic depth=0.002*108/ 0.0035Xp=62mm0.002 * Xu / 0.0035
Area Constant=(((2/3/1.5)*20*108*230)-((2/3/1.5)*20*62/3*230))/20/108/230k1=0.36Constant0.364 * fck * x * b ; == 0.36 cl 38.1 of IS 456-2000 {(((2 / 3 / gc) * fck * X * B) - ((2 / 3 / gc) * fck * X1 / 3 * B))}
Centroid Constant=(108 - (((2/3/1.5) * 20*108*230*(108/2) - ((2/3/1.5) *20*230*62^ 2 /12))/(0.36*20*108*230))) /108k2=0.417Constant0.416 OR say 0.42 as per IS 456 clause 37.1c ((X - (((2 / 3 / gc) * fck * X * B * (X / 2) - ((2 / 3 / gc) * fck * B * X1 ^ 2 / 12)) / (k1 * fck * X * B))) / X)
MR of Concrete=0.36*20*108*230*(225-(0.417*108))Mu,lim=32,144,282N-mm k1 * fck * xu * B * (d - (k2 * xu))
Steel Required
Steel Percentage %=0.205pt=0.205%ptMin = 0.205 produces higher Moment of Resistance than 6040000
MR Produced > than Factored Moment= 230*(225^2) * ((415/1.15 ) * (0.205/100 ) * (1-(0.416 * (415/1.15) / (0.36*20) * (0.205/100))))MRs=8,245,662N mmB * (d ^ 2) * ((fy / gs) * (pt / 100) * (1 - (k2 * (fy / gs) / (k1 * fck) * (pt / 100))))
Section 7=
Min Eff d REQD for under-reinforced
MR Coefft=32144282/(20*230*225^ 2)k= 0.138Constant0.138 for fe 415 (= Mu/ fck * B * de^2)
Min Depth=Sqrt(6,040,000/ (0.138*20*230))dr=98mmUsing formula Mu = k * fck * B * d^2
Steel Provided
No of bars reqd 12mm dia=106/ (PI() *12^ 2 / 4)φ=2NrLimited to min 2
Area providedAst=226mm^2
No of bars reqd 12mm diaφ=2NrLimited to min 2
Area providedAsc=0mm^2
Sagging @1.76
***********************************************************=****************************
DESIGN FLEXURE
***********************************************************=****************************
Factored moment=3.8*10^6Mu=3,800,000N mm
Stress Block
Eff depth=250-25-12/2d=225mmde = Dg - dc - barDia/2
Ultimate strain in steel=(415/1.15/200000/)+0.002esu=0.0038Constant((fy / gs / Es) + 0.002
Limiting depth of N-A=(0.0035 / (0.0035 +0.0038)) *225Xu=108mm(0.0035 / (0.0035 + esu)) * d OR 0.48d
Parabolic depth=0.002*108/ 0.0035Xp=62mm0.002 * Xu / 0.0035
Area Constant=(((2/3/1.5)*20*108*230)-((2/3/1.5)*20*62/3*230))/20/108/230k1=0.36Constant0.364 * fck * x * b ; == 0.36 cl 38.1 of IS 456-2000 {(((2 / 3 / gc) * fck * X * B) - ((2 / 3 / gc) * fck * X1 / 3 * B))}
Centroid Constant=(108 - (((2/3/1.5) * 20*108*230*(108/2) - ((2/3/1.5) *20*230*62^ 2 /12))/(0.36*20*108*230))) /108k2=0.417Constant0.416 OR say 0.42 as per IS 456 clause 37.1c ((X - (((2 / 3 / gc) * fck * X * B * (X / 2) - ((2 / 3 / gc) * fck * B * X1 ^ 2 / 12)) / (k1 * fck * X * B))) / X)
TEE Section
LEFT spanInput GeometryLlt=2500mm
RIGHT spanInput GeometryLrt=3000mm
Dist btw point of 0 Moments=0.7*2644Lrt=1851mm
Width of Flange TEE=1851/6+230+6*125bf=1288mm23.1.2a IS 456
Xu,lim < Df case
Moment of ResistanceT/L sectionMu,lim=180,007,979Nmm=0.7*2644
Steel Required
Steel Percentage %=0.205pt=0.205%ptMin = 0.205 produces higher Moment of Resistance than 3800000
MR Produced > than Factored Moment= 230*(225^2) * ((415/1.15 ) * (0.205/100 ) * (1-(0.416 * (415/1.15) / (0.36*20) * (0.205/100))))MRs=8,245,662N mmB * (d ^ 2) * ((fy / gs) * (pt / 100) * (1 - (k2 * (fy / gs) / (k1 * fck) * (pt / 100))))
Section 8=
Min Eff d REQD for under-reinforced
MR Coefft=180007979/(20*1288*225^ 2)k= 0.138Constant0.138 for fe 415 (= Mu/ fck * B * de^2)
Min Depth=Sqrt(3,800,000/ (0.138*20*230))dr=77mmUsing formula Mu = k * fck * B * d^2
Steel Provided
No of bars reqd 12mm dia=106/ (PI() *12^ 2 / 4)φ=2NrLimited to min 2
Area providedAst=226mm^2
No of bars reqd 12mm diaφ=2NrLimited to min 2
Area providedAsc=0mm^2
***********************************************************=****************************
DESIGN SHEAR
***********************************************************=****************************
Max Shear ForceMax of +Ve & -VeVu=26860NFrom STAAD Analysis
Shear Force factored=26860Vu=26860cl 40 IS 456
Shear Stresstv=0.533
Given % of steelρ=0.12%Read τc from Table 19 of IS 456
beeta Constant= 0.8 * 20/ (6.89 * 0.12)beeta=19.352Constant8 * fck / (6.89 * pt)
Shear strength of concrete=(0.85 * Sqrt(0.8 *20)* (Sqrt(1 + 5 *19.352) - 1)) / (6 * 19.352)tc=0.26N/mm^20.85 * Sqrt(0.8 * fck * (Sqrt(1 + 5 * beeta) - 1)) / (6 * beeta)
Shear reinforcement required since0.26<0.533
Tie Legslegs=2nr
Stirrups Provided#8@150 mm c/c=
Hogging @1.76
***********************************************************=****************************
DESIGN FLEXURE
***********************************************************=****************************
Factored moment=-9.82*10^6Mu=9,820,000N mm
Stress Block
Eff depth=250-25-12/2d=225mmde = Dg - dc - barDia/2
Ultimate strain in steel=(415/1.15/200000/)+0.002esu=0.0038Constant((fy / gs / Es) + 0.002
Limiting depth of N-A=(0.0035 / (0.0035 +0.0038)) *225Xu=108mm(0.0035 / (0.0035 + esu)) * d OR 0.48d
Parabolic depth=0.002*108/ 0.0035Xp=62mm0.002 * Xu / 0.0035
Area Constant=(((2/3/1.5)*20*108*230)-((2/3/1.5)*20*62/3*230))/20/108/230k1=0.36Constant0.364 * fck * x * b ; == 0.36 cl 38.1 of IS 456-2000 {(((2 / 3 / gc) * fck * X * B) - ((2 / 3 / gc) * fck * X1 / 3 * B))}
Centroid Constant=(108 - (((2/3/1.5) * 20*108*230*(108/2) - ((2/3/1.5) *20*230*62^ 2 /12))/(0.36*20*108*230))) /108k2=0.417Constant0.416 OR say 0.42 as per IS 456 clause 37.1c ((X - (((2 / 3 / gc) * fck * X * B * (X / 2) - ((2 / 3 / gc) * fck * B * X1 ^ 2 / 12)) / (k1 * fck * X * B))) / X)
MR of Concrete=0.36*20*108*230*(225-(0.417*108))Mu,lim=32,144,282N-mm k1 * fck * xu * B * (d - (k2 * xu))
Steel Required
Steel Percentage %=0.265pt=0.265%By trials; pt = 0.245 produces lower Moment of Resistance than 9820000
MR with steel % 0.265= 230*(225^2) * ((415/1.15 ) * (0.265/100 ) * (1-(0.416 * (415/1.15) / (0.36*20) * (0.265/100))))MR=10,519,727N mmB * (d ^ 2) * ((fy / gs) * (pt / 100) * (1 - (k2 * (fy / gs) / (k1 * fck) * (pt / 100))))
Steel Area=0.265*230*225/100Ast=137mm^2Ast = pt * B * d / 100
Section 9=
Min Eff d REQD for under-reinforced
MR Coefft=32144282/(20*230*225^ 2)k= 0.138Constant0.138 for fe 415 (= Mu/ fck * B * de^2)
Min Depth=Sqrt(9,820,000/ (0.138*20*230))dr=124mmUsing formula Mu = k * fck * B * d^2
Steel Provided
No of bars reqd 12mm dia=137/ (PI() *12^ 2 / 4)φ=2NrLimited to min 2
Area providedAst=226mm^2
No of bars reqd 12mm diaφ=2NrLimited to min 2
Area providedAsc=0mm^2
Sagging @2.2
***********************************************************=****************************
DESIGN FLEXURE
***********************************************************=****************************
Factored moment=11.97*10^6Mu=11,970,000N mm
Stress Block
Eff depth=250-25-12/2d=225mmde = Dg - dc - barDia/2
Ultimate strain in steel=(415/1.15/200000/)+0.002esu=0.0038Constant((fy / gs / Es) + 0.002
Limiting depth of N-A=(0.0035 / (0.0035 +0.0038)) *225Xu=108mm(0.0035 / (0.0035 + esu)) * d OR 0.48d
Parabolic depth=0.002*108/ 0.0035Xp=62mm0.002 * Xu / 0.0035
Area Constant=(((2/3/1.5)*20*108*230)-((2/3/1.5)*20*62/3*230))/20/108/230k1=0.36Constant0.364 * fck * x * b ; == 0.36 cl 38.1 of IS 456-2000 {(((2 / 3 / gc) * fck * X * B) - ((2 / 3 / gc) * fck * X1 / 3 * B))}
Centroid Constant=(108 - (((2/3/1.5) * 20*108*230*(108/2) - ((2/3/1.5) *20*230*62^ 2 /12))/(0.36*20*108*230))) /108k2=0.417Constant0.416 OR say 0.42 as per IS 456 clause 37.1c ((X - (((2 / 3 / gc) * fck * X * B * (X / 2) - ((2 / 3 / gc) * fck * B * X1 ^ 2 / 12)) / (k1 * fck * X * B))) / X)
TEE Section
LEFT spanInput GeometryLlt=2500mm
RIGHT spanInput GeometryLrt=3000mm
Dist btw point of 0 Moments=0.7*2644Lrt=1851mm
Width of Flange TEE=1851/6+230+6*125bf=1288mm23.1.2a IS 456
Xu,lim < Df case
Moment of ResistanceT/L sectionMu,lim=180,007,979Nmm=0.7*2644
Steel Required
Steel Percentage %=0.305pt=0.305%By trials; pt = 0.285 produces lower Moment of Resistance than 11970000
MR with steel % 0.305= 230*(225^2) * ((415/1.15 ) * (0.305/100 ) * (1-(0.416 * (415/1.15) / (0.36*20) * (0.305/100))))MR=12,000,726N mmB * (d ^ 2) * ((fy / gs) * (pt / 100) * (1 - (k2 * (fy / gs) / (k1 * fck) * (pt / 100))))
Steel Area=0.305*230*225/100Ast=158mm^2Ast = pt * B * d / 100
Section 10=
Min Eff d REQD for under-reinforced
MR Coefft=180007979/(20*1288*225^ 2)k= 0.138Constant0.138 for fe 415 (= Mu/ fck * B * de^2)
Min Depth=Sqrt(11,970,000/ (0.138*20*230))dr=137mmUsing formula Mu = k * fck * B * d^2
Steel Provided
No of bars reqd 12mm dia=158/ (PI() *12^ 2 / 4)φ=2NrLimited to min 2
Area providedAst=226mm^2
No of bars reqd 12mm diaφ=2NrLimited to min 2
Area providedAsc=0mm^2
***********************************************************=****************************
DESIGN SHEAR
***********************************************************=****************************
Max Shear ForceMax of +Ve & -VeVu=26860NFrom STAAD Analysis
Shear Force factored=26860Vu=26860cl 40 IS 456
Shear Stresstv=0.533
Given % of steelρ=0.12%Read τc from Table 19 of IS 456
beeta Constant= 0.8 * 20/ (6.89 * 0.12)beeta=19.352Constant8 * fck / (6.89 * pt)
Shear strength of concrete=(0.85 * Sqrt(0.8 *20)* (Sqrt(1 + 5 *19.352) - 1)) / (6 * 19.352)tc=0.26N/mm^20.85 * Sqrt(0.8 * fck * (Sqrt(1 + 5 * beeta) - 1)) / (6 * beeta)
Shear reinforcement required since0.26<0.533
Tie Legslegs=2nr
Stirrups Provided#8@150 mm c/c=
Hogging @2.2
***********************************************************=****************************
DESIGN FLEXURE
***********************************************************=****************************
Factored moment=-12.14*10^6Mu=12,140,000N mm
Stress Block
Eff depth=250-25-12/2d=225mmde = Dg - dc - barDia/2
Ultimate strain in steel=(415/1.15/200000/)+0.002esu=0.0038Constant((fy / gs / Es) + 0.002
Limiting depth of N-A=(0.0035 / (0.0035 +0.0038)) *225Xu=108mm(0.0035 / (0.0035 + esu)) * d OR 0.48d
Parabolic depth=0.002*108/ 0.0035Xp=62mm0.002 * Xu / 0.0035
Area Constant=(((2/3/1.5)*20*108*230)-((2/3/1.5)*20*62/3*230))/20/108/230k1=0.36Constant0.364 * fck * x * b ; == 0.36 cl 38.1 of IS 456-2000 {(((2 / 3 / gc) * fck * X * B) - ((2 / 3 / gc) * fck * X1 / 3 * B))}
Centroid Constant=(108 - (((2/3/1.5) * 20*108*230*(108/2) - ((2/3/1.5) *20*230*62^ 2 /12))/(0.36*20*108*230))) /108k2=0.417Constant0.416 OR say 0.42 as per IS 456 clause 37.1c ((X - (((2 / 3 / gc) * fck * X * B * (X / 2) - ((2 / 3 / gc) * fck * B * X1 ^ 2 / 12)) / (k1 * fck * X * B))) / X)
MR of Concrete=0.36*20*108*230*(225-(0.417*108))Mu,lim=32,144,282N-mm k1 * fck * xu * B * (d - (k2 * xu))
Steel Required
Steel Percentage %=0.325pt=0.325%By trials; pt = 0.305 produces lower Moment of Resistance than 12140000
MR with steel % 0.325= 230*(225^2) * ((415/1.15 ) * (0.325/100 ) * (1-(0.416 * (415/1.15) / (0.36*20) * (0.325/100))))MR=12,730,712N mmB * (d ^ 2) * ((fy / gs) * (pt / 100) * (1 - (k2 * (fy / gs) / (k1 * fck) * (pt / 100))))
Steel Area=0.325*230*225/100Ast=168mm^2Ast = pt * B * d / 100
Section 11=
Min Eff d REQD for under-reinforced
MR Coefft=32144282/(20*230*225^ 2)k= 0.138Constant0.138 for fe 415 (= Mu/ fck * B * de^2)
Min Depth=Sqrt(12,140,000/ (0.138*20*230))dr=138mmUsing formula Mu = k * fck * B * d^2
Steel Provided
No of bars reqd 12mm dia=168/ (PI() *12^ 2 / 4)φ=2NrLimited to min 2
Area providedAst=226mm^2
No of bars reqd 12mm diaφ=2NrLimited to min 2
Area providedAsc=0mm^2
Sagging @2.64
***********************************************************=****************************
DESIGN FLEXURE
***********************************************************=****************************
Factored moment=24.98*10^6Mu=24,980,000N mm
Stress Block
Eff depth=250-25-12/2d=225mmde = Dg - dc - barDia/2
Ultimate strain in steel=(415/1.15/200000/)+0.002esu=0.0038Constant((fy / gs / Es) + 0.002
Limiting depth of N-A=(0.0035 / (0.0035 +0.0038)) *225Xu=108mm(0.0035 / (0.0035 + esu)) * d OR 0.48d
Parabolic depth=0.002*108/ 0.0035Xp=62mm0.002 * Xu / 0.0035
Area Constant=(((2/3/1.5)*20*108*230)-((2/3/1.5)*20*62/3*230))/20/108/230k1=0.36Constant0.364 * fck * x * b ; == 0.36 cl 38.1 of IS 456-2000 {(((2 / 3 / gc) * fck * X * B) - ((2 / 3 / gc) * fck * X1 / 3 * B))}
Centroid Constant=(108 - (((2/3/1.5) * 20*108*230*(108/2) - ((2/3/1.5) *20*230*62^ 2 /12))/(0.36*20*108*230))) /108k2=0.417Constant0.416 OR say 0.42 as per IS 456 clause 37.1c ((X - (((2 / 3 / gc) * fck * X * B * (X / 2) - ((2 / 3 / gc) * fck * B * X1 ^ 2 / 12)) / (k1 * fck * X * B))) / X)
TEE Section
LEFT spanInput GeometryLlt=2500mm
RIGHT spanInput GeometryLrt=3000mm
Dist btw point of 0 Moments=0.7*2644Lrt=1851mm
Width of Flange TEE=1851/6+230+6*125bf=1288mm23.1.2a IS 456
Xu,lim < Df case
Moment of ResistanceT/L sectionMu,lim=180,007,979Nmm=0.7*2644
Steel Required
Steel Percentage %=0.705pt=0.705%By trials; pt = 0.685 produces lower Moment of Resistance than 24980000
MR with steel % 0.705= 230*(225^2) * ((415/1.15 ) * (0.705/100 ) * (1-(0.416 * (415/1.15) / (0.36*20) * (0.705/100))))MR=25,268,777N mmB * (d ^ 2) * ((fy / gs) * (pt / 100) * (1 - (k2 * (fy / gs) / (k1 * fck) * (pt / 100))))
Steel Area=0.705*230*225/100Ast=365mm^2Ast = pt * B * d / 100
Section 12=
Min Eff d REQD for under-reinforced
MR Coefft=180007979/(20*1288*225^ 2)k= 0.138Constant0.138 for fe 415 (= Mu/ fck * B * de^2)
Min Depth=Sqrt(24,980,000/ (0.138*20*230))dr=198mmUsing formula Mu = k * fck * B * d^2
Steel Provided
No of bars reqd 12mm dia=365/ (PI() *12^ 2 / 4)φ=4NrLimited to min 2
Area providedAst=452mm^2
No of bars reqd 12mm diaφ=2NrLimited to min 2
Area providedAsc=0mm^2
***********************************************************=****************************
DESIGN SHEAR
***********************************************************=****************************
Max Shear ForceMax of +Ve & -VeVu=26860NFrom STAAD Analysis
Shear Force factored=26860Vu=26860cl 40 IS 456
Shear Stresstv=0.533
Given % of steelρ=0.12%Read τc from Table 19 of IS 456
beeta Constant= 0.8 * 20/ (6.89 * 0.12)beeta=19.352Constant8 * fck / (6.89 * pt)
Shear strength of concrete=(0.85 * Sqrt(0.8 *20)* (Sqrt(1 + 5 *19.352) - 1)) / (6 * 19.352)tc=0.26N/mm^20.85 * Sqrt(0.8 * fck * (Sqrt(1 + 5 * beeta) - 1)) / (6 * beeta)
Shear reinforcement required since0.26<0.533
Tie Legslegs=2nr
Stirrups Provided#8@150 mm c/c=
Hogging @2.64
***********************************************************=****************************
DESIGN FLEXURE
***********************************************************=****************************
Factored moment=-14.39*10^6Mu=14,390,000N mm
Stress Block
Eff depth=250-25-12/2d=225mmde = Dg - dc - barDia/2
Ultimate strain in steel=(415/1.15/200000/)+0.002esu=0.0038Constant((fy / gs / Es) + 0.002
Limiting depth of N-A=(0.0035 / (0.0035 +0.0038)) *225Xu=108mm(0.0035 / (0.0035 + esu)) * d OR 0.48d
Parabolic depth=0.002*108/ 0.0035Xp=62mm0.002 * Xu / 0.0035
Area Constant=(((2/3/1.5)*20*108*230)-((2/3/1.5)*20*62/3*230))/20/108/230k1=0.36Constant0.364 * fck * x * b ; == 0.36 cl 38.1 of IS 456-2000 {(((2 / 3 / gc) * fck * X * B) - ((2 / 3 / gc) * fck * X1 / 3 * B))}
Centroid Constant=(108 - (((2/3/1.5) * 20*108*230*(108/2) - ((2/3/1.5) *20*230*62^ 2 /12))/(0.36*20*108*230))) /108k2=0.417Constant0.416 OR say 0.42 as per IS 456 clause 37.1c ((X - (((2 / 3 / gc) * fck * X * B * (X / 2) - ((2 / 3 / gc) * fck * B * X1 ^ 2 / 12)) / (k1 * fck * X * B))) / X)
MR of Concrete=0.36*20*108*230*(225-(0.417*108))Mu,lim=32,144,282N-mm k1 * fck * xu * B * (d - (k2 * xu))
Steel Required
Steel Percentage %=0.385pt=0.385%By trials; pt = 0.365 produces lower Moment of Resistance than 14390000
MR with steel % 0.385= 230*(225^2) * ((415/1.15 ) * (0.385/100 ) * (1-(0.416 * (415/1.15) / (0.36*20) * (0.385/100))))MR=14,878,618N mmB * (d ^ 2) * ((fy / gs) * (pt / 100) * (1 - (k2 * (fy / gs) / (k1 * fck) * (pt / 100))))
Steel Area=0.385*230*225/100Ast=199mm^2Ast = pt * B * d / 100
Section 13=
Min Eff d REQD for under-reinforced
MR Coefft=32144282/(20*230*225^ 2)k= 0.138Constant0.138 for fe 415 (= Mu/ fck * B * de^2)
Min Depth=Sqrt(14,390,000/ (0.138*20*230))dr=151mmUsing formula Mu = k * fck * B * d^2
Steel Provided
No of bars reqd 12mm dia=199/ (PI() *12^ 2 / 4)φ=2NrLimited to min 2
Area providedAst=226mm^2
No of bars reqd 12mm diaφ=2NrLimited to min 2
Area providedAsc=0mm^2
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SLENDERNESS CHECKS
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Slender checkspan: 2644is less than the lower of 60 *230 and 250 *230^ 2/219=PASS
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SERVICEABILITY CHECKS Annex F of IS 456
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Dist from compression face=250a=250mma=Dg >> Clause 43.1 & 26.3.2
Initial fy strain @ level considered=1/0e1=Infinitye1 = 1 / Ast.Value
Ave fy strain @ level considered= Infinity-((230*(250-0)*(250-0))/(3 *0*200000*(219-0)))em=NaNe1 - ((b.Value * (Dg.Value - Xu.Value) * (a.Value - Xu.Value)) / (3 * Ast.Value * Es.Value * (D.Value - Xu.Value)))
Eff cover corner=25+12/ 2effCover=31mmeffCover = dc.Value + m_bar.Value / 2
Dist surface of bar =Sqrt(2 * 31^ 2)-12 / 2acr=37.84mmSqrt(2 * effCover ^ 2) - m_bar / 2
Crack width at mid span bottom corner=3 *37.84*NaN/ (1 + (2 *37.84-25)/(250-0))Wcr=NaNmm Annex-F of IS 456
Dist surface of bar=25dc=25mm= dc
Crack width at mid span soffit=3 *25*NaN/ (1 + (2 *25-25)/(250-0))Wcr=NaNmm Annex-F of IS 456
The crack width is with in limits
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RESULTS REPORTED
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Main Steel
Section Sagging at 0AstReq=396mm^2
AstProv=452mm^2
AscReq=0mm^2
AscProv=0mm^2
pt=0.897%
pc=0.000%
Section Hogging at 0AstReq=210mm^2
AstProv=226mm^2
AscReq=0mm^2
AscProv=0mm^2
pt=0.449%
pc=0.000%
Section Sagging at 0.44AstReq=179mm^2
AstProv=226mm^2
AscReq=0mm^2
AscProv=0mm^2
pt=0.449%
pc=0.000%
Section Hogging at 0.44AstReq=179mm^2
AstProv=226mm^2
AscReq=0mm^2
AscProv=0mm^2
pt=0.449%
pc=0.000%
Section Sagging at 0.88AstReq=106mm^2
AstProv=226mm^2
AscReq=0mm^2
AscProv=0mm^2
pt=0.449%
pc=0.000%
Section Hogging at 0.88AstReq=147mm^2
AstProv=226mm^2
AscReq=0mm^2
AscProv=0mm^2
pt=0.449%
pc=0.000%
Section Sagging at 1.32AstReq=106mm^2
AstProv=226mm^2
AscReq=0mm^2
AscProv=0mm^2
pt=0.449%
pc=0.000%
Section Hogging at 1.32AstReq=106mm^2
AstProv=226mm^2
AscReq=0mm^2
AscProv=0mm^2
pt=0.449%
pc=0.000%
Section Sagging at 1.76AstReq=106mm^2
AstProv=226mm^2
AscReq=0mm^2
AscProv=0mm^2
pt=0.449%
pc=0.000%
Section Hogging at 1.76AstReq=137mm^2
AstProv=226mm^2
AscReq=0mm^2
AscProv=0mm^2
pt=0.449%
pc=0.000%
Section Sagging at 2.2AstReq=158mm^2
AstProv=226mm^2
AscReq=0mm^2
AscProv=0mm^2
pt=0.449%
pc=0.000%
Section Hogging at 2.2AstReq=168mm^2
AstProv=226mm^2
AscReq=0mm^2
AscProv=0mm^2
pt=0.449%
pc=0.000%
Section Sagging at 2.64AstReq=365mm^2
AstProv=452mm^2
AscReq=0mm^2
AscProv=0mm^2
pt=0.897%
pc=0.000%
Section Hogging at 2.64AstReq=199mm^2
AstProv=226mm^2
AscReq=0mm^2
AscProv=0mm^2
pt=0.449%
pc=0.000%
Section Sagging at 0AstReq=396mm^2
AstProv=452mm^2
AscReq=0mm^2
AscProv=0mm^2
pt=0.897%
pc=0.000%
Section Hogging at 0AstReq=210mm^2
AstProv=226mm^2
AscReq=0mm^2
AscProv=0mm^2
pt=0.449%
pc=0.000%
Section Sagging at 0.44AstReq=179mm^2
AstProv=226mm^2
AscReq=0mm^2
AscProv=0mm^2
pt=0.449%
pc=0.000%
Section Hogging at 0.44AstReq=179mm^2
AstProv=226mm^2
AscReq=0mm^2
AscProv=0mm^2
pt=0.449%
pc=0.000%
Section Sagging at 0.88AstReq=106mm^2
AstProv=226mm^2
AscReq=0mm^2
AscProv=0mm^2
pt=0.449%
pc=0.000%
Section Hogging at 0.88AstReq=147mm^2
AstProv=226mm^2
AscReq=0mm^2
AscProv=0mm^2
pt=0.449%
pc=0.000%
Section Sagging at 1.32AstReq=106mm^2
AstProv=226mm^2
AscReq=0mm^2
AscProv=0mm^2
pt=0.449%
pc=0.000%
Section Hogging at 1.32AstReq=106mm^2
AstProv=226mm^2
AscReq=0mm^2
AscProv=0mm^2
pt=0.449%
pc=0.000%
Section Sagging at 1.76AstReq=106mm^2
AstProv=226mm^2
AscReq=0mm^2
AscProv=0mm^2
pt=0.449%
pc=0.000%
Section Hogging at 1.76AstReq=137mm^2
AstProv=226mm^2
AscReq=0mm^2
AscProv=0mm^2
pt=0.449%
pc=0.000%
Section Sagging at 2.2AstReq=158mm^2
AstProv=226mm^2
AscReq=0mm^2
AscProv=0mm^2
pt=0.449%
pc=0.000%
Section Hogging at 2.2AstReq=168mm^2
AstProv=226mm^2
AscReq=0mm^2
AscProv=0mm^2
pt=0.449%
pc=0.000%
Section Sagging at 2.64AstReq=365mm^2
AstProv=452mm^2
AscReq=0mm^2
AscProv=0mm^2
pt=0.897%
pc=0.000%
Section Hogging at 2.64AstReq=199mm^2
AstProv=226mm^2
AscReq=0mm^2
AscProv=0mm^2
pt=0.449%
pc=0.000%
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Shear Reinforcement