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T-beam and L - beam designs
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Out Put:Note : DRS = Doubly Reinforced Section, SRS = Singly Reinforced Section, NA = Not Applicable
Rqd. tensile Steel Reinforecement, Ast 7700.34 mm2
Provide 25 Ф bar 15.69 Nos. Say 16.00 Nos. Matching
Rqd. Compressive Steel Reinforecement, Asc 981.74 mm2
Provide 25 Ф bar 2.00 Nos. Say 2.00 Nos.
Stirrups Provided:
Provide 8 Ф bar Spacing 200.00 mm @ C/C Leg = 2
Crack Width Calculation:Stress in tensile reinforced level fsb 116.01 N/mm
2
Spacing of reinforcement S 21.933 mm
acr = ((S / 2)^2+d'^2)^0.5 - Dia /2 = 48.986 mm
Ɛ1b = [fs*((a' - xu) / [(d-xu)*2*10 ^5] 0.0006332
Ɛ2b= bt*(a'-xu)*(D-xu) / [600000*Ast*(d - xu)] 0.0001848
Ɛmb = Ɛ1b-Ɛ2b 0.0004484
0.0652253
Stress in tensile reinforced level fst 124.704 N/mm2
Ɛ1t= fs*(a' - (-D)) / [(d- (-D))*2*10 ^5] 0.0006499
Ɛ2t= bt*(a'-(-D))*(D-(-D)) / [600000*Ast*(d - (-D))] 0.0003655
Ɛmt = Ɛ1t-Ɛ2t 0.0002844
0.0415899
0.1068152 < 0.2
INPUT DATA:- Governing Load Case For Design LC 228
INPUT DATA:- Axial force, Torsion Moments, Bending moments and Shear force:
Design Shear force, Fy 351.31 KN LC 219
Design Torsional Moment for shear Tu=Mx 58.92 KNm LC 219
Moment M'uz 3598.39 KN LC 228
Design Torsional Moment for moment Tu=Mx 23.81 KNm LC 228
Axial Force, Fx 1440.39 KN T LC 228
Bending in another direction Muy 27.56 KNm LC 228
INPUT DATA:- Material Properties :
Characteristic Strength of concrete, fck 25.00 N/mm2
Grade of Steel, fy 415.00 N/mm2
INPUT DATA:- Material Properties and Dimensions of Beam:
Thickness of flange, Df 200.00 mm
Total Depth of T- Beam, D 1800.00 mm
Width of Flange, bf 2400.00 mm
Width of web in compression fibre, bcw 450.00 mm
Width of web in tension, btw' 450.00 mm
Layer of bar in tension zone 4.00
MOLUNG KHOLA BRIDGE MEMBER
T - Beam with Trapezoidal Web, memb. No. 13 (6.5m)
Wcrb = 3*acr*Ɛm/ [1+2*(acr - Cmin) / (D - xu)]
Wcrt = 3*acr x Ɛm / [1+2*(acr - Cmin) / (D - (-D))]
Wcr =Wcrb+Wcrt
Cover, C 40.00 mm
Stirrups of Design purpose 8.00 mm
Dia of bar for design purpose 25.00 mm
Spacer for vertical spacing 32.00 mm
Calculations of required Design Moments, Shear forces:
Resultant Moment of ( Muy and Muz') = M''uz 2111.64 KNm
Design Moment Mu 2181.67 KNm
Design shear force Vu 560.80 KN
Calculations of required Section properties:
Width of web in reiforcement level in tension, btw 450.00 mm
Width of Web, Average btw 450.00 mm
Effective Depth , d (Calculated) 1654.00 mm
Width of small portion in the flange, bs 0.000 mm
Centroid of Section from Compression fibre Cc 621.687 mm
Centoid of section from tension fibre Ct 1178.313 mm
Df/d (Calculated) 0.121
RESULT IN ACCORDANCE WITH DIFFERENT CONDITIONS:
1. Condition: If Neutral Axis lies in the flange? YES
Muf, lim= 0.36*fck*bf*Df*(d-0.416*Df) 6785.89 KNm
4604.216 KNm
Neutral Axis lies in the Flange? YES
For Mu or Mu,lim Area of Steel, Ast 3710.89 mm2
For Tension Area of Steel, Ast2 3989.45 mm2
for BM+Tension, total rqd. Steel, Ast 7700.34 mm2
Neutral Axis Ratio, Xu/d 0.03751
Neutral Axis, Xu 62.034 mm
Due to Mu Compressive strain Ɛcc 0.00027
Total Strain due to (Mu+Fx) Ɛcct 0.00040 < 0.0035 OK
for BM+compression, TrialTotal Rqd. Steel, Ast 10455.000 mm2
Due To Fx, Additional compressive stress fsc NA N/mm2
Additional compressive stress fcc NA N/mm2
Pu NA KN
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00012170 NA
Test : Fx-Pu =0 NA
for BM+compression, Extra Increased area Ast 0.000 mm2
Required Ast 7700.339 mm2
2. Condition: If Neutral Axis lies in the webNeutral Axis lies in the Web NA
Neutral axis depth ratio α = Xu,max/d 0.4791
Maximum Neutral Axis for balanced design Xu,max 792.44 mm NA
yf,max 248.87 mm NA
Test : Muf,lim > Mu for Neutral in flange
Compressive force for straight portion, C1 1704.04 KN NA
Compressive force fo rParabolic portion, C2 1514.70 KN NA
Compressive force Trap. Web, Cu = C1+C2 3218.74 KN NA
Compressive force for Flange portion, C3 4348.50 KN NA
Compressive force for Small Flange portion, C4 0.00 KN NA
Total Compressive force, C 7567.24 KN NA
Moment of C1 about Neutral Axis, Integration I1 1060992.17 KNmm NA
Moment C2 about Neutral Axis Integration I2 428683.70 KNmm NA
Moment f Cu about neutral axis Integration Iu 1489675.87 KNmm NA
CG of Cu from Neutral axis ,Y 462.814 mm NA
CG of Cu from Extreme Compression fibre X 329.630 mm NA
For average web only X/d 0.19929 NA
CG C from Extreme Compression fibre X 197.673 mm NA
11020.28 KNm NA
Capacity Mu, lim (Only for trapezodal Web) 4262.80 KNm NA
Capacity Mu, lim (trapezodal Web + Flange) 11020.37 KNm NA
-8838.70 KNm SRS
1456.478 mm NA
1456.327 mm NA
20956.625 mm2
NA
20958.972 mm2
NA
-0.001929
11.66904
-8549.985
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a 853.018 mm
yf=0.15*xu+0.65*Df 257.953 mm
Lever Arm z = jd 1643.994
18566.429 mm2
NA GO TO 1
Hit and Trial α = Xu/d 0.300000 SRS-NA
0.00000 SRS-NA
Neutral Axis for balanced design Xu 496.20 mm SRS-NA
yf,max 204.43 mm SRS-NA
Compressive force for straight portion, C1 0.00 KN SRS-NA
Compressive force fo rParabolic portion, C2 0.00 KN SRS-NA
Compressive force Trap.Web, Cu = C1+C2 0.00 KN SRS-NA
Compressive force for Flange portion, C3 0.00 KN SRS-NA
Compressive force for Small Flange portion, C4 0.00 KN SRS-NA
Total Compressive force, C 0.00 KN SRS-NA
Capacity if average web +flange Muw, lim=
0.36*fck*bw*Xu,max*(d-0.416*Xu,max) + 0.446*fck*(bf-
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast,max
For (web +Flange) balanced section Ast,max
a= - 0.14976*fck*bw - 0.0050175*fck*(bf - bw)
b= 0.36*fck*bw*d + 0.00669*fck*(bf - bw)
c= 0.2899*fck*Df*(bf - bw)*(d-0.325*Df)-Mu
For Df/d > 0.2 Ast
2 (A) IF Df/d > 0.2
α is chosen to make Test : C = T
Moment of C1 about Neutral Axis, Integration I1 NA KNmm SRS-NA
Moment C2 about Neutral Axis Integration I2 0.00 KNmm SRS-NA
Moment f Cu about neutral axis Integration Iu 0.00 KNmm SRS-NA
CG of Cu from Neutral axis ,Y 0.000 mm SRS-NA
CG of Cu from Extreme Comprssion fibre X 0.000 mm SRS-NA
For average web only X/d 0.00000 SRS-NA
CG C from Extreme Compression fibre X 0.000 mm SRS-NA
0.00 KNm SRS-NA
Mu(Only for trapezodal Web) 0.00 KNm SRS-NA
Mu,lim (trapezodal Web + Flange) 0.00 KNm SRS-NA
0.00 KNm SRS-NA
0.000 mm SRS-NA
0.000 mm SRS-NA
0.000 mm2
SRS-NA
0.00 mm2
SRS-NA
For Tension Area of Steel, Ast2 3989.45 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 3989.45 mm2
SRS-NA
NA KN SRS-NA
Neutral Axis, Xu 0.00 mm SRS-NA
Due to Mu Compressive strain Ɛcc 0.00000 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00002 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 1300.000 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc NA N/mm2
SRS-NA
Additional compressive stress fcc NA N/mm2
SRS-NA
Pu 0.000 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00001938 YES SRS-NA
Test : Fx-Pu =0 NA SRS-NA
Extra Increased area 0.000 mm2
SRS-NA
Required Singly reinforced Ast 3989.447 mm2
SRS-NA
-0.001929 SRS-NA
11.66904 SRS-NA
2309.679 SRS-NA
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a -191.847 mm SRS-NA
yf=0.15*xu+0.65*Df 101.223 mm SRS-NA
Lever Arm z = jd 1532.220 SRS-NA
3943.667 mm2
SRS-NA
NA GO TO 1
Hit and Trial α = Xu/d 0.2500 SRS-NA
α is chosen to make Test : C - T = 0 0.0000 SRS-NA
average web +flange Muw= 0.36*fck*bw*Xu,max*(d-
0.416*Xu,max) + 0.446*fck*(bf-bw)*yf*(d-0.5*yf,max)
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast,max
For (web +Flange) balanced section Ast,max
Force of Tension, T
a= - 0.14976*fck*bw - 0.0050175*fck*(bf - bw)
b= 0.36*fck*bw*d + 0.00669*fck*(bf - bw)
c= 0.2899*fck*Df*(bf - bw)*(d-0.325*Df)-Mu
For Df/d > 0.2 Ast
2 (B) IF Df/d < = 0.2
Neutral Axis for balanced design Xu 0.00 mm SRS-NA
yf 0.00 mm SRS-NA
Compressive force for straight portion, C1 0.00 KN SRS-NA
Compressive force fo rParabolic portion, C2 0.00 KN SRS-NA
Compressive force Trap.Web, Cu = C1+C2 0.00 KN SRS-NA
Compressive force for Flange portion, C3 0.00 KN SRS-NA
Compressive force for Small Flange portion, C4 0.00 KN SRS-NA
Total Compressive force, C 0.00 KN SRS-NA
Moment of C1 about Neutral Axis, Integration I1 0.00 KNmm SRS-NA
Moment C2 about Neutral Axis Integration I2 0.00 KNmm SRS-NA
Moment f Cu about neutral axis Integration Iu 0.00 KNmm SRS-NA
CG of Cu from Neutral axis ,Y 0.000 mm SRS-NA
CG of Cu from Extreme Comprssion fibre X 0.000 mm SRS-NA
For average web only X/d 0.0000000 SRS-NA
CG C from Extreme Compression fibre Xmax 0.000 mm SRS-NA
0.00 KNm SRS-NA
Mu (Only for trapezodal Web) 0.00 KNm SRS-NA
Mu,lim (trapezodal Web + Flange) 0.00 KNm SRS-NA
0.00 KNm SRS-NA
0.000 mm SRS-NA
0.000 mm SRS-NA
0.000 mm2
SRS-NA
0.000 mm2
SRS-NA
For Tension Area of Steel, Ast2 3989.45 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 3989.45 mm2
SRS-NA
0.00 KN SRS-NA
Neutral Axis, Xu 0.000 SRS-NA
Due to Mu Compressive strain Ɛcc 0.00000 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00014 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 3000.000 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc 0.00 N/mm2
SRS-NA
Additional compressive stress fcc 0.000 N/mm2
SRS-NA
Pu 0.000 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00013902 SRS-NA SRS-NA
Test : Fx-Pu =0 0.000000 SRS-NA
Extra Increased area 0.000 mm2
SRS-NA
Required Singly reinforced Ast 3989.447 mm2
SRS-NA
0.000000000 SRS-NA
b= 0.36*fck*bw*d 0.00000000 SRS-NA
0.00000 SRS-NA
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a 0.000 SRS-NA
Lever Arm z = jd 0.000 SRS-NA
average web +flange Muw = 0.36*fck*bw*Xu,max*(d-
0.416*Xu,max) + 0.446*fck*(bf-bw)*yf*(d-0.5*yf,max)
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast
For (web +Flange) balanced section Ast
Force of Tension, T
a= -0.14976*fck*bw
c= 0.446*fck*Df*(bf - bw)*(d-0.5*Df)-Mu
0.000 mm2
SRS-NA
2 (C) Condition: Doubly Reinforced Section GO TO 1
Number of Layer of Comression bar 1.00 No. SRS-NA
Dia of Main reinforcement in compression 32 mm SRS-NA
Spacer for Vertical spacing 32 mm SRS-NA
Dia of Stirrups 8.00 mm SRS-NA
Clear cover, C 40.00 mm SRS-NA
Charactertistics strength of Concrete fck 25.00 N/mm2 SRS-NA
Yield stress of steel fy 415.00 N/mm2 SRS-NA
Helping calculation, d'' 64.00 mm SRS-NA
Effective depth from in compression side d' 64.00 mm SRS-NA
Effective depth at tension side d 1654.00 mm SRS-NA
Neutral Axis depth ration Xu,max/d 0.479 SRS-NA
Neutral Axis Depth Xu.max 792.44 mmm SRS-NA
Compression level strain Ɛsc Or Ɛcc 0.00322 SRS-NA
Compressive level stress of steel fsc 355.993 N/mm2 SRS-NA
Compressive level stress of concrete fcc=446*fck*(Ԑcc-250*Ԑcc^2)11.150 N/mm2 SRS-NA
Area of compressive stress Asc -16120.178 mm2
SRS-NA
-15396.566 mm2
SRS-NA
For DRS Total Area of tension steel Ast 5562.407 mm2
SRS-NA
for Tension, Area of Steel, Ast3 19386.01 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 24948.42 mm2
SRS-NA
Neutral Axis, Xu 792.444 mm SRS-NA
Due to Mu Compressive strain Ɛcc 0.00350 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00362 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 11749.484 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc NA N/mm2
SRS-NA
Additional compressive stress fcc NA N/mm2
SRS-NA
Pu 0.000 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00011915 YES SRS-NA
Test : Fx-Pu =0 0.000000 SRS-NA
Extra Increased area 0.000 mm2
SRS-NA
Required Double reinforced Ast 24948.420 mm2
SRS-NA
Check for Shear forceDesign Shear force 560.80 KN
Shear stress 0.753 N/mm2
Percentage of tension steel, pt 1.055 %
Percentage of compressive steel, pc 0.132 %
For Df/d < 0.2 Ast
for Asc, Area of tension steel Ast2
Percentage of tension and compressive steel, pt 4.907 %
α=0.8*fck/6.89*pt 0.592
tc = 0.85*SQRT(0.8*fck)*(SQRT(1+5*α)-1)/6*α 1.060 N/mm2
1.00 x 1.060 = 1.060
> 0.753 Not OK
Shear Reinforcement is required.
Dia of of Vertical Stirrups 8.00 mm
Number of leg 2.00
Planned area to Provide Asv 100.53 mm2
Required spacing of stirrups Svreqd. -263.411 mm
Plan to Provide, spacing of stirrups Sv 200.000
Minimum required Asv 0.4*b*Sv/0.87*fy 99.7092 mm2
Ф 7.9672 mm
Rqd. Stirrups Ф 8.00 Leg 2.000 200.00 mm C/C
Permissible shear stress,
K´tc =
Out Put:Note : DRS = Doubly Reinforced Section, SRS = Singly Reinforced Section, NA = Not Applicable
Rqd. tensile Steel Reinforecement, Ast 8064.86 mm2
Provide 25 Ф bar 16.43 Nos. Say 16.00 Nos.
Rqd. Compressive Steel Reinforecement, Asc 981.74 mm2
Provide 25 Ф bar 2.00 Nos. Say 2.00 Nos.
Stirrups Provided:
Provide 8 Ф bar Spacing 200.00 mm @ C/C Leg = 2
Crack Width Calculation:Stress in tensile reinforced level fsb 118.68 N/mm
2
Spacing of reinforcement S 21.933 mm
acr = ((S / 2)^2+d'^2)^0.5 - Dia /2 = 48.986 mm
Ɛ1b = [fs*((a' - xu) / [(d-xu)*2*10 ^5] 0.0006480
Ɛ2b= bt*(a'-xu)*(D-xu) / [600000*Ast*(d - xu)] 0.0001760
Ɛmb = Ɛ1b-Ɛ2b 0.0004719
0.0686417
Stress in tensile reinforced level fst 122.032 N/mm2
Ɛ1t= fs*(a' - (-D)) / [(d- (-D))*2*10 ^5] 0.0006360
Ɛ2t= bt*(a'-(-D))*(D-(-D)) / [600000*Ast*(d - (-D))] 0.0003489
Ɛmt = Ɛ1t-Ɛ2t 0.0002870
0.0419697
0.1106114 < 0.2
INPUT DATA:- Governing Load Case For Design LC 232
INPUT DATA:- Axial force, Torsion Moments, Bending moments and Shear force:
Design Shear force, Fy 361.30 KN LC 231
Design Torsional Moment for shear Tu=Mx 24.55 KNm LC 231
Moment M'uz 3834.74 KN LC 232
Design Torsional Moment for moment Tu=Mx 8.15 KNm LC 232
Axial Force, Fx 1476.26 KN T LC 232
Bending in another direction Muy 29.41 KNm LC 232
INPUT DATA:- Material Properties :
Characteristic Strength of concrete, fck 25.00 N/mm2
Grade of Steel, fy 415.00 N/mm2
INPUT DATA:- Material Properties and Dimensions of Beam:
Thickness of flange, Df 200.00 mm
Total Depth of T- Beam, D 1800.00 mm
Width of Flange, bf 2400.00 mm
Width of web in compression fibre, bcw 450.00 mm
Width of web in tension, btw' 450.00 mm
Layer of bar in tension zone 4.00
MOLUNG KHOLA BRIDGE MEMBER
T - Beam with Trapezoidal Web, memb. No. 25 (12.5m)
Wcrb = 3*acr*Ɛm/ [1+2*(acr - Cmin) / (D - xu)]
Wcrt = 3*acr x Ɛm / [1+2*(acr - Cmin) / (D - (-D))]
Wcr =Wcrb+Wcrt
Cover, C 40.00 mm
Stirrups of Design purpose 8.00 mm
Dia of bar for design purpose 25.00 mm
Spacer for vertical spacing 32.00 mm
Calculations of required Design Moments, Shear forces:
Resultant Moment of ( Muy and Muz') = M''uz 2310.96 KNm
Design Moment Mu 2334.93 KNm
Design shear force Vu 448.59 KN
Calculations of required Section properties:
Width of web in reiforcement level in tension, btw 450.00 mm
Width of Web, Average btw 450.00 mm
Effective Depth , d (Calculated) 1654.00 mm
Width of small portion in the flange, bs 0.000 mm
Centroid of Section from Compression fibre Cc 621.687 mm
Centoid of section from tension fibre Ct 1178.313 mm
Df/d (Calculated) 0.121
RESULT IN ACCORDANCE WITH DIFFERENT CONDITIONS:
1. Condition: If Neutral Axis lies in the flange? YES
Muf, lim= 0.36*fck*bf*Df*(d-0.416*Df) 6785.89 KNm
4450.950 KNm
Neutral Axis lies in the Flange? YES
For Mu or Mu,lim Area of Steel, Ast 3976.07 mm2
For Tension Area of Steel, Ast2 4088.80 mm2
for BM+Tension, total rqd. Steel, Ast 8064.86 mm2
Neutral Axis Ratio, Xu/d 0.04019
Neutral Axis, Xu 66.467 mm
Due to Mu Compressive strain Ɛcc 0.00029
Total Strain due to (Mu+Fx) Ɛcct 0.00042 < 0.0035 OK
for BM+compression, TrialTotal Rqd. Steel, Ast 10455.000 mm2
Due To Fx, Additional compressive stress fsc NA N/mm2
Additional compressive stress fcc NA N/mm2
Pu NA KN
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00012170 NA
Test : Fx-Pu =0 NA
for BM+compression, Extra Increased area Ast 0.000 mm2
Required Ast 8064.863 mm2
2. Condition: If Neutral Axis lies in the webNeutral Axis lies in the Web NA
Neutral axis depth ratio α = Xu,max/d 0.4791
Maximum Neutral Axis for balanced design Xu,max 792.44 mm NA
yf,max 248.87 mm NA
Test : Muf,lim > Mu for Neutral in flange
Compressive force for straight portion, C1 1704.04 KN NA
Compressive force fo rParabolic portion, C2 1514.70 KN NA
Compressive force Trap. Web, Cu = C1+C2 3218.74 KN NA
Compressive force for Flange portion, C3 4348.50 KN NA
Compressive force for Small Flange portion, C4 0.00 KN NA
Total Compressive force, C 7567.24 KN NA
Moment of C1 about Neutral Axis, Integration I1 1060992.17 KNmm NA
Moment C2 about Neutral Axis Integration I2 428683.70 KNmm NA
Moment f Cu about neutral axis Integration Iu 1489675.87 KNmm NA
CG of Cu from Neutral axis ,Y 462.814 mm NA
CG of Cu from Extreme Compression fibre X 329.630 mm NA
For average web only X/d 0.19929 NA
CG C from Extreme Compression fibre X 197.673 mm NA
11020.28 KNm NA
Capacity Mu, lim (Only for trapezodal Web) 4262.80 KNm NA
Capacity Mu, lim (trapezodal Web + Flange) 11020.37 KNm NA
-8685.43 KNm SRS
1456.478 mm NA
1456.327 mm NA
20956.625 mm2
NA
20958.972 mm2
NA
-0.001929
11.66904
-8549.985
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a 853.018 mm
yf=0.15*xu+0.65*Df 257.953 mm
Lever Arm z = jd 1643.994
18566.429 mm2
NA GO TO 1
Hit and Trial α = Xu/d 0.300000 SRS-NA
0.00000 SRS-NA
Neutral Axis for balanced design Xu 496.20 mm SRS-NA
yf,max 204.43 mm SRS-NA
Compressive force for straight portion, C1 0.00 KN SRS-NA
Compressive force fo rParabolic portion, C2 0.00 KN SRS-NA
Compressive force Trap.Web, Cu = C1+C2 0.00 KN SRS-NA
Compressive force for Flange portion, C3 0.00 KN SRS-NA
Compressive force for Small Flange portion, C4 0.00 KN SRS-NA
Total Compressive force, C 0.00 KN SRS-NA
Capacity if average web +flange Muw, lim=
0.36*fck*bw*Xu,max*(d-0.416*Xu,max) + 0.446*fck*(bf-
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast,max
For (web +Flange) balanced section Ast,max
a= - 0.14976*fck*bw - 0.0050175*fck*(bf - bw)
b= 0.36*fck*bw*d + 0.00669*fck*(bf - bw)
c= 0.2899*fck*Df*(bf - bw)*(d-0.325*Df)-Mu
For Df/d > 0.2 Ast
2 (A) IF Df/d > 0.2
α is chosen to make Test : C = T
Moment of C1 about Neutral Axis, Integration I1 NA KNmm SRS-NA
Moment C2 about Neutral Axis Integration I2 0.00 KNmm SRS-NA
Moment f Cu about neutral axis Integration Iu 0.00 KNmm SRS-NA
CG of Cu from Neutral axis ,Y 0.000 mm SRS-NA
CG of Cu from Extreme Comprssion fibre X 0.000 mm SRS-NA
For average web only X/d 0.00000 SRS-NA
CG C from Extreme Compression fibre X 0.000 mm SRS-NA
0.00 KNm SRS-NA
Mu(Only for trapezodal Web) 0.00 KNm SRS-NA
Mu,lim (trapezodal Web + Flange) 0.00 KNm SRS-NA
0.00 KNm SRS-NA
0.000 mm SRS-NA
0.000 mm SRS-NA
0.000 mm2
SRS-NA
0.00 mm2
SRS-NA
For Tension Area of Steel, Ast2 4088.80 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 4088.80 mm2
SRS-NA
NA KN SRS-NA
Neutral Axis, Xu 0.00 mm SRS-NA
Due to Mu Compressive strain Ɛcc 0.00000 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00002 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 1300.000 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc NA N/mm2
SRS-NA
Additional compressive stress fcc NA N/mm2
SRS-NA
Pu 0.000 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00001938 YES SRS-NA
Test : Fx-Pu =0 NA SRS-NA
Extra Increased area 0.000 mm2
SRS-NA
Required Singly reinforced Ast 4088.797 mm2
SRS-NA
-0.001929 SRS-NA
11.66904 SRS-NA
2156.413 SRS-NA
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a -179.472 mm SRS-NA
yf=0.15*xu+0.65*Df 103.079 mm SRS-NA
Lever Arm z = jd 1541.886 SRS-NA
4194.258 mm2
SRS-NA
NA GO TO 1
Hit and Trial α = Xu/d 0.2650 SRS-NA
α is chosen to make Test : C - T = 0 0.0000 SRS-NA
average web +flange Muw= 0.36*fck*bw*Xu,max*(d-
0.416*Xu,max) + 0.446*fck*(bf-bw)*yf*(d-0.5*yf,max)
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast,max
For (web +Flange) balanced section Ast,max
Force of Tension, T
a= - 0.14976*fck*bw - 0.0050175*fck*(bf - bw)
b= 0.36*fck*bw*d + 0.00669*fck*(bf - bw)
c= 0.2899*fck*Df*(bf - bw)*(d-0.325*Df)-Mu
For Df/d > 0.2 Ast
2 (B) IF Df/d < = 0.2
Neutral Axis for balanced design Xu 0.00 mm SRS-NA
yf 0.00 mm SRS-NA
Compressive force for straight portion, C1 0.00 KN SRS-NA
Compressive force fo rParabolic portion, C2 0.00 KN SRS-NA
Compressive force Trap.Web, Cu = C1+C2 0.00 KN SRS-NA
Compressive force for Flange portion, C3 0.00 KN SRS-NA
Compressive force for Small Flange portion, C4 0.00 KN SRS-NA
Total Compressive force, C 0.00 KN SRS-NA
Moment of C1 about Neutral Axis, Integration I1 0.00 KNmm SRS-NA
Moment C2 about Neutral Axis Integration I2 0.00 KNmm SRS-NA
Moment f Cu about neutral axis Integration Iu 0.00 KNmm SRS-NA
CG of Cu from Neutral axis ,Y 0.000 mm SRS-NA
CG of Cu from Extreme Comprssion fibre X 0.000 mm SRS-NA
For average web only X/d 0.0000000 SRS-NA
CG C from Extreme Compression fibre Xmax 0.000 mm SRS-NA
0.00 KNm SRS-NA
Mu (Only for trapezodal Web) 0.00 KNm SRS-NA
Mu,lim (trapezodal Web + Flange) 0.00 KNm SRS-NA
0.00 KNm SRS-NA
0.000 mm SRS-NA
0.000 mm SRS-NA
0.000 mm2
SRS-NA
0.000 mm2
SRS-NA
For Tension Area of Steel, Ast2 4088.80 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 4088.80 mm2
SRS-NA
0.00 KN SRS-NA
Neutral Axis, Xu 0.000 SRS-NA
Due to Mu Compressive strain Ɛcc 0.00000 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00014 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 3000.000 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc 0.00 N/mm2
SRS-NA
Additional compressive stress fcc 0.000 N/mm2
SRS-NA
Pu 0.000 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00013902 SRS-NA SRS-NA
Test : Fx-Pu =0 0.000000 SRS-NA
Extra Increased area 0.000 mm2
SRS-NA
Required Singly reinforced Ast 4088.797 mm2
SRS-NA
0.000000000 SRS-NA
b= 0.36*fck*bw*d 0.00000000 SRS-NA
0.00000 SRS-NA
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a 0.000 SRS-NA
Lever Arm z = jd 0.000 SRS-NA
average web +flange Muw = 0.36*fck*bw*Xu,max*(d-
0.416*Xu,max) + 0.446*fck*(bf-bw)*yf*(d-0.5*yf,max)
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast
For (web +Flange) balanced section Ast
Force of Tension, T
a= -0.14976*fck*bw
c= 0.446*fck*Df*(bf - bw)*(d-0.5*Df)-Mu
0.000 mm2
SRS-NA
2 (C) Condition: Doubly Reinforced Section GO TO 1
Number of Layer of Comression bar 1.00 No. SRS-NA
Dia of Main reinforcement in compression 32 mm SRS-NA
Spacer for Vertical spacing 32 mm SRS-NA
Dia of Stirrups 8.00 mm SRS-NA
Clear cover, C 40.00 mm SRS-NA
Charactertistics strength of Concrete fck 25.00 N/mm2 SRS-NA
Yield stress of steel fy 415.00 N/mm2 SRS-NA
Helping calculation, d'' 64.00 mm SRS-NA
Effective depth from in compression side d' 64.00 mm SRS-NA
Effective depth at tension side d 1654.00 mm SRS-NA
Neutral Axis depth ration Xu,max/d 0.479 SRS-NA
Neutral Axis Depth Xu.max 792.44 mmm SRS-NA
Compression level strain Ɛsc Or Ɛcc 0.00322 SRS-NA
Compressive level stress of steel fsc 355.993 N/mm2 SRS-NA
Compressive level stress of concrete fcc=446*fck*(Ԑcc-250*Ԑcc^2) 11.150 N/mm2 SRS-NA
Area of compressive stress Asc -15840.649 mm2
SRS-NA
-15129.584 mm2
SRS-NA
For DRS Total Area of tension steel Ast 5829.388 mm2
SRS-NA
for Tension, Area of Steel, Ast3 19218.38 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 25047.77 mm2
SRS-NA
Neutral Axis, Xu 792.444 mm SRS-NA
Due to Mu Compressive strain Ɛcc 0.00350 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00362 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 11749.484 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc NA N/mm2
SRS-NA
Additional compressive stress fcc NA N/mm2
SRS-NA
Pu 0.000 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00011915 YES SRS-NA
Test : Fx-Pu =0 0.000000 SRS-NA
Extra Increased area 0.000 mm2
SRS-NA
Required Double reinforced Ast 25047.769 mm2
SRS-NA
Check for Shear forceDesign Shear force 448.59 KN
Shear stress 0.603 N/mm2
Percentage of tension steel, pt 1.055 %
Percentage of compressive steel, pc 0.132 %
For Df/d < 0.2 Ast
for Asc, Area of tension steel Ast2
Percentage of tension and compressive steel, pt 4.907 %
α=0.8*fck/6.89*pt 0.592
tc = 0.85*SQRT(0.8*fck)*(SQRT(1+5*α)-1)/6*α 1.060 N/mm2
1.00 x 1.060 = 1.060
> 0.603 OK
Shear Reinforcement is NOT required.
Dia of of Vertical Stirrups 8.00 mm
Number of leg 2.00
Planned area to Provide Asv 100.53 mm2
Required spacing of stirrups Svreqd. -176.507 mm
Plan to Provide, spacing of stirrups Sv 200.000
Minimum required Asv 0.4*b*Sv/0.87*fy 99.7092 mm2
Ф 7.9672 mm
Rqd. Stirrups Ф 8.00 Leg 2.000 200.00 mm C/C
Permissible shear stress,
K´tc =
Out Put:Note : DRS = Doubly Reinforced Section, SRS = Singly Reinforced Section, NA = Not Applicable
Rqd. tensile Steel Reinforecement, Ast 2603.14 mm2
Provide 25 Ф bar 5.30 Nos. Say 5.00 Nos.
Rqd. Compressive Steel Reinforecement, Asc 1963.48 mm2
Provide 25 Ф bar 4.00 Nos. Say 4.00 Nos.
Stirrups Provided:
Provide 8 Ф bar Spacing 200.00 mm @ C/C Leg = 2
Crack Width Calculation:Stress in tensile reinforced level fsb 176.22 N/mm
2
Spacing of reinforcement S 82.250 mm
acr = ((S / 2)^2+d'^2)^0.5 - Dia /2 = 60.654 mm
Ɛ1b = [fs*((a' - xu) / [(d-xu)*2*10 ^5] 0.0009278
Ɛ2b= bt*(a'-xu)*(D-xu) / [600000*Ast*(d - xu)] 0.0005364
Ɛmb = Ɛ1b-Ɛ2b 0.0003914
0.0695856
Stress in tensile reinforced level fst 64.491 N/mm2
Ɛ1t= fs*(a' - (-D)) / [(d- (-D))*2*10 ^5] 0.0003306
Ɛ2t= bt*(a'-(-D))*(D-(-D)) / [600000*Ast*(d - (-D))] 0.0010635
Ɛmt = Ɛ1t-Ɛ2t -0.0007329
-0.1318418
-0.0622561 < 0.2
INPUT DATA:- Governing Load Case For Design LC 556
INPUT DATA:- Axial force, Torsion Moments, Bending moments and Shear force:
Design Shear force, Fy 873.28 KN LC 515
Design Torsional Moment for shear Tu=Mx 58.18 KNm LC 515
Moment M'uz 1382.96 KN LC 556
Design Torsional Moment for moment Tu=Mx 20.22 KNm LC 556
Axial Force, Fx 251.82 KN T LC 556
Bending in another direction Muy 10.73 KNm LC 556
INPUT DATA:- Material Properties :
Characteristic Strength of concrete, fck 25.00 N/mm2
Grade of Steel, fy 415.00 N/mm2
INPUT DATA:- Material Properties and Dimensions of Beam:
Thickness of flange, Df 200.00 mm
Total Depth of T- Beam, D 1800.00 mm
Width of Flange, bf 2400.00 mm
Width of web in compression fibre, bcw 450.00 mm
Width of web in tension, btw' 450.00 mm
Layer of bar in tension zone 2.00
MOLUNG KHOLA BRIDGE MEMBER
T - Beam with Trapezoidal Web, memb. No. 38 (19m)
Wcrb = 3*acr*Ɛm/ [1+2*(acr - Cmin) / (D - xu)]
Wcrt = 3*acr x Ɛm / [1+2*(acr - Cmin) / (D - (-D))]
Wcr =Wcrb+Wcrt
Cover, C 40.00 mm
Stirrups of Design purpose 8.00 mm
Dia of bar for design purpose 25.00 mm
Spacer for vertical spacing 32.00 mm
Calculations of required Design Moments, Shear forces:
Resultant Moment of ( Muy and Muz') = M''uz 1108.70 KNm
Design Moment Mu 1168.17 KNm
Design shear force Vu 1080.14 KN
Calculations of required Section properties:
Width of web in reiforcement level in tension, btw 450.00 mm
Width of Web, Average btw 450.00 mm
Effective Depth , d (Calculated) 1711.00 mm
Width of small portion in the flange, bs 0.000 mm
Centroid of Section from Compression fibre Cc 621.687 mm
Centoid of section from tension fibre Ct 1178.313 mm
Df/d (Calculated) 0.117
RESULT IN ACCORDANCE WITH DIFFERENT CONDITIONS:
1. Condition: If Neutral Axis lies in the flange? YES
Muf, lim= 0.36*fck*bf*Df*(d-0.416*Df) 7032.13 KNm
5863.950 KNm
Neutral Axis lies in the Flange? YES
For Mu or Mu,lim Area of Steel, Ast 1905.68 mm2
For Tension Area of Steel, Ast2 697.47 mm2
for BM+Tension, total rqd. Steel, Ast 2603.14 mm2
Neutral Axis Ratio, Xu/d 0.01862
Neutral Axis, Xu 31.855 mm
Due to Mu Compressive strain Ɛcc 0.00014
Total Strain due to (Mu+Fx) Ɛcct 0.00026 < 0.0035 OK
for BM+compression, TrialTotal Rqd. Steel, Ast 10455.000 mm2
Due To Fx, Additional compressive stress fsc NA N/mm2
Additional compressive stress fcc NA N/mm2
Pu NA KN
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00012170 NA
Test : Fx-Pu =0 NA
for BM+compression, Extra Increased area Ast 0.000 mm2
Required Ast 2603.142 mm2
2. Condition: If Neutral Axis lies in the webNeutral Axis lies in the Web NA
Neutral axis depth ratio α = Xu,max/d 0.4791
Maximum Neutral Axis for balanced design Xu,max 819.75 mm NA
yf,max 252.96 mm NA
Test : Muf,lim > Mu for Neutral in flange
Compressive force for straight portion, C1 1762.76 KN NA
Compressive force fo rParabolic portion, C2 1566.90 KN NA
Compressive force Trap. Web, Cu = C1+C2 3329.66 KN NA
Compressive force for Flange portion, C3 4348.50 KN NA
Compressive force for Small Flange portion, C4 0.00 KN NA
Total Compressive force, C 7678.16 KN NA
Moment of C1 about Neutral Axis, Integration I1 1135379.86 KNmm NA
Moment C2 about Neutral Axis Integration I2 458739.34 KNmm NA
Moment f Cu about neutral axis Integration Iu 1594119.20 KNmm NA
CG of Cu from Neutral axis ,Y 478.763 mm NA
CG of Cu from Extreme Compression fibre X 340.990 mm NA
For average web only X/d 0.19929 NA
CG C from Extreme Compression fibre X 204.506 mm NA
11567.01 KNm NA
Capacity Mu, lim (Only for trapezodal Web) 4561.67 KNm NA
Capacity Mu, lim (trapezodal Web + Flange) 11567.10 KNm NA
-10398.93 KNm SRS
1506.654 mm NA
1506.494 mm NA
21263.770 mm2
NA
21266.198 mm2
NA
-0.001929
12.08578
-8935.608
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a 856.446 mm
yf=0.15*xu+0.65*Df 258.467 mm
Lever Arm z = jd 1700.989
18834.573 mm2
NA GO TO 1
Hit and Trial α = Xu/d 0.300000 SRS-NA
0.00000 SRS-NA
Neutral Axis for balanced design Xu 513.30 mm SRS-NA
yf,max 207.00 mm SRS-NA
Compressive force for straight portion, C1 0.00 KN SRS-NA
Compressive force fo rParabolic portion, C2 0.00 KN SRS-NA
Compressive force Trap.Web, Cu = C1+C2 0.00 KN SRS-NA
Compressive force for Flange portion, C3 0.00 KN SRS-NA
Compressive force for Small Flange portion, C4 0.00 KN SRS-NA
Total Compressive force, C 0.00 KN SRS-NA
a= - 0.14976*fck*bw - 0.0050175*fck*(bf - bw)
b= 0.36*fck*bw*d + 0.00669*fck*(bf - bw)
c= 0.2899*fck*Df*(bf - bw)*(d-0.325*Df)-Mu
For Df/d > 0.2 Ast
2 (A) IF Df/d > 0.2
α is chosen to make Test : C = T
Capacity if average web +flange Muw, lim=
0.36*fck*bw*Xu,max*(d-0.416*Xu,max) + 0.446*fck*(bf-
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast,max
For (web +Flange) balanced section Ast,max
Moment of C1 about Neutral Axis, Integration I1 NA KNmm SRS-NA
Moment C2 about Neutral Axis Integration I2 0.00 KNmm SRS-NA
Moment f Cu about neutral axis Integration Iu 0.00 KNmm SRS-NA
CG of Cu from Neutral axis ,Y 0.000 mm SRS-NA
CG of Cu from Extreme Comprssion fibre X 0.000 mm SRS-NA
For average web only X/d 0.00000 SRS-NA
CG C from Extreme Compression fibre X 0.000 mm SRS-NA
0.00 KNm SRS-NA
Mu(Only for trapezodal Web) 0.00 KNm SRS-NA
Mu,lim (trapezodal Web + Flange) 0.00 KNm SRS-NA
0.00 KNm SRS-NA
0.000 mm SRS-NA
0.000 mm SRS-NA
0.000 mm2
SRS-NA
0.00 mm2
SRS-NA
For Tension Area of Steel, Ast2 697.47 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 697.47 mm2
SRS-NA
NA KN SRS-NA
Neutral Axis, Xu 0.00 mm SRS-NA
Due to Mu Compressive strain Ɛcc 0.00000 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00002 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 1300.000 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc NA N/mm2
SRS-NA
Additional compressive stress fcc NA N/mm2
SRS-NA
Pu 0.000 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00001938 YES SRS-NA
Test : Fx-Pu =0 NA SRS-NA
Extra Increased area 0.000 mm2
SRS-NA
Required Singly reinforced Ast 697.466 mm2
SRS-NA
-0.001929 SRS-NA
12.08578 SRS-NA
3484.285 SRS-NA
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a -276.124 mm SRS-NA
yf=0.15*xu+0.65*Df 88.581 mm SRS-NA
Lever Arm z = jd 1446.340 SRS-NA
2237.022 mm2
SRS-NA
NA GO TO 1
Hit and Trial α = Xu/d 0.2650 SRS-NA
α is chosen to make Test : C - T = 0 0.0000 SRS-NA
Force of Tension, T
a= - 0.14976*fck*bw - 0.0050175*fck*(bf - bw)
b= 0.36*fck*bw*d + 0.00669*fck*(bf - bw)
c= 0.2899*fck*Df*(bf - bw)*(d-0.325*Df)-Mu
For Df/d > 0.2 Ast
2 (B) IF Df/d < = 0.2
average web +flange Muw= 0.36*fck*bw*Xu,max*(d-
0.416*Xu,max) + 0.446*fck*(bf-bw)*yf*(d-0.5*yf,max)
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast,max
For (web +Flange) balanced section Ast,max
Neutral Axis for balanced design Xu 0.00 mm SRS-NA
yf 0.00 mm SRS-NA
Compressive force for straight portion, C1 0.00 KN SRS-NA
Compressive force fo rParabolic portion, C2 0.00 KN SRS-NA
Compressive force Trap.Web, Cu = C1+C2 0.00 KN SRS-NA
Compressive force for Flange portion, C3 0.00 KN SRS-NA
Compressive force for Small Flange portion, C4 0.00 KN SRS-NA
Total Compressive force, C 0.00 KN SRS-NA
Moment of C1 about Neutral Axis, Integration I1 0.00 KNmm SRS-NA
Moment C2 about Neutral Axis Integration I2 0.00 KNmm SRS-NA
Moment f Cu about neutral axis Integration Iu 0.00 KNmm SRS-NA
CG of Cu from Neutral axis ,Y 0.000 mm SRS-NA
CG of Cu from Extreme Comprssion fibre X 0.000 mm SRS-NA
For average web only X/d 0.0000000 SRS-NA
CG C from Extreme Compression fibre Xmax 0.000 mm SRS-NA
0.00 KNm SRS-NA
Mu (Only for trapezodal Web) 0.00 KNm SRS-NA
Mu,lim (trapezodal Web + Flange) 0.00 KNm SRS-NA
0.00 KNm SRS-NA
0.000 mm SRS-NA
0.000 mm SRS-NA
0.000 mm2
SRS-NA
0.000 mm2
SRS-NA
For Tension Area of Steel, Ast2 697.47 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 697.47 mm2
SRS-NA
0.00 KN SRS-NA
Neutral Axis, Xu 0.000 SRS-NA
Due to Mu Compressive strain Ɛcc 0.00000 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00014 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 3000.000 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc 0.00 N/mm2
SRS-NA
Additional compressive stress fcc 0.000 N/mm2
SRS-NA
Pu 0.000 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00013902 SRS-NA SRS-NA
Test : Fx-Pu =0 0.000000 SRS-NA
Extra Increased area 0.000 mm2
SRS-NA
Required Singly reinforced Ast 697.466 mm2
SRS-NA
0.000000000 SRS-NA
b= 0.36*fck*bw*d 0.00000000 SRS-NA
0.00000 SRS-NA
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a 0.000 SRS-NA
Lever Arm z = jd 0.000 SRS-NA
Force of Tension, T
a= -0.14976*fck*bw
c= 0.446*fck*Df*(bf - bw)*(d-0.5*Df)-Mu
average web +flange Muw = 0.36*fck*bw*Xu,max*(d-
0.416*Xu,max) + 0.446*fck*(bf-bw)*yf*(d-0.5*yf,max)
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast
For (web +Flange) balanced section Ast
0.000 mm2
SRS-NA
2 (C) Condition: Doubly Reinforced Section GO TO 1
Number of Layer of Comression bar 1.00 No. SRS-NA
Dia of Main reinforcement in compression 32 mm SRS-NA
Spacer for Vertical spacing 32 mm SRS-NA
Dia of Stirrups 8.00 mm SRS-NA
Clear cover, C 40.00 mm SRS-NA
Charactertistics strength of Concrete fck 25.00 N/mm2 SRS-NA
Yield stress of steel fy 415.00 N/mm2 SRS-NA
Helping calculation, d'' 64.00 mm SRS-NA
Effective depth from in compression side d' 64.00 mm SRS-NA
Effective depth at tension side d 1711.00 mm SRS-NA
Neutral Axis depth ration Xu,max/d 0.479 SRS-NA
Neutral Axis Depth Xu.max 819.75 mmm SRS-NA
Compression level strain Ɛsc Or Ɛcc 0.00323 SRS-NA
Compressive level stress of steel fsc 356.075 N/mm2 SRS-NA
Compressive level stress of concrete fcc=446*fck*(Ԑcc-250*Ԑcc^2) 11.150 N/mm2 SRS-NA
Area of compressive stress Asc -18305.041 mm2
SRS-NA
-17487.496 mm2
SRS-NA
For DRS Total Area of tension steel Ast 3778.702 mm2
SRS-NA
for Tension, Area of Steel, Ast3 18184.96 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 21963.66 mm2
SRS-NA
Neutral Axis, Xu 819.753 mm SRS-NA
Due to Mu Compressive strain Ɛcc 0.00350 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00362 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 11749.484 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc NA N/mm2
SRS-NA
Additional compressive stress fcc NA N/mm2
SRS-NA
Pu 0.000 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00011915 YES SRS-NA
Test : Fx-Pu =0 0.000000 SRS-NA
Extra Increased area 0.000 mm2
SRS-NA
Required Double reinforced Ast 21963.663 mm2
SRS-NA
Check for Shear forceDesign Shear force 1080.14 KN
Shear stress 1.403 N/mm2
Percentage of tension steel, pt 0.319 %
Percentage of compressive steel, pc 0.255 %
For Df/d < 0.2 Ast
for Asc, Area of tension steel Ast2
Percentage of tension and compressive steel, pt 4.294 %
α=0.8*fck/6.89*pt 0.676
tc = 0.85*SQRT(0.8*fck)*(SQRT(1+5*α)-1)/6*α 1.024 N/mm2
1.00 x 1.024 = 1.024
> 1.403 NOT OK
Shear Reinforcement is required.
Dia of of Vertical Stirrups 8.00 mm
Number of leg 2.00
Planned area to Provide Asv 100.53 mm2
Required spacing of stirrups Svreqd. 213.016 mm
Plan to Provide, spacing of stirrups Sv 200.000
Minimum required Asv 0.4*b*Sv/0.87*fy 99.7092 mm2
Ф 7.9672 mm
Rqd. Stirrups Ф 8.00 Leg 2.000 200.00 mm C/C
Permissible shear stress,
K´tc =
Out Put:Note : DRS = Doubly Reinforced Section, SRS = Singly Reinforced Section, NA = Not Applicable
Rqd. tensile Steel Reinforecement, Ast 12063.72 mm2
Provide 32 Ф bar 15.00 Nos. Say 15.00 Nos.
Rqd. Compressive Steel Reinforecement, Asc 8728.57 mm2
Provide 25 Ф bar 17.78 Nos. Say 18.00 Nos.
Stirrups Provided:
Provide 10 Ф bar Spacing 199.07 mm @ C/C Leg = 2
Crack Width Calculation:Stress in tensile reinforced level fsb 698.31 N/mm
2
Spacing of reinforcement S 10.035 mm
acr = ((S / 2)^2+d'^2)^0.5 - Dia /2 = 48.196 mm
Ɛ1b = [fs*((a' - xu) / [(d-xu)*2*10 ^5] 0.0040228
Ɛ2b= bt*(a'-xu)*(D-xu) / [600000*Ast*(d - xu)] 0.0000354
Ɛmb = Ɛ1b-Ɛ2b 0.0039874
0.5661088
Stress in tensile reinforced level fst 0.000 N/mm2
Ɛ1t= fs*(a' - (-D)) / [(d- (-D))*2*10 ^5] 0.0000000
Ɛ2t= bt*(a'-(-D))*(D-(-D)) / [600000*Ast*(d - (-D))] 0.0001147
Ɛmt = Ɛ1t-Ɛ2t -0.0001147
-0.0165052
0.5496036 < 0.2
INPUT DATA:- Governing Load Case For Design LC 530
INPUT DATA:- Axial force, Torsion Moments, Bending moments and Shear force:
Design Shear force, Fy 1152.88 KN LC 567
Design Torsional Moment for shear Tu=Mx 0.00 KNm LC 567
Moment M'uz 15000.00 KN LC 530
Design Torsional Moment for moment Tu=Mx 0.00 KNm LC 530
Axial Force, Fx 0.00 KN C LC 530
Bending in another direction Muy 0 KNm LC 530
INPUT DATA:- Material Properties :
Characteristic Strength of concrete, fck 25.00 N/mm2
Grade of Steel, fy 415.00 N/mm2
INPUT DATA:- Material Properties and Dimensions of Beam:
Thickness of flange, Df 225.00 mm
Total Depth of T- Beam, D 1600.00 mm
Width of Flange, bf 2500.00 mm
Width of web in compression fibre, bcw 600.00 mm
Width of web in tension, btw' 250.00 mm
Layer of bar in tension zone 3.00
MOLUNG KHOLA BRIDGE MEMBER
T - Beam with Trapezoidal Web, memb. No. 46 (23m)
Wcrb = 3*acr*Ɛm/ [1+2*(acr - Cmin) / (D - xu)]
Wcrt = 3*acr x Ɛm / [1+2*(acr - Cmin) / (D - (-D))]
Wcr =Wcrb+Wcrt
Cover, C 40.00 mm
Stirrups of Design purpose 8.00 mm
Dia of bar for design purpose 25.00 mm
Spacer for vertical spacing 32.00 mm
Calculations of required Design Moments, Shear forces:
Resultant Moment of ( Muy and Muz') = M''uz 15000.00 KNm
Design Moment Mu 15000.00 KNm
Design shear force Vu 1152.88 KN
Calculations of required Section properties:
Width of web in reiforcement level in tension, btw 268.48 mm
Width of Web, Average btw 425.00 mm
Effective Depth , d (Calculated) 1482.50 mm
Width of small portion in the flange, bs 49.219 mm
Centroid of Section from Compression fibre Cc 450.396 mm
Centoid of section from tension fibre Ct 1149.604 mm
Df/d (Calculated) 0.152
RESULT IN ACCORDANCE WITH DIFFERENT CONDITIONS:
1. Condition: If Neutral Axis lies in the flange? GO TO 2 (C)
Muf, lim= 0.36*fck*bf*Df*(d-0.416*Df) 7031.34 KNm DRS-NA
-7968.655 KNm DRS-NA
Neutral Axis lies in the Flange? NO DRS-NA
For Mu or Mu,lim Area of Steel, Ast 14016.31 mm2
DRS-NA
For Tension Area of Steel, Ast2 0.00 mm2
DRS-NA
for BM+Tension, total rqd. Steel, Ast 14016.31 mm2
DRS-NA
Neutral Axis Ratio, Xu/d 0.15177 DRS-NA
Neutral Axis, Xu 225.000 mm DRS-NA
Due to Mu Compressive strain Ɛcc 0.00111 DRS-NA
Total Strain due to (Mu+Fx) Ɛcct 0.00123 < 0.0035 DRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 10455.000 mm2
DRS-NA
Due To Fx, Additional compressive stress fsc 24.41 N/mm2
DRS-NA
Additional compressive stress fcc 1.316 N/mm2
DRS-NA
Pu 1750.370 KN DRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00012170 NA DRS-NA
Test : Fx-Pu =0 0.000000 DRS-NA
for BM+compression, Extra Increased area Ast 0.000 mm2
DRS-NA
Required Ast 10455.000 mm2
DRS-NA
2. Condition: If Neutral Axis lies in the webNeutral Axis lies in the Web YES
Neutral axis depth ratio α = Xu,max/d 0.4791
Maximum Neutral Axis for balanced design Xu,max 710.28 mm
yf,max 252.79 mm
Test : Muf,lim > Mu for Neutral in flange
Compressive force for straight portion, C1 1920.95 KN
Compressive force fo rParabolic portion, C2 1502.14 KN
Compressive force Trap. Web, Cu = C1+C2 3423.08 KN
Compressive force for Flange portion, C3 4766.63 KN
Compressive force for Small Flange portion, C4 61.74 KN
Total Compressive force, C 8251.45 KN
Moment of C1 about Neutral Axis, Integration I1 1077891.84 KNmm
Moment C2 about Neutral Axis Integration I2 387646.83 KNmm
Moment f Cu about neutral axis Integration Iu 1465538.67 KNmm
CG of Cu from Neutral axis ,Y 428.134 mm
CG of Cu from Extreme Compression fibre X 282.143 mm
For average web only X/d 0.19032
CG C from Extreme Compression fibre X 183.156 mm
10366.05 KNm
Capacity Mu, lim (Only for trapezodal Web) 4108.92 KNm
Capacity Mu, lim (trapezodal Web + Flange) 10721.47 KNm
4278.53 KNm DRS
1307.253 mm
1299.344 mm
21962.731 mm2
22854.032 mm2
-0.001871 DRS-NA
10.65773 DRS-NA
-8283.401 DRS-NA
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a 928.613 mm DRS-NA
yf=0.15*xu+0.65*Df 285.542 mm DRS-NA
Lever Arm z = jd 1475.432 DRS-NA
20126.475 mm2
DRS-NA
DRS-NA GO TO 2 (C)
Hit and Trial α = Xu/d 0.300000 DRS-NA
0.00000 DRS-NA
Neutral Axis for balanced design Xu 444.75 mm DRS-NA
yf,max 212.96 mm DRS-NA
Compressive force for straight portion, C1 0.00 KN DRS-NA
Compressive force fo rParabolic portion, C2 0.00 KN DRS-NA
Compressive force Trap.Web, Cu = C1+C2 0.00 KN DRS-NA
Compressive force for Flange portion, C3 0.00 KN DRS-NA
Compressive force for Small Flange portion, C4 0.00 KN DRS-NA
Total Compressive force, C 0.00 KN DRS-NA
a= - 0.14976*fck*bw - 0.0050175*fck*(bf - bw)
b= 0.36*fck*bw*d + 0.00669*fck*(bf - bw)
c= 0.2899*fck*Df*(bf - bw)*(d-0.325*Df)-Mu
For Df/d > 0.2 Ast
2 (A) IF Df/d > 0.2
α is chosen to make Test : C = T
Capacity if average web +flange Muw, lim=
0.36*fck*bw*Xu,max*(d-0.416*Xu,max) + 0.446*fck*(bf-
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast,max
For (web +Flange) balanced section Ast,max
Moment of C1 about Neutral Axis, Integration I1 0.00 KNmm DRS-NA
Moment C2 about Neutral Axis Integration I2 0.00 KNmm DRS-NA
Moment f Cu about neutral axis Integration Iu 0.00 KNmm DRS-NA
CG of Cu from Neutral axis ,Y 0.000 mm DRS-NA
CG of Cu from Extreme Comprssion fibre X 0.000 mm DRS-NA
For average web only X/d 0.00000 DRS-NA
CG C from Extreme Compression fibre X 0.000 mm DRS-NA
0.00 KNm DRS-NA
Mu(Only for trapezodal Web) 0.00 KNm DRS-NA
Mu,lim (trapezodal Web + Flange) 0.00 KNm DRS-NA
0.00 KNm DRS-NA
0.000 mm DRS-NA
0.000 mm DRS-NA
0.000 mm2
DRS-NA
0.00 mm2
DRS-NA
For Tension Area of Steel, Ast2 0.00 mm2
DRS-NA
for BM+Tension, total rqd. Steel, Ast 0.00 mm2
DRS-NA
0.00 KN DRS-NA
Neutral Axis, Xu 0.00 mm DRS-NA
Due to Mu Compressive strain Ɛcc 0.00000 DRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00002 < 0.0035 DRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 1300.000 mm2
DRS-NA
Due To Fx, Additional compressive stress fsc 3.89 N/mm2
DRS-NA
Additional compressive stress fcc 0.215 N/mm2
DRS-NA
Pu 251.367 KN DRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00001938 YES DRS-NA
Test : Fx-Pu =0 0.000000 DRS-NA
Extra Increased area 0.000 mm2
DRS-NA
Required Singly reinforced Ast 1300.000 mm2
DRS-NA
-0.001871 DRS-NA
10.65773 DRS-NA
-9871.419 DRS-NA
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a 1164.157 mm DRS-NA
yf=0.15*xu+0.65*Df 320.874 mm DRS-NA
Lever Arm z = jd 1237.686 DRS-NA
33567.070 mm2
DRS-NA
DRS-NA GO TO 2 (C)
Hit and Trial α = Xu/d 0.2201 DRS-NA
α is chosen to make Test : C - T = 0 -51.3282 DRS-NA
Force of Tension, T
a= - 0.14976*fck*bw - 0.0050175*fck*(bf - bw)
b= 0.36*fck*bw*d + 0.00669*fck*(bf - bw)
c= 0.2899*fck*Df*(bf - bw)*(d-0.325*Df)-Mu
For Df/d > 0.2 Ast
2 (B) IF Df/d < = 0.2
average web +flange Muw= 0.36*fck*bw*Xu,max*(d-
0.416*Xu,max) + 0.446*fck*(bf-bw)*yf*(d-0.5*yf,max)
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast,max
For (web +Flange) balanced section Ast,max
Neutral Axis for balanced design Xu 326.24 mm DRS-NA
yf 195.19 mm DRS-NA
Compressive force for straight portion, C1 911.02 KN DRS-NA
Compressive force fo rParabolic portion, C2 766.47 KN DRS-NA
Compressive force Trap.Web, Cu = C1+C2 1677.49 KN DRS-NA
Compressive force for Flange portion, C3 4135.03 KN DRS-NA
Compressive force for Small Flange portion, C4 53.56 KN DRS-NA
Total Compressive force, C 5866.08 KN DRS-NA
Moment of C1 about Neutral Axis, Integration I1 234094.27 KNmm DRS-NA
Moment C2 about Neutral Axis Integration I2 89945.16 KNmm DRS-NA
Moment f Cu about neutral axis Integration Iu 324039.43 KNmm DRS-NA
CG of Cu from Neutral axis ,Y 193.170 mm DRS-NA
CG of Cu from Extreme Comprssion fibre X 133.075 mm DRS-NA
For average web only X/d 0.0897641 DRS-NA
CG C from Extreme Compression fibre Xmax 118.726 mm DRS-NA
7934.72 KNm DRS-NA
Mu (Only for trapezodal Web) 2263.64 KNm DRS-NA
Mu,lim (trapezodal Web + Flange) 8000.00 KNm DRS-NA
-7000.00 KNm DRS-NA
1376.652 mm DRS-NA
1363.774 mm DRS-NA
15963.928 mm2
DRS-NA
16247.265 mm2
DRS-NA
For Tension Area of Steel, Ast2 0.00 mm2
DRS-NA
for BM+Tension, total rqd. Steel, Ast 16247.27 mm2
DRS-NA
10998.89 KN DRS-NA
Neutral Axis, Xu 285.422 DRS-NA
Due to Mu Compressive strain Ɛcc 0.00141 DRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00154 <= 0.0035 DRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 6916.530 mm2
DRS-NA
Due To Fx, Additional compressive stress fsc 26.59 N/mm2
DRS-NA
Additional compressive stress fcc 1.429 N/mm2
DRS-NA
Pu 1813.324 KN DRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00013259 DRS-NA DRS-NA
Test : Fx-Pu =0 0.000000 DRS-NA
Extra Increased area 0.000 mm2
DRS-NA
Required Singly reinforced Ast 6916.530 mm2
DRS-NA
-0.001005206 DRS-NA
b= 0.36*fck*bw*d 3.58225277 DRS-NA
-7330.30869 DRS-NA
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a #NUM! DRS-NA
Force of Tension, T
a= -0.14976*fck*bw
c= 0.446*fck*Df*(bf - bw)*(d-0.5*Df)-Mu
average web +flange Muw = 0.36*fck*bw*Xu,max*(d-
0.416*Xu,max) + 0.446*fck*(bf-bw)*yf*(d-0.5*yf,max)
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast
For (web +Flange) balanced section Ast
Lever Arm z = jd #NUM! DRS-NA
#NUM! mm2
DRS-NA
2 (C) Condition: Doubly Reinforced Section YES
Number of Layer of Comression bar 1.00 No.
Dia of Main reinforcement in compression 25 mm
Spacer for Vertical spacing 32 mm
Dia of Stirrups 8.00 mm
Clear cover, C 40.00 mm
Charactertistics strength of Concrete fck 25.00 N/mm2
Yield stress of steel fy 415.00 N/mm2
Helping calculation, d'' 57.00 mm
Effective depth from in compression side d' 60.50 mm
Effective depth at tension side d 1482.50 mm
Neutral Axis depth ration Xu,max/d 0.479
Neutral Axis Depth Xu.max 710.28 mmm
Compression level strain Ɛsc Or Ɛcc 0.00320
Compressive level stress of steel fsc 355.859 N/mm2
Compressive level stress of concrete fcc=446*fck*(Ԑcc-250*Ԑcc^2) 11.150 N/mm2
Area of compressive stress Asc 8728.566 mm2
8333.510 mm2
For DRS Total Area of tension steel Ast 31187.542 mm2
for Tension, Area of Steel, Ast3 0.00 mm2
for BM+Tension, total rqd. Steel, Ast 31187.54 mm2
Neutral Axis, Xu 710.277 mm
Due to Mu Compressive strain Ɛcc 0.00350
Total Strain due to (Mu+P) Ɛcct 0.00350 < 0.0035 OK
for BM+compression, TrialTotal Rqd. Steel, Ast 12063.716 mm2
Due To Fx, Additional compressive stress fsc 0.00 N/mm2
Additional compressive stress fcc 0.000 N/mm2
Pu 0.000 KN
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00000000 YES
Test : Fx-Pu =0 -0.000010
Extra Increased area -19123.826 mm2
Required Double reinforced Ast 12063.716 mm2
Check for Shear forceDesign Shear force 1152.88 KN
Shear stress 1.830 N/mm2
Percentage of tension steel, pt 1.915 %
For Df/d < 0.2 Ast
for Asc, Area of tension steel Ast2
Percentage of compressive steel, pc 1.402 %
Percentage of tension and compressive steel, pt 7.256 %
α=0.8*fck/6.89*pt 0.400
tc = 0.85*SQRT(0.8*fck)*(SQRT(1+5*α)-1)/6*α 1.159 N/mm2
1.00 x 1.159 = 1.159
> 1.830 NOT OK
Shear Reinforcement is required.
Dia of of Vertical Stirrups 10.00 mm
Number of leg 2.00
Planned area to Provide Asv 157.08 mm2
Required spacing of stirrups Svreqd. 199.071 mm
Plan to Provide, spacing of stirrups Sv 200.000
Minimum required Asv 0.4*b*Sv/0.87*fy 94.1698 mm2
Ф 7.7428 mm
Rqd. Stirrups Ф 10.00 Leg 2.000 199.07 mm C/C
Permissible shear stress,
K´tc =
Out Put:Note : DRS = Doubly Reinforced Section, SRS = Singly Reinforced Section, NA = Not Applicable
Rqd. tensile Steel Reinforecement, Ast 12867.96 mm2
Provide 25 Ф bar 26.21 Nos. Say 26.00 Nos.
Rqd. Compressive Steel Reinforecement, Asc 2293.97 mm2
Provide 25 Ф bar 4.67 Nos. Say 5.00 Nos.
Stirrups Provided:
Provide 8 Ф bar Spacing 100.00 mm @ C/C Leg = 2
Crack Width Calculation:Stress in tensile reinforced level fsb 240.39 N/mm
2
Spacing of reinforcement S 15.160 mm
acr = ((S / 2)^2+d'^2)^0.5 - Dia /2 = 48.473 mm
Ɛ1b = [fs*((a' - xu) / [(d-xu)*2*10 ^5] 0.0012822
Ɛ2b= bt*(a'-xu)*(D-xu) / [600000*Ast*(d - xu)] 0.0000668
Ɛmb = Ɛ1b-Ɛ2b 0.0012154
0.1737022
Stress in tensile reinforced level fst -91.744 N/mm2
Ɛ1t= fs*(a' - (-D)) / [(d- (-D))*2*10 ^5] -0.0004666
Ɛ2t= bt*(a'-(-D))*(D-(-D)) / [600000*Ast*(d - (-D))] 0.0002371
Ɛmt = Ɛ1t-Ɛ2t -0.0007037
-0.1018498
0.0718524 < 0.2
INPUT DATA:- Governing Load Case For Design LC 268
INPUT DATA:- Axial force, Torsion Moments, Bending moments and Shear force:
Design Shear force, Fy 1397.44 KN LC 538
Design Torsional Moment for shear Tu=Mx 62.88 KNm LC 538
Moment M'uz 6317.18 KN LC 268
Design Torsional Moment for moment Tu=Mx 53.65 KNm LC 268
Axial Force, Fx 1770.85 KN C LC 268
Bending in another direction Muy 72.28 KNm LC 268
INPUT DATA:- Material Properties :
Characteristic Strength of concrete, fck 25.00 N/mm2
Grade of Steel, fy 415.00 N/mm2
INPUT DATA:- Material Properties and Dimensions of Beam:
Thickness of flange, Df 200.00 mm
Total Depth of T- Beam, D 1800.00 mm
Width of Flange, bf 500.00 mm Approx.Effective
Width of web in compression fibre, bcw 500.00 mm Approx.Effective
Width of web in tension, btw' 500.00 mm Approx.Effective
Layer of bar in tension zone 1.00
MOLUNG KHOLA BRIDGE MEMBER
T - Beam with Trapezoidal Web, memb. No. 50 (25m)
Wcrb = 3*acr*Ɛm/ [1+2*(acr - Cmin) / (D - xu)]
Wcrt = 3*acr x Ɛm / [1+2*(acr - Cmin) / (D - (-D))]
Wcr =Wcrb+Wcrt
Cover, C 40.00 mm
Stirrups of Design purpose 8.00 mm
Dia of bar for design purpose 25.00 mm
Spacer for vertical spacing 32.00 mm
Calculations of required Design Moments, Shear forces:
Resultant Moment of ( Muy and Muz') = M''uz 6317.59 KNm
Design Moment Mu 6462.76 KNm
Design shear force Vu 1598.66 KN
Calculations of required Section properties:
Width of web in reiforcement level in tension, btw 500.00 mm
Width of Web, Average btw 500.00 mm
Effective Depth , d (Calculated) 1739.50 mm
Width of small portion in the flange, bs 0.000 mm
Centroid of Section from Compression fibre Cc 859.649 mm
Centoid of section from tension fibre Ct 940.351 mm
Df/d (Calculated) 0.115
RESULT IN ACCORDANCE WITH DIFFERENT CONDITIONS:
1. Condition: If Neutral Axis lies in the flange? GO TO 2 (C)
Muf, lim= 0.36*fck*bf*Df*(d-0.416*Df) 1490.68 KNm DRS-NA
-4972.088 KNm DRS-NA
Neutral Axis lies in the Flange? NO DRS-NA
For Mu or Mu,lim Area of Steel, Ast 2492.04 mm2
DRS-NA
For Tension Area of Steel, Ast2 0.00 mm2
DRS-NA
for BM+Tension, total rqd. Steel, Ast 2492.04 mm2
DRS-NA
Neutral Axis Ratio, Xu/d 0.11498 DRS-NA
Neutral Axis, Xu 200.000 mm DRS-NA
Due to Mu Compressive strain Ɛcc 0.00084 DRS-NA
Total Strain due to (Mu+Fx) Ɛcct 0.00096 < 0.0035 DRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 10455.000 mm2
DRS-NA
Due To Fx, Additional compressive stress fsc 24.41 N/mm2
DRS-NA
Additional compressive stress fcc 1.316 N/mm2
DRS-NA
Pu 1425.564 KN DRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00012170 NA DRS-NA
Test : Fx-Pu =0 0.000000 DRS-NA
for BM+compression, Extra Increased area Ast 0.000 mm2
DRS-NA
Required Ast 10455.000 mm2
DRS-NA
2. Condition: If Neutral Axis lies in the webNeutral Axis lies in the Web YES
Neutral axis depth ratio α = Xu,max/d 0.4791
Maximum Neutral Axis for balanced design Xu,max 833.41 mm
yf,max 255.01 mm
Test : Muf,lim > Mu for Neutral in flange
Compressive force for straight portion, C1 1991.25 KN
Compressive force fo rParabolic portion, C2 1770.00 KN
Compressive force Trap. Web, Cu = C1+C2 3761.25 KN
Compressive force for Flange portion, C3 0.00 KN
Compressive force for Small Flange portion, C4 0.00 KN
Total Compressive force, C 3761.25 KN
Moment of C1 about Neutral Axis, Integration I1 1303909.73 KNmm
Moment C2 about Neutral Axis Integration I2 526832.21 KNmm
Moment f Cu about neutral axis Integration Iu 1830741.94 KNmm
CG of Cu from Neutral axis ,Y 486.738 mm
CG of Cu from Extreme Compression fibre X 346.669 mm
For average web only X/d 0.19929
CG C from Extreme Compression fibre X 346.669 mm
5238.67 KNm
Capacity Mu, lim (Only for trapezodal Web) 5238.78 KNm
Capacity Mu, lim (trapezodal Web + Flange) 5238.78 KNm
1223.98 KNm DRS
1392.802 mm
1392.831 mm
10417.525 mm2
10417.525 mm2
-0.001872 DRS-NA
7.82775 DRS-NA
-5238.780 DRS-NA
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a 836.663 mm DRS-NA
yf=0.15*xu+0.65*Df 255.499 mm DRS-NA
Lever Arm z = jd 1391.448 DRS-NA
10427.874 mm2
DRS-NA
DRS-NA GO TO 2 (C)
Hit and Trial α = Xu/d 0.300000 DRS-NA
0.00000 DRS-NA
Neutral Axis for balanced design Xu 521.85 mm DRS-NA
yf,max 208.28 mm DRS-NA
Compressive force for straight portion, C1 0.00 KN DRS-NA
Compressive force fo rParabolic portion, C2 0.00 KN DRS-NA
Compressive force Trap.Web, Cu = C1+C2 0.00 KN DRS-NA
Compressive force for Flange portion, C3 0.00 KN DRS-NA
Compressive force for Small Flange portion, C4 0.00 KN DRS-NA
Total Compressive force, C 0.00 KN DRS-NA
a= - 0.14976*fck*bw - 0.0050175*fck*(bf - bw)
b= 0.36*fck*bw*d + 0.00669*fck*(bf - bw)
c= 0.2899*fck*Df*(bf - bw)*(d-0.325*Df)-Mu
For Df/d > 0.2 Ast
2 (A) IF Df/d > 0.2
α is chosen to make Test : C = T
Capacity if average web +flange Muw, lim=
0.36*fck*bw*Xu,max*(d-0.416*Xu,max) + 0.446*fck*(bf-
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast,max
For (web +Flange) balanced section Ast,max
Moment of C1 about Neutral Axis, Integration I1 0.00 KNmm DRS-NA
Moment C2 about Neutral Axis Integration I2 0.00 KNmm DRS-NA
Moment f Cu about neutral axis Integration Iu 0.00 KNmm DRS-NA
CG of Cu from Neutral axis ,Y 0.000 mm DRS-NA
CG of Cu from Extreme Comprssion fibre X 0.000 mm DRS-NA
For average web only X/d 0.00000 DRS-NA
CG C from Extreme Compression fibre X 0.000 mm DRS-NA
0.00 KNm DRS-NA
Mu(Only for trapezodal Web) 0.00 KNm DRS-NA
Mu,lim (trapezodal Web + Flange) 0.00 KNm DRS-NA
0.00 KNm DRS-NA
0.000 mm DRS-NA
0.000 mm DRS-NA
0.000 mm2
DRS-NA
0.00 mm2
DRS-NA
For Tension Area of Steel, Ast2 0.00 mm2
DRS-NA
for BM+Tension, total rqd. Steel, Ast 0.00 mm2
DRS-NA
0.00 KN DRS-NA
Neutral Axis, Xu 0.00 mm DRS-NA
Due to Mu Compressive strain Ɛcc 0.00000 DRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00002 < 0.0035 DRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 1300.000 mm2
DRS-NA
Due To Fx, Additional compressive stress fsc 3.89 N/mm2
DRS-NA
Additional compressive stress fcc 0.215 N/mm2
DRS-NA
Pu 198.286 KN DRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00001938 YES DRS-NA
Test : Fx-Pu =0 0.000000 DRS-NA
Extra Increased area 0.000 mm2
DRS-NA
Required Singly reinforced Ast 1300.000 mm2
DRS-NA
-0.001872 DRS-NA
7.82775 DRS-NA
-6462.764 DRS-NA
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a 1132.161 mm DRS-NA
yf=0.15*xu+0.65*Df 299.824 mm DRS-NA
Lever Arm z = jd 1268.521 DRS-NA
14110.852 mm2
DRS-NA
DRS-NA GO TO 2 (C)
Hit and Trial α = Xu/d 0.2698 DRS-NA
α is chosen to make Test : C - T = 0 -20.6699 DRS-NA
Force of Tension, T
a= - 0.14976*fck*bw - 0.0050175*fck*(bf - bw)
b= 0.36*fck*bw*d + 0.00669*fck*(bf - bw)
c= 0.2899*fck*Df*(bf - bw)*(d-0.325*Df)-Mu
For Df/d > 0.2 Ast
2 (B) IF Df/d < = 0.2
average web +flange Muw= 0.36*fck*bw*Xu,max*(d-
0.416*Xu,max) + 0.446*fck*(bf-bw)*yf*(d-0.5*yf,max)
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast,max
For (web +Flange) balanced section Ast,max
Neutral Axis for balanced design Xu 469.29 mm DRS-NA
yf 200.39 mm DRS-NA
Compressive force for straight portion, C1 1121.27 KN DRS-NA
Compressive force fo rParabolic portion, C2 996.68 KN DRS-NA
Compressive force Trap.Web, Cu = C1+C2 2117.96 KN DRS-NA
Compressive force for Flange portion, C3 0.00 KN DRS-NA
Compressive force for Small Flange portion, C4 0.00 KN DRS-NA
Total Compressive force, C 2117.96 KN DRS-NA
Moment of C1 about Neutral Axis, Integration I1 413444.48 KNmm DRS-NA
Moment C2 about Neutral Axis Integration I2 167048.28 KNmm DRS-NA
Moment f Cu about neutral axis Integration Iu 580492.76 KNmm DRS-NA
CG of Cu from Neutral axis ,Y 274.082 mm DRS-NA
CG of Cu from Extreme Comprssion fibre X 195.209 mm DRS-NA
For average web only X/d 0.1122215 DRS-NA
CG C from Extreme Compression fibre Xmax 195.209 mm DRS-NA
3261.21 KNm DRS-NA
Mu (Only for trapezodal Web) 3270.74 KNm DRS-NA
Mu,lim (trapezodal Web + Flange) 3270.74 KNm DRS-NA
-3192.03 KNm DRS-NA
1544.275 mm DRS-NA
1544.291 mm DRS-NA
5849.078 mm2
DRS-NA
5866.099 mm2
DRS-NA
For Tension Area of Steel, Ast2 0.00 mm2
DRS-NA
for BM+Tension, total rqd. Steel, Ast 5866.10 mm2
DRS-NA
4184.94 KN DRS-NA
Neutral Axis, Xu 469.291 DRS-NA
Due to Mu Compressive strain Ɛcc 0.00197 DRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00211 < 0.0035 DRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 3000.000 mm2
DRS-NA
Due To Fx, Additional compressive stress fsc 27.88 N/mm2
DRS-NA
Additional compressive stress fcc 1.496 N/mm2
DRS-NA
Pu 1425.719 KN DRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00013902 DRS-NA DRS-NA
Test : Fx-Pu =0 0.000000 DRS-NA
Extra Increased area 0.000 mm2
DRS-NA
Required Singly reinforced Ast 3000.000 mm2
DRS-NA
-0.001872000 DRS-NA
b= 0.36*fck*bw*d 7.82775000 DRS-NA
-6462.76408 DRS-NA
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a 1132.161 DRS-NA
Lever Arm z = jd 1268.521 DRS-NA
Force of Tension, T
a= -0.14976*fck*bw
c= 0.446*fck*Df*(bf - bw)*(d-0.5*Df)-Mu
average web +flange Muw = 0.36*fck*bw*Xu,max*(d-
0.416*Xu,max) + 0.446*fck*(bf-bw)*yf*(d-0.5*yf,max)
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast
For (web +Flange) balanced section Ast
14110.852 mm2
DRS-NA
2 (C) Condition: Doubly Reinforced Section YES
Number of Layer of Comression bar 5.00 No.
Dia of Main reinforcement in compression 25 mm
Spacer for Vertical spacing 32 mm
Dia of Stirrups 8.00 mm
Clear cover, C 40.00 mm
Charactertistics strength of Concrete fck 25.00 N/mm2
Yield stress of steel fy 415.00 N/mm2
Helping calculation, d'' 57.00 mm
Effective depth from in compression side d' 174.50 mm
Effective depth at tension side d 1739.50 mm
Neutral Axis depth ration Xu,max/d 0.479
Neutral Axis Depth Xu.max 833.41 mmm
Compression level strain Ɛsc Or Ɛcc 0.00277
Compressive level stress of steel fsc 352.086 N/mm2
Compressive level stress of concrete fcc=446*fck*(Ԑcc-250*Ԑcc^2) 11.150 N/mm2
Area of compressive stress Asc 2293.975 mm2
2166.178 mm2
For DRS Total Area of tension steel Ast 12583.702 mm2
for Tension, Area of Steel, Ast3 0.00 mm2
for BM+Tension, total rqd. Steel, Ast 12583.70 mm2
Neutral Axis, Xu 833.407 mm
Due to Mu Compressive strain Ɛcc 0.00350
Total Strain due to (Mu+P) Ɛcct 0.00350 <= 0.0035 OK
for BM+compression, TrialTotal Rqd. Steel, Ast 12867.960 mm2
Due To Fx, Additional compressive stress fsc 31.96 N/mm2
Additional compressive stress fcc 1.706 N/mm2
Pu 1924.355 KN
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00015932 YES
Test : Fx-Pu =0 -153.508599
Extra Increased area 284.258 mm2
Required Double reinforced Ast 12867.960 mm2
Check for Shear forceDesign Shear force 1598.66 KN
Shear stress 1.671 N/mm2
Percentage of tension steel, pt 1.467 %
Percentage of compressive steel, pc 0.282 %
For Df/d < 0.2 Ast
for Asc, Area of tension steel Ast2
Percentage of tension and compressive steel, pt 5.098 %
α=0.8*fck/6.89*pt 0.569
tc = 0.85*SQRT(0.8*fck)*(SQRT(1+5*α)-1)/6*α 1.070 N/mm2
1.00 x 1.070 = 1.070
> 1.671 NOT OK
Shear Reinforcement is required.
Dia of of Vertical Stirrups 8.00 mm
Number of leg 2.00
Planned area to Provide Asv 100.53 mm2
Required spacing of stirrups Svreqd. 120.731 mm
Plan to Provide, spacing of stirrups Sv 100.000
Minimum required Asv 0.4*b*Sv/0.87*fy 55.3940 mm2
Ф 5.9384 mm
Rqd. Stirrups Ф 8.00 Leg 2.000 100.00 mm C/C
Permissible shear stress,
K´tc =
Out Put:Note : DRS = Doubly Reinforced Section, SRS = Singly Reinforced Section, NA = Not Applicable
Rqd. tensile Steel Reinforecement, Ast 3093.46 mm2
Provide 25 Ф bar 6.30 Nos. Say 6.00 Nos.
Rqd. Compressive Steel Reinforecement, Asc 3216.99 mm2
Provide 25 Ф bar 6.55 Nos. Say 7.00 Nos.
Stirrups Provided:
Provide 8 Ф bar Spacing 200.00 mm @ C/C Leg = 2
Crack Width Calculation:Stress in tensile reinforced level fsb 164.44 N/mm
2
Spacing of reinforcement S 65.800 mm
acr = ((S / 2)^2+d'^2)^0.5 - Dia /2 = 56.367 mm
Ɛ1b = [fs*((a' - xu) / [(d-xu)*2*10 ^5] 0.0008659
Ɛ2b= bt*(a'-xu)*(D-xu) / [600000*Ast*(d - xu)] 0.0004506
Ɛmb = Ɛ1b-Ɛ2b 0.0004153
0.0689500
Stress in tensile reinforced level fst 76.267 N/mm2
Ɛ1t= fs*(a' - (-D)) / [(d- (-D))*2*10 ^5] 0.0003910
Ɛ2t= bt*(a'-(-D))*(D-(-D)) / [600000*Ast*(d - (-D))] 0.0008949
Ɛmt = Ɛ1t-Ɛ2t -0.0005039
-0.0844476
-0.0154975 < 0.2
INPUT DATA:- Governing Load Case For Design LC 554
INPUT DATA:- Axial force, Torsion Moments, Bending moments and Shear force:
Design Shear force, Fy 721.95 KN LC 251
Design Torsional Moment for shear Tu=Mx 60.62 KNm LC 251
Moment M'uz 1633.01 KN LC 554
Design Torsional Moment for moment Tu=Mx 15.92 KNm LC 554
Axial Force, Fx 353.89 KN T LC 554
Bending in another direction Muy 5.37 KNm LC 554
INPUT DATA:- Material Properties :
Characteristic Strength of concrete, fck 25.00 N/mm2
Grade of Steel, fy 415.00 N/mm2
INPUT DATA:- Material Properties and Dimensions of Beam:
Thickness of flange, Df 200.00 mm
Total Depth of T- Beam, D 1800.00 mm
Width of Flange, bf 2400.00 mm
Width of web in compression fibre, bcw 450.00 mm
Width of web in tension, btw' 450.00 mm
Layer of bar in tension zone 2.00
MOLUNG KHOLA BRIDGE MEMBER
T - Beam with Trapezoidal Web, memb. No. 65 (32.5m)
Wcrb = 3*acr*Ɛm/ [1+2*(acr - Cmin) / (D - xu)]
Wcrt = 3*acr x Ɛm / [1+2*(acr - Cmin) / (D - (-D))]
Wcr =Wcrb+Wcrt
Cover, C 40.00 mm
Stirrups of Design purpose 8.00 mm
Dia of bar for design purpose 25.00 mm
Spacer for vertical spacing 32.00 mm
Calculations of required Design Moments, Shear forces:
Resultant Moment of ( Muy and Muz') = M''uz 1247.52 KNm
Design Moment Mu 1294.34 KNm
Design shear force Vu 937.49 KN
Calculations of required Section properties:
Width of web in reiforcement level in tension, btw 450.00 mm
Width of Web, Average btw 450.00 mm
Effective Depth , d (Calculated) 1711.00 mm
Width of small portion in the flange, bs 0.000 mm
Centroid of Section from Compression fibre Cc 621.687 mm
Centoid of section from tension fibre Ct 1178.313 mm
Df/d (Calculated) 0.117
RESULT IN ACCORDANCE WITH DIFFERENT CONDITIONS:
1. Condition: If Neutral Axis lies in the flange? YES
Muf, lim= 0.36*fck*bf*Df*(d-0.416*Df) 7032.13 KNm
5737.784 KNm
Neutral Axis lies in the Flange? YES
For Mu or Mu,lim Area of Steel, Ast 2113.28 mm2
For Tension Area of Steel, Ast2 980.18 mm2
for BM+Tension, total rqd. Steel, Ast 3093.46 mm2
Neutral Axis Ratio, Xu/d 0.02065
Neutral Axis, Xu 35.326 mm
Due to Mu Compressive strain Ɛcc 0.00015
Total Strain due to (Mu+Fx) Ɛcct 0.00027 < 0.0035 OK
for BM+compression, TrialTotal Rqd. Steel, Ast 10455.000 mm2
Due To Fx, Additional compressive stress fsc NA N/mm2
Additional compressive stress fcc NA N/mm2
Pu NA KN
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00012170 NA
Test : Fx-Pu =0 NA
for BM+compression, Extra Increased area Ast 0.000 mm2
Required Ast 3093.460 mm2
2. Condition: If Neutral Axis lies in the webNeutral Axis lies in the Web NA
Neutral axis depth ratio α = Xu,max/d 0.4791
Maximum Neutral Axis for balanced design Xu,max 819.75 mm NA
yf,max 252.96 mm NA
Test : Muf,lim > Mu for Neutral in flange
Compressive force for straight portion, C1 1762.76 KN NA
Compressive force fo rParabolic portion, C2 1566.90 KN NA
Compressive force Trap. Web, Cu = C1+C2 3329.66 KN NA
Compressive force for Flange portion, C3 4348.50 KN NA
Compressive force for Small Flange portion, C4 0.00 KN NA
Total Compressive force, C 7678.16 KN NA
Moment of C1 about Neutral Axis, Integration I1 1135379.86 KNmm NA
Moment C2 about Neutral Axis Integration I2 458739.34 KNmm NA
Moment f Cu about neutral axis Integration Iu 1594119.20 KNmm NA
CG of Cu from Neutral axis ,Y 478.763 mm NA
CG of Cu from Extreme Compression fibre X 340.990 mm NA
For average web only X/d 0.19929 NA
CG C from Extreme Compression fibre X 204.506 mm NA
11567.01 KNm NA
Capacity Mu, lim (Only for trapezodal Web) 4561.67 KNm NA
Capacity Mu, lim (trapezodal Web + Flange) 11567.10 KNm NA
-10272.76 KNm SRS
1506.654 mm NA
1506.494 mm NA
21263.770 mm2
NA
21266.198 mm2
NA
-0.001929
12.08578
-8935.608
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a 856.446 mm
yf=0.15*xu+0.65*Df 258.467 mm
Lever Arm z = jd 1700.989
18834.573 mm2
NA GO TO 1
Hit and Trial α = Xu/d 0.300000 SRS-NA
0.00000 SRS-NA
Neutral Axis for balanced design Xu 513.30 mm SRS-NA
yf,max 207.00 mm SRS-NA
Compressive force for straight portion, C1 0.00 KN SRS-NA
Compressive force fo rParabolic portion, C2 0.00 KN SRS-NA
Compressive force Trap.Web, Cu = C1+C2 0.00 KN SRS-NA
Compressive force for Flange portion, C3 0.00 KN SRS-NA
Compressive force for Small Flange portion, C4 0.00 KN SRS-NA
Total Compressive force, C 0.00 KN SRS-NA
a= - 0.14976*fck*bw - 0.0050175*fck*(bf - bw)
b= 0.36*fck*bw*d + 0.00669*fck*(bf - bw)
c= 0.2899*fck*Df*(bf - bw)*(d-0.325*Df)-Mu
For Df/d > 0.2 Ast
2 (A) IF Df/d > 0.2
α is chosen to make Test : C = T
Capacity if average web +flange Muw, lim=
0.36*fck*bw*Xu,max*(d-0.416*Xu,max) + 0.446*fck*(bf-
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast,max
For (web +Flange) balanced section Ast,max
Moment of C1 about Neutral Axis, Integration I1 NA KNmm SRS-NA
Moment C2 about Neutral Axis Integration I2 0.00 KNmm SRS-NA
Moment f Cu about neutral axis Integration Iu 0.00 KNmm SRS-NA
CG of Cu from Neutral axis ,Y 0.000 mm SRS-NA
CG of Cu from Extreme Comprssion fibre X 0.000 mm SRS-NA
For average web only X/d 0.00000 SRS-NA
CG C from Extreme Compression fibre X 0.000 mm SRS-NA
0.00 KNm SRS-NA
Mu(Only for trapezodal Web) 0.00 KNm SRS-NA
Mu,lim (trapezodal Web + Flange) 0.00 KNm SRS-NA
0.00 KNm SRS-NA
0.000 mm SRS-NA
0.000 mm SRS-NA
0.000 mm2
SRS-NA
0.00 mm2
SRS-NA
For Tension Area of Steel, Ast2 980.18 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 980.18 mm2
SRS-NA
NA KN SRS-NA
Neutral Axis, Xu 0.00 mm SRS-NA
Due to Mu Compressive strain Ɛcc 0.00000 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00002 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 1300.000 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc NA N/mm2
SRS-NA
Additional compressive stress fcc NA N/mm2
SRS-NA
Pu 0.000 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00001938 YES SRS-NA
Test : Fx-Pu =0 NA SRS-NA
Extra Increased area 0.000 mm2
SRS-NA
Required Singly reinforced Ast 980.178 mm2
SRS-NA
-0.001929 SRS-NA
12.08578 SRS-NA
3358.119 SRS-NA
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a -266.517 mm SRS-NA
yf=0.15*xu+0.65*Df 90.022 mm SRS-NA
Lever Arm z = jd 1474.332 SRS-NA
2431.566 mm2
SRS-NA
NA GO TO 1
Hit and Trial α = Xu/d 0.0967 SRS-NA
α is chosen to make Test : C - T = 0 0.0000 SRS-NA
Force of Tension, T
a= - 0.14976*fck*bw - 0.0050175*fck*(bf - bw)
b= 0.36*fck*bw*d + 0.00669*fck*(bf - bw)
c= 0.2899*fck*Df*(bf - bw)*(d-0.325*Df)-Mu
For Df/d > 0.2 Ast
2 (B) IF Df/d < = 0.2
average web +flange Muw= 0.36*fck*bw*Xu,max*(d-
0.416*Xu,max) + 0.446*fck*(bf-bw)*yf*(d-0.5*yf,max)
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast,max
For (web +Flange) balanced section Ast,max
Neutral Axis for balanced design Xu 0.00 mm SRS-NA
yf 0.00 mm SRS-NA
Compressive force for straight portion, C1 0.00 KN SRS-NA
Compressive force fo rParabolic portion, C2 0.00 KN SRS-NA
Compressive force Trap.Web, Cu = C1+C2 0.00 KN SRS-NA
Compressive force for Flange portion, C3 0.00 KN SRS-NA
Compressive force for Small Flange portion, C4 0.00 KN SRS-NA
Total Compressive force, C 0.00 KN SRS-NA
Moment of C1 about Neutral Axis, Integration I1 0.00 KNmm SRS-NA
Moment C2 about Neutral Axis Integration I2 0.00 KNmm SRS-NA
Moment f Cu about neutral axis Integration Iu 0.00 KNmm SRS-NA
CG of Cu from Neutral axis ,Y 0.000 mm SRS-NA
CG of Cu from Extreme Comprssion fibre X 0.000 mm SRS-NA
For average web only X/d 0.0000000 SRS-NA
CG C from Extreme Compression fibre Xmax 0.000 mm SRS-NA
0.00 KNm SRS-NA
Mu (Only for trapezodal Web) 0.00 KNm SRS-NA
Mu,lim (trapezodal Web + Flange) 0.00 KNm SRS-NA
0.00 KNm SRS-NA
0.000 mm SRS-NA
0.000 mm SRS-NA
0.000 mm2
SRS-NA
0.000 mm2
SRS-NA
For Tension Area of Steel, Ast2 980.18 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 980.18 mm2
SRS-NA
0.00 KN SRS-NA
Neutral Axis, Xu 0.000 SRS-NA
Due to Mu Compressive strain Ɛcc 0.00000 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00014 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 3000.000 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc 0.00 N/mm2
SRS-NA
Additional compressive stress fcc 0.000 N/mm2
SRS-NA
Pu 0.000 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00013902 SRS-NA SRS-NA
Test : Fx-Pu =0 0.000000 SRS-NA
Extra Increased area 0.000 mm2
SRS-NA
Required Singly reinforced Ast 980.178 mm2
SRS-NA
0.000000000 SRS-NA
b= 0.36*fck*bw*d 0.00000000 SRS-NA
0.00000 SRS-NA
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a 0.000 SRS-NA
Lever Arm z = jd 0.000 SRS-NA
Force of Tension, T
a= -0.14976*fck*bw
c= 0.446*fck*Df*(bf - bw)*(d-0.5*Df)-Mu
average web +flange Muw = 0.36*fck*bw*Xu,max*(d-
0.416*Xu,max) + 0.446*fck*(bf-bw)*yf*(d-0.5*yf,max)
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast
For (web +Flange) balanced section Ast
0.000 mm2
SRS-NA
2 (C) Condition: Doubly Reinforced Section GO TO 1
Number of Layer of Comression bar 1.00 No. SRS-NA
Dia of Main reinforcement in compression 32 mm SRS-NA
Spacer for Vertical spacing 32 mm SRS-NA
Dia of Stirrups 8.00 mm SRS-NA
Clear cover, C 40.00 mm SRS-NA
Charactertistics strength of Concrete fck 25.00 N/mm2 SRS-NA
Yield stress of steel fy 415.00 N/mm2 SRS-NA
Helping calculation, d'' 64.00 mm SRS-NA
Effective depth from in compression side d' 64.00 mm SRS-NA
Effective depth at tension side d 1711.00 mm SRS-NA
Neutral Axis depth ration Xu,max/d 0.479 SRS-NA
Neutral Axis Depth Xu.max 819.75 mmm SRS-NA
Compression level strain Ɛsc Or Ɛcc 0.00323 SRS-NA
Compressive level stress of steel fsc 356.075 N/mm2 SRS-NA
Compressive level stress of concrete fcc=446*fck*(Ԑcc-250*Ԑcc^2) 11.150 N/mm2 SRS-NA
Area of compressive stress Asc -18082.953 mm2
SRS-NA
-17275.327 mm2
SRS-NA
For DRS Total Area of tension steel Ast 3990.871 mm2
SRS-NA
for Tension, Area of Steel, Ast3 18255.51 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 22246.38 mm2
SRS-NA
Neutral Axis, Xu 819.753 mm SRS-NA
Due to Mu Compressive strain Ɛcc 0.00350 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00362 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 12063.716 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc NA N/mm2
SRS-NA
Additional compressive stress fcc NA N/mm2
SRS-NA
Pu 0.000 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00012335 YES SRS-NA
Test : Fx-Pu =0 0.000000 SRS-NA
Extra Increased area 0.000 mm2
SRS-NA
Required Double reinforced Ast 22246.376 mm2
SRS-NA
Check for Shear forceDesign Shear force 937.49 KN
Shear stress 1.218 N/mm2
Percentage of tension steel, pt 0.383 %
Percentage of compressive steel, pc 0.446 %
For Df/d < 0.2 Ast
for Asc, Area of tension steel Ast2
Percentage of tension and compressive steel, pt 4.549 %
α=0.8*fck/6.89*pt 0.638
tc = 0.85*SQRT(0.8*fck)*(SQRT(1+5*α)-1)/6*α 1.040 N/mm2
1.00 x 1.040 = 1.040
> 1.218 NOT OK
Shear Reinforcement is required.
Dia of of Vertical Stirrups 8.00 mm
Number of leg 2.00
Planned area to Provide Asv 100.53 mm2
Required spacing of stirrups Svreqd. 453.162 mm
Plan to Provide, spacing of stirrups Sv 200.000
Minimum required Asv 0.4*b*Sv/0.87*fy 99.7092 mm2
Ф 7.9672 mm
Rqd. Stirrups Ф 8.00 Leg 2.000 200.00 mm C/C
Permissible shear stress,
K´tc =
Out Put:Note : DRS = Doubly Reinforced Section, SRS = Singly Reinforced Section, NA = Not Applicable
Rqd. tensile Steel Reinforecement, Ast 7122.37 mm2
Provide 25 Ф bar 14.51 Nos. Say 15.00 Nos.
Rqd. Compressive Steel Reinforecement, Asc 981.74 mm2
Provide 25 Ф bar 2.00 Nos. Say 2.00 Nos.
Stirrups Provided:
Provide 8 Ф bar Spacing 200.00 mm @ C/C Leg = 2
Crack Width Calculation:Stress in tensile reinforced level fsb 117.62 N/mm
2
Spacing of reinforcement S 23.214 mm
acr = ((S / 2)^2+d'^2)^0.5 - Dia /2 = 51.069 mm
Ɛ1b = [fs*((a' - xu) / [(d-xu)*2*10 ^5] 0.0006427
Ɛ2b= bt*(a'-xu)*(D-xu) / [600000*Ast*(d - xu)] 0.0002004
Ɛmb = Ɛ1b-Ɛ2b 0.0004422
0.0669026
Stress in tensile reinforced level fst 123.094 N/mm2
Ɛ1t= fs*(a' - (-D)) / [(d- (-D))*2*10 ^5] 0.0006419
Ɛ2t= bt*(a'-(-D))*(D-(-D)) / [600000*Ast*(d - (-D))] 0.0003953
Ɛmt = Ɛ1t-Ɛ2t 0.0002465
0.0375372
0.1044398 < 0.2
INPUT DATA:- Governing Load Case For Design LC 548
INPUT DATA:- Axial force, Torsion Moments, Bending moments and Shear force:
Design Shear force, Fy 219.58 KN LC 268
Design Torsional Moment for shear Tu=Mx 6.32 KNm LC 268
Moment M'uz 3342.74 KN LC 548
Design Torsional Moment for moment Tu=Mx 19.49 KNm LC 548
Axial Force, Fx 1315.08 KN T LC 548
Bending in another direction Muy 34.48 KNm LC 548
INPUT DATA:- Material Properties :
Characteristic Strength of concrete, fck 25.00 N/mm2
Grade of Steel, fy 415.00 N/mm2
INPUT DATA:- Material Properties and Dimensions of Beam:
Thickness of flange, Df 200.00 mm
Total Depth of T- Beam, D 1800.00 mm
Width of Flange, bf 2400.00 mm
Width of web in compression fibre, bcw 450.00 mm
Width of web in tension, btw' 450.00 mm
Layer of bar in tension zone 4.00
MOLUNG KHOLA BRIDGE MEMBER
T - Beam with Trapezoidal Web, memb. No. 80 (40m)
Wcrb = 3*acr*Ɛm/ [1+2*(acr - Cmin) / (D - xu)]
Wcrt = 3*acr x Ɛm / [1+2*(acr - Cmin) / (D - (-D))]
Wcr =Wcrb+Wcrt
Cover, C 40.00 mm
Stirrups of Design purpose 10.00 mm
Dia of bar for design purpose 25.00 mm
Spacer for vertical spacing 32.00 mm
Calculations of required Design Moments, Shear forces:
Resultant Moment of ( Muy and Muz') = M''uz 1988.09 KNm
Design Moment Mu 2045.41 KNm
Design shear force Vu 242.05 KN
Calculations of required Section properties:
Width of web in reiforcement level in tension, btw 450.00 mm
Width of Web, Average btw 450.00 mm
Effective Depth , d (Calculated) 1652.00 mm
Width of small portion in the flange, bs 0.000 mm
Centroid of Section from Compression fibre Cc 621.687 mm
Centoid of section from tension fibre Ct 1178.313 mm
Df/d (Calculated) 0.121
RESULT IN ACCORDANCE WITH DIFFERENT CONDITIONS:
1. Condition: If Neutral Axis lies in the flange? YES
Muf, lim= 0.36*fck*bf*Df*(d-0.416*Df) 6777.25 KNm
4731.834 KNm
Neutral Axis lies in the Flange? YES
For Mu or Mu,lim Area of Steel, Ast 3479.99 mm2
For Tension Area of Steel, Ast2 3642.39 mm2
for BM+Tension, total rqd. Steel, Ast 7122.37 mm2
Neutral Axis Ratio, Xu/d 0.03521
Neutral Axis, Xu 58.174 mm
Due to Mu Compressive strain Ɛcc 0.00026
Total Strain due to (Mu+Fx) Ɛcct 0.00038 < 0.0035 OK
for BM+compression, TrialTotal Rqd. Steel, Ast 10455.000 mm2
Due To Fx, Additional compressive stress fsc NA N/mm2
Additional compressive stress fcc NA N/mm2
Pu NA KN
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00012170 NA
Test : Fx-Pu =0 NA
for BM+compression, Extra Increased area Ast 0.000 mm2
Required Ast 7122.372 mm2
2. Condition: If Neutral Axis lies in the webNeutral Axis lies in the Web NA
Neutral axis depth ratio α = Xu,max/d 0.4791
Maximum Neutral Axis for balanced design Xu,max 791.49 mm NA
yf,max 248.72 mm NA
Test : Muf,lim > Mu for Neutral in flange
Compressive force for straight portion, C1 1701.98 KN NA
Compressive force fo rParabolic portion, C2 1512.87 KN NA
Compressive force Trap. Web, Cu = C1+C2 3214.84 KN NA
Compressive force for Flange portion, C3 4348.50 KN NA
Compressive force for Small Flange portion, C4 0.00 KN NA
Total Compressive force, C 7563.34 KN NA
Moment of C1 about Neutral Axis, Integration I1 1058427.84 KNmm NA
Moment C2 about Neutral Axis Integration I2 427647.61 KNmm NA
Moment f Cu about neutral axis Integration Iu 1486075.45 KNmm NA
CG of Cu from Neutral axis ,Y 462.254 mm NA
CG of Cu from Extreme Compression fibre X 329.231 mm NA
For average web only X/d 0.19929 NA
CG C from Extreme Compression fibre X 197.436 mm NA
11001.28 KNm NA
Capacity Mu, lim (Only for trapezodal Web) 4252.50 KNm NA
Capacity Mu, lim (trapezodal Web + Flange) 11001.37 KNm NA
-8955.96 KNm SRS
1454.715 mm NA
1454.564 mm NA
20945.848 mm2
NA
20948.192 mm2
NA
-0.001929
11.65441
-8536.638
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a 852.913 mm
yf=0.15*xu+0.65*Df 257.937 mm
Lever Arm z = jd 1641.995
18556.993 mm2
NA GO TO 1
Hit and Trial α = Xu/d 0.300000 SRS-NA
0.00000 SRS-NA
Neutral Axis for balanced design Xu 495.60 mm SRS-NA
yf,max 204.34 mm SRS-NA
Compressive force for straight portion, C1 0.00 KN SRS-NA
Compressive force fo rParabolic portion, C2 0.00 KN SRS-NA
Compressive force Trap.Web, Cu = C1+C2 0.00 KN SRS-NA
Compressive force for Flange portion, C3 0.00 KN SRS-NA
Compressive force for Small Flange portion, C4 0.00 KN SRS-NA
Total Compressive force, C 0.00 KN SRS-NA
a= - 0.14976*fck*bw - 0.0050175*fck*(bf - bw)
b= 0.36*fck*bw*d + 0.00669*fck*(bf - bw)
c= 0.2899*fck*Df*(bf - bw)*(d-0.325*Df)-Mu
For Df/d > 0.2 Ast
2 (A) IF Df/d > 0.2
α is chosen to make Test : C = T
Capacity if average web +flange Muw, lim=
0.36*fck*bw*Xu,max*(d-0.416*Xu,max) + 0.446*fck*(bf-
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast,max
For (web +Flange) balanced section Ast,max
Moment of C1 about Neutral Axis, Integration I1 NA KNmm SRS-NA
Moment C2 about Neutral Axis Integration I2 0.00 KNmm SRS-NA
Moment f Cu about neutral axis Integration Iu 0.00 KNmm SRS-NA
CG of Cu from Neutral axis ,Y 0.000 mm SRS-NA
CG of Cu from Extreme Comprssion fibre X 0.000 mm SRS-NA
For average web only X/d 0.00000 SRS-NA
CG C from Extreme Compression fibre X 0.000 mm SRS-NA
0.00 KNm SRS-NA
Mu(Only for trapezodal Web) 0.00 KNm SRS-NA
Mu,lim (trapezodal Web + Flange) 0.00 KNm SRS-NA
0.00 KNm SRS-NA
0.000 mm SRS-NA
0.000 mm SRS-NA
0.000 mm2
SRS-NA
0.00 mm2
SRS-NA
For Tension Area of Steel, Ast2 3642.39 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 3642.39 mm2
SRS-NA
NA KN SRS-NA
Neutral Axis, Xu 0.00 mm SRS-NA
Due to Mu Compressive strain Ɛcc 0.00000 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00002 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 1300.000 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc NA N/mm2
SRS-NA
Additional compressive stress fcc NA N/mm2
SRS-NA
Pu 0.000 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00001938 YES SRS-NA
Test : Fx-Pu =0 NA SRS-NA
Extra Increased area 0.000 mm2
SRS-NA
Required Singly reinforced Ast 3642.386 mm2
SRS-NA
-0.001929 SRS-NA
11.65441 SRS-NA
2440.284 SRS-NA
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a -202.592 mm SRS-NA
yf=0.15*xu+0.65*Df 99.611 mm SRS-NA
Lever Arm z = jd 1520.416 SRS-NA
3726.068 mm2
SRS-NA
NA GO TO 1
Hit and Trial α = Xu/d 0.2545 SRS-NA
α is chosen to make Test : C - T = 0 0.0000 SRS-NA
Force of Tension, T
a= - 0.14976*fck*bw - 0.0050175*fck*(bf - bw)
b= 0.36*fck*bw*d + 0.00669*fck*(bf - bw)
c= 0.2899*fck*Df*(bf - bw)*(d-0.325*Df)-Mu
For Df/d > 0.2 Ast
2 (B) IF Df/d < = 0.2
average web +flange Muw= 0.36*fck*bw*Xu,max*(d-
0.416*Xu,max) + 0.446*fck*(bf-bw)*yf*(d-0.5*yf,max)
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast,max
For (web +Flange) balanced section Ast,max
Neutral Axis for balanced design Xu 0.00 mm SRS-NA
yf 0.00 mm SRS-NA
Compressive force for straight portion, C1 0.00 KN SRS-NA
Compressive force fo rParabolic portion, C2 0.00 KN SRS-NA
Compressive force Trap.Web, Cu = C1+C2 0.00 KN SRS-NA
Compressive force for Flange portion, C3 0.00 KN SRS-NA
Compressive force for Small Flange portion, C4 0.00 KN SRS-NA
Total Compressive force, C 0.00 KN SRS-NA
Moment of C1 about Neutral Axis, Integration I1 0.00 KNmm SRS-NA
Moment C2 about Neutral Axis Integration I2 0.00 KNmm SRS-NA
Moment f Cu about neutral axis Integration Iu 0.00 KNmm SRS-NA
CG of Cu from Neutral axis ,Y 0.000 mm SRS-NA
CG of Cu from Extreme Comprssion fibre X 0.000 mm SRS-NA
For average web only X/d 0.0000000 SRS-NA
CG C from Extreme Compression fibre Xmax 0.000 mm SRS-NA
0.00 KNm SRS-NA
Mu (Only for trapezodal Web) 0.00 KNm SRS-NA
Mu,lim (trapezodal Web + Flange) 0.00 KNm SRS-NA
0.00 KNm SRS-NA
0.000 mm SRS-NA
0.000 mm SRS-NA
0.000 mm2
SRS-NA
0.000 mm2
SRS-NA
For Tension Area of Steel, Ast2 3642.39 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 3642.39 mm2
SRS-NA
0.00 KN SRS-NA
Neutral Axis, Xu 0.000 SRS-NA
Due to Mu Compressive strain Ɛcc 0.00000 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00014 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 3000.000 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc 0.00 N/mm2
SRS-NA
Additional compressive stress fcc 0.000 N/mm2
SRS-NA
Pu 0.000 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00013902 SRS-NA SRS-NA
Test : Fx-Pu =0 0.000000 SRS-NA
Extra Increased area 0.000 mm2
SRS-NA
Required Singly reinforced Ast 3642.386 mm2
SRS-NA
0.000000000 SRS-NA
b= 0.36*fck*bw*d 0.00000000 SRS-NA
0.00000 SRS-NA
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a 0.000 SRS-NA
Lever Arm z = jd 0.000 SRS-NA
Force of Tension, T
a= -0.14976*fck*bw
c= 0.446*fck*Df*(bf - bw)*(d-0.5*Df)-Mu
average web +flange Muw = 0.36*fck*bw*Xu,max*(d-
0.416*Xu,max) + 0.446*fck*(bf-bw)*yf*(d-0.5*yf,max)
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast
For (web +Flange) balanced section Ast
0.000 mm2
SRS-NA
2 (C) Condition: Doubly Reinforced Section GO TO 1
Number of Layer of Comression bar 1.00 No. SRS-NA
Dia of Main reinforcement in compression 32 mm SRS-NA
Spacer for Vertical spacing 32 mm SRS-NA
Dia of Stirrups 10.00 mm SRS-NA
Clear cover, C 40.00 mm SRS-NA
Charactertistics strength of Concrete fck 25.00 N/mm2 SRS-NA
Yield stress of steel fy 415.00 N/mm2 SRS-NA
Helping calculation, d'' 64.00 mm SRS-NA
Effective depth from in compression side d' 66.00 mm SRS-NA
Effective depth at tension side d 1652.00 mm SRS-NA
Neutral Axis depth ration Xu,max/d 0.479 SRS-NA
Neutral Axis Depth Xu.max 791.49 mmm SRS-NA
Compression level strain Ɛsc Or Ɛcc 0.00321 SRS-NA
Compressive level stress of steel fsc 355.913 N/mm2 SRS-NA
Compressive level stress of concrete fcc=446*fck*(Ԑcc-250*Ԑcc^2) 11.150 N/mm2 SRS-NA
Area of compressive stress Asc -16379.017 mm2
SRS-NA
-15640.169 mm2
SRS-NA
For DRS Total Area of tension steel Ast 5308.023 mm2
SRS-NA
for Tension, Area of Steel, Ast3 19282.55 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 24590.58 mm2
SRS-NA
Neutral Axis, Xu 791.486 mm SRS-NA
Due to Mu Compressive strain Ɛcc 0.00350 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00362 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 12063.716 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc NA N/mm2
SRS-NA
Additional compressive stress fcc NA N/mm2
SRS-NA
Pu 0.000 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00012335 YES SRS-NA
Test : Fx-Pu =0 0.000000 SRS-NA
Extra Increased area 0.000 mm2
SRS-NA
Required Double reinforced Ast 24590.578 mm2
SRS-NA
Check for Shear forceDesign Shear force 242.05 KN
Shear stress 0.326 N/mm2
Percentage of tension steel, pt 0.990 %
Percentage of compressive steel, pc 0.132 %
For Df/d < 0.2 Ast
for Asc, Area of tension steel Ast2
Percentage of tension and compressive steel, pt 4.843 %
α=0.8*fck/6.89*pt 0.599
tc = 0.85*SQRT(0.8*fck)*(SQRT(1+5*α)-1)/6*α 1.056 N/mm2
1.00 x 1.056 = 1.056
> 0.326 OK
Shear Reinforcement is NOT required.
Dia of of Vertical Stirrups 8.00 mm
Number of leg 2.00
Planned area to Provide Asv 100.53 mm2
Required spacing of stirrups Svreqd. -110.404 mm
Plan to Provide, spacing of stirrups Sv 200.000
Minimum required Asv 0.4*b*Sv/0.87*fy 99.7092 mm2
Ф 7.9672 mm
Rqd. Stirrups Ф 8.00 Leg 2.000 200.00 mm C/C
Permissible shear stress,
K´tc =
Out Put:Note : DRS = Doubly Reinforced Section, SRS = Singly Reinforced Section, NA = Not Applicable
Rqd. tensile Steel Reinforecement, Ast 7261.75 mm2
Provide 25 Ф bar 14.79 Nos. Say 15.00 Nos.
Rqd. Compressive Steel Reinforecement, Asc 981.74 mm2
Provide 25 Ф bar 2.00 Nos. Say 2.00 Nos.
Stirrups Provided:
Provide 8 Ф bar Spacing 200.00 mm @ C/C Leg = 2
Crack Width Calculation:Stress in tensile reinforced level fsb 117.93 N/mm
2
Spacing of reinforcement S 23.500 mm
acr = ((S / 2)^2+d'^2)^0.5 - Dia /2 = 49.130 mm
Ɛ1b = [fs*((a' - xu) / [(d-xu)*2*10 ^5] 0.0006436
Ɛ2b= bt*(a'-xu)*(D-xu) / [600000*Ast*(d - xu)] 0.0001962
Ɛmb = Ɛ1b-Ɛ2b 0.0004474
0.0652607
Stress in tensile reinforced level fst 122.779 N/mm2
Ɛ1t= fs*(a' - (-D)) / [(d- (-D))*2*10 ^5] 0.0006398
Ɛ2t= bt*(a'-(-D))*(D-(-D)) / [600000*Ast*(d - (-D))] 0.0003875
Ɛmt = Ɛ1t-Ɛ2t 0.0002523
0.0370019
0.1022627 < 0.2
INPUT DATA:- Governing Load Case For Design LC 528
INPUT DATA:- Axial force, Torsion Moments, Bending moments and Shear force:
Design Shear force, Fy 276.23 KN LC 519
Design Torsional Moment for shear Tu=Mx 57.13 KNm LC 519
Moment M'uz 3453.01 KN LC 528
Design Torsional Moment for moment Tu=Mx 21.07 KNm LC 528
Axial Force, Fx 1337.39 KN T LC 528
Bending in another direction Muy 35.09 KNm LC 528
INPUT DATA:- Material Properties :
Characteristic Strength of concrete, fck 25.00 N/mm2
Grade of Steel, fy 415.00 N/mm2
INPUT DATA:- Material Properties and Dimensions of Beam:
Thickness of flange, Df 250.00 mm
Total Depth of T- Beam, D 1800.00 mm
Width of Flange, bf 2400.00 mm
Width of web in compression fibre, bcw 450.00 mm
Width of web in tension, btw' 450.00 mm
Layer of bar in tension zone 4.00
MOLUNG KHOLA BRIDGE MEMBER
T - Beam with Trapezoidal Web, memb. No. 173 (6.5m)
Wcrb = 3*acr*Ɛm/ [1+2*(acr - Cmin) / (D - xu)]
Wcrt = 3*acr x Ɛm / [1+2*(acr - Cmin) / (D - (-D))]
Wcr =Wcrb+Wcrt
Cover, C 40.00 mm
Stirrups of Design purpose 8.00 mm
Dia of bar for design purpose 25.00 mm
Spacer for vertical spacing 32.00 mm
Calculations of required Design Moments, Shear forces:
Resultant Moment of ( Muy and Muz') = M''uz 2030.93 KNm
Design Moment Mu 2092.90 KNm
Design shear force Vu 479.36 KN
Calculations of required Section properties:
Width of web in reiforcement level in tension, btw 450.00 mm
Width of Web, Average btw 450.00 mm
Effective Depth , d (Calculated) 1654.00 mm
Width of small portion in the flange, bs 0.000 mm
Centroid of Section from Compression fibre Cc 590.443 mm
Centoid of section from tension fibre Ct 1209.557 mm
Df/d (Calculated) 0.151
RESULT IN ACCORDANCE WITH DIFFERENT CONDITIONS:
1. Condition: If Neutral Axis lies in the flange? YES
Muf, lim= 0.36*fck*bf*Df*(d-0.416*Df) 8370.05 KNm
6277.149 KNm
Neutral Axis lies in the Flange? YES
For Mu or Mu,lim Area of Steel, Ast 3557.58 mm2
For Tension Area of Steel, Ast2 3704.17 mm2
for BM+Tension, total rqd. Steel, Ast 7261.75 mm2
Neutral Axis Ratio, Xu/d 0.03596
Neutral Axis, Xu 59.471 mm
Due to Mu Compressive strain Ɛcc 0.00026
Total Strain due to (Mu+Fx) Ɛcct 0.00038 < 0.0035 OK
for BM+compression, TrialTotal Rqd. Steel, Ast 10455.000 mm2
Due To Fx, Additional compressive stress fsc NA N/mm2
Additional compressive stress fcc NA N/mm2
Pu NA KN
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00012170 NA
Test : Fx-Pu =0 NA
for BM+compression, Extra Increased area Ast 0.000 mm2
Required Ast 7261.747 mm2
2. Condition: If Neutral Axis lies in the webNeutral Axis lies in the Web NA
Neutral axis depth ratio α = Xu,max/d 0.4791
Maximum Neutral Axis for balanced design Xu,max 792.44 mm NA
yf,max 281.37 mm NA
Test : Muf,lim > Mu for Neutral in flange
Compressive force for straight portion, C1 1704.04 KN NA
Compressive force fo rParabolic portion, C2 1514.70 KN NA
Compressive force Trap. Web, Cu = C1+C2 3218.74 KN NA
Compressive force for Flange portion, C3 5435.63 KN NA
Compressive force for Small Flange portion, C4 0.00 KN NA
Total Compressive force, C 8654.36 KN NA
Moment of C1 about Neutral Axis, Integration I1 1060992.17 KNmm NA
Moment C2 about Neutral Axis Integration I2 428683.70 KNmm NA
Moment f Cu about neutral axis Integration Iu 1489675.87 KNmm NA
CG of Cu from Neutral axis ,Y 462.814 mm NA
CG of Cu from Extreme Compression fibre X 329.630 mm NA
For average web only X/d 0.19929 NA
CG C from Extreme Compression fibre X 201.106 mm NA
12573.78 KNm NA
Capacity Mu, lim (Only for trapezodal Web) 4262.80 KNm NA
Capacity Mu, lim (trapezodal Web + Flange) 12573.87 KNm NA
-10480.97 KNm SRS
1453.023 mm NA
1452.894 mm NA
23967.691 mm2
NA
23969.982 mm2
NA
-0.001929
11.56304
-9485.891
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a 980.914 mm
yf=0.15*xu+0.65*Df 309.637 mm
Lever Arm z = jd 1644.067
21182.742 mm2
NA GO TO 1
Hit and Trial α = Xu/d 0.300000 SRS-NA
0.00000 SRS-NA
Neutral Axis for balanced design Xu 496.20 mm SRS-NA
yf,max 236.93 mm SRS-NA
Compressive force for straight portion, C1 0.00 KN SRS-NA
Compressive force fo rParabolic portion, C2 0.00 KN SRS-NA
Compressive force Trap.Web, Cu = C1+C2 0.00 KN SRS-NA
Compressive force for Flange portion, C3 0.00 KN SRS-NA
Compressive force for Small Flange portion, C4 0.00 KN SRS-NA
Total Compressive force, C 0.00 KN SRS-NA
a= - 0.14976*fck*bw - 0.0050175*fck*(bf - bw)
b= 0.36*fck*bw*d + 0.00669*fck*(bf - bw)
c= 0.2899*fck*Df*(bf - bw)*(d-0.325*Df)-Mu
For Df/d > 0.2 Ast
2 (A) IF Df/d > 0.2
α is chosen to make Test : C = T
Capacity if average web +flange Muw, lim=
0.36*fck*bw*Xu,max*(d-0.416*Xu,max) + 0.446*fck*(bf-
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast,max
For (web +Flange) balanced section Ast,max
Moment of C1 about Neutral Axis, Integration I1 NA KNmm SRS-NA
Moment C2 about Neutral Axis Integration I2 0.00 KNmm SRS-NA
Moment f Cu about neutral axis Integration Iu 0.00 KNmm SRS-NA
CG of Cu from Neutral axis ,Y 0.000 mm SRS-NA
CG of Cu from Extreme Comprssion fibre X 0.000 mm SRS-NA
For average web only X/d 0.00000 SRS-NA
CG C from Extreme Compression fibre X 0.000 mm SRS-NA
0.00 KNm SRS-NA
Mu(Only for trapezodal Web) 0.00 KNm SRS-NA
Mu,lim (trapezodal Web + Flange) 0.00 KNm SRS-NA
0.00 KNm SRS-NA
0.000 mm SRS-NA
0.000 mm SRS-NA
0.000 mm2
SRS-NA
0.00 mm2
SRS-NA
For Tension Area of Steel, Ast2 3704.17 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 3704.17 mm2
SRS-NA
NA KN SRS-NA
Neutral Axis, Xu 0.00 mm SRS-NA
Due to Mu Compressive strain Ɛcc 0.00000 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00002 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 1300.000 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc NA N/mm2
SRS-NA
Additional compressive stress fcc NA N/mm2
SRS-NA
Pu 0.000 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00001938 YES SRS-NA
Test : Fx-Pu =0 NA SRS-NA
Extra Increased area 0.000 mm2
SRS-NA
Required Singly reinforced Ast 3704.168 mm2
SRS-NA
-0.001929 SRS-NA
11.56304 SRS-NA
3463.875 SRS-NA
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a -285.923 mm SRS-NA
yf=0.15*xu+0.65*Df 119.612 mm SRS-NA
Lever Arm z = jd 1450.716 SRS-NA
3995.747 mm2
SRS-NA
NA GO TO 1
Hit and Trial α = Xu/d 0.2552 SRS-NA
α is chosen to make Test : C - T = 0 0.0000 SRS-NA
Force of Tension, T
a= - 0.14976*fck*bw - 0.0050175*fck*(bf - bw)
b= 0.36*fck*bw*d + 0.00669*fck*(bf - bw)
c= 0.2899*fck*Df*(bf - bw)*(d-0.325*Df)-Mu
For Df/d > 0.2 Ast
2 (B) IF Df/d < = 0.2
average web +flange Muw= 0.36*fck*bw*Xu,max*(d-
0.416*Xu,max) + 0.446*fck*(bf-bw)*yf*(d-0.5*yf,max)
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast,max
For (web +Flange) balanced section Ast,max
Neutral Axis for balanced design Xu 0.00 mm SRS-NA
yf 0.00 mm SRS-NA
Compressive force for straight portion, C1 0.00 KN SRS-NA
Compressive force fo rParabolic portion, C2 0.00 KN SRS-NA
Compressive force Trap.Web, Cu = C1+C2 0.00 KN SRS-NA
Compressive force for Flange portion, C3 0.00 KN SRS-NA
Compressive force for Small Flange portion, C4 0.00 KN SRS-NA
Total Compressive force, C 0.00 KN SRS-NA
Moment of C1 about Neutral Axis, Integration I1 0.00 KNmm SRS-NA
Moment C2 about Neutral Axis Integration I2 0.00 KNmm SRS-NA
Moment f Cu about neutral axis Integration Iu 0.00 KNmm SRS-NA
CG of Cu from Neutral axis ,Y 0.000 mm SRS-NA
CG of Cu from Extreme Comprssion fibre X 0.000 mm SRS-NA
For average web only X/d 0.0000000 SRS-NA
CG C from Extreme Compression fibre Xmax 0.000 mm SRS-NA
0.00 KNm SRS-NA
Mu (Only for trapezodal Web) 0.00 KNm SRS-NA
Mu,lim (trapezodal Web + Flange) 0.00 KNm SRS-NA
0.00 KNm SRS-NA
0.000 mm SRS-NA
0.000 mm SRS-NA
0.000 mm2
SRS-NA
0.000 mm2
SRS-NA
For Tension Area of Steel, Ast2 3704.17 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 3704.17 mm2
SRS-NA
0.00 KN SRS-NA
Neutral Axis, Xu 0.000 SRS-NA
Due to Mu Compressive strain Ɛcc 0.00000 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00014 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 3000.000 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc 0.00 N/mm2
SRS-NA
Additional compressive stress fcc 0.000 N/mm2
SRS-NA
Pu 0.000 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00013902 SRS-NA SRS-NA
Test : Fx-Pu =0 0.000000 SRS-NA
Extra Increased area 0.000 mm2
SRS-NA
Required Singly reinforced Ast 3704.168 mm2
SRS-NA
0.000000000 SRS-NA
b= 0.36*fck*bw*d 0.00000000 SRS-NA
0.00000 SRS-NA
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a 0.000 SRS-NA
Lever Arm z = jd 0.000 SRS-NA
Force of Tension, T
a= -0.14976*fck*bw
c= 0.446*fck*Df*(bf - bw)*(d-0.5*Df)-Mu
average web +flange Muw = 0.36*fck*bw*Xu,max*(d-
0.416*Xu,max) + 0.446*fck*(bf-bw)*yf*(d-0.5*yf,max)
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast
For (web +Flange) balanced section Ast
0.000 mm2
SRS-NA
2 (C) Condition: Doubly Reinforced Section GO TO 1
Number of Layer of Comression bar 1.00 No. SRS-NA
Dia of Main reinforcement in compression 32 mm SRS-NA
Spacer for Vertical spacing 32 mm SRS-NA
Dia of Stirrups 8.00 mm SRS-NA
Clear cover, C 40.00 mm SRS-NA
Charactertistics strength of Concrete fck 25.00 N/mm2 SRS-NA
Yield stress of steel fy 415.00 N/mm2 SRS-NA
Helping calculation, d'' 64.00 mm SRS-NA
Effective depth from in compression side d' 64.00 mm SRS-NA
Effective depth at tension side d 1654.00 mm SRS-NA
Neutral Axis depth ration Xu,max/d 0.479 SRS-NA
Neutral Axis Depth Xu.max 792.44 mmm SRS-NA
Compression level strain Ɛsc Or Ɛcc 0.00322 SRS-NA
Compressive level stress of steel fsc 355.993 N/mm2 SRS-NA
Compressive level stress of concrete fcc=446*fck*(Ԑcc-250*Ԑcc^2) 11.150 N/mm2 SRS-NA
Area of compressive stress Asc -19115.387 mm2
SRS-NA
-18257.323 mm2
SRS-NA
For DRS Total Area of tension steel Ast 5712.658 mm2
SRS-NA
for Tension, Area of Steel, Ast3 21961.49 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 27674.15 mm2
SRS-NA
Neutral Axis, Xu 792.444 mm SRS-NA
Due to Mu Compressive strain Ɛcc 0.00350 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00362 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 12063.716 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc NA N/mm2
SRS-NA
Additional compressive stress fcc NA N/mm2
SRS-NA
Pu 0.000 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00012335 YES SRS-NA
Test : Fx-Pu =0 0.000000 SRS-NA
Extra Increased area 0.000 mm2
SRS-NA
Required Double reinforced Ast 27674.150 mm2
SRS-NA
Check for Shear forceDesign Shear force 479.36 KN
Shear stress 0.644 N/mm2
Percentage of tension steel, pt 0.989 %
Percentage of compressive steel, pc 0.132 %
For Df/d < 0.2 Ast
for Asc, Area of tension steel Ast2
Percentage of tension and compressive steel, pt 4.841 %
α=0.8*fck/6.89*pt 0.600
tc = 0.85*SQRT(0.8*fck)*(SQRT(1+5*α)-1)/6*α 1.056 N/mm2
1.00 x 1.056 = 1.056
> 0.644 OK
Shear Reinforcement is NOT required.
Dia of of Vertical Stirrups 8.00 mm
Number of leg 2.00
Planned area to Provide Asv 100.53 mm2
Required spacing of stirrups Svreqd. -195.743 mm
Plan to Provide, spacing of stirrups Sv 200.000
Minimum required Asv 0.4*b*Sv/0.87*fy 99.7092 mm2
Ф 7.9672 mm
Rqd. Stirrups Ф 8.00 Leg 2.000 200.00 mm C/C
Permissible shear stress,
K´tc =
Out Put:Note : DRS = Doubly Reinforced Section, SRS = Singly Reinforced Section, NA = Not Applicable
Rqd. tensile Steel Reinforecement, Ast 7700.20 mm2
Provide 25 Ф bar 15.69 Nos. Say 16.00 Nos.
Rqd. Compressive Steel Reinforecement, Asc 1963.48 mm2
Provide 25 Ф bar 4.00 Nos. Say 4.00 Nos.
Stirrups Provided:
Provide 8 Ф bar Spacing 200.00 mm @ C/C Leg = 2
Crack Width Calculation:Stress in tensile reinforced level fsb 119.54 N/mm
2
Spacing of reinforcement S 21.933 mm
acr = ((S / 2)^2+d'^2)^0.5 - Dia /2 = 48.986 mm
Ɛ1b = [fs*((a' - xu) / [(d-xu)*2*10 ^5] 0.0006526
Ɛ2b= bt*(a'-xu)*(D-xu) / [600000*Ast*(d - xu)] 0.0001846
Ɛmb = Ɛ1b-Ɛ2b 0.0004680
0.0680647
Stress in tensile reinforced level fst 121.172 N/mm2
Ɛ1t= fs*(a' - (-D)) / [(d- (-D))*2*10 ^5] 0.0006315
Ɛ2t= bt*(a'-(-D))*(D-(-D)) / [600000*Ast*(d - (-D))] 0.0003655
Ɛmt = Ɛ1t-Ɛ2t 0.0002660
0.0388975
0.1069622 < 0.2
INPUT DATA:- Governing Load Case For Design LC 508
INPUT DATA:- Axial force, Torsion Moments, Bending moments and Shear force:
Design Shear force, Fy 361.08 KN LC 206
Design Torsional Moment for shear Tu=Mx 4.78 KNm LC 206
Moment M'uz 3722.93 KN LC 508
Design Torsional Moment for moment Tu=Mx 4.25 KNm LC 508
Axial Force, Fx 1399.57 KN T LC 508
Bending in another direction Muy 17.72 KNm LC 508
INPUT DATA:- Material Properties :
Characteristic Strength of concrete, fck 25.00 N/mm2
Grade of Steel, fy 415.00 N/mm2
INPUT DATA:- Material Properties and Dimensions of Beam:
Thickness of flange, Df 250.00 mm
Total Depth of T- Beam, D 1800.00 mm
Width of Flange, bf 2400.00 mm
Width of web in compression fibre, bcw 450.00 mm
Width of web in tension, btw' 450.00 mm
Layer of bar in tension zone 4.00
MOLUNG KHOLA BRIDGE MEMBER
T - Beam with Trapezoidal Web, memb. No.185 (12.5m)
Wcrb = 3*acr*Ɛm/ [1+2*(acr - Cmin) / (D - xu)]
Wcrt = 3*acr x Ɛm / [1+2*(acr - Cmin) / (D - (-D))]
Wcr =Wcrb+Wcrt
Cover, C 40.00 mm
Stirrups of Design purpose 8.00 mm
Dia of bar for design purpose 25.00 mm
Spacer for vertical spacing 32.00 mm
Calculations of required Design Moments, Shear forces:
Resultant Moment of ( Muy and Muz') = M''uz 2234.48 KNm
Design Moment Mu 2246.98 KNm
Design shear force Vu 378.08 KN
Calculations of required Section properties:
Width of web in reiforcement level in tension, btw 450.00 mm
Width of Web, Average btw 450.00 mm
Effective Depth , d (Calculated) 1654.00 mm
Width of small portion in the flange, bs 0.000 mm
Centroid of Section from Compression fibre Cc 590.443 mm
Centoid of section from tension fibre Ct 1209.557 mm
Df/d (Calculated) 0.151
RESULT IN ACCORDANCE WITH DIFFERENT CONDITIONS:
1. Condition: If Neutral Axis lies in the flange? YES
Muf, lim= 0.36*fck*bf*Df*(d-0.416*Df) 8370.05 KNm
6123.067 KNm
Neutral Axis lies in the Flange? YES
For Mu or Mu,lim Area of Steel, Ast 3823.81 mm2
For Tension Area of Steel, Ast2 3876.39 mm2
for BM+Tension, total rqd. Steel, Ast 7700.20 mm2
Neutral Axis Ratio, Xu/d 0.03865
Neutral Axis, Xu 63.922 mm
Due to Mu Compressive strain Ɛcc 0.00028
Total Strain due to (Mu+Fx) Ɛcct 0.00040 < 0.0035 OK
for BM+compression, TrialTotal Rqd. Steel, Ast 10455.000 mm2
Due To Fx, Additional compressive stress fsc NA N/mm2
Additional compressive stress fcc NA N/mm2
Pu NA KN
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00012170 NA
Test : Fx-Pu =0 NA
for BM+compression, Extra Increased area Ast 0.000 mm2
Required Ast 7700.201 mm2
2. Condition: If Neutral Axis lies in the webNeutral Axis lies in the Web NA
Neutral axis depth ratio α = Xu,max/d 0.4791
Maximum Neutral Axis for balanced design Xu,max 792.44 mm NA
yf,max 281.37 mm NA
Test : Muf,lim > Mu for Neutral in flange
Compressive force for straight portion, C1 1704.04 KN NA
Compressive force fo rParabolic portion, C2 1514.70 KN NA
Compressive force Trap. Web, Cu = C1+C2 3218.74 KN NA
Compressive force for Flange portion, C3 5435.63 KN NA
Compressive force for Small Flange portion, C4 0.00 KN NA
Total Compressive force, C 8654.36 KN NA
Moment of C1 about Neutral Axis, Integration I1 1060992.17 KNmm NA
Moment C2 about Neutral Axis Integration I2 428683.70 KNmm NA
Moment f Cu about neutral axis Integration Iu 1489675.87 KNmm NA
CG of Cu from Neutral axis ,Y 462.814 mm NA
CG of Cu from Extreme Compression fibre X 329.630 mm NA
For average web only X/d 0.19929 NA
CG C from Extreme Compression fibre X 201.106 mm NA
12573.78 KNm NA
Capacity Mu, lim (Only for trapezodal Web) 4262.80 KNm NA
Capacity Mu, lim (trapezodal Web + Flange) 12573.87 KNm NA
-10326.89 KNm SRS
1453.023 mm NA
1452.894 mm NA
23967.691 mm2
NA
23969.982 mm2
NA
-0.001929
11.56304
-9485.891
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a 980.914 mm
yf=0.15*xu+0.65*Df 309.637 mm
Lever Arm z = jd 1644.067
21182.742 mm2
NA GO TO 1
Hit and Trial α = Xu/d 0.300000 SRS-NA
0.00000 SRS-NA
Neutral Axis for balanced design Xu 496.20 mm SRS-NA
yf,max 236.93 mm SRS-NA
Compressive force for straight portion, C1 0.00 KN SRS-NA
Compressive force fo rParabolic portion, C2 0.00 KN SRS-NA
Compressive force Trap.Web, Cu = C1+C2 0.00 KN SRS-NA
Compressive force for Flange portion, C3 0.00 KN SRS-NA
Compressive force for Small Flange portion, C4 0.00 KN SRS-NA
Total Compressive force, C 0.00 KN SRS-NA
Capacity if average web +flange Muw, lim=
0.36*fck*bw*Xu,max*(d-0.416*Xu,max) + 0.446*fck*(bf-
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast,max
For (web +Flange) balanced section Ast,max
a= - 0.14976*fck*bw - 0.0050175*fck*(bf - bw)
b= 0.36*fck*bw*d + 0.00669*fck*(bf - bw)
c= 0.2899*fck*Df*(bf - bw)*(d-0.325*Df)-Mu
For Df/d > 0.2 Ast
2 (A) IF Df/d > 0.2
α is chosen to make Test : C = T
Moment of C1 about Neutral Axis, Integration I1 NA KNmm SRS-NA
Moment C2 about Neutral Axis Integration I2 0.00 KNmm SRS-NA
Moment f Cu about neutral axis Integration Iu 0.00 KNmm SRS-NA
CG of Cu from Neutral axis ,Y 0.000 mm SRS-NA
CG of Cu from Extreme Comprssion fibre X 0.000 mm SRS-NA
For average web only X/d 0.00000 SRS-NA
CG C from Extreme Compression fibre X 0.000 mm SRS-NA
0.00 KNm SRS-NA
Mu(Only for trapezodal Web) 0.00 KNm SRS-NA
Mu,lim (trapezodal Web + Flange) 0.00 KNm SRS-NA
0.00 KNm SRS-NA
0.000 mm SRS-NA
0.000 mm SRS-NA
0.000 mm2
SRS-NA
0.00 mm2
SRS-NA
For Tension Area of Steel, Ast2 3876.39 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 3876.39 mm2
SRS-NA
NA KN SRS-NA
Neutral Axis, Xu 0.00 mm SRS-NA
Due to Mu Compressive strain Ɛcc 0.00000 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00002 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 1300.000 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc NA N/mm2
SRS-NA
Additional compressive stress fcc NA N/mm2
SRS-NA
Pu 0.000 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00001938 YES SRS-NA
Test : Fx-Pu =0 NA SRS-NA
Extra Increased area 0.000 mm2
SRS-NA
Required Singly reinforced Ast 3876.388 mm2
SRS-NA
-0.001929 SRS-NA
11.56304 SRS-NA
3309.793 SRS-NA
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a -273.736 mm SRS-NA
yf=0.15*xu+0.65*Df 121.440 mm SRS-NA
Lever Arm z = jd 1466.916 SRS-NA
4242.542 mm2
SRS-NA
NA GO TO 1
Hit and Trial α = Xu/d 0.2659 SRS-NA
α is chosen to make Test : C - T = 0 0.0000 SRS-NA
average web +flange Muw= 0.36*fck*bw*Xu,max*(d-
0.416*Xu,max) + 0.446*fck*(bf-bw)*yf*(d-0.5*yf,max)
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast,max
For (web +Flange) balanced section Ast,max
Force of Tension, T
a= - 0.14976*fck*bw - 0.0050175*fck*(bf - bw)
b= 0.36*fck*bw*d + 0.00669*fck*(bf - bw)
c= 0.2899*fck*Df*(bf - bw)*(d-0.325*Df)-Mu
For Df/d > 0.2 Ast
2 (B) IF Df/d < = 0.2
Neutral Axis for balanced design Xu 0.00 mm SRS-NA
yf 0.00 mm SRS-NA
Compressive force for straight portion, C1 0.00 KN SRS-NA
Compressive force fo rParabolic portion, C2 0.00 KN SRS-NA
Compressive force Trap.Web, Cu = C1+C2 0.00 KN SRS-NA
Compressive force for Flange portion, C3 0.00 KN SRS-NA
Compressive force for Small Flange portion, C4 0.00 KN SRS-NA
Total Compressive force, C 0.00 KN SRS-NA
Moment of C1 about Neutral Axis, Integration I1 0.00 KNmm SRS-NA
Moment C2 about Neutral Axis Integration I2 0.00 KNmm SRS-NA
Moment f Cu about neutral axis Integration Iu 0.00 KNmm SRS-NA
CG of Cu from Neutral axis ,Y 0.000 mm SRS-NA
CG of Cu from Extreme Comprssion fibre X 0.000 mm SRS-NA
For average web only X/d 0.0000000 SRS-NA
CG C from Extreme Compression fibre Xmax 0.000 mm SRS-NA
0.00 KNm SRS-NA
Mu (Only for trapezodal Web) 0.00 KNm SRS-NA
Mu,lim (trapezodal Web + Flange) 0.00 KNm SRS-NA
0.00 KNm SRS-NA
0.000 mm SRS-NA
0.000 mm SRS-NA
0.000 mm2
SRS-NA
0.000 mm2
SRS-NA
For Tension Area of Steel, Ast2 3876.39 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 3876.39 mm2
SRS-NA
0.00 KN SRS-NA
Neutral Axis, Xu 0.000 SRS-NA
Due to Mu Compressive strain Ɛcc 0.00000 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00014 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 3000.000 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc 0.00 N/mm2
SRS-NA
Additional compressive stress fcc 0.000 N/mm2
SRS-NA
Pu 0.000 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00013902 SRS-NA SRS-NA
Test : Fx-Pu =0 0.000000 SRS-NA
Extra Increased area 0.000 mm2
SRS-NA
Required Singly reinforced Ast 3876.388 mm2
SRS-NA
0.000000000 SRS-NA
b= 0.36*fck*bw*d 0.00000000 SRS-NA
0.00000 SRS-NA
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a 0.000 SRS-NA
Lever Arm z = jd 0.000 SRS-NA
average web +flange Muw = 0.36*fck*bw*Xu,max*(d-
0.416*Xu,max) + 0.446*fck*(bf-bw)*yf*(d-0.5*yf,max)
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast
For (web +Flange) balanced section Ast
Force of Tension, T
a= -0.14976*fck*bw
c= 0.446*fck*Df*(bf - bw)*(d-0.5*Df)-Mu
0.000 mm2
SRS-NA
2 (C) Condition: Doubly Reinforced Section GO TO 1
Number of Layer of Comression bar 1.00 No. SRS-NA
Dia of Main reinforcement in compression 32 mm SRS-NA
Spacer for Vertical spacing 32 mm SRS-NA
Dia of Stirrups 8.00 mm SRS-NA
Clear cover, C 40.00 mm SRS-NA
Charactertistics strength of Concrete fck 25.00 N/mm2 SRS-NA
Yield stress of steel fy 415.00 N/mm2 SRS-NA
Helping calculation, d'' 64.00 mm SRS-NA
Effective depth from in compression side d' 64.00 mm SRS-NA
Effective depth at tension side d 1654.00 mm SRS-NA
Neutral Axis depth ration Xu,max/d 0.479 SRS-NA
Neutral Axis Depth Xu.max 792.44 mmm SRS-NA
Compression level strain Ɛsc Or Ɛcc 0.00322 SRS-NA
Compressive level stress of steel fsc 355.993 N/mm2 SRS-NA
Compressive level stress of concrete fcc=446*fck*(Ԑcc-250*Ԑcc^2) 11.150 N/mm2 SRS-NA
Area of compressive stress Asc -18834.371 mm2
SRS-NA
-17988.921 mm2
SRS-NA
For DRS Total Area of tension steel Ast 5981.060 mm2
SRS-NA
for Tension, Area of Steel, Ast3 21865.31 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 27846.37 mm2
SRS-NA
Neutral Axis, Xu 792.444 mm SRS-NA
Due to Mu Compressive strain Ɛcc 0.00350 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00362 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 12063.716 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc NA N/mm2
SRS-NA
Additional compressive stress fcc NA N/mm2
SRS-NA
Pu 0.000 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00012335 YES SRS-NA
Test : Fx-Pu =0 0.000000 SRS-NA
Extra Increased area 0.000 mm2
SRS-NA
Required Double reinforced Ast 27846.370 mm2
SRS-NA
Check for Shear forceDesign Shear force 378.08 KN
Shear stress 0.508 N/mm2
Percentage of tension steel, pt 1.055 %
Percentage of compressive steel, pc 0.264 %
For Df/d < 0.2 Ast
for Asc, Area of tension steel Ast2
Percentage of tension and compressive steel, pt 5.039 %
α=0.8*fck/6.89*pt 0.576
tc = 0.85*SQRT(0.8*fck)*(SQRT(1+5*α)-1)/6*α 1.067 N/mm2
1.00 x 1.067 = 1.067
> 0.508 OK
Shear Reinforcement is NOT required.
Dia of of Vertical Stirrups 8.00 mm
Number of leg 2.00
Planned area to Provide Asv 100.53 mm2
Required spacing of stirrups Svreqd. -144.372 mm
Plan to Provide, spacing of stirrups Sv 200.000
Minimum required Asv 0.4*b*Sv/0.87*fy 99.7092 mm2
Ф 7.9672 mm
Rqd. Stirrups Ф 8.00 Leg 2.000 200.00 mm C/C
Permissible shear stress,
K´tc =
Out Put:Note : DRS = Doubly Reinforced Section, SRS = Singly Reinforced Section, NA = Not Applicable
Rqd. tensile Steel Reinforecement, Ast 2731.67 mm2
Provide 25 Ф bar 5.56 Nos. Say 6.00 Nos.
Rqd. Compressive Steel Reinforecement, Asc 1963.48 mm2
Provide 25 Ф bar 4.00 Nos. Say 4.00 Nos.
Stirrups Provided:
Provide 8 Ф bar Spacing 200.00 mm @ C/C Leg = 2
Crack Width Calculation:Stress in tensile reinforced level fsb 168.55 N/mm
2
Spacing of reinforcement S 65.800 mm
acr = ((S / 2)^2+d'^2)^0.5 - Dia /2 = 56.367 mm
Ɛ1b = [fs*((a' - xu) / [(d-xu)*2*10 ^5] 0.0008874
Ɛ2b= bt*(a'-xu)*(D-xu) / [600000*Ast*(d - xu)] 0.0005112
Ɛmb = Ɛ1b-Ɛ2b 0.0003763
0.0624692
Stress in tensile reinforced level fst 72.158 N/mm2
Ɛ1t= fs*(a' - (-D)) / [(d- (-D))*2*10 ^5] 0.0003699
Ɛ2t= bt*(a'-(-D))*(D-(-D)) / [600000*Ast*(d - (-D))] 0.0010135
Ɛmt = Ɛ1t-Ɛ2t -0.0006435
-0.1078396
-0.0453704 < 0.2
INPUT DATA:- Governing Load Case For Design LC 560
INPUT DATA:- Axial force, Torsion Moments, Bending moments and Shear force:
Design Shear force, Fy 706.48 KN LC 515
Design Torsional Moment for shear Tu=Mx 68.67 KNm LC 515
Moment M'uz 1470.91 KN LC 560
Design Torsional Moment for moment Tu=Mx 11.18 KNm LC 560
Axial Force, Fx 295.67 KN T LC 560
Bending in another direction Muy 1.61 KNm LC 560
INPUT DATA:- Material Properties :
Characteristic Strength of concrete, fck 25.00 N/mm2
Grade of Steel, fy 415.00 N/mm2
INPUT DATA:- Material Properties and Dimensions of Beam:
Thickness of flange, Df 250.00 mm
Total Depth of T- Beam, D 1800.00 mm
Width of Flange, bf 2400.00 mm
Width of web in compression fibre, bcw 450.00 mm
Width of web in tension, btw' 450.00 mm
Layer of bar in tension zone 2.00
MOLUNG KHOLA BRIDGE MEMBER
T - Beam with Trapezoidal Web, memb. No. 198 (19m)
Wcrb = 3*acr*Ɛm/ [1+2*(acr - Cmin) / (D - xu)]
Wcrt = 3*acr x Ɛm / [1+2*(acr - Cmin) / (D - (-D))]
Wcr =Wcrb+Wcrt
Cover, C 40.00 mm
Stirrups of Design purpose 8.00 mm
Dia of bar for design purpose 25.00 mm
Spacer for vertical spacing 32.00 mm
Calculations of required Design Moments, Shear forces:
Resultant Moment of ( Muy and Muz') = M''uz 1139.60 KNm
Design Moment Mu 1172.48 KNm
Design shear force Vu 950.64 KN
Calculations of required Section properties:
Width of web in reiforcement level in tension, btw 450.00 mm
Width of Web, Average btw 450.00 mm
Effective Depth , d (Calculated) 1711.00 mm
Width of small portion in the flange, bs 0.000 mm
Centroid of Section from Compression fibre Cc 590.443 mm
Centoid of section from tension fibre Ct 1209.557 mm
Df/d (Calculated) 0.146
RESULT IN ACCORDANCE WITH DIFFERENT CONDITIONS:
1. Condition: If Neutral Axis lies in the flange? YES
Muf, lim= 0.36*fck*bf*Df*(d-0.416*Df) 8677.85 KNm
7505.364 KNm
Neutral Axis lies in the Flange? YES
For Mu or Mu,lim Area of Steel, Ast 1912.76 mm2
For Tension Area of Steel, Ast2 818.92 mm2
for BM+Tension, total rqd. Steel, Ast 2731.67 mm2
Neutral Axis Ratio, Xu/d 0.01869
Neutral Axis, Xu 31.974 mm
Due to Mu Compressive strain Ɛcc 0.00014
Total Strain due to (Mu+Fx) Ɛcct 0.00026 < 0.0035 OK
for BM+compression, TrialTotal Rqd. Steel, Ast 10455.000 mm2
Due To Fx, Additional compressive stress fsc NA N/mm2
Additional compressive stress fcc NA N/mm2
Pu NA KN
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00012170 NA
Test : Fx-Pu =0 NA
for BM+compression, Extra Increased area Ast 0.000 mm2
Required Ast 2731.674 mm2
2. Condition: If Neutral Axis lies in the webNeutral Axis lies in the Web NA
Neutral axis depth ratio α = Xu,max/d 0.4791
Maximum Neutral Axis for balanced design Xu,max 819.75 mm NA
yf,max 285.46 mm NA
Test : Muf,lim > Mu for Neutral in flange
Compressive force for straight portion, C1 1762.76 KN NA
Compressive force fo rParabolic portion, C2 1566.90 KN NA
Compressive force Trap. Web, Cu = C1+C2 3329.66 KN NA
Compressive force for Flange portion, C3 5435.63 KN NA
Compressive force for Small Flange portion, C4 0.00 KN NA
Total Compressive force, C 8765.29 KN NA
Moment of C1 about Neutral Axis, Integration I1 1135379.86 KNmm NA
Moment C2 about Neutral Axis Integration I2 458739.34 KNmm NA
Moment f Cu about neutral axis Integration Iu 1594119.20 KNmm NA
CG of Cu from Neutral axis ,Y 478.763 mm NA
CG of Cu from Extreme Compression fibre X 340.990 mm NA
For average web only X/d 0.19929 NA
CG C from Extreme Compression fibre X 207.048 mm NA
13182.48 KNm NA
Capacity Mu, lim (Only for trapezodal Web) 4561.67 KNm NA
Capacity Mu, lim (trapezodal Web + Flange) 13182.57 KNm NA
-12010.09 KNm SRS
1504.090 mm NA
1503.952 mm NA
24274.821 mm2
NA
24277.207 mm2
NA
-0.001929
11.97979
-9893.202
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a 980.733 mm
yf=0.15*xu+0.65*Df 309.610 mm
Lever Arm z = jd 1701.067
21464.036 mm2
NA GO TO 1
Hit and Trial α = Xu/d 0.300000 SRS-NA
0.00000 SRS-NA
Neutral Axis for balanced design Xu 513.30 mm SRS-NA
yf,max 239.50 mm SRS-NA
Compressive force for straight portion, C1 0.00 KN SRS-NA
Compressive force fo rParabolic portion, C2 0.00 KN SRS-NA
Compressive force Trap.Web, Cu = C1+C2 0.00 KN SRS-NA
Compressive force for Flange portion, C3 0.00 KN SRS-NA
Compressive force for Small Flange portion, C4 0.00 KN SRS-NA
Total Compressive force, C 0.00 KN SRS-NA
a= - 0.14976*fck*bw - 0.0050175*fck*(bf - bw)
b= 0.36*fck*bw*d + 0.00669*fck*(bf - bw)
c= 0.2899*fck*Df*(bf - bw)*(d-0.325*Df)-Mu
For Df/d > 0.2 Ast
2 (A) IF Df/d > 0.2
α is chosen to make Test : C = T
Capacity if average web +flange Muw, lim=
0.36*fck*bw*Xu,max*(d-0.416*Xu,max) + 0.446*fck*(bf-
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast,max
For (web +Flange) balanced section Ast,max
Moment of C1 about Neutral Axis, Integration I1 NA KNmm SRS-NA
Moment C2 about Neutral Axis Integration I2 0.00 KNmm SRS-NA
Moment f Cu about neutral axis Integration Iu 0.00 KNmm SRS-NA
CG of Cu from Neutral axis ,Y 0.000 mm SRS-NA
CG of Cu from Extreme Comprssion fibre X 0.000 mm SRS-NA
For average web only X/d 0.00000 SRS-NA
CG C from Extreme Compression fibre X 0.000 mm SRS-NA
0.00 KNm SRS-NA
Mu(Only for trapezodal Web) 0.00 KNm SRS-NA
Mu,lim (trapezodal Web + Flange) 0.00 KNm SRS-NA
0.00 KNm SRS-NA
0.000 mm SRS-NA
0.000 mm SRS-NA
0.000 mm2
SRS-NA
0.00 mm2
SRS-NA
For Tension Area of Steel, Ast2 818.92 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 818.92 mm2
SRS-NA
NA KN SRS-NA
Neutral Axis, Xu 0.00 mm SRS-NA
Due to Mu Compressive strain Ɛcc 0.00000 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00002 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 1300.000 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc NA N/mm2
SRS-NA
Additional compressive stress fcc NA N/mm2
SRS-NA
Pu 0.000 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00001938 YES SRS-NA
Test : Fx-Pu =0 NA SRS-NA
Extra Increased area 0.000 mm2
SRS-NA
Required Singly reinforced Ast 818.917 mm2
SRS-NA
-0.001929 SRS-NA
11.97979 SRS-NA
4585.680 SRS-NA
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a -361.713 mm SRS-NA
yf=0.15*xu+0.65*Df 108.243 mm SRS-NA
Lever Arm z = jd 1319.563 SRS-NA
2460.983 mm2
SRS-NA
NA GO TO 1
Hit and Trial α = Xu/d 0.2698 SRS-NA
α is chosen to make Test : C - T = 0 0.0000 SRS-NA
Force of Tension, T
a= - 0.14976*fck*bw - 0.0050175*fck*(bf - bw)
b= 0.36*fck*bw*d + 0.00669*fck*(bf - bw)
c= 0.2899*fck*Df*(bf - bw)*(d-0.325*Df)-Mu
For Df/d > 0.2 Ast
2 (B) IF Df/d < = 0.2
average web +flange Muw= 0.36*fck*bw*Xu,max*(d-
0.416*Xu,max) + 0.446*fck*(bf-bw)*yf*(d-0.5*yf,max)
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast,max
For (web +Flange) balanced section Ast,max
Neutral Axis for balanced design Xu 0.00 mm SRS-NA
yf 0.00 mm SRS-NA
Compressive force for straight portion, C1 0.00 KN SRS-NA
Compressive force fo rParabolic portion, C2 0.00 KN SRS-NA
Compressive force Trap.Web, Cu = C1+C2 0.00 KN SRS-NA
Compressive force for Flange portion, C3 0.00 KN SRS-NA
Compressive force for Small Flange portion, C4 0.00 KN SRS-NA
Total Compressive force, C 0.00 KN SRS-NA
Moment of C1 about Neutral Axis, Integration I1 0.00 KNmm SRS-NA
Moment C2 about Neutral Axis Integration I2 0.00 KNmm SRS-NA
Moment f Cu about neutral axis Integration Iu 0.00 KNmm SRS-NA
CG of Cu from Neutral axis ,Y 0.000 mm SRS-NA
CG of Cu from Extreme Comprssion fibre X 0.000 mm SRS-NA
For average web only X/d 0.0000000 SRS-NA
CG C from Extreme Compression fibre Xmax 0.000 mm SRS-NA
0.00 KNm SRS-NA
Mu (Only for trapezodal Web) 0.00 KNm SRS-NA
Mu,lim (trapezodal Web + Flange) 0.00 KNm SRS-NA
0.00 KNm SRS-NA
0.000 mm SRS-NA
0.000 mm SRS-NA
0.000 mm2
SRS-NA
0.000 mm2
SRS-NA
For Tension Area of Steel, Ast2 818.92 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 818.92 mm2
SRS-NA
0.00 KN SRS-NA
Neutral Axis, Xu 0.000 SRS-NA
Due to Mu Compressive strain Ɛcc 0.00000 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00014 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 3000.000 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc 0.00 N/mm2
SRS-NA
Additional compressive stress fcc 0.000 N/mm2
SRS-NA
Pu 0.000 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00013902 SRS-NA SRS-NA
Test : Fx-Pu =0 0.000000 SRS-NA
Extra Increased area 0.000 mm2
SRS-NA
Required Singly reinforced Ast 818.917 mm2
SRS-NA
0.000000000 SRS-NA
b= 0.36*fck*bw*d 0.00000000 SRS-NA
0.00000 SRS-NA
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a 0.000 SRS-NA
Lever Arm z = jd 0.000 SRS-NA
Force of Tension, T
a= -0.14976*fck*bw
c= 0.446*fck*Df*(bf - bw)*(d-0.5*Df)-Mu
average web +flange Muw = 0.36*fck*bw*Xu,max*(d-
0.416*Xu,max) + 0.446*fck*(bf-bw)*yf*(d-0.5*yf,max)
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast
For (web +Flange) balanced section Ast
0.000 mm2
SRS-NA
2 (C) Condition: Doubly Reinforced Section GO TO 1
Number of Layer of Comression bar 1.00 No. SRS-NA
Dia of Main reinforcement in compression 32 mm SRS-NA
Spacer for Vertical spacing 32 mm SRS-NA
Dia of Stirrups 8.00 mm SRS-NA
Clear cover, C 40.00 mm SRS-NA
Charactertistics strength of Concrete fck 25.00 N/mm2 SRS-NA
Yield stress of steel fy 415.00 N/mm2 SRS-NA
Helping calculation, d'' 64.00 mm SRS-NA
Effective depth from in compression side d' 64.00 mm SRS-NA
Effective depth at tension side d 1711.00 mm SRS-NA
Neutral Axis depth ration Xu,max/d 0.479 SRS-NA
Neutral Axis Depth Xu.max 819.75 mmm SRS-NA
Compression level strain Ɛsc Or Ɛcc 0.00323 SRS-NA
Compressive level stress of steel fsc 356.075 N/mm2 SRS-NA
Compressive level stress of concrete fcc=446*fck*(Ԑcc-250*Ԑcc^2) 11.150 N/mm2 SRS-NA
Area of compressive stress Asc -21141.137 mm2
SRS-NA
-20196.926 mm2
SRS-NA
For DRS Total Area of tension steel Ast 4080.281 mm2
SRS-NA
for Tension, Area of Steel, Ast3 21015.84 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 25096.12 mm2
SRS-NA
Neutral Axis, Xu 819.753 mm SRS-NA
Due to Mu Compressive strain Ɛcc 0.00350 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00362 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 12063.716 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc NA N/mm2
SRS-NA
Additional compressive stress fcc NA N/mm2
SRS-NA
Pu 0.000 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00012335 YES SRS-NA
Test : Fx-Pu =0 0.000000 SRS-NA
Extra Increased area 0.000 mm2
SRS-NA
Required Double reinforced Ast 25096.124 mm2
SRS-NA
Check for Shear forceDesign Shear force 950.64 KN
Shear stress 1.235 N/mm2
Percentage of tension steel, pt 0.383 %
Percentage of compressive steel, pc 0.255 %
For Df/d < 0.2 Ast
for Asc, Area of tension steel Ast2
Percentage of tension and compressive steel, pt 4.358 %
α=0.8*fck/6.89*pt 0.666
tc = 0.85*SQRT(0.8*fck)*(SQRT(1+5*α)-1)/6*α 1.028 N/mm2
1.00 x 1.028 = 1.028
> 1.235 NOT OK
Shear Reinforcement is required.
Dia of of Vertical Stirrups 8.00 mm
Number of leg 2.00
Planned area to Provide Asv 100.53 mm2
Required spacing of stirrups Svreqd. 390.564 mm
Plan to Provide, spacing of stirrups Sv 200.000
Minimum required Asv 0.4*b*Sv/0.87*fy 99.7092 mm2
Ф 7.9672 mm
Rqd. Stirrups Ф 8.00 Leg 2.000 200.00 mm C/C
Permissible shear stress,
K´tc =
Out Put:Note : DRS = Doubly Reinforced Section, SRS = Singly Reinforced Section, NA = Not Applicable
Rqd. tensile Steel Reinforecement, Ast 6916.69 mm2
Provide 25 Ф bar 14.09 Nos. Say 14.00 Nos.
Rqd. Compressive Steel Reinforecement, Asc 981.74 mm2
Provide 25 Ф bar 2.00 Nos. Say 2.00 Nos.
Stirrups Provided:
Provide 8 Ф bar Spacing 100.00 mm @ C/C Leg = 2
Crack Width Calculation:Stress in tensile reinforced level fsb 301.10 N/mm
2
Spacing of reinforcement S 25.308 mm
acr = ((S / 2)^2+d'^2)^0.5 - Dia /2 = 49.309 mm
Ɛ1b = [fs*((a' - xu) / [(d-xu)*2*10 ^5] 0.0017588
Ɛ2b= bt*(a'-xu)*(D-xu) / [600000*Ast*(d - xu)] 0.0001284
Ɛmb = Ɛ1b-Ɛ2b 0.0016303
0.2368237
Stress in tensile reinforced level fst -140.694 N/mm2
Ɛ1t= fs*(a' - (-D)) / [(d- (-D))*2*10 ^5] -0.0007332
Ɛ2t= bt*(a'-(-D))*(D-(-D)) / [600000*Ast*(d - (-D))] 0.0004069
Ɛmt = Ɛ1t-Ɛ2t -0.0011401
-0.1677794
0.0690442 < 0.2
INPUT DATA:- Governing Load Case For Design LC 230
INPUT DATA:- Axial force, Torsion Moments, Bending moments and Shear force:
Design Shear force, Fy 1068.57 KN LC 567
Design Torsional Moment for shear Tu=Mx 75.62 KNm LC 567
Moment M'uz 4092.23 KN LC 230
Design Torsional Moment for moment Tu=Mx 18.07 KNm LC 230
Axial Force, Fx 1459.71 KN C LC 230
Bending in another direction Muy 27.65 KNm LC 230
INPUT DATA:- Material Properties :
Characteristic Strength of concrete, fck 25.00 N/mm2
Grade of Steel, fy 415.00 N/mm2
INPUT DATA:- Material Properties and Dimensions of Beam:
Thickness of flange, Df 250.00 mm
Total Depth of T- Beam, D 1800.00 mm
Width of Flange, bf 450.00 mm
Width of web in compression fibre, bcw 450.00 mm
Width of web in tension, btw' 450.00 mm
Layer of bar in tension zone 4.00
MOLUNG KHOLA BRIDGE MEMBER
T - Beam with Trapezoidal Web, memb. No. 210 (25m)
Wcrb = 3*acr*Ɛm/ [1+2*(acr - Cmin) / (D - xu)]
Wcrt = 3*acr x Ɛm / [1+2*(acr - Cmin) / (D - (-D))]
Wcr =Wcrb+Wcrt
Cover, C 40.00 mm
Stirrups of Design purpose 8.00 mm
Dia of bar for design purpose 25.00 mm
Spacer for vertical spacing 32.00 mm
Calculations of required Design Moments, Shear forces:
Resultant Moment of ( Muy and Muz') = M''uz 4092.32 KNm
Design Moment Mu 4145.47 KNm
Design shear force Vu 1337.44 KN
Calculations of required Section properties:
Width of web in reiforcement level in tension, btw 450.00 mm
Width of Web, Average btw 450.00 mm
Effective Depth , d (Calculated) 1654.00 mm
Width of small portion in the flange, bs 0.000 mm
Centroid of Section from Compression fibre Cc 852.381 mm
Centoid of section from tension fibre Ct 947.619 mm
Df/d (Calculated) 0.151
RESULT IN ACCORDANCE WITH DIFFERENT CONDITIONS:
1. Condition: If Neutral Axis lies in the flange? GO TO 2 (B)
Muf, lim= 0.36*fck*bf*Df*(d-0.416*Df) 1569.38 KNm SRS-NA
-2576.087 KNm SRS-NA
Neutral Axis lies in the Flange? NO SRS-NA
For Mu or Mu,lim Area of Steel, Ast 2803.27 mm2
SRS-NA
For Tension Area of Steel, Ast2 0.00 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 2803.27 mm2
SRS-NA
Neutral Axis Ratio, Xu/d 0.15115 SRS-NA
Neutral Axis, Xu 250.000 mm SRS-NA
Due to Mu Compressive strain Ɛcc 0.00110 SRS-NA
Total Strain due to (Mu+Fx) Ɛcct 0.00123 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 10455.000 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc 24.41 N/mm2
SRS-NA
Additional compressive stress fcc 1.316 N/mm2
SRS-NA
Pu 1307.154 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00012170 YES SRS-NA
Test : Fx-Pu =0 152.552663 SRS-NA
for BM+compression, Extra Increased area Ast 7651.732 mm2
SRS-NA
Required Ast 10455.000 mm2
SRS-NA
2. Condition: If Neutral Axis lies in the webNeutral Axis lies in the Web YES
Neutral axis depth ratio α = Xu,max/d 0.4791
Maximum Neutral Axis for balanced design Xu,max 792.44 mm
yf,max 281.37 mm
Test : Muf,lim > Mu for Neutral in flange
Compressive force for straight portion, C1 1704.04 KN
Compressive force fo rParabolic portion, C2 1514.70 KN
Compressive force Trap. Web, Cu = C1+C2 3218.74 KN
Compressive force for Flange portion, C3 0.00 KN
Compressive force for Small Flange portion, C4 0.00 KN
Total Compressive force, C 3218.74 KN
Moment of C1 about Neutral Axis, Integration I1 1060992.17 KNmm
Moment C2 about Neutral Axis Integration I2 428683.70 KNmm
Moment f Cu about neutral axis Integration Iu 1489675.87 KNmm
CG of Cu from Neutral axis ,Y 462.814 mm
CG of Cu from Extreme Compression fibre X 329.630 mm
For average web only X/d 0.19929
CG C from Extreme Compression fibre X 329.630 mm
4262.71 KNm
Capacity Mu, lim (Only for trapezodal Web) 4262.80 KNm
Capacity Mu, lim (trapezodal Web + Flange) 4262.80 KNm
-117.33 KNm SRS
1324.343 mm
1324.370 mm
8914.934 mm2
8914.934 mm2
-0.001685
6.69870
-4262.799
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a 795.539 mm
yf=0.15*xu+0.65*Df 281.831 mm
Lever Arm z = jd 1323.056
8923.791 mm2
NA GO TO 2 (B)
Hit and Trial α = Xu/d 0.300000 SRS-NA
0.00000 SRS-NA
Neutral Axis for balanced design Xu 496.20 mm SRS-NA
yf,max 236.93 mm SRS-NA
Compressive force for straight portion, C1 0.00 KN SRS-NA
Compressive force fo rParabolic portion, C2 0.00 KN SRS-NA
Compressive force Trap.Web, Cu = C1+C2 0.00 KN SRS-NA
Compressive force for Flange portion, C3 0.00 KN SRS-NA
Compressive force for Small Flange portion, C4 0.00 KN SRS-NA
Total Compressive force, C 0.00 KN SRS-NA
a= - 0.14976*fck*bw - 0.0050175*fck*(bf - bw)
b= 0.36*fck*bw*d + 0.00669*fck*(bf - bw)
c= 0.2899*fck*Df*(bf - bw)*(d-0.325*Df)-Mu
For Df/d > 0.2 Ast
2 (A) IF Df/d > 0.2
α is chosen to make Test : C = T
Capacity if average web +flange Muw, lim=
0.36*fck*bw*Xu,max*(d-0.416*Xu,max) + 0.446*fck*(bf-
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast,max
For (web +Flange) balanced section Ast,max
Moment of C1 about Neutral Axis, Integration I1 0.00 KNmm SRS-NA
Moment C2 about Neutral Axis Integration I2 0.00 KNmm SRS-NA
Moment f Cu about neutral axis Integration Iu 0.00 KNmm SRS-NA
CG of Cu from Neutral axis ,Y 0.000 mm SRS-NA
CG of Cu from Extreme Comprssion fibre X 0.000 mm SRS-NA
For average web only X/d 0.00000 SRS-NA
CG C from Extreme Compression fibre X 0.000 mm SRS-NA
0.00 KNm SRS-NA
Mu(Only for trapezodal Web) 0.00 KNm SRS-NA
Mu,lim (trapezodal Web + Flange) 0.00 KNm SRS-NA
0.00 KNm SRS-NA
0.000 mm SRS-NA
0.000 mm SRS-NA
0.000 mm2
SRS-NA
0.00 mm2
SRS-NA
For Tension Area of Steel, Ast2 0.00 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 0.00 mm2
SRS-NA
0.00 KN SRS-NA
Neutral Axis, Xu 0.00 mm SRS-NA
Due to Mu Compressive strain Ɛcc 0.00000 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00002 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 1300.000 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc 3.89 N/mm2
SRS-NA
Additional compressive stress fcc 0.215 N/mm2
SRS-NA
Pu 178.934 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00001938 YES SRS-NA
Test : Fx-Pu =0 1280.772357 SRS-NA
Extra Increased area 1300.000 mm2
SRS-NA
Required Singly reinforced Ast 1300.000 mm2
SRS-NA
-0.001685 SRS-NA
6.69870 SRS-NA
-4145.470 SRS-NA
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a 766.688 mm SRS-NA
yf=0.15*xu+0.65*Df 277.503 mm SRS-NA
Lever Arm z = jd 1335.058 SRS-NA
8600.158 mm2
SRS-NA
0.151 YES
Hit and Trial α = Xu/d 0.4753
α is chosen to make Test : C - T = 0 0.6912
Force of Tension, T
a= - 0.14976*fck*bw - 0.0050175*fck*(bf - bw)
b= 0.36*fck*bw*d + 0.00669*fck*(bf - bw)
c= 0.2899*fck*Df*(bf - bw)*(d-0.325*Df)-Mu
For Df/d > 0.2 Ast
2 (B) IF Df/d < = 0.2
average web +flange Muw= 0.36*fck*bw*Xu,max*(d-
0.416*Xu,max) + 0.446*fck*(bf-bw)*yf*(d-0.5*yf,max)
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast,max
For (web +Flange) balanced section Ast,max
Neutral Axis for balanced design Xu 786.12 mm
yf 280.42 mm
Compressive force for straight portion, C1 1690.45 KN
Compressive force fo rParabolic portion, C2 1502.62 KN
Compressive force Trap.Web, Cu = C1+C2 3193.06 KN
Compressive force for Flange portion, C3 0.00 KN
Compressive force for Small Flange portion, C4 0.00 KN
Total Compressive force, C 3193.06 KN
Moment of C1 about Neutral Axis, Integration I1 1044134.15 KNmm
Moment C2 about Neutral Axis Integration I2 421872.38 KNmm
Moment f Cu about neutral axis Integration Iu 1466006.53 KNmm
CG of Cu from Neutral axis ,Y 459.122 mm
CG of Cu from Extreme Comprssion fibre X 327.001 mm
For average web only X/d 0.1977030
CG C from Extreme Compression fibre Xmax 327.001 mm
4224.81 KNm
Mu (Only for trapezodal Web) 4237.19 KNm
Mu,lim (trapezodal Web + Flange) 4237.19 KNm
91.72 KNm
1326.973 mm
1326.999 mm
8818.165 mm2
8843.826 mm2
For Tension Area of Steel, Ast2 0.00 mm2
for BM+Tension, total rqd. Steel, Ast 8843.83 mm2
3123.94 KN
Neutral Axis, Xu 786.123
Due to Mu Compressive strain Ɛcc 0.00347
Total Strain due to (Mu+P) Ɛcct 0.00360 < 0.0035 OK
for BM+compression, TrialTotal Rqd. Steel, Ast 6916.690 mm2
Due To Fx, Additional compressive stress fsc 26.19 N/mm2
Additional compressive stress fcc 1.408 N/mm2
Pu 1312.216 KN
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00013058 YES
Test : Fx-Pu =0 147.490189
Extra Increased area -1927.136 mm2
Required Singly reinforced Ast 6916.690 mm2
-0.001684800
b= 0.36*fck*bw*d 6.69870000
-4145.47047
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a 766.688
Lever Arm z = jd 1335.058
Force of Tension, T
a= -0.14976*fck*bw
c= 0.446*fck*Df*(bf - bw)*(d-0.5*Df)-Mu
average web +flange Muw = 0.36*fck*bw*Xu,max*(d-
0.416*Xu,max) + 0.446*fck*(bf-bw)*yf*(d-0.5*yf,max)
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast
For (web +Flange) balanced section Ast
8600.158 mm2
2 (C) Condition: Doubly Reinforced Section GO TO 2 (B)
Number of Layer of Comression bar 1.00 No. SRS-NA
Dia of Main reinforcement in compression 32 mm SRS-NA
Spacer for Vertical spacing 32 mm SRS-NA
Dia of Stirrups 8.00 mm SRS-NA
Clear cover, C 40.00 mm SRS-NA
Charactertistics strength of Concrete fck 25.00 N/mm2 SRS-NA
Yield stress of steel fy 415.00 N/mm2 SRS-NA
Helping calculation, d'' 64.00 mm SRS-NA
Effective depth from in compression side d' 64.00 mm SRS-NA
Effective depth at tension side d 1654.00 mm SRS-NA
Neutral Axis depth ration Xu,max/d 0.479 SRS-NA
Neutral Axis Depth Xu.max 792.44 mmm SRS-NA
Compression level strain Ɛsc Or Ɛcc 0.00322 SRS-NA
Compressive level stress of steel fsc 355.993 N/mm2 SRS-NA
Compressive level stress of concrete fcc=446*fck*(Ԑcc-250*Ԑcc^2)11.150 N/mm2 SRS-NA
Area of compressive stress Asc -213.985 mm2
SRS-NA
-204.380 mm2
SRS-NA
For DRS Total Area of tension steel Ast 8710.554 mm2
SRS-NA
for Tension, Area of Steel, Ast3 0.00 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 8710.55 mm2
SRS-NA
Neutral Axis, Xu 792.444 mm SRS-NA
Due to Mu Compressive strain Ɛcc 0.00350 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00362 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 12867.960 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc 23.78 N/mm2
SRS-NA
Additional compressive stress fcc 1.283 N/mm2
SRS-NA
Pu 1328.378 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00011854 YES SRS-NA
Test : Fx-Pu =0 0.000000 SRS-NA
Extra Increased area 4157.406 mm2
SRS-NA
Required Double reinforced Ast 12867.960 mm2
SRS-NA
Check for Shear forceDesign Shear force 1337.44 KN
Shear stress 1.797 N/mm2
Percentage of tension steel, pt 0.923 %
Percentage of compressive steel, pc 0.132 %
For Df/d < 0.2 Ast
for Asc, Area of tension steel Ast2
Percentage of tension and compressive steel, pt 4.775 %
α=0.8*fck/6.89*pt 0.608
tc = 0.85*SQRT(0.8*fck)*(SQRT(1+5*α)-1)/6*α 1.052 N/mm2
1.00 x 1.052 = 1.052
> 1.797 Not OK
Shear Reinforcement is required.
Dia of of Vertical Stirrups 8.00 mm
Number of leg 2.00
Planned area to Provide Asv 100.53 mm2
Required spacing of stirrups Svreqd. 108.351 mm
Plan to Provide, spacing of stirrups Sv 100.000
Minimum required Asv 0.4*b*Sv/0.87*fy 49.8546 mm2
Ф 5.6337 mm
Rqd. Stirrups Ф 8.00 Leg 2.000 100.00 mm C/C
Permissible shear stress,
K´tc =
Out Put:Note : DRS = Doubly Reinforced Section, SRS = Singly Reinforced Section, NA = Not Applicable
Rqd. tensile Steel Reinforecement, Ast 12867.96 mm2
Provide 25 Ф bar 26.21 Nos. Say 26.00 Nos.
Rqd. Compressive Steel Reinforecement, Asc 2263.98 mm2
Provide 25 Ф bar 4.61 Nos. Say 5.00 Nos.
Stirrups Provided:
Provide 8 Ф bar Spacing 100.00 mm @ C/C Leg = 2
Crack Width Calculation:Stress in tensile reinforced level fsb 239.80 N/mm
2
Spacing of reinforcement S 15.160 mm
acr = ((S / 2)^2+d'^2)^0.5 - Dia /2 = 48.473 mm
Ɛ1b = [fs*((a' - xu) / [(d-xu)*2*10 ^5] 0.0012790
Ɛ2b= bt*(a'-xu)*(D-xu) / [600000*Ast*(d - xu)] 0.0000668
Ɛmb = Ɛ1b-Ɛ2b 0.0012123
0.1732484
Stress in tensile reinforced level fst -98.948 N/mm2
Ɛ1t= fs*(a' - (-D)) / [(d- (-D))*2*10 ^5] -0.0005032
Ɛ2t= bt*(a'-(-D))*(D-(-D)) / [600000*Ast*(d - (-D))] 0.0002371
Ɛmt = Ɛ1t-Ɛ2t -0.0007403
-0.1071519
0.0660965 < 0.2
INPUT DATA:- Governing Load Case For Design LC 534
INPUT DATA:- Axial force, Torsion Moments, Bending moments and Shear force:
Design Shear force, Fy 1459.77 KN LC 238
Design Torsional Moment for shear Tu=Mx 30.45 KNm LC 238
Moment M'uz 6357.32 KN LC 534
Design Torsional Moment for moment Tu=Mx 33.01 KNm LC 534
Axial Force, Fx 1909.89 KN C LC 534
Bending in another direction Muy 38.87 KNm LC 534
INPUT DATA:- Material Properties :
Characteristic Strength of concrete, fck 25.00 N/mm2
Grade of Steel, fy 415.00 N/mm2
INPUT DATA:- Material Properties and Dimensions of Beam:
Thickness of flange, Df 250.00 mm
Total Depth of T- Beam, D 1800.00 mm
Width of Flange, bf 500.00 mm Approx.Effective
Width of web in compression fibre, bcw 500.00 mm Approx.Effective
Width of web in tension, btw' 500.00 mm Approx.Effective
Layer of bar in tension zone 1.00
MOLUNG KHOLA BRIDGE MEMBER
T - Beam with Trapezoidal Web, memb. No. 210 (25m)
Wcrb = 3*acr*Ɛm/ [1+2*(acr - Cmin) / (D - xu)]
Wcrt = 3*acr x Ɛm / [1+2*(acr - Cmin) / (D - (-D))]
Wcr =Wcrb+Wcrt
Cover, C 40.00 mm
Stirrups of Design purpose 8.00 mm
Dia of bar for design purpose 25.00 mm
Spacer for vertical spacing 32.00 mm
Calculations of required Design Moments, Shear forces:
Resultant Moment of ( Muy and Muz') = M''uz 6357.44 KNm
Design Moment Mu 6446.76 KNm
Design shear force Vu 1557.21 KN
Calculations of required Section properties:
Width of web in reiforcement level in tension, btw 500.00 mm
Width of Web, Average btw 500.00 mm
Effective Depth , d (Calculated) 1739.50 mm
Width of small portion in the flange, bs 0.000 mm
Centroid of Section from Compression fibre Cc 852.381 mm
Centoid of section from tension fibre Ct 947.619 mm
Df/d (Calculated) 0.144
RESULT IN ACCORDANCE WITH DIFFERENT CONDITIONS:
1. Condition: If Neutral Axis lies in the flange? GO TO 2 (C)
Muf, lim= 0.36*fck*bf*Df*(d-0.416*Df) 1839.95 KNm DRS-NA
-4606.813 KNm DRS-NA
Neutral Axis lies in the Flange? NO DRS-NA
For Mu or Mu,lim Area of Steel, Ast 3114.81 mm2
DRS-NA
For Tension Area of Steel, Ast2 0.00 mm2
DRS-NA
for BM+Tension, total rqd. Steel, Ast 3114.81 mm2
DRS-NA
Neutral Axis Ratio, Xu/d 0.14372 DRS-NA
Neutral Axis, Xu 250.000 mm DRS-NA
Due to Mu Compressive strain Ɛcc 0.00105 DRS-NA
Total Strain due to (Mu+Fx) Ɛcct 0.00117 < 0.0035 DRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 10455.000 mm2
DRS-NA
Due To Fx, Additional compressive stress fsc 24.41 N/mm2
DRS-NA
Additional compressive stress fcc 1.316 N/mm2
DRS-NA
Pu 1425.564 KN DRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00012170 NA DRS-NA
Test : Fx-Pu =0 0.000000 DRS-NA
for BM+compression, Extra Increased area Ast 0.000 mm2
DRS-NA
Required Ast 10455.000 mm2
DRS-NA
2. Condition: If Neutral Axis lies in the webNeutral Axis lies in the Web YES
Neutral axis depth ratio α = Xu,max/d 0.4791
Maximum Neutral Axis for balanced design Xu,max 833.41 mm
yf,max 287.51 mm
Test : Muf,lim > Mu for Neutral in flange
Compressive force for straight portion, C1 1991.25 KN
Compressive force fo rParabolic portion, C2 1770.00 KN
Compressive force Trap. Web, Cu = C1+C2 3761.25 KN
Compressive force for Flange portion, C3 0.00 KN
Compressive force for Small Flange portion, C4 0.00 KN
Total Compressive force, C 3761.25 KN
Moment of C1 about Neutral Axis, Integration I1 1303909.73 KNmm
Moment C2 about Neutral Axis Integration I2 526832.21 KNmm
Moment f Cu about neutral axis Integration Iu 1830741.94 KNmm
CG of Cu from Neutral axis ,Y 486.738 mm
CG of Cu from Extreme Compression fibre X 346.669 mm
For average web only X/d 0.19929
CG C from Extreme Compression fibre X 346.669 mm
5238.67 KNm
Capacity Mu, lim (Only for trapezodal Web) 5238.78 KNm
Capacity Mu, lim (trapezodal Web + Flange) 5238.78 KNm
1207.98 KNm DRS
1392.802 mm
1392.831 mm
10417.525 mm2
10417.525 mm2
-0.001872 DRS-NA
7.82775 DRS-NA
-5238.780 DRS-NA
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a 836.663 mm DRS-NA
yf=0.15*xu+0.65*Df 287.999 mm DRS-NA
Lever Arm z = jd 1391.448 DRS-NA
10427.874 mm2
DRS-NA
DRS-NA GO TO 2 (C)
Hit and Trial α = Xu/d 0.300000 DRS-NA
0.00000 DRS-NA
Neutral Axis for balanced design Xu 521.85 mm DRS-NA
yf,max 240.78 mm DRS-NA
Compressive force for straight portion, C1 0.00 KN DRS-NA
Compressive force fo rParabolic portion, C2 0.00 KN DRS-NA
Compressive force Trap.Web, Cu = C1+C2 0.00 KN DRS-NA
Compressive force for Flange portion, C3 0.00 KN DRS-NA
Compressive force for Small Flange portion, C4 0.00 KN DRS-NA
Total Compressive force, C 0.00 KN DRS-NA
2 (A) IF Df/d > 0.2
α is chosen to make Test : C = T
For avg. web +flange balanced section Ast,max
For (web +Flange) balanced section Ast,max
For Df/d > 0.2 Ast
a= - 0.14976*fck*bw - 0.0050175*fck*(bf - bw)
b= 0.36*fck*bw*d + 0.00669*fck*(bf - bw)
c= 0.2899*fck*Df*(bf - bw)*(d-0.325*Df)-Mu
Capacity if average web +flange Muw, lim=
0.36*fck*bw*Xu,max*(d-0.416*Xu,max) + 0.446*fck*(bf-
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
Moment of C1 about Neutral Axis, Integration I1 0.00 KNmm DRS-NA
Moment C2 about Neutral Axis Integration I2 0.00 KNmm DRS-NA
Moment f Cu about neutral axis Integration Iu 0.00 KNmm DRS-NA
CG of Cu from Neutral axis ,Y 0.000 mm DRS-NA
CG of Cu from Extreme Comprssion fibre X 0.000 mm DRS-NA
For average web only X/d 0.00000 DRS-NA
CG C from Extreme Compression fibre X 0.000 mm DRS-NA
0.00 KNm DRS-NA
Mu(Only for trapezodal Web) 0.00 KNm DRS-NA
Mu,lim (trapezodal Web + Flange) 0.00 KNm DRS-NA
0.00 KNm DRS-NA
0.000 mm DRS-NA
0.000 mm DRS-NA
0.000 mm2
DRS-NA
0.00 mm2
DRS-NA
For Tension Area of Steel, Ast2 0.00 mm2
DRS-NA
for BM+Tension, total rqd. Steel, Ast 0.00 mm2
DRS-NA
0.00 KN DRS-NA
Neutral Axis, Xu 0.00 mm DRS-NA
Due to Mu Compressive strain Ɛcc 0.00000 DRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00002 < 0.0035 DRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 1300.000 mm2
DRS-NA
Due To Fx, Additional compressive stress fsc 3.89 N/mm2
DRS-NA
Additional compressive stress fcc 0.215 N/mm2
DRS-NA
Pu 198.286 KN DRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00001938 YES DRS-NA
Test : Fx-Pu =0 0.000000 DRS-NA
Extra Increased area 0.000 mm2
DRS-NA
Required Singly reinforced Ast 1300.000 mm2
DRS-NA
-0.001872 DRS-NA
7.82775 DRS-NA
-6446.760 DRS-NA
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a 1127.712 mm DRS-NA
yf=0.15*xu+0.65*Df 331.657 mm DRS-NA
Lever Arm z = jd 1270.372 DRS-NA
14055.402 mm2
DRS-NA
DRS-NA GO TO 2 (C)
Hit and Trial α = Xu/d 0.1445 DRS-NA
α is chosen to make Test : C - T = 0 -28.0871 DRS-NA
For avg. web +flange balanced section Ast,max
For (web +Flange) balanced section Ast,max
Force of Tension, T
a= - 0.14976*fck*bw - 0.0050175*fck*(bf - bw)
For Df/d > 0.2 Ast
2 (B) IF Df/d < = 0.2
average web +flange Muw= 0.36*fck*bw*Xu,max*(d-
0.416*Xu,max) + 0.446*fck*(bf-bw)*yf*(d-0.5*yf,max)
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
b= 0.36*fck*bw*d + 0.00669*fck*(bf - bw)
c= 0.2899*fck*Df*(bf - bw)*(d-0.325*Df)-Mu
Neutral Axis for balanced design Xu 251.36 mm DRS-NA
yf 200.20 mm DRS-NA
Compressive force for straight portion, C1 600.57 KN DRS-NA
Compressive force fo rParabolic portion, C2 533.84 KN DRS-NA
Compressive force Trap.Web, Cu = C1+C2 1134.40 KN DRS-NA
Compressive force for Flange portion, C3 0.00 KN DRS-NA
Compressive force for Small Flange portion, C4 0.00 KN DRS-NA
Total Compressive force, C 1134.40 KN DRS-NA
Moment of C1 about Neutral Axis, Integration I1 118608.90 KNmm DRS-NA
Moment C2 about Neutral Axis Integration I2 47922.79 KNmm DRS-NA
Moment f Cu about neutral axis Integration Iu 166531.69 KNmm DRS-NA
CG of Cu from Neutral axis ,Y 146.801 mm DRS-NA
CG of Cu from Extreme Comprssion fibre X 104.556 mm DRS-NA
For average web only X/d 0.0601071 DRS-NA
CG C from Extreme Compression fibre Xmax 104.556 mm DRS-NA
1849.29 KNm DRS-NA
Mu (Only for trapezodal Web) 1854.68 KNm DRS-NA
Mu,lim (trapezodal Web + Flange) 1854.68 KNm DRS-NA
-4592.08 KNm DRS-NA
1634.935 mm DRS-NA
1634.944 mm DRS-NA
3132.834 mm2
DRS-NA
3141.951 mm2
DRS-NA
For Tension Area of Steel, Ast2 0.00 mm2
DRS-NA
for BM+Tension, total rqd. Steel, Ast 3141.95 mm2
DRS-NA
3943.11 KN DRS-NA
Neutral Axis, Xu 251.358 DRS-NA
Due to Mu Compressive strain Ɛcc 0.00106 DRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00119 < 0.0035 DRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 3000.000 mm2
DRS-NA
Due To Fx, Additional compressive stress fsc 27.88 N/mm2
DRS-NA
Additional compressive stress fcc 1.496 N/mm2
DRS-NA
Pu 1425.719 KN DRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00013902 DRS-NA DRS-NA
Test : Fx-Pu =0 0.000000 DRS-NA
Extra Increased area 0.000 mm2
DRS-NA
Required Singly reinforced Ast 3000.000 mm2
DRS-NA
-0.001872000 DRS-NA
b= 0.36*fck*bw*d 7.82775000 DRS-NA
-6446.76001 DRS-NA
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a 1127.712 DRS-NA
Lever Arm z = jd 1270.372 DRS-NA
For (web +Flange) balanced section Ast
average web +flange Muw = 0.36*fck*bw*Xu,max*(d-
0.416*Xu,max) + 0.446*fck*(bf-bw)*yf*(d-0.5*yf,max)
a= -0.14976*fck*bw
c= 0.446*fck*Df*(bf - bw)*(d-0.5*Df)-Mu
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast
Force of Tension, T
14055.402 mm2
DRS-NA
2 (C) Condition: Doubly Reinforced Section YES
Number of Layer of Comression bar 5.00 No.
Dia of Main reinforcement in compression 25 mm
Spacer for Vertical spacing 32 mm
Dia of Stirrups 8.00 mm
Clear cover, C 40.00 mm
Charactertistics strength of Concrete fck 25.00 N/mm2
Yield stress of steel fy 415.00 N/mm2
Helping calculation, d'' 57.00 mm
Effective depth from in compression side d' 174.50 mm
Effective depth at tension side d 1739.50 mm
Neutral Axis depth ration Xu,max/d 0.479
Neutral Axis Depth Xu.max 833.41 mmm
Compression level strain Ɛsc Or Ɛcc 0.00277
Compressive level stress of steel fsc 352.086 N/mm2
Compressive level stress of concrete fcc=446*fck*(Ԑcc-250*Ԑcc^2)11.150 N/mm2
Area of compressive stress Asc 2263.980 mm2
2137.854 mm2
For DRS Total Area of tension steel Ast 12555.379 mm2
for Tension, Area of Steel, Ast3 0.00 mm2
for BM+Tension, total rqd. Steel, Ast 12555.38 mm2
Neutral Axis, Xu 833.407 mm
Due to Mu Compressive strain Ɛcc 0.00350
Total Strain due to (Mu+P) Ɛcct 0.003500 < 0.0035 OK
for BM+compression, TrialTotal Rqd. Steel, Ast 12867.960 mm2
Due To Fx, Additional compressive stress fsc 31.71 N/mm2
Additional compressive stress fcc 1.693 N/mm2
Pu 1909.887 KN
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00015808 YES
Test : Fx-Pu =0 0.000000
Extra Increased area 312.581 mm2
Required Double reinforced Ast 12867.960 mm2
Check for Shear forceDesign Shear force 1557.21 KN
Shear stress 1.628 N/mm2
Percentage of tension steel, pt 1.467 %
Percentage of compressive steel, pc 0.282 %
For Df/d < 0.2 Ast
for Asc, Area of tension steel Ast2
Percentage of tension and compressive steel, pt 5.098 %
α=0.8*fck/6.89*pt 0.569
tc = 0.85*SQRT(0.8*fck)*(SQRT(1+5*α)-1)/6*α 1.070 N/mm2
1.00 x 1.070 = 1.070
> 1.628 Not OK
Shear Reinforcement is required.
Dia of of Vertical Stirrups 8.00 mm
Number of leg 2.00
Planned area to Provide Asv 100.53 mm2
Required spacing of stirrups Svreqd. 130.104 mm
Plan to Provide, spacing of stirrups Sv 100.000
Minimum required Asv 0.4*b*Sv/0.87*fy 55.3940 mm2
Ф 5.9384 mm
Rqd. Stirrups Ф 8.00 Leg 2.000 100.00 mm C/C
Permissible shear stress,
K´tc =
Out Put:Note : DRS = Doubly Reinforced Section, SRS = Singly Reinforced Section, NA = Not Applicable
Rqd. tensile Steel Reinforecement, Ast 3210.46 mm2
Provide 25 Ф bar 6.54 Nos. Say 7.00 Nos.
Rqd. Compressive Steel Reinforecement, Asc 3216.99 mm2
Provide 25 Ф bar 6.55 Nos. Say 7.00 Nos.
Stirrups Provided:
Provide 8 Ф bar Spacing 200.00 mm @ C/C Leg = 2
Crack Width Calculation:Stress in tensile reinforced level fsb 155.29 N/mm
2
Spacing of reinforcement S 54.833 mm
acr = ((S / 2)^2+d'^2)^0.5 - Dia /2 = 53.922 mm
Ɛ1b = [fs*((a' - xu) / [(d-xu)*2*10 ^5] 0.0008176
Ɛ2b= bt*(a'-xu)*(D-xu) / [600000*Ast*(d - xu)] 0.0004343
Ɛmb = Ɛ1b-Ɛ2b 0.0003833
0.0610487
Stress in tensile reinforced level fst 85.422 N/mm2
Ɛ1t= fs*(a' - (-D)) / [(d- (-D))*2*10 ^5] 0.0004379
Ɛ2t= bt*(a'-(-D))*(D-(-D)) / [600000*Ast*(d - (-D))] 0.0008623
Ɛmt = Ɛ1t-Ɛ2t -0.0004244
-0.0681247
-0.0070760 < 0.2
INPUT DATA:- Governing Load Case For Design LC 544
INPUT DATA:- Axial force, Torsion Moments, Bending moments and Shear force:
Design Shear force, Fy 620.99 KN LC 251
Design Torsional Moment for shear Tu=Mx 67.38 KNm LC 251
Moment M'uz 1667.71 KN LC 544
Design Torsional Moment for moment Tu=Mx 21.05 KNm LC 544
Axial Force, Fx 411.36 KN T LC 544
Bending in another direction Muy 12.3 KNm LC 544
INPUT DATA:- Material Properties :
Characteristic Strength of concrete, fck 25.00 N/mm2
Grade of Steel, fy 415.00 N/mm2
INPUT DATA:- Material Properties and Dimensions of Beam:
Thickness of flange, Df 250.00 mm
Total Depth of T- Beam, D 1800.00 mm
Width of Flange, bf 2400.00 mm
Width of web in compression fibre, bcw 450.00 mm
Width of web in tension, btw' 450.00 mm
Layer of bar in tension zone 2.00
MOLUNG KHOLA BRIDGE MEMBER
T - Beam with Trapezoidal Web, memb. No. 225 (32.5m)
Wcrb = 3*acr*Ɛm/ [1+2*(acr - Cmin) / (D - xu)]
Wcrt = 3*acr x Ɛm / [1+2*(acr - Cmin) / (D - (-D))]
Wcr =Wcrb+Wcrt
Cover, C 40.00 mm
Stirrups of Design purpose 8.00 mm
Dia of bar for design purpose 25.00 mm
Spacer for vertical spacing 32.00 mm
Calculations of required Design Moments, Shear forces:
Resultant Moment of ( Muy and Muz') = M''uz 1206.81 KNm
Design Moment Mu 1268.73 KNm
Design shear force Vu 860.56 KN
Calculations of required Section properties:
Width of web in reiforcement level in tension, btw 450.00 mm
Width of Web, Average btw 450.00 mm
Effective Depth , d (Calculated) 1711.00 mm
Width of small portion in the flange, bs 0.000 mm
Centroid of Section from Compression fibre Cc 590.443 mm
Centoid of section from tension fibre Ct 1209.557 mm
Df/d (Calculated) 0.146
RESULT IN ACCORDANCE WITH DIFFERENT CONDITIONS:
1. Condition: If Neutral Axis lies in the flange? YES
Muf, lim= 0.36*fck*bf*Df*(d-0.416*Df) 8677.85 KNm
7409.120 KNm
Neutral Axis lies in the Flange? YES
For Mu or Mu,lim Area of Steel, Ast 2071.10 mm2
For Tension Area of Steel, Ast2 1139.35 mm2
for BM+Tension, total rqd. Steel, Ast 3210.46 mm2
Neutral Axis Ratio, Xu/d 0.02023
Neutral Axis, Xu 34.621 mm
Due to Mu Compressive strain Ɛcc 0.00015
Total Strain due to (Mu+Fx) Ɛcct 0.00027 < 0.0035 OK
for BM+compression, TrialTotal Rqd. Steel, Ast 10455.000 mm2
Due To Fx, Additional compressive stress fsc NA N/mm2
Additional compressive stress fcc NA N/mm2
Pu NA KN
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00012170 NA
Test : Fx-Pu =0 NA
for BM+compression, Extra Increased area Ast 0.000 mm2
Required Ast 3210.455 mm2
2. Condition: If Neutral Axis lies in the webNeutral Axis lies in the Web NA
Neutral axis depth ratio α = Xu,max/d 0.4791
Maximum Neutral Axis for balanced design Xu,max 819.75 mm NA
yf,max 285.46 mm NA
Test : Muf,lim > Mu for Neutral in flange
Compressive force for straight portion, C1 1762.76 KN NA
Compressive force fo rParabolic portion, C2 1566.90 KN NA
Compressive force Trap. Web, Cu = C1+C2 3329.66 KN NA
Compressive force for Flange portion, C3 5435.63 KN NA
Compressive force for Small Flange portion, C4 0.00 KN NA
Total Compressive force, C 8765.29 KN NA
Moment of C1 about Neutral Axis, Integration I1 1135379.86 KNmm NA
Moment C2 about Neutral Axis Integration I2 458739.34 KNmm NA
Moment f Cu about neutral axis Integration Iu 1594119.20 KNmm NA
CG of Cu from Neutral axis ,Y 478.763 mm NA
CG of Cu from Extreme Compression fibre X 340.990 mm NA
For average web only X/d 0.19929 NA
CG C from Extreme Compression fibre X 207.048 mm NA
13182.48 KNm NA
Capacity Mu, lim (Only for trapezodal Web) 4561.67 KNm NA
Capacity Mu, lim (trapezodal Web + Flange) 13182.57 KNm NA
-11913.85 KNm SRS
1504.090 mm NA
1503.952 mm NA
24274.821 mm2
NA
24277.207 mm2
NA
-0.001929
11.97979
-9893.202
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a 980.733 mm
yf=0.15*xu+0.65*Df 309.610 mm
Lever Arm z = jd 1701.067
21464.036 mm2
NA GO TO 1
Hit and Trial α = Xu/d 0.300000 SRS-NA
0.00000 SRS-NA
Neutral Axis for balanced design Xu 513.30 mm SRS-NA
yf,max 239.50 mm SRS-NA
Compressive force for straight portion, C1 0.00 KN SRS-NA
Compressive force fo rParabolic portion, C2 0.00 KN SRS-NA
Compressive force Trap.Web, Cu = C1+C2 0.00 KN SRS-NA
Compressive force for Flange portion, C3 0.00 KN SRS-NA
Compressive force for Small Flange portion, C4 0.00 KN SRS-NA
Total Compressive force, C 0.00 KN SRS-NA
a= - 0.14976*fck*bw - 0.0050175*fck*(bf - bw)
b= 0.36*fck*bw*d + 0.00669*fck*(bf - bw)
c= 0.2899*fck*Df*(bf - bw)*(d-0.325*Df)-Mu
For Df/d > 0.2 Ast
2 (A) IF Df/d > 0.2
α is chosen to make Test : C = T
Capacity if average web +flange Muw, lim=
0.36*fck*bw*Xu,max*(d-0.416*Xu,max) + 0.446*fck*(bf-
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast,max
For (web +Flange) balanced section Ast,max
Moment of C1 about Neutral Axis, Integration I1 NA KNmm SRS-NA
Moment C2 about Neutral Axis Integration I2 0.00 KNmm SRS-NA
Moment f Cu about neutral axis Integration Iu 0.00 KNmm SRS-NA
CG of Cu from Neutral axis ,Y 0.000 mm SRS-NA
CG of Cu from Extreme Comprssion fibre X 0.000 mm SRS-NA
For average web only X/d 0.00000 SRS-NA
CG C from Extreme Compression fibre X 0.000 mm SRS-NA
0.00 KNm SRS-NA
Mu(Only for trapezodal Web) 0.00 KNm SRS-NA
Mu,lim (trapezodal Web + Flange) 0.00 KNm SRS-NA
0.00 KNm SRS-NA
0.000 mm SRS-NA
0.000 mm SRS-NA
0.000 mm2
SRS-NA
0.00 mm2
SRS-NA
For Tension Area of Steel, Ast2 1139.35 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 1139.35 mm2
SRS-NA
NA KN SRS-NA
Neutral Axis, Xu 0.00 mm SRS-NA
Due to Mu Compressive strain Ɛcc 0.00000 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00002 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 1300.000 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc NA N/mm2
SRS-NA
Additional compressive stress fcc NA N/mm2
SRS-NA
Pu 0.000 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00001938 YES SRS-NA
Test : Fx-Pu =0 NA SRS-NA
Extra Increased area 0.000 mm2
SRS-NA
Required Singly reinforced Ast 1139.353 mm2
SRS-NA
-0.001929 SRS-NA
11.97979 SRS-NA
4489.436 SRS-NA
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a -354.510 mm SRS-NA
yf=0.15*xu+0.65*Df 109.324 mm SRS-NA
Lever Arm z = jd 1347.985 SRS-NA
2606.845 mm2
SRS-NA
NA GO TO 1
Hit and Trial α = Xu/d 0.0983 SRS-NA
α is chosen to make Test : C - T = 0 0.0000 SRS-NA
Force of Tension, T
a= - 0.14976*fck*bw - 0.0050175*fck*(bf - bw)
b= 0.36*fck*bw*d + 0.00669*fck*(bf - bw)
c= 0.2899*fck*Df*(bf - bw)*(d-0.325*Df)-Mu
For Df/d > 0.2 Ast
2 (B) IF Df/d < = 0.2
average web +flange Muw= 0.36*fck*bw*Xu,max*(d-
0.416*Xu,max) + 0.446*fck*(bf-bw)*yf*(d-0.5*yf,max)
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast,max
For (web +Flange) balanced section Ast,max
Neutral Axis for balanced design Xu 0.00 mm SRS-NA
yf 0.00 mm SRS-NA
Compressive force for straight portion, C1 0.00 KN SRS-NA
Compressive force fo rParabolic portion, C2 0.00 KN SRS-NA
Compressive force Trap.Web, Cu = C1+C2 0.00 KN SRS-NA
Compressive force for Flange portion, C3 0.00 KN SRS-NA
Compressive force for Small Flange portion, C4 0.00 KN SRS-NA
Total Compressive force, C 0.00 KN SRS-NA
Moment of C1 about Neutral Axis, Integration I1 0.00 KNmm SRS-NA
Moment C2 about Neutral Axis Integration I2 0.00 KNmm SRS-NA
Moment f Cu about neutral axis Integration Iu 0.00 KNmm SRS-NA
CG of Cu from Neutral axis ,Y 0.000 mm SRS-NA
CG of Cu from Extreme Comprssion fibre X 0.000 mm SRS-NA
For average web only X/d 0.0000000 SRS-NA
CG C from Extreme Compression fibre Xmax 0.000 mm SRS-NA
0.00 KNm SRS-NA
Mu (Only for trapezodal Web) 0.00 KNm SRS-NA
Mu,lim (trapezodal Web + Flange) 0.00 KNm SRS-NA
0.00 KNm SRS-NA
0.000 mm SRS-NA
0.000 mm SRS-NA
0.000 mm2
SRS-NA
0.000 mm2
SRS-NA
For Tension Area of Steel, Ast2 1139.35 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 1139.35 mm2
SRS-NA
0.00 KN SRS-NA
Neutral Axis, Xu 0.000 SRS-NA
Due to Mu Compressive strain Ɛcc 0.00000 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00014 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 3000.000 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc 0.00 N/mm2
SRS-NA
Additional compressive stress fcc 0.000 N/mm2
SRS-NA
Pu 0.000 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00013902 SRS-NA SRS-NA
Test : Fx-Pu =0 0.000000 SRS-NA
Extra Increased area 0.000 mm2
SRS-NA
Required Singly reinforced Ast 1139.353 mm2
SRS-NA
0.000000000 SRS-NA
b= 0.36*fck*bw*d 0.00000000 SRS-NA
0.00000 SRS-NA
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a 0.000 SRS-NA
Lever Arm z = jd 0.000 SRS-NA
Force of Tension, T
a= -0.14976*fck*bw
c= 0.446*fck*Df*(bf - bw)*(d-0.5*Df)-Mu
average web +flange Muw = 0.36*fck*bw*Xu,max*(d-
0.416*Xu,max) + 0.446*fck*(bf-bw)*yf*(d-0.5*yf,max)
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast
For (web +Flange) balanced section Ast
0.000 mm2
SRS-NA
2 (C) Condition: Doubly Reinforced Section GO TO 1
Number of Layer of Comression bar 2.00 No. SRS-NA
Dia of Main reinforcement in compression 25 mm SRS-NA
Spacer for Vertical spacing 32 mm SRS-NA
Dia of Stirrups 8.00 mm SRS-NA
Clear cover, C 40.00 mm SRS-NA
Charactertistics strength of Concrete fck 25.00 N/mm2 SRS-NA
Yield stress of steel fy 415.00 N/mm2 SRS-NA
Helping calculation, d'' 57.00 mm SRS-NA
Effective depth from in compression side d' 89.00 mm SRS-NA
Effective depth at tension side d 1711.00 mm SRS-NA
Neutral Axis depth ration Xu,max/d 0.479 SRS-NA
Neutral Axis Depth Xu.max 819.75 mmm SRS-NA
Compression level strain Ɛsc Or Ɛcc 0.00312 SRS-NA
Compressive level stress of steel fsc 355.148 N/mm2 SRS-NA
Compressive level stress of concrete fcc=446*fck*(Ԑcc-250*Ԑcc^2) 11.150 N/mm2 SRS-NA
Area of compressive stress Asc -21352.309 mm2
SRS-NA
-20343.879 mm2
SRS-NA
For DRS Total Area of tension steel Ast 3933.328 mm2
SRS-NA
for Tension, Area of Steel, Ast3 21483.23 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 25416.56 mm2
SRS-NA
Neutral Axis, Xu 819.753 mm SRS-NA
Due to Mu Compressive strain Ɛcc 0.00350 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00362 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 12063.716 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc NA N/mm2
SRS-NA
Additional compressive stress fcc NA N/mm2
SRS-NA
Pu 0.000 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00012335 YES SRS-NA
Test : Fx-Pu =0 0.000000 SRS-NA
Extra Increased area 0.000 mm2
SRS-NA
Required Double reinforced Ast 25416.560 mm2
SRS-NA
Check for Shear forceDesign Shear force 860.56 KN
Shear stress 1.118 N/mm2
Percentage of tension steel, pt 0.446 %
Percentage of compressive steel, pc 0.446 %
For Df/d < 0.2 Ast
for Asc, Area of tension steel Ast2
Percentage of tension and compressive steel, pt 4.613 %
α=0.8*fck/6.89*pt 0.629
tc = 0.85*SQRT(0.8*fck)*(SQRT(1+5*α)-1)/6*α 1.043 N/mm2
1.00 x 1.043 = 1.043
> 1.118 NOT OK
Shear Reinforcement is required.
Dia of of Vertical Stirrups 8.00 mm
Number of leg 2.00
Planned area to Provide Asv 100.53 mm2
Required spacing of stirrups Svreqd. 1084.332 mm
Plan to Provide, spacing of stirrups Sv 200.000
Minimum required Asv 0.4*b*Sv/0.87*fy 99.7092 mm2
Ф 7.9672 mm
Rqd. Stirrups Ф 8.00 Leg 2.000 200.00 mm C/C
Permissible shear stress,
K´tc =
Out Put:Note : DRS = Doubly Reinforced Section, SRS = Singly Reinforced Section, NA = Not Applicable
Rqd. tensile Steel Reinforecement, Ast 6680.54 mm2
Provide 25 Ф bar 13.61 Nos. Say 14.00 Nos.
Rqd. Compressive Steel Reinforecement, Asc 1608.50 mm2
Provide 25 Ф bar 3.28 Nos. Say 3.00 Nos.
Stirrups Provided:
Provide 8 Ф bar Spacing 200.00 mm @ C/C Leg = 2
Crack Width Calculation:Stress in tensile reinforced level fsb 114.33 N/mm
2
Spacing of reinforcement S 25.308 mm
acr = ((S / 2)^2+d'^2)^0.5 - Dia /2 = 49.309 mm
Ɛ1b = [fs*((a' - xu) / [(d-xu)*2*10 ^5] 0.0006293
Ɛ2b= bt*(a'-xu)*(D-xu) / [600000*Ast*(d - xu)] 0.0002159
Ɛmb = Ɛ1b-Ɛ2b 0.0004134
0.0605038
Stress in tensile reinforced level fst 126.381 N/mm2
Ɛ1t= fs*(a' - (-D)) / [(d- (-D))*2*10 ^5] 0.0006613
Ɛ2t= bt*(a'-(-D))*(D-(-D)) / [600000*Ast*(d - (-D))] 0.0004230
Ɛmt = Ɛ1t-Ɛ2t 0.0002383
0.0350757
0.0955795 < 0.2
INPUT DATA:- Governing Load Case For Design LC 224
INPUT DATA:- Axial force, Torsion Moments, Bending moments and Shear force:
Design Shear force, Fy 186.39 KN LC 268
Design Torsional Moment for shear Tu=Mx 8.32 KNm LC 268
Moment M'uz 3173.95 KN LC 224
Design Torsional Moment for moment Tu=Mx 2.97 KNm LC 224
Axial Force, Fx 1266.44 KN T LC 224
Bending in another direction Muy 20.1 KNm LC 224
INPUT DATA:- Material Properties :
Characteristic Strength of concrete, fck 25.00 N/mm2
Grade of Steel, fy 415.00 N/mm2
INPUT DATA:- Material Properties and Dimensions of Beam:
Thickness of flange, Df 250.00 mm
Total Depth of T- Beam, D 1800.00 mm
Width of Flange, bf 2400.00 mm
Width of web in compression fibre, bcw 450.00 mm
Width of web in tension, btw' 450.00 mm
Layer of bar in tension zone 4.00
MOLUNG KHOLA BRIDGE MEMBER
T - Beam with Trapezoidal Web, memb. No. 240 (40m)
Wcrb = 3*acr*Ɛm/ [1+2*(acr - Cmin) / (D - xu)]
Wcrt = 3*acr x Ɛm / [1+2*(acr - Cmin) / (D - (-D))]
Wcr =Wcrb+Wcrt
Cover, C 40.00 mm
Stirrups of Design purpose 8.00 mm
Dia of bar for design purpose 32.00 mm
Spacer for vertical spacing 32.00 mm
Calculations of required Design Moments, Shear forces:
Resultant Moment of ( Muy and Muz') = M''uz 1844.85 KNm
Design Moment Mu 1853.59 KNm
Design shear force Vu 215.97 KN
Calculations of required Section properties:
Width of web in reiforcement level in tension, btw 450.00 mm
Width of Web, Average btw 450.00 mm
Effective Depth , d (Calculated) 1640.00 mm
Width of small portion in the flange, bs 0.000 mm
Centroid of Section from Compression fibre Cc 590.443 mm
Centoid of section from tension fibre Ct 1209.557 mm
Df/d (Calculated) 0.152
RESULT IN ACCORDANCE WITH DIFFERENT CONDITIONS:
1. Condition: If Neutral Axis lies in the flange? YES
Muf, lim= 0.36*fck*bf*Df*(d-0.416*Df) 8294.45 KNm
6440.858 KNm
Neutral Axis lies in the Flange? YES
For Mu or Mu,lim Area of Steel, Ast 3172.87 mm2
For Tension Area of Steel, Ast2 3507.67 mm2
for BM+Tension, total rqd. Steel, Ast 6680.54 mm2
Neutral Axis Ratio, Xu/d 0.03234
Neutral Axis, Xu 53.039 mm
Due to Mu Compressive strain Ɛcc 0.00024
Total Strain due to (Mu+Fx) Ɛcct 0.00036 < 0.0035 OK
for BM+compression, TrialTotal Rqd. Steel, Ast 10455.000 mm2
Due To Fx, Additional compressive stress fsc NA N/mm2
Additional compressive stress fcc NA N/mm2
Pu NA KN
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00012170 NA
Test : Fx-Pu =0 NA
for BM+compression, Extra Increased area Ast 0.000 mm2
Required Ast 6680.540 mm2
2. Condition: If Neutral Axis lies in the webNeutral Axis lies in the Web NA
Neutral axis depth ratio α = Xu,max/d 0.4791
Maximum Neutral Axis for balanced design Xu,max 785.74 mm NA
yf,max 280.36 mm NA
Test : Muf,lim > Mu for Neutral in flange
Compressive force for straight portion, C1 1689.61 KN NA
Compressive force fo rParabolic portion, C2 1501.88 KN NA
Compressive force Trap. Web, Cu = C1+C2 3191.49 KN NA
Compressive force for Flange portion, C3 5435.63 KN NA
Compressive force for Small Flange portion, C4 0.00 KN NA
Total Compressive force, C 8627.12 KN NA
Moment of C1 about Neutral Axis, Integration I1 1043107.01 KNmm NA
Moment C2 about Neutral Axis Integration I2 421457.38 KNmm NA
Moment f Cu about neutral axis Integration Iu 1464564.39 KNmm NA
CG of Cu from Neutral axis ,Y 458.896 mm NA
CG of Cu from Extreme Compression fibre X 326.840 mm NA
For average web only X/d 0.19929 NA
CG C from Extreme Compression fibre X 199.668 mm NA
12425.83 KNm NA
Capacity Mu, lim (Only for trapezodal Web) 4190.94 KNm NA
Capacity Mu, lim (trapezodal Web + Flange) 12425.91 KNm NA
-10572.33 KNm SRS
1440.459 mm NA
1440.332 mm NA
23892.256 mm2
NA
23894.523 mm2
NA
-0.001929
11.46068
-9387.398
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a 981.163 mm
yf=0.15*xu+0.65*Df 309.674 mm
Lever Arm z = jd 1630.066
21113.278 mm2
NA GO TO 1
Hit and Trial α = Xu/d 0.300000 SRS-NA
0.00000 SRS-NA
Neutral Axis for balanced design Xu 492.00 mm SRS-NA
yf,max 236.30 mm SRS-NA
Compressive force for straight portion, C1 0.00 KN SRS-NA
Compressive force fo rParabolic portion, C2 0.00 KN SRS-NA
Compressive force Trap.Web, Cu = C1+C2 0.00 KN SRS-NA
Compressive force for Flange portion, C3 0.00 KN SRS-NA
Compressive force for Small Flange portion, C4 0.00 KN SRS-NA
Total Compressive force, C 0.00 KN SRS-NA
a= - 0.14976*fck*bw - 0.0050175*fck*(bf - bw)
b= 0.36*fck*bw*d + 0.00669*fck*(bf - bw)
c= 0.2899*fck*Df*(bf - bw)*(d-0.325*Df)-Mu
For Df/d > 0.2 Ast
2 (A) IF Df/d > 0.2
α is chosen to make Test : C = T
Capacity if average web +flange Muw, lim=
0.36*fck*bw*Xu,max*(d-0.416*Xu,max) + 0.446*fck*(bf-
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast,max
For (web +Flange) balanced section Ast,max
Moment of C1 about Neutral Axis, Integration I1 NA KNmm SRS-NA
Moment C2 about Neutral Axis Integration I2 0.00 KNmm SRS-NA
Moment f Cu about neutral axis Integration Iu 0.00 KNmm SRS-NA
CG of Cu from Neutral axis ,Y 0.000 mm SRS-NA
CG of Cu from Extreme Comprssion fibre X 0.000 mm SRS-NA
For average web only X/d 0.00000 SRS-NA
CG C from Extreme Compression fibre X 0.000 mm SRS-NA
0.00 KNm SRS-NA
Mu(Only for trapezodal Web) 0.00 KNm SRS-NA
Mu,lim (trapezodal Web + Flange) 0.00 KNm SRS-NA
0.00 KNm SRS-NA
0.000 mm SRS-NA
0.000 mm SRS-NA
0.000 mm2
SRS-NA
0.00 mm2
SRS-NA
For Tension Area of Steel, Ast2 3507.67 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 3507.67 mm2
SRS-NA
NA KN SRS-NA
Neutral Axis, Xu 0.00 mm SRS-NA
Due to Mu Compressive strain Ɛcc 0.00000 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00002 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 1300.000 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc NA N/mm2
SRS-NA
Additional compressive stress fcc NA N/mm2
SRS-NA
Pu 0.000 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00001938 YES SRS-NA
Test : Fx-Pu =0 NA SRS-NA
Extra Increased area 0.000 mm2
SRS-NA
Required Singly reinforced Ast 3507.667 mm2
SRS-NA
-0.001929 SRS-NA
11.46068 SRS-NA
3653.720 SRS-NA
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a -303.316 mm SRS-NA
yf=0.15*xu+0.65*Df 117.003 mm SRS-NA
Lever Arm z = jd 1409.041 SRS-NA
3643.528 mm2
SRS-NA
NA GO TO 1
Hit and Trial α = Xu/d 0.2418 SRS-NA
α is chosen to make Test : C - T = 0 0.0000 SRS-NA
Force of Tension, T
a= - 0.14976*fck*bw - 0.0050175*fck*(bf - bw)
b= 0.36*fck*bw*d + 0.00669*fck*(bf - bw)
c= 0.2899*fck*Df*(bf - bw)*(d-0.325*Df)-Mu
For Df/d > 0.2 Ast
2 (B) IF Df/d < = 0.2
average web +flange Muw= 0.36*fck*bw*Xu,max*(d-
0.416*Xu,max) + 0.446*fck*(bf-bw)*yf*(d-0.5*yf,max)
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast,max
For (web +Flange) balanced section Ast,max
Neutral Axis for balanced design Xu 0.00 mm SRS-NA
yf 0.00 mm SRS-NA
Compressive force for straight portion, C1 0.00 KN SRS-NA
Compressive force fo rParabolic portion, C2 0.00 KN SRS-NA
Compressive force Trap.Web, Cu = C1+C2 0.00 KN SRS-NA
Compressive force for Flange portion, C3 0.00 KN SRS-NA
Compressive force for Small Flange portion, C4 0.00 KN SRS-NA
Total Compressive force, C 0.00 KN SRS-NA
Moment of C1 about Neutral Axis, Integration I1 0.00 KNmm SRS-NA
Moment C2 about Neutral Axis Integration I2 0.00 KNmm SRS-NA
Moment f Cu about neutral axis Integration Iu 0.00 KNmm SRS-NA
CG of Cu from Neutral axis ,Y 0.000 mm SRS-NA
CG of Cu from Extreme Comprssion fibre X 0.000 mm SRS-NA
For average web only X/d 0.0000000 SRS-NA
CG C from Extreme Compression fibre Xmax 0.000 mm SRS-NA
0.00 KNm SRS-NA
Mu (Only for trapezodal Web) 0.00 KNm SRS-NA
Mu,lim (trapezodal Web + Flange) 0.00 KNm SRS-NA
0.00 KNm SRS-NA
0.000 mm SRS-NA
0.000 mm SRS-NA
0.000 mm2
SRS-NA
0.000 mm2
SRS-NA
For Tension Area of Steel, Ast2 3507.67 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 3507.67 mm2
SRS-NA
0.00 KN SRS-NA
Neutral Axis, Xu 0.000 SRS-NA
Due to Mu Compressive strain Ɛcc 0.00000 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00014 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 3000.000 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc 0.00 N/mm2
SRS-NA
Additional compressive stress fcc 0.000 N/mm2
SRS-NA
Pu 0.000 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00013902 SRS-NA SRS-NA
Test : Fx-Pu =0 0.000000 SRS-NA
Extra Increased area 0.000 mm2
SRS-NA
Required Singly reinforced Ast 3507.667 mm2
SRS-NA
0.000000000 SRS-NA
b= 0.36*fck*bw*d 0.00000000 SRS-NA
0.00000 SRS-NA
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a 0.000 SRS-NA
Lever Arm z = jd 0.000 SRS-NA
Force of Tension, T
a= -0.14976*fck*bw
c= 0.446*fck*Df*(bf - bw)*(d-0.5*Df)-Mu
average web +flange Muw = 0.36*fck*bw*Xu,max*(d-
0.416*Xu,max) + 0.446*fck*(bf-bw)*yf*(d-0.5*yf,max)
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast
For (web +Flange) balanced section Ast
0.000 mm2
SRS-NA
2 (C) Condition: Doubly Reinforced Section GO TO 1
Number of Layer of Comression bar 1.00 No. SRS-NA
Dia of Main reinforcement in compression 32 mm SRS-NA
Spacer for Vertical spacing 32 mm SRS-NA
Dia of Stirrups 8.00 mm SRS-NA
Clear cover, C 40.00 mm SRS-NA
Charactertistics strength of Concrete fck 25.00 N/mm2 SRS-NA
Yield stress of steel fy 415.00 N/mm2 SRS-NA
Helping calculation, d'' 64.00 mm SRS-NA
Effective depth from in compression side d' 64.00 mm SRS-NA
Effective depth at tension side d 1640.00 mm SRS-NA
Neutral Axis depth ration Xu,max/d 0.479 SRS-NA
Neutral Axis Depth Xu.max 785.74 mmm SRS-NA
Compression level strain Ɛsc Or Ɛcc 0.00321 SRS-NA
Compressive level stress of steel fsc 355.972 N/mm2 SRS-NA
Compressive level stress of concrete fcc=446*fck*(Ԑcc-250*Ԑcc^2) 11.150 N/mm2 SRS-NA
Area of compressive stress Asc -19454.466 mm2
SRS-NA
-18580.053 mm2
SRS-NA
For DRS Total Area of tension steel Ast 5314.470 mm2
SRS-NA
for Tension, Area of Steel, Ast3 22087.72 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 27402.19 mm2
SRS-NA
Neutral Axis, Xu 785.736 mm SRS-NA
Due to Mu Compressive strain Ɛcc 0.00350 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00362 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 12063.716 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc NA N/mm2
SRS-NA
Additional compressive stress fcc NA N/mm2
SRS-NA
Pu 0.000 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00012335 YES SRS-NA
Test : Fx-Pu =0 0.000000 SRS-NA
Extra Increased area 0.000 mm2
SRS-NA
Required Double reinforced Ast 27402.190 mm2
SRS-NA
Check for Shear forceDesign Shear force 215.97 KN
Shear stress 0.293 N/mm2
Percentage of tension steel, pt 0.931 %
Percentage of compressive steel, pc 0.200 %
For Df/d < 0.2 Ast
for Asc, Area of tension steel Ast2
Percentage of tension and compressive steel, pt 4.851 %
α=0.8*fck/6.89*pt 0.598
tc = 0.85*SQRT(0.8*fck)*(SQRT(1+5*α)-1)/6*α 1.057 N/mm2
1.00 x 1.057 = 1.057
> 0.293 OK
Shear Reinforcement is NOT required.
Dia of of Vertical Stirrups 8.00 mm
Number of leg 2.00
Planned area to Provide Asv 100.53 mm2
Required spacing of stirrups Svreqd. -105.577 mm
Plan to Provide, spacing of stirrups Sv 200.000
Minimum required Asv 0.4*b*Sv/0.87*fy 99.7092 mm2
Ф 7.9672 mm
Rqd. Stirrups Ф 8.00 Leg 2.000 200.00 mm C/C
Permissible shear stress,
K´tc =
Out Put:Note : DRS = Doubly Reinforced Section, SRS = Singly Reinforced Section, NA = Not Applicable
Rqd. tensile Steel Reinforecement, Ast 318.80 mm2
Provide 20 Ф bar 1.01 Nos. Say 1.00 Nos.
Rqd. Compressive Steel Reinforecement, Asc 628.00 mm2
Provide 20 Ф bar 2.00 Nos. Say 2.00 Nos.
Stirrups Provided:
Provide 8 Ф bar Spacing 300.00 mm @ C/C Leg = 2
Crack Width Calculation:Stress in tensile reinforced level fsb 240.72 N/mm
2
Spacing of reinforcement S #DIV/0! mm
acr = ((S / 2)^2+d'^2)^0.5 - Dia /2 = #DIV/0! mm
Ɛ1b = [fs*((a' - xu) / [(d-xu)*2*10 ^5] 0.0012535
Ɛ2b= bt*(a'-xu)*(D-xu) / [600000*Ast*(d - xu)] 0.0023804
Ɛmb = Ɛ1b-Ɛ2b -0.0011269
#DIV/0!
Stress in tensile reinforced level fst 0.000 N/mm2
Ɛ1t= fs*(a' - (-D)) / [(d- (-D))*2*10 ^5] 0.0000000
Ɛ2t= bt*(a'-(-D))*(D-(-D)) / [600000*Ast*(d - (-D))] 0.0047978
Ɛmt = Ɛ1t-Ɛ2t -0.0047978
#DIV/0!
#DIV/0! < 0.2
INPUT DATA:- Governing Load Case For Design LC 248
INPUT DATA:- Axial force, Torsion Moments, Bending moments and Shear force:
Design Shear force, Fy 153.30 KN LC 234
Design Torsional Moment for shear Tu=Mx 0.00 KNm LC 234
Moment M'uz 163.95 KN LC 248
Design Torsional Moment for moment Tu=Mx 0.00 KNm LC 248
Axial Force, Fx 0.00 KN T LC 248
Bending in another direction Muy 0 KNm LC 248
INPUT DATA:- Material Properties :
Characteristic Strength of concrete, fck 25.00 N/mm2
Grade of Steel, fy 415.00 N/mm2
INPUT DATA:- Material Properties and Dimensions of Beam:
Thickness of flange, Df 175.00 mm
Total Depth of T- Beam, D 1500.00 mm
Width of Flange, bf 300.00 mm
Width of web in compression fibre, bcw 300.00 mm
Width of web in tension, btw' 300.00 mm
Layer of bar in tension zone 1.00
MOLUNG KHOLA BRIDGE MEMBER
T - Beam with Trapezoidal Web, memb. No. 80 (40m)
Wcrb = 3*acr*Ɛm/ [1+2*(acr - Cmin) / (D - xu)]
Wcrt = 3*acr x Ɛm / [1+2*(acr - Cmin) / (D - (-D))]
Wcr =Wcrb+Wcrt
Cover, C 40.00 mm
Stirrups of Design purpose 8.00 mm
Dia of bar for design purpose 20.00 mm
Spacer for vertical spacing 32.00 mm
Calculations of required Design Moments, Shear forces:
Resultant Moment of ( Muy and Muz') = M''uz 163.95 KNm
Design Moment Mu 163.95 KNm
Design shear force Vu 153.30 KN
Calculations of required Section properties:
Width of web in reiforcement level in tension, btw 300.00 mm
Width of Web, Average btw 300.00 mm
Effective Depth , d (Calculated) 1442.00 mm
Width of small portion in the flange, bs 0.000 mm
Centroid of Section from Compression fibre Cc 715.092 mm
Centoid of section from tension fibre Ct 784.908 mm
Df/d (Calculated) 0.121
RESULT IN ACCORDANCE WITH DIFFERENT CONDITIONS:
1. Condition: If Neutral Axis lies in the flange? YES
Muf, lim= 0.36*fck*bf*Df*(d-0.416*Df) 646.95 KNm
483.000 KNm
Neutral Axis lies in the Flange? YES
For Mu or Mu,lim Area of Steel, Ast 318.80 mm2
For Tension Area of Steel, Ast2 0.00 mm2
for BM+Tension, total rqd. Steel, Ast 318.80 mm2
Neutral Axis Ratio, Xu/d 0.02957
Neutral Axis, Xu 42.634 mm
Due to Mu Compressive strain Ɛcc 0.00022
Total Strain due to (Mu+Fx) Ɛcct 0.00034 < 0.0035 OK
for BM+compression, TrialTotal Rqd. Steel, Ast 331.010 mm2
Due To Fx, Additional compressive stress fsc NA N/mm2
Additional compressive stress fcc NA N/mm2
Pu NA KN
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00012170 NA
Test : Fx-Pu =0 NA
for BM+compression, Extra Increased area Ast 0.000 mm2
Required Ast 318.805 mm2
2. Condition: If Neutral Axis lies in the webNeutral Axis lies in the Web NA
Neutral axis depth ratio α = Xu,max/d 0.4791
Maximum Neutral Axis for balanced design Xu,max 690.87 mm NA
yf,max 217.38 mm NA
Test : Muf,lim > Mu for Neutral in flange
Compressive force for straight portion, C1 990.42 KN NA
Compressive force fo rParabolic portion, C2 880.37 KN NA
Compressive force Trap. Web, Cu = C1+C2 1870.79 KN NA
Compressive force for Flange portion, C3 0.00 KN NA
Compressive force for Small Flange portion, C4 0.00 KN NA
Total Compressive force, C 1870.79 KN NA
Moment of C1 about Neutral Axis, Integration I1 537626.21 KNmm NA
Moment C2 about Neutral Axis Integration I2 217222.71 KNmm NA
Moment f Cu about neutral axis Integration Iu 754848.92 KNmm NA
CG of Cu from Neutral axis ,Y 403.493 mm NA
CG of Cu from Extreme Compression fibre X 287.380 mm NA
For average web only X/d 0.19929 NA
CG C from Extreme Compression fibre X 287.380 mm NA
2160.00 KNm NA
Capacity Mu, lim (Only for trapezodal Web) 2160.05 KNm NA
Capacity Mu, lim (trapezodal Web + Flange) 2160.05 KNm NA
-1996.10 KNm SRS
1154.597 mm NA
1154.620 mm NA
5181.513 mm2
NA
5181.513 mm2
NA
-0.001123
3.89340
-2160.046
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a 693.572 mm
yf=0.15*xu+0.65*Df 217.786 mm
Lever Arm z = jd 1153.474
5186.661 mm2
NA GO TO 1
Hit and Trial α = Xu/d 0.300000 SRS-NA
0.00000 SRS-NA
Neutral Axis for balanced design Xu 432.60 mm SRS-NA
yf,max 178.64 mm SRS-NA
Compressive force for straight portion, C1 0.00 KN SRS-NA
Compressive force fo rParabolic portion, C2 0.00 KN SRS-NA
Compressive force Trap.Web, Cu = C1+C2 0.00 KN SRS-NA
Compressive force for Flange portion, C3 0.00 KN SRS-NA
Compressive force for Small Flange portion, C4 0.00 KN SRS-NA
Total Compressive force, C 0.00 KN SRS-NA
Capacity if average web +flange Muw, lim=
0.36*fck*bw*Xu,max*(d-0.416*Xu,max) + 0.446*fck*(bf-
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast,max
For (web +Flange) balanced section Ast,max
a= - 0.14976*fck*bw - 0.0050175*fck*(bf - bw)
b= 0.36*fck*bw*d + 0.00669*fck*(bf - bw)
c= 0.2899*fck*Df*(bf - bw)*(d-0.325*Df)-Mu
For Df/d > 0.2 Ast
2 (A) IF Df/d > 0.2
α is chosen to make Test : C = T
Moment of C1 about Neutral Axis, Integration I1 NA KNmm SRS-NA
Moment C2 about Neutral Axis Integration I2 0.00 KNmm SRS-NA
Moment f Cu about neutral axis Integration Iu 0.00 KNmm SRS-NA
CG of Cu from Neutral axis ,Y 0.000 mm SRS-NA
CG of Cu from Extreme Comprssion fibre X 0.000 mm SRS-NA
For average web only X/d 0.00000 SRS-NA
CG C from Extreme Compression fibre X 0.000 mm SRS-NA
0.00 KNm SRS-NA
Mu(Only for trapezodal Web) 0.00 KNm SRS-NA
Mu,lim (trapezodal Web + Flange) 0.00 KNm SRS-NA
0.00 KNm SRS-NA
0.000 mm SRS-NA
0.000 mm SRS-NA
0.000 mm2
SRS-NA
0.00 mm2
SRS-NA
For Tension Area of Steel, Ast2 0.00 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 0.00 mm2
SRS-NA
NA KN SRS-NA
Neutral Axis, Xu 0.00 mm SRS-NA
Due to Mu Compressive strain Ɛcc 0.00000 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00002 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 1300.000 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc NA N/mm2
SRS-NA
Additional compressive stress fcc NA N/mm2
SRS-NA
Pu 0.000 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00001938 YES SRS-NA
Test : Fx-Pu =0 NA SRS-NA
Extra Increased area 0.000 mm2
SRS-NA
Required Singly reinforced Ast 0.000 mm2
SRS-NA
-0.001123 SRS-NA
3.89340 SRS-NA
-163.950 SRS-NA
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a 42.634 mm SRS-NA
yf=0.15*xu+0.65*Df 120.145 mm SRS-NA
Lever Arm z = jd 1424.264 SRS-NA
318.826 mm2
SRS-NA
NA GO TO 1
Hit and Trial α = Xu/d 0.2545 SRS-NA
α is chosen to make Test : C - T = 0 0.0000 SRS-NA
average web +flange Muw= 0.36*fck*bw*Xu,max*(d-
0.416*Xu,max) + 0.446*fck*(bf-bw)*yf*(d-0.5*yf,max)
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast,max
For (web +Flange) balanced section Ast,max
Force of Tension, T
a= - 0.14976*fck*bw - 0.0050175*fck*(bf - bw)
b= 0.36*fck*bw*d + 0.00669*fck*(bf - bw)
c= 0.2899*fck*Df*(bf - bw)*(d-0.325*Df)-Mu
For Df/d > 0.2 Ast
2 (B) IF Df/d < = 0.2
Neutral Axis for balanced design Xu 0.00 mm SRS-NA
yf 0.00 mm SRS-NA
Compressive force for straight portion, C1 0.00 KN SRS-NA
Compressive force fo rParabolic portion, C2 0.00 KN SRS-NA
Compressive force Trap.Web, Cu = C1+C2 0.00 KN SRS-NA
Compressive force for Flange portion, C3 0.00 KN SRS-NA
Compressive force for Small Flange portion, C4 0.00 KN SRS-NA
Total Compressive force, C 0.00 KN SRS-NA
Moment of C1 about Neutral Axis, Integration I1 0.00 KNmm SRS-NA
Moment C2 about Neutral Axis Integration I2 0.00 KNmm SRS-NA
Moment f Cu about neutral axis Integration Iu 0.00 KNmm SRS-NA
CG of Cu from Neutral axis ,Y 0.000 mm SRS-NA
CG of Cu from Extreme Comprssion fibre X 0.000 mm SRS-NA
For average web only X/d 0.0000000 SRS-NA
CG C from Extreme Compression fibre Xmax 0.000 mm SRS-NA
0.00 KNm SRS-NA
Mu (Only for trapezodal Web) 0.00 KNm SRS-NA
Mu,lim (trapezodal Web + Flange) 0.00 KNm SRS-NA
0.00 KNm SRS-NA
0.000 mm SRS-NA
0.000 mm SRS-NA
0.000 mm2
SRS-NA
0.000 mm2
SRS-NA
For Tension Area of Steel, Ast2 0.00 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 0.00 mm2
SRS-NA
0.00 KN SRS-NA
Neutral Axis, Xu 0.000 SRS-NA
Due to Mu Compressive strain Ɛcc 0.00000 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00014 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 3000.000 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc 0.00 N/mm2
SRS-NA
Additional compressive stress fcc 0.000 N/mm2
SRS-NA
Pu 0.000 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00013902 SRS-NA SRS-NA
Test : Fx-Pu =0 0.000000 SRS-NA
Extra Increased area 0.000 mm2
SRS-NA
Required Singly reinforced Ast 0.000 mm2
SRS-NA
0.000000000 SRS-NA
b= 0.36*fck*bw*d 0.00000000 SRS-NA
0.00000 SRS-NA
Neutral Axis Xu=(-b+√(b2-4*a*c))/2*a 0.000 SRS-NA
Lever Arm z = jd 0.000 SRS-NA
average web +flange Muw = 0.36*fck*bw*Xu,max*(d-
0.416*Xu,max) + 0.446*fck*(bf-bw)*yf*(d-0.5*yf,max)
Test, Mu > Mu,lim (Doubly or Singly), Mu - Mu,lim=
for average web Lever Arm z= jd
for (Trap. Web+ Flange) Lever Arm z= jd
For avg. web +flange balanced section Ast
For (web +Flange) balanced section Ast
Force of Tension, T
a= -0.14976*fck*bw
c= 0.446*fck*Df*(bf - bw)*(d-0.5*Df)-Mu
0.000 mm2
SRS-NA
2 (C) Condition: Doubly Reinforced Section GO TO 1
Number of Layer of Comression bar 1.00 No. SRS-NA
Dia of Main reinforcement in compression 32 mm SRS-NA
Spacer for Vertical spacing 32 mm SRS-NA
Dia of Stirrups 8.00 mm SRS-NA
Clear cover, C 40.00 mm SRS-NA
Charactertistics strength of Concrete fck 25.00 N/mm2 SRS-NA
Yield stress of steel fy 415.00 N/mm2 SRS-NA
Helping calculation, d'' 64.00 mm SRS-NA
Effective depth from in compression side d' 64.00 mm SRS-NA
Effective depth at tension side d 1442.00 mm SRS-NA
Neutral Axis depth ration Xu,max/d 0.479 SRS-NA
Neutral Axis Depth Xu.max 690.87 mmm SRS-NA
Compression level strain Ɛsc Or Ɛcc 0.00318 SRS-NA
Compressive level stress of steel fsc 355.632 N/mm2 SRS-NA
Compressive level stress of concrete fcc=446*fck*(Ԑcc-250*Ԑcc^2) 11.150 N/mm2 SRS-NA
Area of compressive stress Asc -4204.994 mm2
SRS-NA
-4012.037 mm2
SRS-NA
For DRS Total Area of tension steel Ast 1169.476 mm2
SRS-NA
for Tension, Area of Steel, Ast3 4012.04 mm2
SRS-NA
for BM+Tension, total rqd. Steel, Ast 5181.51 mm2
SRS-NA
Neutral Axis, Xu 690.873 mm SRS-NA
Due to Mu Compressive strain Ɛcc 0.00350 SRS-NA
Total Strain due to (Mu+P) Ɛcct 0.00362 < 0.0035 SRS-NA
for BM+compression, TrialTotal Rqd. Steel, Ast 12063.716 mm2
SRS-NA
Due To Fx, Additional compressive stress fsc NA N/mm2
SRS-NA
Additional compressive stress fcc NA N/mm2
SRS-NA
Pu 0.000 KN SRS-NA
Hit and trial, Extra Comprssve strain due to P, Ɛcc 0.00012335 YES SRS-NA
Test : Fx-Pu =0 0.000000 SRS-NA
Extra Increased area 0.000 mm2
SRS-NA
Required Double reinforced Ast 5181.513 mm2
SRS-NA
Check for Shear forceDesign Shear force 153.30 KN
Shear stress 0.354 N/mm2
Percentage of tension steel, pt 0.073 %
Percentage of compressive steel, pc 0.145 %
For Df/d < 0.2 Ast
for Asc, Area of tension steel Ast2
Percentage of tension and compressive steel, pt 0.218 %
α=0.8*fck/6.89*pt 13.324
tc = 0.85*SQRT(0.8*fck)*(SQRT(1+5*α)-1)/6*α 0.343 N/mm2
1.00 x 0.343 = 0.343
> 0.354 NOT OK
Shear Reinforcement is required.
Dia of of Vertical Stirrups 8.00 mm
Number of leg 2.00
Planned area to Provide Asv 100.53 mm2
Required spacing of stirrups Svreqd. 11092.042 mm
Plan to Provide, spacing of stirrups Sv 300.000
Minimum required Asv 0.4*b*Sv/0.87*fy 99.7092 mm2
Ф 7.9672 mm
Rqd. Stirrups Ф 8.00 Leg 2.000 300.00 mm C/C
Permissible shear stress,
K´tc =
P/fck 0.07864
1.9660 % As
Total number of bar 21 No. area of one bar
500 mm Face As
1800 mm Face Bar No.
40 mm Number of row
1735.6232 mm Spacing of bar, Sy
8 mm Spacing of bar, Sx
64.376777 mm Percentage of one bar
25 N/mm2
reqd. dia Ф in mm
415 N/mm2 Puz
831.57855 mm Pu,x
0.4619881
0.6136042
Total Strain due to (Mu+P) Ɛcct 0.003500
ku,b = Xu,b/D g C1 C2 Xu Mc, KN
0.4619881 292.4 0.1672 0.1922 831.579 2084.881
0.190805 5.8 0.0691 0.0794 343.448 1176.652
######### 0.0 0.4470 0.5000 ######### 0.000
k = Xu/D g C1 C2 Xu Mc, KN
0.571488 15.99 0.2069 0.2377 1028.679 2197.376
Find Mux1 0.000 check Mux1 3379.311 For As
Find Mux1 0.000 Check Mux1 3379.311 For As
N. Axis ratio Cntrod Cff. N. Axis
k = Xu/D g C1 C2 Xu Mc, KN
0.571 15.99 0.2069 0.2377 1028.679 2197.376
ku,0.002
Go on putting value of k here, get locus of ∑ Mi and ∑ Pi for drawing Mcap against Pcap
DATA Prepared for INTERACTION DIAGRAM
For Compression
Ties
depth in compression d'x
Concrete grade fck
Yield Stress of Steel , fy
Xu,b
ku,b
Interaction Diagram Program
Percentage of Steel, p
Dimention of Column, b
Dimention of Column, D
Cover of Bar, C
Effective depth dx
0.300 19.753086 0.1086 0.1248 540 1650.242
0.400 400.000 0.145 0.166 720.00 1956.364
0.600 11.111 0.217 0.250 1080.00 2202.669
0.800 2.367 0.290 0.333 1440.00 1961.055
1.000 1.000 0.362 0.416 1800.00 1231.524
1.200 0.549 0.400 0.458 2160.00 675.737
1.400 0.346 0.418 0.475 2520.00 426.135
1.600 0.238 0.427 0.483 2880.00 293.047
1.800 0.174 0.432 0.488 3240.00 213.807
2.000 0.132 0.436 0.491 3600.000 162.847
4.000 0.026 0.445 0.498 7200.000 31.527
10.000 0.004 0.447 0.500 18000.000 4.390
15.000 0.002 0.447 0.500 27000.000 1.894
######### 0.000 0.447 0.500 ######### 0.000
Used Col. Used Col. Imp col. Used Col. Used Col.
INPUT Formulated Formulated Formulated
Rows As y Ԑsi fsi, N/mm2 fci(N/mm2)
1 4825.49 835.62 0.003281 356.545 11.175
2 0 517.29 0.002198 335.182 11.175
3 0 198.96 0.001115 223.602 8.986
4 0 -119.37 0.000032 6.350 0.351
5 0 -437.71 -0.001051 -210.902 0.000
6 0 -756.04 -0.002135 -332.849 0.000
7 0 0.00 0.000438 87.819 4.357
0 0 0.00 0.000438 87.819 4.357
1 0 0.00 0.000438 87.819 4.357
2 0 756.04 0.003010 354.195 11.175
3 0 437.71 0.001927 325.206 11.160
4 0 119.37 0.000844 169.289 7.442
5 0 -198.96 -0.000239 -47.963 0.000
6 0 -517.29 -0.001322 -265.215 0.000
7 12867.963 -835.62 -0.002405 -342.825 0.000
Check 17693.449
Design Value ((Moment and Compression Load)
CONFIGURATION of Steel for INTERACTION DIAGRAM OF RECTANGULAR COLUMN
INPUT of FORMULATED
% 1.966
∑ Mi∑ Pi
For, k 0.5714883 5078.952 -2744.88 For, k
Ԑsi fsi, N/mm2 fci(N/mm2) Ԑ'si f'sci, N/mm
2 Ԑsi
0.00328 356.545 11.175 0.00328 356.545 0.00151
0.00220 335.182 11.175 0.00220 335.182 0.00050
0.00111 223.602 8.986 0.00111 223.602 -0.00051
0.00003 6.350 0.351 0.00003 6.350 -0.00153
-0.00105 -210.902 0.000 0.00105 210.902 -0.00254
-0.00213 -332.849 0.000 0.00213 332.849 -0.00355
0.00044 87.819 4.357 0.00044 87.819 -0.00115
0.00044 87.819 4.357 0.00044 87.819 -0.00115
0.00044 87.819 4.357 0.00044 87.819 -0.00115
0.00301 354.195 11.175 0.00301 354.195 0.00126
0.00193 325.206 11.160 0.00193 325.206 0.00025
0.00084 169.289 7.442 0.00084 169.289 -0.00077
-0.00024 -47.963 0.000 0.00024 47.963 -0.00178
-0.00132 -265.215 0.000 0.00132 265.215 -0.00279
-0.00241 -342.825 0.000 0.00241 342.825 -0.00381
∑ Mi∑ Pi
For, k 1.000 1140.503 1976.17 For, k
Ԑsi fsi, N/mm2 fci(N/mm2) Ԑ'si f'sci, N/mm
2 Ԑsi
0.00337 357.360 11.175 0.00337 357.360 0.00302
0.00276 351.917 11.175 0.00276 351.917 0.00256
0.00214 332.935 11.175 0.00214 332.935 0.00210
0.00152 296.240 10.526 0.00152 296.240 0.00164
0.00090 180.305 7.788 0.00090 180.305 0.00118
0.00028 56.148 2.909 0.00028 56.148 0.00073
0.00175 314.363 11.000 0.00175 314.363 0.00181
0.00175 314.363 11.000 0.00175 314.363 0.00181
0.00175 314.363 11.000 0.00175 314.363 0.00181
0.00322 356.017 11.175 0.00322 356.017 0.00290
0.00260 347.926 11.175 0.00260 347.926 0.00245
0.00198 327.234 11.174 0.00198 327.234 0.00199
0.00136 273.423 10.042 0.00136 273.423 0.00153
0.00074 149.266 6.769 0.00074 149.266 0.00107
0.00013 25.108 1.355 0.00013 25.108 0.00061
∑ Mi∑ Pi
For, k 2.000 -1389.672 4887.83 For, k
Ԑsi fsi, N/mm2 fci(N/mm2) Ԑ'si f'sci, N/mm
2 Ԑsi
0.00250 345.317 11.175 0.00250 345.317 0.00222
0.00227 338.018 11.175 0.00227 338.018 0.00212
0.00205 329.726 11.175 0.00205 329.726 0.00202
0.00182 319.012 11.089 0.00182 319.012 0.00192
0.00160 304.004 10.727 0.00160 304.004 0.00182
0.00137 275.705 10.082 0.00137 275.705 0.00172
0.00191 324.266 11.152 0.00191 324.266 0.00196
0.00191 324.266 11.152 0.00191 324.266 0.00196
0.00191 324.266 11.152 0.00191 324.266 0.00196
0.00244 343.866 11.175 0.00244 343.866 0.00220
0.00222 335.945 11.175 0.00222 335.945 0.00210
0.00199 327.653 11.175 0.00199 327.653 0.00200
0.00177 315.509 11.025 0.00177 315.509 0.00190
0.00154 298.658 10.592 0.00154 298.658 0.00180
0.00132 264.418 9.876 0.00132 264.418 0.00170
17694.000 mm2
area of one bar 842.57 mm2
3580.9 mm2
Face Bar No. 4 Nos.
Number of row 6 N0s
Spacing of bar, Sy 318.3 mm
Spacing of bar, Sx 70.7 mm
Percentage of one bar 0.093619 %
reqd. dia Ф in mm 32.754
15433.20 KN
1909.890 KN
Pc, KN ∑ Mi∑ Pi Mu, KN Pu, KN 3-IMP Value
3762.893 5078.952 -2744.883 7163.833 1018.010 IMP Pub
1554.104 2064.172 -3971.600 3240.824 -2417.496 IMP, Mp
10057.500 0.000 7648.724 0.000 17706.224 IMP Puz
Pc, KN ∑ Mi∑ Pi Mcap, KN Pcap, KN TEST
4654.772 5078.952 -2744.883 7276.329 1909.890 Trialing
1.966 %, K 0.2629259
1.966 %, Xu 262.92594
Pc, KN ∑ Mi∑ Pi Mcap, KN Pcap, KN At k
4654.772 5078.952 -2744.883 7276.3 1909.890 0.239300
Go on putting value of k here, get locus of ∑ Mi and ∑ Pi for drawing Mcap against Pcap
DATA Prepared for INTERACTION DIAGRAM
For Compression PASTE here OUTPUT Interaction Diagram
Interaction Diagram Program
-2000.000
0.000
2000.000
4000.000
6000.000
8000.000
10000.000
12000.000
14000.000
16000.000
18000.000
-4000.0 -2000.0 0.0 2000.0 4000.0 6000.0
2443.500 5032.791 -3269.157 6683.0 -825.7
3258.000 5225.103 -3039.015 7181.5 219.0
4887.000 4968.149 -2611.411 7170.8 2275.6
6516.000 2944.563 -185.394 4905.6 6330.6
8145.000 1140.503 1976.168 2372.0 10121.2
9006.354 127.32 3158.79 803.1 12165.1
9394.623 -475.29 3862.39 -49.2 13257.0
9601.649 -880.99 4321.57 -587.9 13923.2
9724.911 -1172.023 4645.513 -958.2 14370.4
9804.182 -1389.67 4887.83 -1226.8 14692.0
10008.458 -1919.59 5432.03 -1888.1 15440.5
10050.672 -2063.61 5555.36 -2059.2 15606.0
10054.554 -2091.52 5578.75 -2089.6 15633.3
10057.500 -2128.493 5603.822 ######### 15661.3
6357.32 1909.89
Help Col. Help Col.
Formulated Formulated Formulated Formulated Formulated Formulated
Ԑ'si f'sci, N/mm2 ∑ Mi
∑ Pi Mu, KN Pu, KN
0.00328 356.545 5078.952 -2744.883 7276.329 1909.890
0.00220 335.182
0.00111 223.602
0.00003 6.350
0.00105 210.902
0.00213 332.849 IF($A$24<=1,IF($A$24<$D$14,0.003805*($A$24-0.5+$C51/$D$6)/($D$8/$D$6-$A$24),0.0035*($A$24-0.5+$C51/$D$6)/$A$24),0.002*(1+($C51/$D$6-1/14)/($A$24-3/7)))
0.00044 87.819
0.00044 87.819
0.00044 87.819
0.00301 354.195
0.00193 325.206
0.00084 169.289
0.00024 47.963
0.00132 265.215
0.00241 342.825
Design Value ((Moment and Compression Load)
CONFIGURATION of Steel for INTERACTION DIAGRAM OF RECTANGULAR COLUMNOUT PUT TO BE PASTED CHECK
∑ Mi∑ Pi
0.300 5032.791 -3269.16 For, k 0.400
fsi, N/mm2 fci(N/mm2) Ԑ'si f'sci, N/mm
2 Ԑsi fsi, N/mm2
295.837 10.514 0.00151 295.837 0.00246 344.191
100.406 4.894 0.00050 100.406 0.00126 253.467
-102.800 0.000 0.00051 102.800 0.00007 14.246
-296.971 0.000 0.00153 296.971 -0.00112 -224.974
-346.315 0.000 0.00254 346.315 -0.00231 -339.469
-358.895 0.000 0.00355 358.895 -0.00351 -358.506
-229.804 0.000 0.00115 229.804 -0.00067 -135.266
-229.804 0.000 0.00115 229.804 -0.00067 -135.266
-229.804 0.000 0.00115 229.804 -0.00067 -135.266
252.810 9.647 0.00126 252.810 0.00216 333.718
49.604 2.593 0.00025 49.604 0.00097 193.662
-153.602 0.000 0.00077 153.602 -0.00023 -45.559
-316.158 0.000 0.00178 316.158 -0.00142 -284.779
-352.301 0.000 0.00279 352.301 -0.00261 -348.217
-361.050 0.000 0.00381 361.050 -0.00381 -361.050
∑ Mi∑ Pi
1.200 127.324 3158.79 For, k 1.400
fsi, N/mm2 fci(N/mm2) Ԑ'si f'sci, N/mm
2 Ԑsi fsi, N/mm2
354.266 11.175 0.00302 354.266 0.00281 352.447
346.863 11.175 0.00256 346.863 0.00244 343.890
331.627 11.175 0.00210 331.627 0.00208 330.858
307.694 10.819 0.00164 307.694 0.00172 312.271
237.565 9.316 0.00118 237.565 0.00135 271.248
145.597 6.640 0.00073 145.597 0.00099 198.214
318.397 11.079 0.00181 318.397 0.00185 320.771
318.397 11.079 0.00181 318.397 0.00185 320.771
318.397 11.079 0.00181 318.397 0.00185 320.771
353.271 11.175 0.00290 353.271 0.00272 350.933
343.907 11.175 0.00245 343.907 0.00235 340.919
327.404 11.175 0.00199 327.404 0.00199 327.505
297.225 10.553 0.00153 297.225 0.00163 306.453
214.573 8.757 0.00107 214.573 0.00126 252.990
122.605 5.787 0.00061 122.605 0.00090 179.956
∑ Mi∑ Pi
4.000 -1919.585 5432.03 For, k 10.000
fsi, N/mm2 fci(N/mm2) Ԑ'si f'sci, N/mm
2 Ԑsi fsi, N/mm2
335.997 11.175 0.00222 335.997 0.00208 330.916
332.348 11.175 0.00212 332.348 0.00205 329.555
328.699 11.175 0.00202 328.699 0.00201 328.193
325.050 11.158 0.00192 325.050 0.00197 326.832
318.958 11.088 0.00182 318.958 0.00193 325.470
312.793 10.963 0.00172 312.793 0.00190 323.532
326.419 11.171 0.00196 326.419 0.00199 327.342
326.419 11.171 0.00196 326.419 0.00199 327.342
326.419 11.171 0.00196 326.419 0.00199 327.342
335.084 11.175 0.00220 335.084 0.00207 330.576
331.436 11.175 0.00210 331.436 0.00204 329.214
327.787 11.175 0.00200 327.787 0.00200 327.853
323.582 11.146 0.00190 323.582 0.00196 326.492
317.417 11.062 0.00180 317.417 0.00193 325.130
311.252 10.924 0.00170 311.252 0.00189 322.957
Mu,b KN
7163.83
6255.60
Mu,b KN
7276.33
Wrong points
Wrong points
8000.0
Series1
6729.19
7035.32
7281.62
7040.01
6310.48
5754.69
5505.09
5372.00
5292.76
5241.80
5110.48
5083.34
5080.85
5078.95
IF($A$24<=1,IF($A$24<$D$14,0.003805*($A$24-0.5+$C51/$D$6)/($D$8/$D$6-$A$24),0.0035*($A$24-0.5+$C51/$D$6)/$A$24),0.002*(1+($C51/$D$6-1/14)/($A$24-3/7)))
∑ Mi∑ Pi ∑ Mi
5225.103 -3039.01 For, k 0.600 4968.149
fci(N/mm2) Ԑ'si f'sci, N/mm2 Ԑsi fsi, N/mm
2 fci(N/mm2)
11.175 0.00246 344.191 0.00329 356.636 11.175
9.660 0.00126 253.467 0.00226 337.462 11.175
0.780 0.00007 14.246 0.00123 246.337 9.510
0.000 0.00112 224.974 0.00020 39.409 2.088
0.000 0.00231 339.469 -0.00084 -167.520 0.000
0.000 0.00351 358.506 -0.00187 -321.633 0.000
0.000 0.00067 135.266 0.00058 117.007 5.568
0.000 0.00067 135.266 0.00058 117.007 5.568
0.000 0.00067 135.266 0.00058 117.007 5.568
11.175 0.00216 333.718 0.00303 354.397 11.175
8.185 0.00097 193.662 0.00200 327.960 11.175
0.000 0.00023 45.559 0.00097 194.605 8.212
0.000 0.00142 284.779 -0.00006 -12.323 0.000
0.000 0.00261 348.217 -0.00109 -219.252 0.000
0.000 0.00381 361.050 -0.00212 -332.487 0.000
∑ Mi∑ Pi ∑ Mi
-475.294 3862.39 For, k 1.600 -880.987
fci(N/mm2) Ԑ'si f'sci, N/mm2 Ԑsi fsi, N/mm
2 fci(N/mm2)
11.175 0.00281 352.447 0.00267 349.719 11.175
11.175 0.00244 343.890 0.00237 341.476 11.175
11.175 0.00208 330.858 0.00207 330.352 11.175
10.950 0.00172 312.271 0.00176 315.285 11.020
10.003 0.00135 271.248 0.00146 291.014 10.369
8.315 0.00099 198.214 0.00116 232.865 9.208
11.115 0.00185 320.771 0.00188 322.334 11.133
11.115 0.00185 320.771 0.00188 322.334 11.133
11.115 0.00185 320.771 0.00188 322.334 11.133
11.175 0.00272 350.933 0.00260 347.773 11.175
11.175 0.00235 340.919 0.00229 338.695 11.175
11.175 0.00199 327.505 0.00199 327.571 11.175
10.783 0.00163 306.453 0.00169 310.586 10.905
9.650 0.00126 252.990 0.00139 278.288 10.127
7.777 0.00090 179.956 0.00109 217.724 8.838
∑ Mi∑ Pi ∑ Mi
-2063.611 5555.36 For, k 15.000 -2091.520
fci(N/mm2) Ԑ'si f'sci, N/mm2 Ԑsi fsi, N/mm
2 fci(N/mm2)
11.175 0.00208 330.916 0.00205 329.879 11.175
11.175 0.00205 329.555 0.00203 328.984 11.175
11.175 0.00201 328.193 0.00201 328.090 11.175
11.173 0.00197 326.832 0.00198 327.196 11.174
11.163 0.00193 325.470 0.00196 326.302 11.170
11.146 0.00190 323.532 0.00193 325.407 11.162
11.174 0.00199 327.342 0.00199 327.531 11.175
11.174 0.00199 327.342 0.00199 327.531 11.175
11.174 0.00199 327.342 0.00199 327.531 11.175
11.175 0.00207 330.576 0.00205 329.655 11.175
11.175 0.00204 329.214 0.00202 328.761 11.175
11.175 0.00200 327.853 0.00200 327.867 11.175
11.171 0.00196 326.492 0.00198 326.972 11.173
11.159 0.00193 325.130 0.00195 326.078 11.168
11.140 0.00189 322.957 0.00193 325.184 11.160
0.000
Pu,b KN
1018.01
-1190.78
Pu,b KN
1909.89
Wrong points
Wrong points
-301.38
513.12
2142.12
3771.12
5400.12
6261.47
6649.74
6856.77
6980.03
7059.30
7263.58
7305.79
7309.67
7312.62
IF($A$24<=1,IF($A$24<$D$14,0.003805*($A$24-0.5+$C51/$D$6)/($D$8/$D$6-$A$24),0.0035*($A$24-0.5+$C51/$D$6)/$A$24),0.002*(1+($C51/$D$6-1/14)/($A$24-3/7)))
∑ Pi ∑ Mi∑ Pi
-2611.41 For, k 0.800 2944.563 -185.39
Ԑ'si f'sci, N/mm2 Ԑsi fsi, N/mm
2 fci(N/mm2) Ԑ'si
0.00329 356.636 0.00334 357.088 11.175 0.00334
0.00226 337.462 0.00257 347.119 11.175 0.00257
0.00123 246.337 0.00180 317.231 11.059 0.00180
0.00020 39.409 0.00102 205.067 8.505 0.00102
0.00084 167.520 0.00025 49.871 2.606 0.00025
0.00187 321.633 -0.00053 -105.326 0.000 0.00053
0.00058 117.007 0.00131 263.266 9.855 0.00131
0.00058 117.007 0.00131 263.266 9.855 0.00131
0.00058 117.007 0.00131 263.266 9.855 0.00131
0.00303 354.397 0.00315 355.409 11.175 0.00315
0.00200 327.960 0.00238 341.759 11.175 0.00238
0.00097 194.605 0.00160 304.294 10.734 0.00160
0.00006 12.323 0.00083 166.268 7.344 0.00083
0.00109 219.252 0.00006 11.072 0.608 0.00006
0.00212 332.487 -0.00072 -144.125 0.000 0.00072
∑ Pi ∑ Mi∑ Pi
4321.57 For, k 1.800 -1172.023 4645.51
Ԑ'si f'sci, N/mm2 Ԑsi fsi, N/mm
2 fci(N/mm2) Ԑ'si
0.00267 349.719 0.00257 347.197 11.175 0.00257
0.00237 341.476 0.00231 339.495 11.175 0.00231
0.00207 330.352 0.00206 329.993 11.175 0.00206
0.00176 315.285 0.00180 317.420 11.062 0.00180
0.00146 291.014 0.00154 298.456 10.587 0.00154
0.00116 232.865 0.00128 257.409 9.740 0.00128
0.00188 322.334 0.00190 323.441 11.145 0.00190
0.00188 322.334 0.00190 323.441 11.145 0.00190
0.00188 322.334 0.00190 323.441 11.145 0.00190
0.00260 347.773 0.00251 345.534 11.175 0.00251
0.00229 338.695 0.00225 337.120 11.175 0.00225
0.00199 327.571 0.00199 327.618 11.175 0.00199
0.00169 310.586 0.00173 313.406 10.978 0.00173
0.00139 278.288 0.00148 292.330 10.410 0.00148
0.00109 217.724 0.00122 244.476 9.470 0.00122
∑ Pi ∑ Mi∑ Pi
5578.75 For, k ######### -2128.493 5603.82
Ԑ'si f'sci, N/mm2 Ԑsi fsi, N/mm
2 fci(N/mm2) Ԑ'si
0.00205 329.879 0.00200 327.892 11.175 0.00200
0.00203 328.984 0.00200 327.892 11.175 0.00200
0.00201 328.090 0.00200 327.892 11.175 0.00200
0.00198 327.196 0.00200 327.892 11.175 0.00200
0.00196 326.302 0.00200 327.892 11.175 0.00200
0.00193 325.407 0.00200 327.892 11.175 0.00200
0.00199 327.531 0.00200 327.892 11.175 0.00200
0.00199 327.531 0.00200 327.892 11.175 0.00200
0.00199 327.531 0.00200 327.892 11.175 0.00200
0.00205 329.655 0.00200 327.892 11.175 0.00200
0.00202 328.761 0.00200 327.892 11.175 0.00200
0.00200 327.867 0.00200 327.892 11.175 0.00200
0.00198 326.972 0.00200 327.892 11.175 0.00200
0.00195 326.078 0.00200 327.892 11.175 0.00200
0.00193 325.184 0.00200 327.892 11.175 0.00200
f'sci, N/mm2
357.088
347.119
317.231
205.067
49.871
105.326
263.266
263.266
263.266
355.409
341.759
304.294
166.268
11.072
144.125
f'sci, N/mm2
347.197
339.495
329.993
317.420
298.456
257.409
323.441
323.441
323.441
345.534
337.120
327.618
313.406
292.330
244.476
f'sci, N/mm2
327.892
327.892
327.892
327.892
327.892
327.892
327.892
327.892
327.892
327.892
327.892
327.892
327.892
327.892
327.892
