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Input
Breadth (B) 1000 mmDepth (D) 150 mmEffective Cover 25 mm
125 mmGrade of Concrete 25Grade of Steel 500Length of Beam (L) 2550 mm
3.5Modulus of Elasticity of concrete 25000Modulus of Elasticity of Steel 200000
Modular Ratio, (m) 8
62 kNm
Ast at top of beam 1600
250
Effective Depth (d' )N/mm2
N/mm2
Flexural strength (fcr) N/mm2
N/mm2
N/mm2
Support moment M1
mm2
Asc at bottom of the beam mm2
ckf7.0
ckf5000
c
s
EE
Gross Moment of inertia At Left end and Right of the Beam
= 2.813E+08
CRACKING MOMENT OF RESISTANCE
To find depth of neutal Axis
To find kd
At Left top
1.313E+07 N-mmA 500B 14550C 1643750
Kd 44.6 mmk/d 0.357j 0.881
At left support
112985705.69 mm4
2.813E+08 mm4
1.313E+07 N-mm
Igr mm4
(Mcr)
Mcr
X1
Cracked Moment of Inertia (Ir)=
Ir
Igr
Mr
12* 3DB
yIf grcr *
)(**)'(**)1(2
* 2
kddAmdkdAmKdBstsc
)(**)'(**)1(2
*02
kddAmdkdAmKdBstsc
DEFLECTION CALCULATIONS WITH MODIFIED I EFFECTIVE
2.813E+08
1.313E+07 N mm
1.130E+08
Mr/M 2.12 N-mm
k/d 0.36
j 0.88
2.800E+11
Ieff 2.800E+11
Ieff 2.813E+08 Final
Short Term Deflection
Short Term Deflection = 14.33440 mm
GROSS MOMENT OF INERTIA (corrected)
Igr mm4
CRACKING MOMENT OF RESISTANCE (corrected)
Mr
CRACKED MOMENT OF INERTIA (corrected)
Ir mm4
At Middle of the Beam
Ieff
effIElM
**4* 2
1
Deflection due to creep
1.6
= 9615.4
m = 20.8 For Creep
At Left top
1.313E+07 N-mmA 500B 38230C 4283750
Kd 61.915 mmk/d 0.4953j 0.8349
At left support
218306813.92 mm4
2.813E+08 mm4
1.313E+07 N-mm
Creep coffecient (ɵ)
Ece
Mcr
X1
Cracked Moment of Inertia (Ir)=
Ir
Igr
Mr
ce
S
EE
m
)1( C
ceE
E
DEFLECTION CALCULATIONS WITH MODIFIED I EFFECTIVE
2.813E+08
1.313E+07 N mm
2.183E+08
Mr/M 2.12 N-mm
k/d 0.50
j 0.83
7.087E+08
Ieff 7.087E+08
Ieff 2.813E+08 Final
37.26944 mm
Ieff 2.813E+08
Ec 25000
14.3 mm
= ai,cc perm - ai, perm
= 37.269 - 14.3
= 22.935
GROSS MOMENT OF INERTIA (corrected)
Igr mm4
CRACKING MOMENT OF RESISTANCE (corrected)
Mr
CRACKED MOMENT OF INERTIA (corrected)
Ir mm4
Ieff
long Term Deflection ai,cc perm
long Term Deflection ai,cc perm
I effective for ai Perm (sam as per Short term deflection)
long Term Deflection ai, perm
long Term Deflection ai,perm
acc perm
acc perm
effIElM
**4* 2
1
effIElM
**4* 2
1
SHRINKAGE DEFLECTION
1.28
0.2
k3 0.5
1.08
k4 0.7354k4 0.7354
0.0003
D 150 mm
Ψcs 1.47078E-06
Span 2550 mm
4.78188031845 mm
With Corrected Ieff 14.33 22.94 4.78 42.05 27.72
PERMISSIBLE LIMITS AS PER IS - 456
Total Deflection(mm) SPAN/250 10.2 MM
Long Term Deflection(mm) 20 MM
Shrinkage Deflection(acs)= K3 * Ψcs *l2
Pt
Pc
Pt-Pc
Єcs=
Shrinkage Deflection(acs)=
Short Term Deflection (mm)
Creep Deflection(mm
)
Shrinkage Deflection(mm
)Total
Deflection(mm)Long Term
Deflection(mm)
SPAN/350 OR 20 MM WHICHEVER IS LESS
Input
Breadth (B) 1200 mmDepth (D) 1000 mm
1200 mmEffective Cover 50 mm
0 mm950 mm
1000Grade of Concrete 25Bw/BF 1Grade of Steel 500Length of Beam (L) 4010 mm
3.5Modulus of Elasticity of concrete 25000Modulus of Elasticity of Steel 200000
Modular Ratio, (m) 8
Asc 7125
4040 kNm
Asc 0Ast at bottom of beam 18000
Asc 0Calculations
Breadth of Flange (Bf)
Depth of Flange(Df)=Effective Depth (d' ) Depth of Web (Dw)
N/mm2
N/mm2
Flexural strength (fcr) N/mm2
N/mm2
N/mm2
mm2
Span moment Mo
mm2 mm2 mm2
ckf7.0
ckf5000
c
s
EE
Gross Moment of inertia At Left end and Right of the Beam
= 1.000E+11
Gross Moment of inertiaat middle of the beam
Distance of axis to extremefibre y
Distance of axis to extreme = 500.0 mmfibre y
Gross Moment of inertiaIgr = 1.000E+11 For T beam Action
at middle of the beam
CRACKING MOMENT OF RESISTANCE
To find depth of neutal Axis
To find kd
At Left top At Middle At Right top
7.000E+08 N-mm Mcr 7.000E+08 N-mm Mcr 7.000E+08 N-mmA 600 A 600 A 600B 0 B 193875 B 0C 0 C 139293750 C 0
Kd 0 mm Kd 346.63 mm Kd 0 mmk/d 0 k/d 0.3649 k/d 0j 1 j 0.8784 j 1
At left support At mid span
0 mm4 Ir 73471805157.4 Ir 0
1.000E+11 mm4 Igr 1.000E+11 mm4 Igr 1.000E+11 mm4
7.000E+08 N-mm Mr 7.000E+08 N-mm Mr 7.000E+08 mm4
Igr mm4
mm4
(Mcr)
Mcr
X1 X0 X2
Cracked Moment of Inertia (Ir)=
Cracked Moment of Inertia (Ir)=
Cracked Moment of Inertia (Ir)=
Ir mm4 mm4
Igr
Mr
12* 3DB
333 ***31
fff DyDBByDByB
)**(*2)(** 22
BDDBBBDDB
Dwff
ff
yIf grcr *
)(**)'(**)1(2
* 2
kddAmdkdAmKdBstsc
)(**)'(**)1(2
*02
kddAmdkdAmKdBstsc
DEFLECTION CALCULATIONS WITH MODIFIED I EFFECTIVE
AS per IS 456
#DIV/0!
0 From table 25 IS 456
1.000E+11
7.000E+08 N mm
7.347E+10
Mr/M 1.73 N-mm
k/d 0.36
j 0.88
3.148E+11
Ieff 3.148E+11
Ieff 1.000E+11 Final
Short Term Deflection
Short Term Deflection = 6.49636 mm
K2
K1
GROSS MOMENT OF INERTIA (corrected)
Igr mm4
CRACKING MOMENT OF RESISTANCE (corrected)
Mr
CRACKED MOMENT OF INERTIA (corrected)
Ir mm4
At Middle of the Beam
Ieff
10*
**48*5 21
2 MMMo
IEl
eff
oe XkXXkX *)1(2
* 121
1
Deflection due to creep
1.6
= 9615.4
m = 20.8 For Creep
At Left top At Middle At Right top
7.000E+08 N-mm Mcr 7.000E+08 N-mm Mcr 7.000E+08 N-mmA 600 A 600 A 600B 0 B 515475 B 0C 0 C 362733750 C 0
Kd 0 mm Kd 458.74 mm Kd 0 mmk/d 0 k/d 0.4829 k/d 0j 1 j 0.839 j 1
At left support At mid span
0 mm4 Ir 152540852653 Ir 0
1.000E+11 mm4 Igr 1.000E+11 mm4 Igr 1.000E+11 mm4
7.000E+08 N-mm Mr 7.000E+08 N-mm Mr 7.000E+08 mm4
DEFLECTION CALCULATIONS WITH MODIFIED I EFFECTIVE
AS per IS 456
#DIV/0!
0 From table 25 IS 456
Creep coffecient (ɵ)
Ece
Mcr
X1 X0 X2
Cracked Moment of Inertia (Ir)=
Cracked Moment of Inertia (Ir)=
Cracked Moment of Inertia (Ir)=
Ir mm4 mm4
Igr
Mr
K2
K1
ce
S
EE
m
)1( C
ceE
E
oe XkXXkX *)1(2
* 121
1
1.000E+11
7.000E+08 N mm
1.525E+11
Mr/M 1.73 N-mm
k/d 0.48
j 0.84
3.403E+11
Ieff 3.403E+11
Ieff 1.000E+11 Final
16.89054 mm
Ieff 1.000E+11
Ec 25000
6.5 mm
= ai,cc perm - ai, perm
= 16.891 - 6.5
= 10.394
GROSS MOMENT OF INERTIA (corrected)
Igr mm4
CRACKING MOMENT OF RESISTANCE (corrected)
Mr
CRACKED MOMENT OF INERTIA (corrected)
Ir mm4
At Middle of the Beam
Ieff
long Term Deflection ai,cc perm
long Term Deflection ai,cc perm
I effective for ai Perm (sam as per Short term deflection)
long Term Deflection ai, perm
long Term Deflection ai,perm
acc perm
acc perm
10*
**48*5 21
2 MMMo
IEl
eff
10
***48
*5 212 MM
MoIE
l
eff
SHRINKAGE DEFLECTION
1.579
0.625
k3 0.5
0.9539
k4 0.5466k4 0.5466
0.0003
D 1000 mm
Ψcs 1.63981E-07
Span 4010 mm
1.31841789204 mm
With Corrected Ieff 6.50 10.39 1.32 18.21 11.71
PERMISSIBLE LIMITS AS PER IS - 456
Total Deflection(mm) SPAN/250 16.04 MM
Long Term Deflection(mm) 20 MM
Shrinkage Deflection(acs)= K3 * Ψcs *l2
Pt
Pc
Pt-Pc
Єcs=
Shrinkage Deflection(acs)=
Short Term Deflection (mm)
Creep Deflection(m
m)
Shrinkage Deflection(mm
)Total
Deflection(mm)Long Term
Deflection(mm)
SPAN/350 OR 20 MM WHICHEVER IS LESS
