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Equivalent compressive strength of concrete
Ref: ACI-562 & 214.4R
Equivalent in place concrete strength

= compressive strength of concrete core*l/d factor
Compressive
Equivalent inplace
strength of Length diameter
Sample Number L/d ratio Compressive strength
concrete core factor
(Psi)
(Psi)
1 3870 1.93 0.994 3847.57

2 5350 1.93 0.994 5318.99
3 3470 1.90 0.992 3441.84
4 5900 1.93 0.994 5865.80
5
6
7
8
n 4
Average f'c 4618.54637681159
Sigma 1158.34719149858
V 0.250803412371112
Kc 1.28
Equivalent concrete strength (fceq)

th of concrete
Variation Modification Factors

(Kc) table
n Kc
2 2.4
3 1.47
4 1.28
5 1.2
6 1.15
7 1.125
8 1.1
10 1.08
12 1.06
16 1.05
20 1.03
3279 Psi
ACI Method of Mix Design
Entity for which retrofitting is to be done= column
Maximum Size of the coarse agreegate= 0.5 inch
Expected Strength of concrete= 45 Mpa
Water Cement Ratio from the above chart= 0.4

To maintain workability superplasticizer should be used.
From the above table slump value is assumed to be= 1-2 mm

From the above table ammount of mixing water = 335 lb/cubic yard
198.7476 Kg/ Cubic meter
Ammount of cement to be used= 496.8690026 Kg/ Cubic meter
Determination of the ammount of coarse Aggregate
Fine ness modulus of fine aggregate (Sylhet Sand)= 2.6
From the above table we have the bulk volume of

oven dry rodded CA with a minimum size of 12.5mm is= 0.57 inch
Minimum Bulk density of coarse aggregate= 1600 Kg/Cubic meter
Hence ammount of CA= 912 Kg/Cubic meter
Note:
Specific gravity of cement= 3.15
Specific gravity of CA= 2.64
Specific gravity of FA= 2.58
Determination of ammount of fine aggregate
Volume of water= 0.1987476 cubic meter

Solid Volume of cement= 0.1577362 cubic meter
Solid Volume of CA= 0.3454545 cubic meter
Volume of entraped air = 0.025 cubic meter
(From fig-3)
So volume of FA= 0.2730617 cubic meter
Mass of FA 704.49909 Kg/Cubicmeter
So the resulting ammount of estimated mass in per cubicmeter are as followes
Water 198.7476 Kg/cubic meter

Cement 496.869 Kg/cubic meter
Coarse aggregate Dry 912 Kg/cubic meter
Fine aggregate 704.49909 Kg/cubic meter
Therefore the density

of concrete is= 2312.1157 kg/cubic meter
Load Data
Slab thickness 6 inch
Floor finish 25 Psf
Live load 80 Psf
Other Dead load 40 psf
Beam dimension
Width 12 inch
Depth 20 inch
Beam selfweight 175 lb/ft
Beam length 36 feet
Load over beam 450 lb/ft
Load due to beam 22500 lb
Effective loading area 189.75 sq feet
Load due to slab 41745 lb Prop design data
Total Gravity load 65 Kip bf 125 mm
Load on each prop 16.25 Kip tf 8 mm
hw 250 mm
tw 8 mm
Cross sectional properties
Ixx 37834603 mm^4
Iyy 2614150.7 mm^5
rx 98.85 mm
ry 25.98 mm
Area 3872 mm^2
Yeild strength of steel 36 ksi

Allowable stess 18 ksi
Axial force stress 2.7076059 Ksi
Axial check status Ok
Buckling Check
Applied Load 16.25 Kip Beam Shear Check
Support con factor (k) = 1 Concrete Grade 2250 Psi
Unsupported length 10 feet Shear resisted by conr. 17 kip
Factor of safety 2.5 Total factored load 94.5 Kip
Critical load capacity X 1806.723 Kip Shear on each beam 47.25 Kip
Critical load capacity Y 124.834 Kip Vs 35.6 Kip
FS x dirrection 111 Vc2= 8*phi*√(f'c)*b*d 69.7 Kip
FS y dirrection 7 So Vs<Vc2
Buckling Check Status OK So it is not required to increase beam section
125
Cross sectional Properties
8 Ixx 37834603 mm^4 MOMEN
Iyy 2614150.7 mm^4 Applied Moment
Area 3872 mm^2 Ixx
rxx 98.85 mm Iyy
ryy 25.98 mm Stress Developed
C 125 mm
250
8 Yeild Strength
7Fclv2
arpK
othendfix(k=0.5)O
B
RESULTS
AXIAL FORCE
Applied Load
Area
Stress Developed
Yeild Strength
RESULT
BUCKLING CALCULATION
MOMENT
Applied Moment 0 Kip-ft Axial Load 16.25 Kip
Ixx 90.9 inch^4
Support
Iyy 6.3 inch^4 Condition 1
Stress Developed 0.00 Ksi factor
Yeild Strength 36 Ksi

Unsupported
length
10 feet
Effective
10 feet
RESULTS OK Length
E 29000 Ksi
Ixx 90.9 inch^4
AXIAL FORCE CHECK Iyy 6.3 inch^4
Applied Load 16.25 Kip Pcr X 1806.7 Kip
Area 6.00 inch^2 PcrY 124.8 Kip
Stress Developed 2.7076059 Ksi X axis OK
Y axis OK
Yeild Strength 18 Ksi FS 2.5
RESULT OK
125
IXX IYY
8 1 A1 1000 A1
I1 5333.333 I1
d1 121
Icc1 14646333
250
8 b2 8 b2
h2 234 h2
2 I2 8541936 I2
Total I 37834603 Total I
Atotal 3872
rxx 98.85005 ryy

1000
1302083
8
234
9984
2614151
25.9835

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Equivalent compressive strength of concrete

Ref: ACI-562 & 214.4R

Equivalent in place concrete strength

1 3870 1.93 0.994 3847.57

Equivalent concrete strength (fceq)

Variation Modification Factors

Water Cement Ratio from the above chart= 0.4

From the above table slump value is assumed to be= 1-2 mm

Ammount of cement to be used= 496.8690026 Kg/ Cubic meter

Determination of the ammount of coarse Aggregate

Fine ness modulus of fine aggregate (Sylhet Sand)= 2.6

From the above table we have the bulk volume of

Determination of ammount of fine aggregate

Volume of water= 0.1987476 cubic meter

So the resulting ammount of estimated mass in per cubicmeter are as followes

Water 198.7476 Kg/cubic meter

Therefore the density

Yeild strength of steel 36 ksi

Yeild Strength 36 Ksi

Total I 37834603 Total I

rxx 98.85005 ryy

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