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ANALYTICAL INVESTIGATION OF STRUCTURAL
BEHAVIOR OF REINFORCED CONCRETE COLUMN
USING DIAMOND TIE CONFIGURATION UNDER
ELEVATED TEMPERATURES
Under The Supervision of
ER. HIMMI GUPTA
(Assistant Professor)
Presented By
Sudesh Kumar
(171327-Modular)
Reg. No. 17-TTC-51
Department of Civil Engineering
National Institute of Technical Teachers Training and Research
Sector-26, Chandigarh - 160019
CONTENT
 INTRODUCTION
 LITERATURE REVIEW
 PROPOSED WORK
 RESULT AND DISCUSSION
 CONCLUSION
 REFERENCES
INTRODUCTION
GENERAL
 A total of 2,500 citizens in India die per year as a result of
building fire occurrences . Fire causes thousands of deaths
and loss of property.
 The fire incidents across the world have been seen which
results in the large amount of damage to reinforced
cement concrete framed structures.
 Column being one of the most important loads bearing
member, the whole structure fails due to the failure of the
columns.
 The increased use of cement in building design results in
the need to research the behavior of structures in
reinforced concrete.
 Fire prevention and post fire maintenance should be taken
into account in the structure (retrofitting).
 Many buildings suffer harm that cannot be repaired
because of inadequate fire laws.
FACTORS AFFECTING FIRE RESISTANCE
OF RCC COLUMNS
 Aggregate Type
 Concrete Grade
 Lateral Strengthening
 Longitudinal reinforcement
 Intensity of fire
 Intensity and type of load
 Concrete cover
 Column size
THE STIRRUPS COMMONLY FOUND IN
COLUMN DESIGN
Fig 1: Types of stirrups
LITERATURE REVIEW
SR.
NO.
TITLE AUTHOR CONCLUSION
1. Permeability of
Heated Fiber-
Reinforced
High-Strength
Concrete
Sofren Leo
Suhaendi
et. Al
(2004)
In his investigation, the combination of
polypropylene fibres was found to be an
appropriate way to mitigate the process of
explosive spalling failure mechanism.
When high-resistance concrete is heated,
the runoff losses become more explosive.
The findings of a study on the residual
qualities of high strength fibre reinforced
concrete are presented in this publication..
Fiber length, fibre volume ratio, and fibre
content are only a few examples. Results
confirmed that explosive spalling might
take place inconsistently on HSC under
elevated temperature condition.
SR.
NO.
TITLE AUTHOR CONCLUSION
2. The Effect of
Elevated
Temperature
on Concrete
Materials and
Structures-A
Literature
Review
D. J. Naus
(2005)
this short study seeks to provide an
examination of the effect of high heats on
the analysis of RC elements. The study is
primarily focused on the performance of
reinforced concrete elements in designs of
new generation reactor concepts in which
the concrete may be exposed to long-term
steady-state temperatures in excess of the
present ASME Code limit of 65°C. The
longer the duration of heating before
testing, the larger the loss in strength.
However, the loss in strength stabilizes
after a period of isothermal exposure.
Also concrete specimens loaded during
heating loose less strength than unloaded
specimens.
SR.
NO.
TITLE AUTHOR CONCLUSION
3. Flexural
capacity of
singly
reinforced
beam with
150 MPa ultra
high-strength
concrete
Sungwoo
Shin et Al
(2010)
examine the hysteretic behavior of
ultrahigh-strength concrete tied columns
under stress to determine the effect of the
volumetric ratio of transverse
reinforcements on column deformability.
A reasonable method to enhance the
strength and ductility of tied columns is to
increase the amount of transverse
reinforcement confining the core concrete
and to take the transverse reinforcement
configuration into account when
designing the columns.
SR.
NO.
TITLE AUTHOR CONCLUSION
4. Comparative
Study of
Calculation
Models for
the Fire
Resistance of
Hollow Steel
Columns
Filled with
Concrete
Farid Fellah
et. Al (2011)
focuses on empty steel columns with
reinforced concrete linings, which are
often utilized in high-rise building
construction. In Europe and North
America, many investigations on the steel
reinforcement of these profiles have been
performed. Design engineers, on the other
hand, need more practical tools than
coders. Because the trial findings are
widely dispersed, developing such a
method would be difficult. His study looks
at three distinct methods, each of which is
based on a different procedure. We
compared the test results to the outcomes
of the three techniques. Each talent is
assessed for its potential, but it should
either be utilized with care or avoided
altogether.
SR.
NO.
TITLE AUTHOR CONCLUSION
5. Review on
storage
materials and
thermal
performance
enhancement
techniques for
high
temperature
phase change
thermal
storage
systems
Wasim
Khalik
(2012)
carried out the experimental and
numerical study on performance
characterization of high performance
concretes under fire conditions at both
material and structural level (specifically
columns). Results from fire resistance
tests show that plain HPC columns exhibit
lower fire resistance due to occurrence of
fire induced spalling and faster
degradation of strength. However,
presence of different fiber combinations in
HPC columns can significantly enhance
the fire resistance of the columns.
SR.
NO.
TITLE AUTHOR CONCLUSION
6. Analysis of
fire resistance
of concrete
with
polypropylen
e or steel
fibers
Ruben
Serrano and.
Al (2016)
Continuous development and enlargement
of structural elements is slowed by direct
contact to altitudes of up to 400 degrees
Celsius. By adding steel fibres or
polypropylene fibres into concrete, his
study seeks to address these issues.
Because it enhances both strength and fire
behavior and avoids cracking and
explosive concrete breaking, compression
crack test findings on cylindrical concrete
specimens indicate that polypropylene or
steel fibre reinforced concrete is a feasible
alternative to conventional concrete.
SR.
NO.
TITLE AUTHOR CONCLUSION
7. Effect of
temperature
on strength
and elastic
modulus of
high-strength
steel
Kodur
Venkatesh et
al. (2013)
studied that the high strength concrete
(HSC) columns exhibit lower fire
resistance, as compared to conventional
normal strength concrete columns, due to
occurrence of fire induced spalling and
faster degradation of strength and stiffness
properties of concrete with temperature.
Results show that HSC columns with 135o
bent ties exhibit higher fire resistance than
those HSC columns with 90o bent ties.
SR. NO. TITLE AUTHOR CONCLUSION
8. Performance
of insulated
FRP-
strengthened
concrete
flexural
members
under fire
conditions
Pratik Bhatt
and. Al
(2019)
develops a finite element (FE) based
numerical model in ABAQUS, to evaluate
the response of steel fiber reinforced
concrete (SFRC) columns under
combined effects of fire and structural
loading. Addition of steel fibers improves
the ductility, tensile strength and
toughness properties of concrete, and
thus, increases fire resistance of the HSC
column. Presence of the steel fibres in the
HSC columns can help to achieve up to
four hours of fire resistance.
SR. NO. TITLE AUTHOR CONCLUSION
9. Fire
Resistance of
Eccentrically
Loaded
Reinforced
Concrete
Columns
Shujaat
Hussain
Butch and
Umesh
Sharma
(2019)
observed that at ambient temperatures,
decrease in tie spacing is beneficial as it
increases moment capacity of the section
leading to better confinement. It is
observed that there is an improvement in
fire resistance by 150% for column with
diamond configuration as compared to
rectangular tie configuration with
crossties. it is observed that there was no
appreciable variation in the amount of
spalling for columns with diamond
configuration.
SR. NO. TITLE AUTHOR CONCLUSION
10. Experimental
Study of
Behavior of
Reinforced
Concrete
Columns with
added Steel
Fiber after
Fire Exposure
Mostafa
Abdel
Megied
Osman and.
Al (2020)
evaluates the improvement of the
behavior of reinforced concrete columns
strengthen by steel fibers after exposing
to fire. Ten R.C. columns with a circular
cross-section of 200 mm in Dia. and
1250 mm in Height with varying ratios of
steel fibers added in concrete mix
(0.50%, 1.0% and 1.50%), were
fabricated, then exposed to fire (Elevated
Temperature), and different methods of
fire resistance were loaded up to failure.
Results show that the strengthening with
steel fiber increased the load capacity and
stiffness of R.C. columns compared to
control specimens.
FINDINGS FROM LITERATURE
REVIEW
 The inclusion of steel fibers in HSC columns may aid in
achieving up to 4 hours of fire resistance.
 It was found that columns having diamond tie
configurations perform better in terms of fire resistance
than those having rectangular tie configurations including
crossties.
 HSC columns with 135o bent ties are more resistant to fire
than with 90o bent ties.
 Simple high performance concrete columns show
decreased fire resistance owing to the development of
fire-induced spalling and accelerated strength
deterioration. However, the inclusion of various fibre
mixes in high performance concrete columns may
substantially improve the columns' fire resistance.
 Raising the longitudinal reinforcement proportion of RC
columns improves their fire resistance.
RESEARCH GAPS IDENTIFIED FROM
LITERATURE REVIEW
The fire resistance of RC columns are never been
explored for variation in tie diameter.
No comparison is carried out between experimental and
numerical study to clarify the behavior of reinforced
concrete columns with variation in tie diameter subjected
to fire.
3D finite element (FE) modeling approach is never been
used to predict the mechanical response of various types of
the RC columns with variation in tie diameter of the
diamond tie configuration exposed to fire with sufficient
accuracy.
 There is lack of data on high temperature properties
specific to different types of HPC (plain and with fibers).
Also, there is no methodology to account for the effect of
tie configuration on fire resistance of RC columns.
NEED AND SCOPE OF THE STUDY
 The fire incidents across the world have been seen which
results in the large amount of damage to RCC framed
structures. Column being one of the most important load
bearing member losses strength during fire. The whole
structure fails due to the failure of the columns.
 In this research, an attempt will be made to increase the
fire resistance of the RCC columns with the use of
diamond ties. The structures should be designed keeping
in consideration the fire preventive measures and the
repairs after fire. Many structures get damaged which not
remains in the condition of repair due to poor fire
regulations.
PROPOSED OBJECTIVES
The objective of the proposed thesis work is:
 To determine the stress-strain relation for RC columns at
elevated temperature.
 To study the response of normal strength concrete column,
high strength concrete column and steel fiber reinforced
concrete columns under fire conditions and compare their
structural behavior.
 To analytically study the effect of use of diamond tie
configuration as lateral reinforcement in columns as
compared to lateral tie configuration on structural
behavior of the column using finite element analysis
approach.
RESEARCH METHODOLOGY
The following measures will be taken to carry out the
work:
 Using the FEM software ANSYS, a 3D Finite Element
(FE) dependent computational model is created.
 The ANSYS component is designed to follow the reaction
of the RC Columns through static elastic to fire failure
phase.
 The study is conducted in small gradual times utilizing a
thermal-mechanical analysis technique sequentially
coupled.
 Thermal load (fire exposed) is added to the column in
thermal analysis with the help of a given fire scenario
(duration ratios), whereby transversal temperature are
calculated.
 The calculated pass heats are given for mechanical
analysis inputs whereby, in relation to the thermal
stresses, there are mechanical loading and constraints
added and column axial and side displacements and axial
potential are calculated.
 The study takes into account the composite material's
physical and chemical thermal characteristics, as well as
deformations caused by insulating deformations.
 The column's reaction to all potential failure limiting
states is compared at each point, and the period at which a
fault limiting condition is violated is taken by means of a
steel reinforcement (i.e., column failure time).
PROBLEM STATEMENT
 All the columns were 3.81m long and had 305 mm X 305
mm square cross section. The columns were reinforced
with four steel bars of 25mm diameter in longitudinal
direction at a clear cover of 40 mm. The bars were tied
with lateral ties of 10 mm diameter at a spacing of 75 mm
in 650 mm length near the supports, and 145 mm spacing
in the middle of the column height. The HYSD500
should be checked in the ANSYS program for two legged
stirrups and diamond stirrups with a load of 1700 KN and
the thermal analysis should also be performed to verify
the impact of columns after temperature stresses.
RESULT AND DISCUSSION
 MODELS PREPARED IN ANSYS
MODEL 1 COLUMN WITH NSC
MODEL 2 COLUMN WITH HSC
MODEL 3 COLUMN WITH SFRC
MODEL 4 COLUMN WITH DIAMOND STIRRUP NSC
MODEL 5 COLUMN WITH DIAMOND STIRRUP HSC
MODEL 6 COLUMN WITH DIAMOND STIRRUP SFRC
MODEL 1: COLUMN WITH NSC:
Fig 2: Total Deformation
NSC
Fig 3: Normal Stress
NSC
MODEL 2: COLUMN WITH HSC
Fig 4 : Strain Energy
HSC
Fig 5: Maximum
Principal Stress HSC
MODEL 3: COLUMN WITH SFRC
Fig 6: Shear Stress SFRC Fig 7: Equivalent Stress SFRC
 MODEL 4: COLUMN WITH DIAMOND
STIRRUP NSC
Fig 8:Total Deformation
Diamond Stirrup NSC
Fig 9: Normal Stress
Diamond Stirrup NSC
 MODEL 5: COLUMN WITH DIAMOND
STIRRUP HSC
Fig 10: Strain Energy
Diamond Stirrup HSC
Fig 11: Maximum Principal
Stress Diamond Stirrup HSC
MODEL 6: COLUMN WITH DIAMOND
STIRRUP SFRC
Fig 12: Shear Stress Diamond
Stirrup SFRC
Fig 13: Equivalent Stress
Diamond Stirrup SFRC
RESULT ANALYSIS IN ANSYS
Total Deformation mm
Time
(sec)
NSC HSC SFRC Diamond NSC Diamond HSC
Diamond
SFRC
1 0.00 0.00 0.00 0.00 0.00 0.00
2 4.53 3.73 2.01 2.39 1.95 1.90
3 5.09 4.19 2.31 2.74 2.24 2.16
4 5.72 4.70 2.66 3.15 2.57 2.46
5 6.42 5.29 3.05 3.62 2.96 2.79
6 7.22 5.94 3.51 4.17 3.40 3.17
7 8.11 6.67 4.03 4.79 3.91 3.61
8 9.11 7.50 4.64 5.50 4.49 4.10
9 10.23 8.43 5.33 6.33 5.16 4.66
10 11.50 9.47 6.13 7.27 5.93 5.29
11 12.92 10.64 7.04 8.36 6.82 6.01
12 14.52 11.95 8.09 9.61 7.84 6.83
13 16.31 13.43 9.30 11.04 9.01 7.77
14 18.33 15.09 10.69 12.69 10.35 8.83
15 20.59 16.95 12.29 14.59 11.90 10.03
16 23.14 19.05 14.13 16.77 13.68 11.40
17 26.00 21.40 16.24 19.28 15.72 12.95
18 29.21 24.05 18.67 22.16 18.07 14.72
19 32.82 27.02 21.45 25.47 20.77 16.72
20 36.88 30.36 24.66 29.27 23.87 19.00
Table 1: Total Deformation
 Above graph shows the result for Total Deformation in mm for
columns having simple lateral ties with two legged stirrups and
diamond stirrups. From the results it concludes that Total
Deformation for two legged stirrups in NSC is greater than
diamond NSC by 47.24%. Total Deformation for two legged
stirrups in HSC is greater than diamond HSC by 47.72%. Total
Deformation for two legged stirrups in SFRC is greater than
diamond SFRC by 5.47%.
Graph 1: Total Deformation
Table 2: Normal Stress (MPa) :
Normal Stress Mpa
Time NSC HSC SFRC Diamond NSC Diamond HSC Diamond SFRC
1 0 0 0 0 0 0
2 41.851 51.017 50.828 50.986 50.797 41.349
3 47.024 56.686 56.476 56.651 56.441 46.460
4 52.836 62.984 62.751 62.945 62.712 52.202
5 59.366 69.982 69.723 69.939 69.680 58.654
6 66.704 77.758 77.470 77.710 77.422 65.904
7 74.948 86.398 86.078 86.345 86.024 74.049
8 84.211 95.998 95.642 95.938 95.583 83.201
9 94.620 106.664 106.269 106.598 106.203 93.484
10 106.314 118.516 118.076 118.443 118.003 105.039
11 119.454 131.684 131.196 131.603 131.115 118.021
12 134.218 146.316 145.773 146.225 145.683 132.608
13 150.807 162.573 161.970 162.473 161.870 148.998
14 169.446 180.637 179.967 180.525 179.856 167.413
15 190.389 200.708 199.964 200.584 199.840 188.105
16 213.920 223.008 222.182 222.871 222.044 211.354
17 240.359 247.787 246.869 247.634 246.715 237.476
18 270.066 275.319 274.298 275.149 274.128 266.827
19 303.446 305.910 304.776 305.721 304.587 299.805
20 340.950 339.900 338.640 339.690 338.430 336.860
 Above graph shows the result for Normal Stress for columns
having simple lateral ties with two legged stirrups and diamond
stirrups. From the results it concludes that Normal Stress for
diamond NSC is greater than two legged stirrups in NSC by
17.91%. Normal Stress for two legged stirrups in HSC is greater
than diamond HSC by 0.43%. Normal Stress for two legged
stirrups in SFRC is greater than diamond SFRC by 18.64%.
Graph 2: Normal Stress (mm)
Table 3: Strain Energy (Mpa)
Strain Energy Mpa
Time NSC HSC SFRC Diamond NSC Diamond HSC Diamond SFRC
1 0 0 0 0 0 0
2 1.288 1.105 0.945 1.075 0.923 1.994
3 1.370 1.176 1.005 1.143 0.981 2.015
4 1.457 1.251 1.069 1.216 1.044 2.035
5 1.550 1.330 1.138 1.294 1.111 2.055
6 1.649 1.415 1.210 1.376 1.182 2.076
7 1.754 1.506 1.287 1.464 1.257 2.097
8 1.866 1.602 1.370 1.558 1.337 2.118
9 1.985 1.704 1.457 1.657 1.423 2.140
10 2.112 1.813 1.550 1.763 1.514 2.161
11 2.247 1.928 1.649 1.875 1.610 2.183
12 2.390 2.052 1.754 1.995 1.713 2.205
13 2.543 2.182 1.866 2.122 1.822 2.228
14 2.705 2.322 1.985 2.258 1.939 2.250
15 2.878 2.470 2.112 2.402 2.062 2.273
16 3.062 2.628 2.247 2.555 2.194 2.296
17 3.257 2.795 2.390 2.718 2.334 2.319
18 3.465 2.974 2.543 2.892 2.483 2.342
19 3.686 3.164 2.705 3.077 2.641 2.366
20 3.922 3.366 2.878 3.273 2.810 2.390
 Above graph shows the result for Strain Energy in mm for
columns having simple lateral ties with two legged stirrups and
diamond stirrups. From the results it concludes that Strain Energy
for two legged stirrups in NSC is greater than diamond NSC by
16.45%. Strain Energy for two legged stirrups in HSC is greater
than diamond HSC by 16.47%. Strain Energy for diamond SFRC
is greater than two legged stirrups in SFRC by 52.6%.
Graph 3: Strain Energy (Mpa)
Table 4: Maximum Principal Stress
Maximum Principal Stress Mpa
Time NSC HSC SFRC Diamond NSC Diamond HSC Diamond SFRC
1 0.00 0.00 0.00 0.00 0.00 0.00
2 82.71 82.42 82.08 82.36 82.02 81.59
3 93.99 93.66 93.27 93.60 93.20 92.71
4 106.80 106.43 105.99 106.36 105.91 105.36
5 121.37 120.95 120.44 120.86 120.36 119.72
6 137.92 137.44 136.86 137.34 136.77 136.05
7 156.73 156.18 155.53 156.07 155.42 154.60
8 178.10 177.48 176.74 177.36 176.61 175.68
9 202.38 201.68 200.84 201.54 200.69 199.64
10 229.98 229.18 228.22 229.02 228.06 226.86
11 261.34 260.43 259.34 260.25 259.16 257.80
12 296.98 295.95 294.71 295.74 294.50 292.95
13 337.48 336.30 334.90 336.07 334.66 332.90
14 383.50 382.16 380.57 381.90 380.30 378.30
15 435.79 434.28 432.46 433.98 432.15 429.89
16 495.22 493.50 491.43 493.15 491.08 488.51
17 562.75 560.79 558.45 560.40 558.05 555.12
18 639.48 637.26 634.60 636.82 634.15 630.82
19 726.69 724.16 721.13 723.66 720.62 716.84
20 825.78 822.91 819.47 822.34 818.89 814.59
 Above graph shows the result for Maximum Principal Stress for
columns having simple lateral ties with two legged stirrups and
diamond stirrups. From the results it concludes that Maximum
Principal Stress for two legged stirrups in NSC is greater than
diamond NSC by 0.42%. Maximum Principal Stress for two
legged stirrups in HSC is greater than diamond HSC by 0.48%.
Maximum Principal Stress for two legged stirrups in SFRC is
greater than diamond SFRC by 0.59%.
Graph 4: Maximum Principal Stress
Table 2: Shear Stress
Shear Stress Mpa
Time NSC HSC SFRC Diamond NSC Diamond HSC Diamond SFRC
1 0 0 0 0 0 0
2 24.796 24.622 15.985 16.098 15.963 10.236
3 28.833 28.631 19.030 19.164 19.003 12.483
4 33.527 33.291 22.655 22.815 22.623 15.223
5 38.985 38.711 26.970 27.160 26.932 18.565
6 45.331 45.013 32.108 32.334 32.062 22.640
7 52.710 52.340 38.223 38.493 38.169 27.610
8 61.291 60.861 45.504 45.825 45.440 33.670
9 71.269 70.768 54.171 54.553 54.095 41.062
10 82.871 82.289 64.490 64.944 64.399 50.075
11 96.361 95.685 76.773 77.315 76.665 61.067
12 112.048 111.261 91.397 92.041 91.268 74.472
13 130.289 129.373 108.806 109.573 108.652 90.820
14 151.498 150.434 129.531 130.444 129.348 110.756
15 176.161 174.924 154.203 155.290 153.986 135.068
16 204.838 203.400 183.575 184.870 183.316 164.717
17 238.184 236.511 218.542 220.083 218.234 200.874
18 276.958 275.013 260.169 262.003 259.802 244.969
19 322.044 319.782 309.725 311.909 309.288 298.742
20 374.470 371.840 368.720 371.320 368.200 364.320
 Above graph shows the result for Shear Stress for columns
having simple lateral ties with two legged stirrups and diamond
stirrups. From the results it concludes that Shear Stress for two
legged stirrups in NSC is greater than diamond NSC by 35.07%.
Shear Stress for two legged stirrups in HSC is greater than
diamond HSC by 35.16%. Shear Stress for two legged stirrups in
SFRC is greater than diamond SFRC by 35.96%.
Graph 2: Shear Stress
Table 3: Equivalent Stress
Equivalent Stress Mpa
Time NSC HSC SFRC Diamond NSC Diamond HSC Diamond SFRC
1 0 0 0 0 0 0
2 140.563 140.923 141.394 141.003 141.484 142.125
3 159.730 160.140 160.675 160.231 160.777 161.506
4 181.512 181.977 182.585 182.081 182.701 183.529
5 206.263 206.792 207.483 206.910 207.615 208.556
6 234.390 234.991 235.776 235.125 235.926 236.995
7 266.352 267.035 267.927 267.187 268.098 269.313
8 302.673 303.449 304.463 303.622 304.657 306.037
9 343.946 344.829 345.981 345.025 346.201 347.770
10 390.848 391.851 393.160 392.074 393.410 395.193
11 444.146 445.285 446.773 445.538 447.057 449.083
12 504.711 506.006 507.696 506.293 508.020 510.321
13 573.535 575.007 576.927 575.334 577.295 579.911
14 651.745 653.417 655.599 653.788 656.017 658.989
15 740.619 742.519 744.999 742.941 745.474 748.852
16 841.612 843.771 846.590 844.251 847.130 850.968
17 956.378 958.831 962.034 959.376 962.647 967.009
18 1086.793 1089.581 1093.220 1090.200 1093.917 1098.874
19 1234.992 1238.160 1242.296 1238.864 1243.088 1248.720
20 1403.400 1407.000 1411.700 1407.800 1412.600 1419.000
 Above graph shows the result for Equivalent Stress for columns
having simple lateral ties with two legged stirrups and diamond
stirrups. From the results it concludes that Equivalent Stress for
diamond NSC is greater than two legged stirrups in NSC by
0.31%. Equivalent Stress for diamond HSC is greater than two
legged stirrups in HSC by 0.39%. Equivalent Stress for diamond
SFRC is greater than two legged stirrups in SFRC by 5.17%.
Graph 3: Equivalent Stress
Table 4: Total Heat Flux
Total Heat Flux W/mm^2
Time NSC HSC SFRC Diamond NSC Diamond HSC Diamond SFRC
1 0 0 0 0 0 0
2 0.0051 0.0057 0.0064 0.0062 0.007 0.0078
3 0.0058 0.0065 0.0072 0.0071 0.0079 0.0088
4 0.0066 0.0074 0.0082 0.008 0.009 0.01
5 0.0075 0.0084 0.0094 0.0091 0.0102 0.0114
6 0.0085 0.0095 0.0106 0.0104 0.0116 0.0129
7 0.0097 0.0108 0.0121 0.0118 0.0132 0.0147
8 0.011 0.0123 0.0137 0.0134 0.015 0.0167
9 0.0125 0.014 0.0156 0.0153 0.017 0.019
10 0.0142 0.0159 0.0177 0.0173 0.0193 0.0216
11 0.0162 0.0181 0.0201 0.0197 0.022 0.0245
12 0.0184 0.0205 0.0229 0.0224 0.025 0.0279
13 0.0209 0.0233 0.026 0.0254 0.0284 0.0317
14 0.0238 0.0265 0.0296 0.0289 0.0322 0.036
15 0.027 0.0301 0.0336 0.0328 0.0366 0.0409
16 0.0307 0.0342 0.0382 0.0373 0.0416 0.0465
17 0.0349 0.0389 0.0434 0.0424 0.0473 0.0528
18 0.0396 0.0442 0.0493 0.0482 0.0537 0.06
19 0.045 0.0502 0.056 0.0548 0.0611 0.0682
20 0.051151 0.057058 0.063637 0.062231 0.06939 0.077535
 Above graph shows the result for Total Heat Flux for columns
having simple lateral ties with two legged stirrups and diamond
stirrups. From the results it concludes that Total Heat Flux for
diamond NSC is greater than two legged stirrups in NSC by
17.74%. Total Heat Flux for diamond HSC is greater than two
legged stirrups in HSC by 18.57%. Total Heat Flux for diamond
SFRC is greater than two legged stirrups in SFRC by 17.94%.
Graph 4: Total Heat Flux
CONCLUSION
 The results are taken for Total Heat Flux for columns
having simple lateral ties with two legged stirrups and
diamond stirrups. From the results it concludes that Total
Heat Flux for diamond NSC is greater than two legged
stirrups in NSC by 17.74%. Total Heat Flux for diamond
HSC is greater than two legged stirrups in HSC by
18.57%. Total Heat Flux for diamond SFRC is greater
than two legged stirrups in SFRC by 17.94%.
 The results are taken for Equivalent Stress for columns
having simple lateral ties with two legged stirrups and
diamond stirrups. From the results it concludes that
Equivalent Stress for diamond NSC is greater than two
legged stirrups in NSC by 0.31%. Equivalent Stress for
diamond HSC is greater than two legged stirrups in HSC
by 0.39%. Equivalent Stress for diamond SFRC is greater
than two legged stirrups in SFRC by 5.17%.
 The results are taken for Shear Stress for columns having simple
lateral ties with two legged stirrups and diamond stirrups. From
the results it concludes that Shear Stress for two legged stirrups
in NSC is greater than diamond NSC by 35.07%. Shear Stress for
two legged stirrups in HSC is greater than diamond HSC by
35.16%. Shear Stress for two legged stirrups in SFRC is greater
than diamond SFRC by 35.96%.
 The results are taken for Maximum Principal Stress for columns
having simple lateral ties with two legged stirrups and diamond
stirrups. From the results it concludes that Maximum Principal
Stress for two legged stirrups in NSC is greater than diamond
NSC by 0.42%. Maximum Principal Stress for two legged
stirrups in HSC is greater than diamond HSC by 0.48%.
Maximum Principal Stress for two legged stirrups in SFRC is
greater than diamond SFRC by 0.59%.
 The results are taken for Strain Energy in mm for columns having
simple lateral ties with two legged stirrups and diamond stirrups.
From the results it concludes that Strain Energy for two legged
stirrups in NSC is greater than diamond NSC by 16.45%. Strain
Energy for two legged stirrups in HSC is greater than diamond
HSC by 16.47%. Strain Energy for diamond SFRC is greater than
two legged stirrups in SFRC by 52.6%.
 The results are taken for Normal Stress for columns having
simple lateral ties with two legged stirrups and diamond stirrups.
From the results it concludes that Normal Stress for diamond
NSC is greater than two legged stirrups in NSC by 17.91%.
Normal Stress for two legged stirrups in HSC is greater than
diamond HSC by 0.43%. Normal Stress for two legged stirrups in
SFRC is greater than diamond SFRC by 18.64%.
 The results are taken for Total Deformation in mm for columns
having simple lateral ties with two legged stirrups and diamond
stirrups. From the results it concludes that Total Deformation for
two legged stirrups in NSC is greater than diamond NSC by
47.24%. Total Deformation for two legged stirrups in HSC is
greater than diamond HSC by 47.72%. Total Deformation for two
legged stirrups in SFRC is greater than diamond SFRC by 5.47%.
FUTURE SCOPE
 Further studies can be undertaken for configurations of
lateral reinforcement other than diamond shape done here.
Other column shapes can also be considered for future
study.
REFERENCES
 Kodur, V.K.R. and Lie, T.T. (1998), Fire Resistance of Fiber-Reinforced Concrete.
Fiber Reinforced Concrete: Present and the Future, Canadian Society of Civil
Engineers, pp. 189-213.
 Phan, L.T. and Carino, N.J. (1998) "Review of Mechanical Properties of HSC at
Elevated Temperature” Journal of Materials in Civil Engineering, Vol. 10, No. 1, pp.
4 58-64.
 Kodur, V. K. R. (2000). "Spalling in High Strength Concrete Exposed to Fire-
Concerns, Causes, Critical Parameters and Cures." in Proceedings of the ASCE
Structures Congress: Advanced Technology in Structural Engineering, Philadelphia,
Pennsylvania (PA), USA. 1-9.
 Kodur, V.K.R. and McGrath, R. (2001) Performance of High Strength Concrete
Columns under Severe Fire Conditions. Proceedings Third International Conference
on Concrete under Severe Conditions, Vancouver, BC, Canada, pp. 254-268.
 Kodur, V. K. R and Sultan, M. A, (2003) “Effect of Temperature on Thermal
Properties of High-Strength Concrete”, Journal of Materials in Civil Engineering,
Vol. 15, No. 2, pp. 101 20 – 107.
 Suhaendi, S.L. and Horiguchi, T. (2004), “Fiber-reinforced High-strength Concrete
under Elevated Temperature―Effect of Fibers on Residual Properties” Proceedings
of the Japan Concrete Institute, , Kochi, Japan
 Naus, D.J.(2005), “The Effect of Elevated Temperature on Concrete Materials and
Structures-A Literature Review.” U.S. Nuclear Regulatory Commission, Office of
Nuclear Regulatory Research, Washington (DC), USA.
 Shin, S., Kim, J. and Ahn, J. (2010), “Transverse Reinforcement of RC Columns
Considering Effective Lateral Confining Reduction Factor” Journal of Asian
Architecture and Building Engineering, 501-508.
 Martins, A. M. B. and Rodrigues, J. P.C. (2010), “Behavior Of Concrete Columns
Subjected To Fire” University of Coimbra.
 Khaliq, W. (2012), “Performance Characterization of High Performance Concretes
Under Fire Conditions” Michigan State University.
 Baolin Yu, B. (2013), “Fire Response of Reinforced Concrete Columns
Strengthened With Near-Surface Mounted FRP Reinforcement” Michigan State
University.
 Kodur, V. K. R., Khaliq, W., Raut, N. (2013). “An approach to account for tie
configuration in predicting fire resistance of reinforced concrete columns”
Retrieved 15 July 2020, from https://www.researchgate.net/publication/263466983
 Bhatt, P, Kodur, V.K.R., and Matsagar, V.(2019), “Numerical approach to evaluate
elevated temperature behavior of steel fiber reinforced concrete columns.” The
Indian concrete journal, 8-15.
Rapid hardening cement (RHC) is a type of cement
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Rapid hardening cement (RHC) is a type of cement

  • 1. ANALYTICAL INVESTIGATION OF STRUCTURAL BEHAVIOR OF REINFORCED CONCRETE COLUMN USING DIAMOND TIE CONFIGURATION UNDER ELEVATED TEMPERATURES Under The Supervision of ER. HIMMI GUPTA (Assistant Professor) Presented By Sudesh Kumar (171327-Modular) Reg. No. 17-TTC-51 Department of Civil Engineering National Institute of Technical Teachers Training and Research Sector-26, Chandigarh - 160019
  • 2. CONTENT  INTRODUCTION  LITERATURE REVIEW  PROPOSED WORK  RESULT AND DISCUSSION  CONCLUSION  REFERENCES
  • 3. INTRODUCTION GENERAL  A total of 2,500 citizens in India die per year as a result of building fire occurrences . Fire causes thousands of deaths and loss of property.  The fire incidents across the world have been seen which results in the large amount of damage to reinforced cement concrete framed structures.  Column being one of the most important loads bearing member, the whole structure fails due to the failure of the columns.
  • 4.  The increased use of cement in building design results in the need to research the behavior of structures in reinforced concrete.  Fire prevention and post fire maintenance should be taken into account in the structure (retrofitting).  Many buildings suffer harm that cannot be repaired because of inadequate fire laws.
  • 5. FACTORS AFFECTING FIRE RESISTANCE OF RCC COLUMNS  Aggregate Type  Concrete Grade  Lateral Strengthening  Longitudinal reinforcement  Intensity of fire  Intensity and type of load  Concrete cover  Column size
  • 6. THE STIRRUPS COMMONLY FOUND IN COLUMN DESIGN Fig 1: Types of stirrups
  • 7. LITERATURE REVIEW SR. NO. TITLE AUTHOR CONCLUSION 1. Permeability of Heated Fiber- Reinforced High-Strength Concrete Sofren Leo Suhaendi et. Al (2004) In his investigation, the combination of polypropylene fibres was found to be an appropriate way to mitigate the process of explosive spalling failure mechanism. When high-resistance concrete is heated, the runoff losses become more explosive. The findings of a study on the residual qualities of high strength fibre reinforced concrete are presented in this publication.. Fiber length, fibre volume ratio, and fibre content are only a few examples. Results confirmed that explosive spalling might take place inconsistently on HSC under elevated temperature condition.
  • 8. SR. NO. TITLE AUTHOR CONCLUSION 2. The Effect of Elevated Temperature on Concrete Materials and Structures-A Literature Review D. J. Naus (2005) this short study seeks to provide an examination of the effect of high heats on the analysis of RC elements. The study is primarily focused on the performance of reinforced concrete elements in designs of new generation reactor concepts in which the concrete may be exposed to long-term steady-state temperatures in excess of the present ASME Code limit of 65°C. The longer the duration of heating before testing, the larger the loss in strength. However, the loss in strength stabilizes after a period of isothermal exposure. Also concrete specimens loaded during heating loose less strength than unloaded specimens.
  • 9. SR. NO. TITLE AUTHOR CONCLUSION 3. Flexural capacity of singly reinforced beam with 150 MPa ultra high-strength concrete Sungwoo Shin et Al (2010) examine the hysteretic behavior of ultrahigh-strength concrete tied columns under stress to determine the effect of the volumetric ratio of transverse reinforcements on column deformability. A reasonable method to enhance the strength and ductility of tied columns is to increase the amount of transverse reinforcement confining the core concrete and to take the transverse reinforcement configuration into account when designing the columns.
  • 10. SR. NO. TITLE AUTHOR CONCLUSION 4. Comparative Study of Calculation Models for the Fire Resistance of Hollow Steel Columns Filled with Concrete Farid Fellah et. Al (2011) focuses on empty steel columns with reinforced concrete linings, which are often utilized in high-rise building construction. In Europe and North America, many investigations on the steel reinforcement of these profiles have been performed. Design engineers, on the other hand, need more practical tools than coders. Because the trial findings are widely dispersed, developing such a method would be difficult. His study looks at three distinct methods, each of which is based on a different procedure. We compared the test results to the outcomes of the three techniques. Each talent is assessed for its potential, but it should either be utilized with care or avoided altogether.
  • 11. SR. NO. TITLE AUTHOR CONCLUSION 5. Review on storage materials and thermal performance enhancement techniques for high temperature phase change thermal storage systems Wasim Khalik (2012) carried out the experimental and numerical study on performance characterization of high performance concretes under fire conditions at both material and structural level (specifically columns). Results from fire resistance tests show that plain HPC columns exhibit lower fire resistance due to occurrence of fire induced spalling and faster degradation of strength. However, presence of different fiber combinations in HPC columns can significantly enhance the fire resistance of the columns.
  • 12. SR. NO. TITLE AUTHOR CONCLUSION 6. Analysis of fire resistance of concrete with polypropylen e or steel fibers Ruben Serrano and. Al (2016) Continuous development and enlargement of structural elements is slowed by direct contact to altitudes of up to 400 degrees Celsius. By adding steel fibres or polypropylene fibres into concrete, his study seeks to address these issues. Because it enhances both strength and fire behavior and avoids cracking and explosive concrete breaking, compression crack test findings on cylindrical concrete specimens indicate that polypropylene or steel fibre reinforced concrete is a feasible alternative to conventional concrete.
  • 13. SR. NO. TITLE AUTHOR CONCLUSION 7. Effect of temperature on strength and elastic modulus of high-strength steel Kodur Venkatesh et al. (2013) studied that the high strength concrete (HSC) columns exhibit lower fire resistance, as compared to conventional normal strength concrete columns, due to occurrence of fire induced spalling and faster degradation of strength and stiffness properties of concrete with temperature. Results show that HSC columns with 135o bent ties exhibit higher fire resistance than those HSC columns with 90o bent ties.
  • 14. SR. NO. TITLE AUTHOR CONCLUSION 8. Performance of insulated FRP- strengthened concrete flexural members under fire conditions Pratik Bhatt and. Al (2019) develops a finite element (FE) based numerical model in ABAQUS, to evaluate the response of steel fiber reinforced concrete (SFRC) columns under combined effects of fire and structural loading. Addition of steel fibers improves the ductility, tensile strength and toughness properties of concrete, and thus, increases fire resistance of the HSC column. Presence of the steel fibres in the HSC columns can help to achieve up to four hours of fire resistance.
  • 15. SR. NO. TITLE AUTHOR CONCLUSION 9. Fire Resistance of Eccentrically Loaded Reinforced Concrete Columns Shujaat Hussain Butch and Umesh Sharma (2019) observed that at ambient temperatures, decrease in tie spacing is beneficial as it increases moment capacity of the section leading to better confinement. It is observed that there is an improvement in fire resistance by 150% for column with diamond configuration as compared to rectangular tie configuration with crossties. it is observed that there was no appreciable variation in the amount of spalling for columns with diamond configuration.
  • 16. SR. NO. TITLE AUTHOR CONCLUSION 10. Experimental Study of Behavior of Reinforced Concrete Columns with added Steel Fiber after Fire Exposure Mostafa Abdel Megied Osman and. Al (2020) evaluates the improvement of the behavior of reinforced concrete columns strengthen by steel fibers after exposing to fire. Ten R.C. columns with a circular cross-section of 200 mm in Dia. and 1250 mm in Height with varying ratios of steel fibers added in concrete mix (0.50%, 1.0% and 1.50%), were fabricated, then exposed to fire (Elevated Temperature), and different methods of fire resistance were loaded up to failure. Results show that the strengthening with steel fiber increased the load capacity and stiffness of R.C. columns compared to control specimens.
  • 17. FINDINGS FROM LITERATURE REVIEW  The inclusion of steel fibers in HSC columns may aid in achieving up to 4 hours of fire resistance.  It was found that columns having diamond tie configurations perform better in terms of fire resistance than those having rectangular tie configurations including crossties.  HSC columns with 135o bent ties are more resistant to fire than with 90o bent ties.
  • 18.  Simple high performance concrete columns show decreased fire resistance owing to the development of fire-induced spalling and accelerated strength deterioration. However, the inclusion of various fibre mixes in high performance concrete columns may substantially improve the columns' fire resistance.  Raising the longitudinal reinforcement proportion of RC columns improves their fire resistance.
  • 19. RESEARCH GAPS IDENTIFIED FROM LITERATURE REVIEW The fire resistance of RC columns are never been explored for variation in tie diameter. No comparison is carried out between experimental and numerical study to clarify the behavior of reinforced concrete columns with variation in tie diameter subjected to fire.
  • 20. 3D finite element (FE) modeling approach is never been used to predict the mechanical response of various types of the RC columns with variation in tie diameter of the diamond tie configuration exposed to fire with sufficient accuracy.  There is lack of data on high temperature properties specific to different types of HPC (plain and with fibers). Also, there is no methodology to account for the effect of tie configuration on fire resistance of RC columns.
  • 21. NEED AND SCOPE OF THE STUDY  The fire incidents across the world have been seen which results in the large amount of damage to RCC framed structures. Column being one of the most important load bearing member losses strength during fire. The whole structure fails due to the failure of the columns.  In this research, an attempt will be made to increase the fire resistance of the RCC columns with the use of diamond ties. The structures should be designed keeping in consideration the fire preventive measures and the repairs after fire. Many structures get damaged which not remains in the condition of repair due to poor fire regulations.
  • 22. PROPOSED OBJECTIVES The objective of the proposed thesis work is:  To determine the stress-strain relation for RC columns at elevated temperature.  To study the response of normal strength concrete column, high strength concrete column and steel fiber reinforced concrete columns under fire conditions and compare their structural behavior.  To analytically study the effect of use of diamond tie configuration as lateral reinforcement in columns as compared to lateral tie configuration on structural behavior of the column using finite element analysis approach.
  • 23. RESEARCH METHODOLOGY The following measures will be taken to carry out the work:  Using the FEM software ANSYS, a 3D Finite Element (FE) dependent computational model is created.  The ANSYS component is designed to follow the reaction of the RC Columns through static elastic to fire failure phase.  The study is conducted in small gradual times utilizing a thermal-mechanical analysis technique sequentially coupled.
  • 24.  Thermal load (fire exposed) is added to the column in thermal analysis with the help of a given fire scenario (duration ratios), whereby transversal temperature are calculated.  The calculated pass heats are given for mechanical analysis inputs whereby, in relation to the thermal stresses, there are mechanical loading and constraints added and column axial and side displacements and axial potential are calculated.  The study takes into account the composite material's physical and chemical thermal characteristics, as well as deformations caused by insulating deformations.
  • 25.  The column's reaction to all potential failure limiting states is compared at each point, and the period at which a fault limiting condition is violated is taken by means of a steel reinforcement (i.e., column failure time).
  • 26. PROBLEM STATEMENT  All the columns were 3.81m long and had 305 mm X 305 mm square cross section. The columns were reinforced with four steel bars of 25mm diameter in longitudinal direction at a clear cover of 40 mm. The bars were tied with lateral ties of 10 mm diameter at a spacing of 75 mm in 650 mm length near the supports, and 145 mm spacing in the middle of the column height. The HYSD500 should be checked in the ANSYS program for two legged stirrups and diamond stirrups with a load of 1700 KN and the thermal analysis should also be performed to verify the impact of columns after temperature stresses.
  • 27. RESULT AND DISCUSSION  MODELS PREPARED IN ANSYS MODEL 1 COLUMN WITH NSC MODEL 2 COLUMN WITH HSC MODEL 3 COLUMN WITH SFRC MODEL 4 COLUMN WITH DIAMOND STIRRUP NSC MODEL 5 COLUMN WITH DIAMOND STIRRUP HSC MODEL 6 COLUMN WITH DIAMOND STIRRUP SFRC
  • 28. MODEL 1: COLUMN WITH NSC: Fig 2: Total Deformation NSC Fig 3: Normal Stress NSC
  • 29. MODEL 2: COLUMN WITH HSC Fig 4 : Strain Energy HSC Fig 5: Maximum Principal Stress HSC
  • 30. MODEL 3: COLUMN WITH SFRC Fig 6: Shear Stress SFRC Fig 7: Equivalent Stress SFRC
  • 31.  MODEL 4: COLUMN WITH DIAMOND STIRRUP NSC Fig 8:Total Deformation Diamond Stirrup NSC Fig 9: Normal Stress Diamond Stirrup NSC
  • 32.  MODEL 5: COLUMN WITH DIAMOND STIRRUP HSC Fig 10: Strain Energy Diamond Stirrup HSC Fig 11: Maximum Principal Stress Diamond Stirrup HSC
  • 33. MODEL 6: COLUMN WITH DIAMOND STIRRUP SFRC Fig 12: Shear Stress Diamond Stirrup SFRC Fig 13: Equivalent Stress Diamond Stirrup SFRC
  • 34. RESULT ANALYSIS IN ANSYS Total Deformation mm Time (sec) NSC HSC SFRC Diamond NSC Diamond HSC Diamond SFRC 1 0.00 0.00 0.00 0.00 0.00 0.00 2 4.53 3.73 2.01 2.39 1.95 1.90 3 5.09 4.19 2.31 2.74 2.24 2.16 4 5.72 4.70 2.66 3.15 2.57 2.46 5 6.42 5.29 3.05 3.62 2.96 2.79 6 7.22 5.94 3.51 4.17 3.40 3.17 7 8.11 6.67 4.03 4.79 3.91 3.61 8 9.11 7.50 4.64 5.50 4.49 4.10 9 10.23 8.43 5.33 6.33 5.16 4.66 10 11.50 9.47 6.13 7.27 5.93 5.29 11 12.92 10.64 7.04 8.36 6.82 6.01 12 14.52 11.95 8.09 9.61 7.84 6.83 13 16.31 13.43 9.30 11.04 9.01 7.77 14 18.33 15.09 10.69 12.69 10.35 8.83 15 20.59 16.95 12.29 14.59 11.90 10.03 16 23.14 19.05 14.13 16.77 13.68 11.40 17 26.00 21.40 16.24 19.28 15.72 12.95 18 29.21 24.05 18.67 22.16 18.07 14.72 19 32.82 27.02 21.45 25.47 20.77 16.72 20 36.88 30.36 24.66 29.27 23.87 19.00 Table 1: Total Deformation
  • 35.  Above graph shows the result for Total Deformation in mm for columns having simple lateral ties with two legged stirrups and diamond stirrups. From the results it concludes that Total Deformation for two legged stirrups in NSC is greater than diamond NSC by 47.24%. Total Deformation for two legged stirrups in HSC is greater than diamond HSC by 47.72%. Total Deformation for two legged stirrups in SFRC is greater than diamond SFRC by 5.47%. Graph 1: Total Deformation
  • 36. Table 2: Normal Stress (MPa) : Normal Stress Mpa Time NSC HSC SFRC Diamond NSC Diamond HSC Diamond SFRC 1 0 0 0 0 0 0 2 41.851 51.017 50.828 50.986 50.797 41.349 3 47.024 56.686 56.476 56.651 56.441 46.460 4 52.836 62.984 62.751 62.945 62.712 52.202 5 59.366 69.982 69.723 69.939 69.680 58.654 6 66.704 77.758 77.470 77.710 77.422 65.904 7 74.948 86.398 86.078 86.345 86.024 74.049 8 84.211 95.998 95.642 95.938 95.583 83.201 9 94.620 106.664 106.269 106.598 106.203 93.484 10 106.314 118.516 118.076 118.443 118.003 105.039 11 119.454 131.684 131.196 131.603 131.115 118.021 12 134.218 146.316 145.773 146.225 145.683 132.608 13 150.807 162.573 161.970 162.473 161.870 148.998 14 169.446 180.637 179.967 180.525 179.856 167.413 15 190.389 200.708 199.964 200.584 199.840 188.105 16 213.920 223.008 222.182 222.871 222.044 211.354 17 240.359 247.787 246.869 247.634 246.715 237.476 18 270.066 275.319 274.298 275.149 274.128 266.827 19 303.446 305.910 304.776 305.721 304.587 299.805 20 340.950 339.900 338.640 339.690 338.430 336.860
  • 37.  Above graph shows the result for Normal Stress for columns having simple lateral ties with two legged stirrups and diamond stirrups. From the results it concludes that Normal Stress for diamond NSC is greater than two legged stirrups in NSC by 17.91%. Normal Stress for two legged stirrups in HSC is greater than diamond HSC by 0.43%. Normal Stress for two legged stirrups in SFRC is greater than diamond SFRC by 18.64%. Graph 2: Normal Stress (mm)
  • 38. Table 3: Strain Energy (Mpa) Strain Energy Mpa Time NSC HSC SFRC Diamond NSC Diamond HSC Diamond SFRC 1 0 0 0 0 0 0 2 1.288 1.105 0.945 1.075 0.923 1.994 3 1.370 1.176 1.005 1.143 0.981 2.015 4 1.457 1.251 1.069 1.216 1.044 2.035 5 1.550 1.330 1.138 1.294 1.111 2.055 6 1.649 1.415 1.210 1.376 1.182 2.076 7 1.754 1.506 1.287 1.464 1.257 2.097 8 1.866 1.602 1.370 1.558 1.337 2.118 9 1.985 1.704 1.457 1.657 1.423 2.140 10 2.112 1.813 1.550 1.763 1.514 2.161 11 2.247 1.928 1.649 1.875 1.610 2.183 12 2.390 2.052 1.754 1.995 1.713 2.205 13 2.543 2.182 1.866 2.122 1.822 2.228 14 2.705 2.322 1.985 2.258 1.939 2.250 15 2.878 2.470 2.112 2.402 2.062 2.273 16 3.062 2.628 2.247 2.555 2.194 2.296 17 3.257 2.795 2.390 2.718 2.334 2.319 18 3.465 2.974 2.543 2.892 2.483 2.342 19 3.686 3.164 2.705 3.077 2.641 2.366 20 3.922 3.366 2.878 3.273 2.810 2.390
  • 39.  Above graph shows the result for Strain Energy in mm for columns having simple lateral ties with two legged stirrups and diamond stirrups. From the results it concludes that Strain Energy for two legged stirrups in NSC is greater than diamond NSC by 16.45%. Strain Energy for two legged stirrups in HSC is greater than diamond HSC by 16.47%. Strain Energy for diamond SFRC is greater than two legged stirrups in SFRC by 52.6%. Graph 3: Strain Energy (Mpa)
  • 40. Table 4: Maximum Principal Stress Maximum Principal Stress Mpa Time NSC HSC SFRC Diamond NSC Diamond HSC Diamond SFRC 1 0.00 0.00 0.00 0.00 0.00 0.00 2 82.71 82.42 82.08 82.36 82.02 81.59 3 93.99 93.66 93.27 93.60 93.20 92.71 4 106.80 106.43 105.99 106.36 105.91 105.36 5 121.37 120.95 120.44 120.86 120.36 119.72 6 137.92 137.44 136.86 137.34 136.77 136.05 7 156.73 156.18 155.53 156.07 155.42 154.60 8 178.10 177.48 176.74 177.36 176.61 175.68 9 202.38 201.68 200.84 201.54 200.69 199.64 10 229.98 229.18 228.22 229.02 228.06 226.86 11 261.34 260.43 259.34 260.25 259.16 257.80 12 296.98 295.95 294.71 295.74 294.50 292.95 13 337.48 336.30 334.90 336.07 334.66 332.90 14 383.50 382.16 380.57 381.90 380.30 378.30 15 435.79 434.28 432.46 433.98 432.15 429.89 16 495.22 493.50 491.43 493.15 491.08 488.51 17 562.75 560.79 558.45 560.40 558.05 555.12 18 639.48 637.26 634.60 636.82 634.15 630.82 19 726.69 724.16 721.13 723.66 720.62 716.84 20 825.78 822.91 819.47 822.34 818.89 814.59
  • 41.  Above graph shows the result for Maximum Principal Stress for columns having simple lateral ties with two legged stirrups and diamond stirrups. From the results it concludes that Maximum Principal Stress for two legged stirrups in NSC is greater than diamond NSC by 0.42%. Maximum Principal Stress for two legged stirrups in HSC is greater than diamond HSC by 0.48%. Maximum Principal Stress for two legged stirrups in SFRC is greater than diamond SFRC by 0.59%. Graph 4: Maximum Principal Stress
  • 42. Table 2: Shear Stress Shear Stress Mpa Time NSC HSC SFRC Diamond NSC Diamond HSC Diamond SFRC 1 0 0 0 0 0 0 2 24.796 24.622 15.985 16.098 15.963 10.236 3 28.833 28.631 19.030 19.164 19.003 12.483 4 33.527 33.291 22.655 22.815 22.623 15.223 5 38.985 38.711 26.970 27.160 26.932 18.565 6 45.331 45.013 32.108 32.334 32.062 22.640 7 52.710 52.340 38.223 38.493 38.169 27.610 8 61.291 60.861 45.504 45.825 45.440 33.670 9 71.269 70.768 54.171 54.553 54.095 41.062 10 82.871 82.289 64.490 64.944 64.399 50.075 11 96.361 95.685 76.773 77.315 76.665 61.067 12 112.048 111.261 91.397 92.041 91.268 74.472 13 130.289 129.373 108.806 109.573 108.652 90.820 14 151.498 150.434 129.531 130.444 129.348 110.756 15 176.161 174.924 154.203 155.290 153.986 135.068 16 204.838 203.400 183.575 184.870 183.316 164.717 17 238.184 236.511 218.542 220.083 218.234 200.874 18 276.958 275.013 260.169 262.003 259.802 244.969 19 322.044 319.782 309.725 311.909 309.288 298.742 20 374.470 371.840 368.720 371.320 368.200 364.320
  • 43.  Above graph shows the result for Shear Stress for columns having simple lateral ties with two legged stirrups and diamond stirrups. From the results it concludes that Shear Stress for two legged stirrups in NSC is greater than diamond NSC by 35.07%. Shear Stress for two legged stirrups in HSC is greater than diamond HSC by 35.16%. Shear Stress for two legged stirrups in SFRC is greater than diamond SFRC by 35.96%. Graph 2: Shear Stress
  • 44. Table 3: Equivalent Stress Equivalent Stress Mpa Time NSC HSC SFRC Diamond NSC Diamond HSC Diamond SFRC 1 0 0 0 0 0 0 2 140.563 140.923 141.394 141.003 141.484 142.125 3 159.730 160.140 160.675 160.231 160.777 161.506 4 181.512 181.977 182.585 182.081 182.701 183.529 5 206.263 206.792 207.483 206.910 207.615 208.556 6 234.390 234.991 235.776 235.125 235.926 236.995 7 266.352 267.035 267.927 267.187 268.098 269.313 8 302.673 303.449 304.463 303.622 304.657 306.037 9 343.946 344.829 345.981 345.025 346.201 347.770 10 390.848 391.851 393.160 392.074 393.410 395.193 11 444.146 445.285 446.773 445.538 447.057 449.083 12 504.711 506.006 507.696 506.293 508.020 510.321 13 573.535 575.007 576.927 575.334 577.295 579.911 14 651.745 653.417 655.599 653.788 656.017 658.989 15 740.619 742.519 744.999 742.941 745.474 748.852 16 841.612 843.771 846.590 844.251 847.130 850.968 17 956.378 958.831 962.034 959.376 962.647 967.009 18 1086.793 1089.581 1093.220 1090.200 1093.917 1098.874 19 1234.992 1238.160 1242.296 1238.864 1243.088 1248.720 20 1403.400 1407.000 1411.700 1407.800 1412.600 1419.000
  • 45.  Above graph shows the result for Equivalent Stress for columns having simple lateral ties with two legged stirrups and diamond stirrups. From the results it concludes that Equivalent Stress for diamond NSC is greater than two legged stirrups in NSC by 0.31%. Equivalent Stress for diamond HSC is greater than two legged stirrups in HSC by 0.39%. Equivalent Stress for diamond SFRC is greater than two legged stirrups in SFRC by 5.17%. Graph 3: Equivalent Stress
  • 46. Table 4: Total Heat Flux Total Heat Flux W/mm^2 Time NSC HSC SFRC Diamond NSC Diamond HSC Diamond SFRC 1 0 0 0 0 0 0 2 0.0051 0.0057 0.0064 0.0062 0.007 0.0078 3 0.0058 0.0065 0.0072 0.0071 0.0079 0.0088 4 0.0066 0.0074 0.0082 0.008 0.009 0.01 5 0.0075 0.0084 0.0094 0.0091 0.0102 0.0114 6 0.0085 0.0095 0.0106 0.0104 0.0116 0.0129 7 0.0097 0.0108 0.0121 0.0118 0.0132 0.0147 8 0.011 0.0123 0.0137 0.0134 0.015 0.0167 9 0.0125 0.014 0.0156 0.0153 0.017 0.019 10 0.0142 0.0159 0.0177 0.0173 0.0193 0.0216 11 0.0162 0.0181 0.0201 0.0197 0.022 0.0245 12 0.0184 0.0205 0.0229 0.0224 0.025 0.0279 13 0.0209 0.0233 0.026 0.0254 0.0284 0.0317 14 0.0238 0.0265 0.0296 0.0289 0.0322 0.036 15 0.027 0.0301 0.0336 0.0328 0.0366 0.0409 16 0.0307 0.0342 0.0382 0.0373 0.0416 0.0465 17 0.0349 0.0389 0.0434 0.0424 0.0473 0.0528 18 0.0396 0.0442 0.0493 0.0482 0.0537 0.06 19 0.045 0.0502 0.056 0.0548 0.0611 0.0682 20 0.051151 0.057058 0.063637 0.062231 0.06939 0.077535
  • 47.  Above graph shows the result for Total Heat Flux for columns having simple lateral ties with two legged stirrups and diamond stirrups. From the results it concludes that Total Heat Flux for diamond NSC is greater than two legged stirrups in NSC by 17.74%. Total Heat Flux for diamond HSC is greater than two legged stirrups in HSC by 18.57%. Total Heat Flux for diamond SFRC is greater than two legged stirrups in SFRC by 17.94%. Graph 4: Total Heat Flux
  • 48. CONCLUSION  The results are taken for Total Heat Flux for columns having simple lateral ties with two legged stirrups and diamond stirrups. From the results it concludes that Total Heat Flux for diamond NSC is greater than two legged stirrups in NSC by 17.74%. Total Heat Flux for diamond HSC is greater than two legged stirrups in HSC by 18.57%. Total Heat Flux for diamond SFRC is greater than two legged stirrups in SFRC by 17.94%.
  • 49.  The results are taken for Equivalent Stress for columns having simple lateral ties with two legged stirrups and diamond stirrups. From the results it concludes that Equivalent Stress for diamond NSC is greater than two legged stirrups in NSC by 0.31%. Equivalent Stress for diamond HSC is greater than two legged stirrups in HSC by 0.39%. Equivalent Stress for diamond SFRC is greater than two legged stirrups in SFRC by 5.17%.
  • 50.  The results are taken for Shear Stress for columns having simple lateral ties with two legged stirrups and diamond stirrups. From the results it concludes that Shear Stress for two legged stirrups in NSC is greater than diamond NSC by 35.07%. Shear Stress for two legged stirrups in HSC is greater than diamond HSC by 35.16%. Shear Stress for two legged stirrups in SFRC is greater than diamond SFRC by 35.96%.  The results are taken for Maximum Principal Stress for columns having simple lateral ties with two legged stirrups and diamond stirrups. From the results it concludes that Maximum Principal Stress for two legged stirrups in NSC is greater than diamond NSC by 0.42%. Maximum Principal Stress for two legged stirrups in HSC is greater than diamond HSC by 0.48%. Maximum Principal Stress for two legged stirrups in SFRC is greater than diamond SFRC by 0.59%.
  • 51.  The results are taken for Strain Energy in mm for columns having simple lateral ties with two legged stirrups and diamond stirrups. From the results it concludes that Strain Energy for two legged stirrups in NSC is greater than diamond NSC by 16.45%. Strain Energy for two legged stirrups in HSC is greater than diamond HSC by 16.47%. Strain Energy for diamond SFRC is greater than two legged stirrups in SFRC by 52.6%.  The results are taken for Normal Stress for columns having simple lateral ties with two legged stirrups and diamond stirrups. From the results it concludes that Normal Stress for diamond NSC is greater than two legged stirrups in NSC by 17.91%. Normal Stress for two legged stirrups in HSC is greater than diamond HSC by 0.43%. Normal Stress for two legged stirrups in SFRC is greater than diamond SFRC by 18.64%.
  • 52.  The results are taken for Total Deformation in mm for columns having simple lateral ties with two legged stirrups and diamond stirrups. From the results it concludes that Total Deformation for two legged stirrups in NSC is greater than diamond NSC by 47.24%. Total Deformation for two legged stirrups in HSC is greater than diamond HSC by 47.72%. Total Deformation for two legged stirrups in SFRC is greater than diamond SFRC by 5.47%.
  • 53. FUTURE SCOPE  Further studies can be undertaken for configurations of lateral reinforcement other than diamond shape done here. Other column shapes can also be considered for future study.
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  • 55.  Naus, D.J.(2005), “The Effect of Elevated Temperature on Concrete Materials and Structures-A Literature Review.” U.S. Nuclear Regulatory Commission, Office of Nuclear Regulatory Research, Washington (DC), USA.  Shin, S., Kim, J. and Ahn, J. (2010), “Transverse Reinforcement of RC Columns Considering Effective Lateral Confining Reduction Factor” Journal of Asian Architecture and Building Engineering, 501-508.  Martins, A. M. B. and Rodrigues, J. P.C. (2010), “Behavior Of Concrete Columns Subjected To Fire” University of Coimbra.  Khaliq, W. (2012), “Performance Characterization of High Performance Concretes Under Fire Conditions” Michigan State University.  Baolin Yu, B. (2013), “Fire Response of Reinforced Concrete Columns Strengthened With Near-Surface Mounted FRP Reinforcement” Michigan State University.  Kodur, V. K. R., Khaliq, W., Raut, N. (2013). “An approach to account for tie configuration in predicting fire resistance of reinforced concrete columns” Retrieved 15 July 2020, from https://www.researchgate.net/publication/263466983  Bhatt, P, Kodur, V.K.R., and Matsagar, V.(2019), “Numerical approach to evaluate elevated temperature behavior of steel fiber reinforced concrete columns.” The Indian concrete journal, 8-15.