 Open Access
 Total Downloads : 284
 Authors : Parvesh Gour, Vivek Garg, Abhay Sharma
 Paper ID : IJERTV3IS110120
 Volume & Issue : Volume 03, Issue 11 (November 2014)
 Published (First Online): 06112014
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Detection of Weak Zones in Beams of Existing RC Structure Due to Consideration of Additional Seismic Forces
Parvesh Gour, 
Dr. Vivek Garg, 
Dr. Abhay Sharma 
PG Scholar, 
Assistant Professor 
Associate Professor 
Civil Engineering Department 
Civil Engineering Department 
Civil Engineering Department 
NIT Bhopal, Madhya Pradesh, India. 
NIT Bhopal, Madhya Pradesh, India 
NIT Bhopal, Madhya Pradesh, India 
.Abstract Throughout the globe there are lots of buildings which are vulnerable to damage or damaged by earthquake. There are many buildings which are either designed without consideration of seismic forces or need to be designed with consideration of revised code of earthquake. All such buildings are needed to be retrofied for additional seismic forces developed due to consideration of earthquake loads. The present study investigates the structural behaviour of an RC frame (G+2 Commercial building) under the additional load in the form of seismic forces. The structure is analyzed for two load cases. In first case (Gravity load case) structure is analyzed for only gravity forces and no seismic force is considered in this analysis while in second case (Seismic load case) structure is analyzed with consideration of seismic forces along with gravity forces. The analysis is performed by using structural analysis software i.e. STAAD Pro. The analysis results of structure for gravity and seismic load cases are compared to evaluate the effect of seismic forces on the RC structure. The seismic forces cause substantial change in beam and column forces in the structure. The results indicate that the significant increase is found in the shear force and bending moment in most of the beams. This increase of forces is more significant in plinth beams compared to roof beams. The weak and deficient members are identified and strengthened for the additional forces and moments. The strengthening of beams is done by connecting steel plates at top and bottom of the beams with shear connectors.
Keywords Concrete; Steel; Jacketing; Strengthening.

INTRODUCTION
Earth quake is one of the greatest natural hazards to life on this planet. The effects of the earthquake are very sudden with little or no warning to make alert against damages and collapse of the buildings. There is lots of building which are not designed for earthquake forces or many buildings which are designed for earthquake forces but later on due to change in earthquake code, these buildings need to be retrofied. This paper involves the strengthening demand of
the RC structure by considering seismic forces in addition to gravity forces. The new construction can be built earth quake resistant easily by adopting proper design methodology and quality control in construction but old construction which is not design with code provisions posses enormous seismic risk in particular to human life and historic monuments. Most of the losses of lives in previous earthquakes in different countries have occurred due to collapse of buildings, these buildings are generally nonengineered, those constructed without any concern with the engineer. Most of the small and residential buildings are built rapidly with little or without engineering inputs. So it is highly needed to increase its capacity to bear these forces caused due to earthquake. Many high rise buildings are highly vulnerable to earthquake due to more height and large occupancy. This thesis presents an attempt towards quantitative evaluation of seismic vulnerability of this particular type of buildings and proposes practical solutions to reduce it. The results, with and without strengthening measures, are compared to estimate the effectiveness of the various intervention options.
1.1 Literature Review
Several studies have been carried out to understand the influence of additional forces on the existing structure. These forces may be due to consideration of seismic force, wind load or due to any alteration in the building. Various experimental and analytical investigations have been carried out to understand the behaviour of the retrofitted structure and also to know the amount of retrofitting requires.
Gomes A. and Julio A. J. (1997) studied on strengthening design of RC beams by addition of steel plates, according to him the members which are not having sufficient reinforcement and good quality of concrete can be retrofied with providing external reinforcement. To have additional steel strength with low deformation of the strengthened element it is convenient to use low tensile
strength steel. Adding the plates means increase inertia and the stiffness of element. Additional steel can be connected to beams or columns by inject epoxy resin. High strength steel bolts can be use at the anchorage zone; near the end of plate it is convenient.
Kothandaraman S. and Vasudevan G. (2009) has done experimental study on Flexural retrofitting of RC beams using external bars at soffit level keeping the reinforcement externally at soffit level is found to be viable and the moment carrying capacity of beams could be increased considerably. In case of under reinforced section the capacity can be increased as high as 70%. By doing this the moment carrying capacity can be increased than that of the section in which the entire reinforcement is embedded. It also reduces crack width and the deflection as compare to the reference beam.
Obaidat Y. T. et al (2009) studied on Retrotting of reinforced concrete beams using composite laminates. According to him, the stiffness of the CFRPretrotted beams is enhanced compared to that of the reference beams. Providing externally bonded CFRP plates resulted in an increase in capacity of the maximum load. The crack width of the retrotted beams are decreased compared to the reference beams.
Obaidat Y. T. (2011) studied on use of FRP for structural retrofitting of concrete beam. By his experiments and simulations he shows that retrofitting by FRP can increase load capacity and stiffness. The effect of retrofitting in flexure is more effective than in shear. On the other hand, these simulations showed that an increase in the amount of CFRP will in some cases decrease the maximum load capacity. This means that it is very important to understand the behaviour of a retrofitted structure since an unsuitable arrangement of CFRP can make the situation very dangerous.
Ruano G. et al (2012) has studied on Shear retrofitting of reinforced concrete beam with steel fibre reinforced concrete. The strengthen technique used with self compacting concrete matrix with steel fibre reinforced is feasible to apply at building elements. It is suitable to reduce the thickness of the steel jacketing, it also provides a good surface finish so that plastering can be optional. So it reduce the weight of the plaster or can say it compensate the weight. FRC improves the structural properties of building.

PROPOSED WORK
The present study investigates the structural behaviour of an RC frame (G+2 Commercial building) under the additional load in the form of seismic forces. The structure is analyzed for two load cases. In first case (Gravity load case) structure is analyzed for only gravity forces and no seismic force is considered in this analysis while in second case (Seismic load case) structure is analyzed with consideration of seismic forces along with gravity forces. The analysis is performedby using structural analysis software i.e. STAAD Pro. The analysis results of structure for gravity and seismic load cases are compared to evaluate the effect of seismic forces on the RC structure. Weak zones are detected by comparing the results and retrofitting technique is suggested for the structure. Two cases for the compare of structure are
Case 1: Structure with gravity loads only (STRGR)
Case 2: Structure with earthquake loads of Zone III in addition to gravity loads (STREQ).

Modelling
Modelling is done for the structure, the details of which is illustrated in table
Table 1 Details of structure for modelling
Structure type
RCC commercial building
Storeys
G + 2
Height of each storey
3.5m
Building plan size
21m x 12.5m
Building height
10.5m
Depth of foundation
1.5m below GL
Type of supports
Fixed
Slab thickness each
150mm
Column size each
300mm x 300mm
Beam size
200mm x 400mm
Type of wall separation
Glazed
Dead load of wall taken
Consider brick wall load
Live load on each floor
4 KN m2
Live load on terrace
1.5 KN m2
Seismic zone
Zone III
Live load with seismic force
50% (IS 1893:2002)
Type of existing steel
Fe 415
Characteristic strength of concrete (fck )
25 N mm2
Fig 1 Isometric view of proposed structure
Fig 2 Sections where beams and columns are considered
Fig 3 Member numbering at Section AA
Fig 4 Member numbering at Section BB
Fig 5 Member numbering at Section AA
Fig 6 Member numbering at Section 22
Fig 7 Member numbering at Section 33
Fig 8 Member numbering at Section 44

Load calculation
Dead load and live loads are calculated and tabulated below.
Table 2 Dead load and Live load on structure
Members
Load calculation
Load
Dead load of 200mm wall
0.2 x 3.1 x 20
12.4 kN m
Dead load of 100mm wall
0.1 x 3.1 x 20
6.20 kN m
Dead load of parapet wall of
100 mm
0.1 x 1 x 20
2.00 kN m
Dead load of slab
0.15 x 25
3.75 kN m2
Live load on floors
By IS code
4.00 kN m2
Live load on roof
By IS code
1.50 kN m2
Table 3 Parameters for earthquake load
Sr.
No.
Parameter
Value
1
Location
(ZONE III)
Zone Factor = 0.16
2
Response reduction factor
(Ordinary RC Moment Resisting Frame)
RF = 3
3
Importance factor
(All General Building)
I = 1
4
Rock and soil site factor
(Medium soil)
SS = 2
5
Type of structure
(RC Frame Building)
ST = 1
6
Damping ratio
DM = 0.05

Methodology

Modelling of G+2 structures in staadpro software.

Analyze this structure for the gravity forces only and noted down forces in all beams of the structure.

Apply the seismic force of Zone III in addition to gravity forces at the same structure and noted down forces in all beams of the structure.

Compare the results of both analysis and find deficiencies.

Retrofitting the beams for the additional forces and moments.


Load cases and combinations
According to IS 18932002
Load cases for analysis in staadpro Basic loads
LC 1: EQ X = EQ in +X direction LC 2: EQX = EQ in X direction LC 3: EQ Z = EQ in +Z direction LC 4: EQZ = EQ inZ direction LC 5: DL = Dead load
LC 6: LL = Live load
Combination of loads according to IS 1893:2002 LC 7: 1.5 DL + 1.5 LL
LC 8: 1.2 DL + 1.2 LL + 1.2 EQ X
LC 9: 1.2 DL + 1.2 LL + 1.2 EQX
LC 10: 1.2 DL + 1.2 LL + 1.2 EQ Z
LC 11: 1.2 DL + 1.2 LL + 1.2 EQZ
LC 12: 1.5 DL + 1.5 EQ X
LC 13: 1.5 DL + 1.5 EQX
LC 14: 1.5 DL + 1.5 EQ Z
LC 15: 1.5 DL + 1.5 EQZ
LC 16: 0.9 DL + 1.5 EQ X
LC 17: 0.9 DL + 1.5 EQX
LC 18: 0.9 DL + 1.5 EQ Z
LC 19: 0.9 DL + 1.5 EQZ


RESULTS AND DISCUSSION
The effects of the earthquake forces on structure are studied in addition to gravity forces. The comparison of shear forces, bending moments and reinforcement is done for two cases i.e. for STRGR and STREQ structure and their differences are tabulated to estimate the strengthening requirement for the additional load. Floor wise results are discussed for different beams. Subsequently the retrofitting method is used to strengthen the weak members.
In results STRGR indicates the results of structure analyzed with gravity forces only and STREQ indicates the results of structure analyzed with earthquake force in addition to gravity forces.

Effects of additional seismic force on beams
The shear force, bending moment and area of reinforcing steel in beams of different storeys floors are presented and compared for gravity and seismic load cases.

Effect on shear force in beam
The shear force in both the cases as for STRGR and STR EQ are compared for beams at each floor.

Plinth beams
The shear force in plinth beams for gravity and seismic load cases are discussed. The increase in shear force due to application of earthquake forces in addition to gravity forces are shown in table 4.
Table 4 Comparison of Shear force Fy (kN) in plinth beams between gravity and seismic load case
Beam No
Shear force Fy
Increase in
Shear force
% increase in
shear force
STRGR
STREQ
51
39.10
57.53
18.43
47.14
52
37.57
52.87
15.30
40.72
53
37.51
52.94
15.43
41.14
57
21.61
41.19
19.58
90.61
58
21.25
37.31
16.06
75.58
59
21.24
37.48
16.24
76.46
75
54.34
65.30
10.96
20.17
76
26.78
56.28
29.50
110.16
78
30.43
42.24
11.81
38.81
79
15.16
46.57
31.41
207.19
81
30.41
42.67
12.26
40.32
82
15.16
47.80
32.64
215.30
84
30.40
42.80
12.40
40.79
85
15.16
48.17
33.01
217.74
From the above comparison it is revealed that there is an increase in shear force Fy in all the beams. The maximum increase in shear force is found to be 33.01 kN in beam no 85 with percentage increase of 217.74%.

First floor beams
The shear force in first floor beams for gravity and seismic load cases are discussed. Increase in shear force due to application of earthquake forces in addition to gravity forces are shown in table 6.2.
Table 5 Comparison of Shear force (kN) in first floor beams between gravity and seismic load case
Beam No
Shear force Fy
Increase In Shear force
% increase in
shear force
STRGR
STREQ
151
58.35
67.40
9.05
15.51
152
55.47
67.05
11.58
20.88
153
55.32
67.42
12.10
21.87
157
58.93
69.01
10.08
17.11
158
55.61
62.04
6.43
11.56
159
55.41
62.30
6.89
12.43
175
88.83
88.83
0.00
0.00
176
35.87
69.19
33.32
92.89
178
99.11
99.11
0.00
0.00
179
33.32
64.68
31.36
94.12
181
99.15
99.15
0.00
0.00
182
33.32
66.29
32.97
98.95
184
99.15
99.15
0.00
0.00
185
33.32
66.75
33.43
100.33
From the above comparison it is revealed that there is an increase in shear force Fy in all the beams. The maximum increase in shear force is found to be 33.43 kN in beam no 185 with percentage increase is 100.33%.

Second floor beam
The shear force in second floor beams for gravity and seismic load cases are discussed. Increase in shear force due to application of earthquake forces in addition to gravity forces are shown in table 6.31.
Table 6 Comparison of Shear force (kN) in second floor beams between gravity and seismic load case
Beam No
Shear force Fy
Increase in
Shear force
% increase in
shear force
STRGR
STREQ
251
57.57
65.61
8.04
13.97
252
55.39
60.83
5.44
9.82
253
55.31
60.92
5.61
10.14
257
57.75
60.99
3.24
5.61
258
55.50
56.96
1.46
2.63
259
55.37
56.93
1.56
2.82
275
88.48
88.48
0.00
0.00
276
35.87
57.41
21.54
60.05
278
98.34
98.34
0.00
0.00
279
33.32
52.29
18.97
56.93
281
98.34
98.34
0.00
0.00
282
33.32
53.49
20.17
60.53
284
98.34
98.34
0.00
0.00
285
33.32
53.83
20.51
61.55
From the above comparison it is revealed that there is an increase in shear force Fy in all the beams. The maximum increase in shear force is found to be 21.54 kN in beam no 276 with percentage increase of 60.05%.

Third floor beam
The shear force in third beams for gravity and seismic load cases are discussed. Increase in shear force due to application of earthquake forces in addition to gravity forces are shown in table 6.4.
Table 7 Comparison of Shear force (kN) in third floor beams between gravity and seismic load case
From the above comparison it is revealed that there is an increase in shear force Fy in all the beams. The maximum increase in shear force is found to be 6.34 kN in beam no 376 with percentage increase of 47.17%.
Beam No
Shear force Fy
Increase In
Shear force
% increase in
shear force
STRGR
STREQ
351
22.79
25.78
2.99
13.12
352
22.70
24.55
1.85
8.15
353
22.34
24.19
1.85
8.28
357
29.51
29.82
0.31
1.05
358
28.41
28.41
0.00
0.00
359
28.14
28.14
0.00
0.00
375
38.21
38.21
0.00
0.00
376
13.44
19.78
6.34
47.17
378
53.93
53.93
0.00
0.00
379
15.84
21.14
5.30
33.46
381
54.01
54.01
0.00
0.00
382
15.84
21.56
5.72
36.11
384
54.01
54.01
0.00
0.00
385
15.84
21.67
5.83
36.80


Effect on bending moment in beam
Bending moment and corresponding reinforcement area of steel in beam are discussed. Sagging moment and hogging moment both are compared for the two cases as for STR GR and STREQ. Maximum of two hogging moments from both ends are taken for the comparison.

Plinth level beams
Table 8 Comparison of bending moment Mz (kNm) and corresponding reinforcement area Ast (mm2 ) between Gravity and Seismic analysis in beams at plinth level
Beam no
STRGR
STREQ (Zone III)
Increase in moment/ reinforcement
Max. hogging moment
Max. Sagging moment
Ast Top
Ast Bottom
Max. hogging moment
Max. Sagging moment
Ast Top
Ast Bottom
Hogging moment
Sagging moment
Ast Top
Ast Bottom
1
2
3
4
5
6
7
8
(51)
(62)
(73)
(84)
51
23.00
12.61
226
226
53.00
24.40
565
226
30.00
11.79
339
0
52
22.08
10.86
226
226
48.72
16.31
452
226
26.64
5.45
226
0
53
21.89
10.94
226
226
48.96
16.36
452
226
27.07
5.42
226
0
57
12.34
6.91
226
226
45.32
29.64
402
339
32.98
22.73
176
113
58
12.41
6.21
226
226
40.61
20.84
339
226
28.20
14.63
113
0
59
12.42
6.18
226
226
40.84
21.04
339
226
28.42
14.86
113
0
75
42.68
26.20
402
226
67.26
31.80
603
339
24.58
5.60
201
113
76
17.30
0.00
226
226
54.69
26.18
565
226
37.39
26.18
339
0
78
24.18
14.00
226
226
53.24
22.74
452
226
29.06
8.74
226
0
79
8.60
0.87
226
226
48.85
33.52
452
339
40.25
32.65
226
113
81
24.19
13.92
226
226
54.57
23.13
565
226
30.38
9.21
339
0
82
8.49
0.98
226
226
50.30
35.11
452
339
41.81
34.13
226
113
84
24.19
13.92
226
226
54.94
23.26
565
226
30.75
9.34
339
0
85
8.49
0.99
226
226
50.75
35.57
452
339
42.26
34.58
226
113

First floor beams
Table 9 Comparison of bending moment Mz (kNm) and corresponding reinforcement area Ast (mm2 ) between Gravity and Seismic analysis in beams at first floor
Beam no
STRGR
STREQ (Zone III)
Increase in moment/ reinforcement
Max. hogging moment
Max. Sagging moment
Ast Top
Ast Bottom
Max. hogging moment
Max. Sagging moment
Ast Top
Ast Bottom
Hogging moment
Sagging moment
Ast Top
Ast Bottom
1
2
3
4
5
6
7
8
(51)
(62)
(73)
(84)
151
36.27
22.66
339
226
70.68
37.30
628
339
34.41
14.64
289
113
152
35.35
18.53
339
226
64.86
22.10
565
226
29.51
3.56
226
0
153
34.91
18.71
339
226
65.45
22.10
603
226
30.54
3.36
264
0
157
38.96
25.07
339
226
69.37
42.10
628
402
30.41
17.05
289
176
158
37.78
20.44
339
226
63.09
24.40
565
226
25.31
3.92
226
0
159
37.16
20.72
339
226
63.70
24.80
565
226
26.54
4.11
226
0
175
73.03
52.63
678
452
93.22
52.60
904
452
20.19
0.00
226
0
176
33.08
0.00
339
226
73.70
31.80
678
339
40.62
31.80
339
113
178
86.00
64.96
804
565
99.69
65.00
942
565
13.69
0.00
138
0
179
37.49
0.00
339
226
75.02
36.40
791
339
37.53
36.44
452
113
181
85.99
65.07
804
565
100.90
65.10
981
565
14.91
0.00
177
0
182
37.65
0.00
339
226
77.07
38.40
791
339
39.42
38.43
452
113
184
85.99
65.08
804
565
101.30
65.10
981
565
15.26
0.00
177
0
185
37.66
0.00
339
226
77.66
39.00
791
339
40.00
39.01
452
113

Second floor beam
Table 10 Comparison of bending moment Mz (kNm) and corresponding reinforcement area Ast (mm2 ) between Gravity and Seismic analysis in beams at second floor
Beam no
STRGR
STREQ (Zone III)
Increase in moment/ reinforcement
Max. hogging moment
Max. Sagging moment
Ast Top
Ast Bottom
Max. hogging moment
Max. Sagging moment
Ast Top
Ast Bottom
Hogging moment
Sagging moment
Ast Top
Ast Bottom
1
2
3
4
5
6
7
8
(51)
(62)
(73)
(84)
251
34.96
22.60
339
226
56.50
26.70
565
226
21.54
4.13
226
0
252
35.04
18.69
339
226
54.17
18.70
565
226
19.13
0.00
226
0
253
34.9
18.70
339
226
54.08
18.70
565
226
19.18
0.00
226
0
257
37.28
24.68
339
226
54.70
26.10
565
226
17.42
1.40
226
0
258
37.33
20.70
339
226
52.12
20.70
452
226
14.79
0.00
113
0
259
37.12
20.69
339
226
51.99
20.70
452
226
14.87
0.00
113
0
275
72.7
52.07
678
452
82.64
52.10
791
452
9.94
0.00
113
0
276
32.15
0.00
339
226
58.53
17.40
565
226
26.38
17.35
226
0
278
85.78
63.27
791
565
90.84
63.30
904
565
5.06
0.00
113
0
279
34.94
0.00
339
226
57.85
22.00
565
226
22.91
21.98
226
0
281
85.77
63.28
791
565
91.78
63.30
904
565
6.01
0.00
113
0
282
34.97
0.00
339
226
59.28
23.50
565
226
24.31
23.51
226
0
284
85.77
63.28
791
565
92.04
63.30
904
565
6.27
0.00
113
0
285
34.97
0.00
339
226
59.70
23.90
565
226
24.73
23.94
226
0

Third floor beam


Table 11 Comparison of bending moment Mz (kNm) and corresponding reinforcement area Ast (mm2 ) between Gravity and Seismic analysis in beams at third floor
Beam no
STRGR
STREQ (Zone III)
Increase in moment/ reinforcement
Max. hogging moment
Max. Sagging moment
Ast Top
Ast Bottom
Max. hogging moment
Max. Sagging moment
Ast Top
Ast Bottom
Hogging moment
Sagging moment
Ast Top
Ast Bottom
1
2
3
4
5
6
7
8
(51)
(62)
(73)
(84)
351
13.16
10.76
226
226
21.16
11.80
226
226
8.00
1.04
0
0
352
15.21
8.57
226
226
22.11
8.57
226
226
6.90
0.00
0
0
353
14.96
8.17
226
226
21.65
8.17
226
226
6.69
0.00
0
0
357
18.71
14.70
226
226
25.42
14.70
226
226
6.71
0.00
0
0
358
20.01
11.47
226
226
25.33
11.50
226
226
5.32
0.00
0
0
359
19.79
11.22
226
226
24.95
11.20
226
226
5.16
0.00
0
0
375
31.43
25.94
339
226
36.6
25.90
339
226
5.17
0.00
0
0
376
16.10
0.00
226
226
23.63
2.03
226
226
7.53
2.03
0
0
378
46.49
39.59
402
339
46.88
39.60
402
339
0.39
0.00
0
0
379
23.54
0.00
226
226
29.54
0.00
339
226
6.00
0.00
113
0
381
46.49
39.78
402
339
47.42
39.80
402
339
0.93
0.00
0
0
382
23.82
0.00
226
226
30.28
0.30
339
226
6.46
0.30
113
0
384
46.48
39.79
402
339
47.57
39.80
402
339
1.09
0.00
0
0
385
23.83
0.00
226
226
30.44
0.00
339
226
6.61
0.00
113
0
Table 8 shows the bending moment and corresponding reinforcement area for plinth beams. Here the increase in hogging moment is maximum for beam no 85 as the value is increased by
42.26 kNm. Maximum increase in sagging moment is in the same beam with the value is increased by 34.58 kNm. The increase in reinforcement area for maximum increase in hogging moment at this level beams is 339 mm2 in beam no 51, 76, 81, 84 and increase in reinforcement area for maximum increase in sagging moment at this level beam is 113 mm2 in beam no (57, 75, 79, 82, 85).
Table 9 shows the bending moment and corresponding reinforcement area for first floor beams. Here the increase in hogging moment is maximum for beam no 176 as the value is increased by 40.62 kNm. Maximum increase in sagging moment is in beam no 185 with the value is increased by 39.01 kNm. The increase in reinforcement area for maximum increase in hogging moment at this floor beams is 452 mm2 in beams no 179, 182, 185 and increase in reinforcement area for maximum increase in sagging moment at this level beam is 176 mm2 in beam no 157.
Table 10 shows the bending moment and corresponding reinforcement area for second floor beams. Here the increase in hogging moment is maximum for beam no 276 as the value is increased by 26.38 kNm. Maximum increase in sagging moment is in beam no 285 with the value is increased by 23.94 kNm. The increase in reinforcement area for maximum increase in hogging moment at this floor beam is 226 mm2 in beams no 251, 252, 253, 257, 276, 279, 282, 285 and there is no increase in reinforcement area for sagging moment in any beam.
Similarly equivalent area of mild steel, as given in table below Design of steel plate for required additional reinforcement Select different range from the tables for additional Ast (mm2 ) of fy = 250 N mm2
Table 12 Plate sizes showing for different range of equivalent mild steel area
Serial Number
Additional reinforcement area required (Fe 415)
Corresponding mild steel area required
(Fe 250)
Plate size used
1
Up to 400
664
100 x 8
2
400600
996
100 x 10
3
600 800
1328
100 x 12
3.2.2 Design of shear connector for flexure
Shear connector has to be design for every beam column joints for the maximum moment in that beam. Shear connector will transfer the additional force coming at existing reinforcement level to the outer plate which is designed for different beams. So the amount of force is to be found for which shear connector will be design. These connectors are used for either top plate for hogging moment or bottom plate for sagging moment. As every beam will have different additional moment, the force for which shear connector will design will be different. Here the design of shear connector is design for the maximum moment developed among all the beams of the structure.
So for this, we have
Table 11 shows the bending moment and corresponding
Force = moment
Lever arm
… 1
reinforcement area for third floor beams. Here the increase in
hogging moment is maximum for beam no 351 as the value is increased by 8 kNm. Maximum increase in sagging moment is in beam no 376 with the value is increased by 2.03 kNm. The increase in reinforcement area for maximum increase in hogging moment at this floor beam is 113 mm2 . In beams no 379, 382, 385 and there is no increase in reinforcement area for sagging moment in any beam.
3.2 Strengthening of beams
Strengthening of beams is done for the flexure and shear, to reach the strength of the structural member up to the require strength.
3.2.1 Strengthening of beams for flexure
Retrofitting is done for beams by adding steel plate of equivalent area of reinforced bars. Plate is designed for the additional area of steel required.
Equivalent mild steel area
The additional area of reinforcement bars are found by the comparison of both analysis, but this required steel is of tor steel, but as retrofitting is done by the mild steel plate, the area of equivalent mild steel plate is to be found by force equilibrium.
1 1
For tor steel (Fe 415 N mm2 ) area up to 400 mm2 Ast = 400mm2 , fy = 415 N mm2 ,
fy 2
2 = 250 N mm
Ast2 = Area of Mild steel
Here lever arm L.A. = (d0.42 ) . 2 But for ,
M = 0.36 x b x (d0.42 ) .. 3
Maximum additional moment = 42.26 kNm
Calculation of force for this maximum additional moment is given below,
Finding for max of sagging and hogging moment by 3 Max hogging moment = 42.26 kNm
Therefore we have,
42.26 x 106 = 0.36 x 25 x 200 x (367 0.42 )
42.26 x 106 = 660600 756 2
= 69.50 mm
Put this in 2
L.A. = 367 0.42 x 69.50
L.A. = 337.81 mm
Now additional force which is to be carried by stud
F = M
6
L.A.
F = 42.26 x 10
337.81
F = 125099.91 N
Therefore,
F = 125.10 kN
Now esigning the shear connector for the above force using IS 11384:1985 code
From table 1, we have
So Ast2
= (415) Ã— 400 = 664 mm2
250
For 22 mm diameter of stud, 100 mm height and for M25 concrete
Strength of Shear connector F = 77.5 kN
Provide 2 shear connectors to resist the design shear force.
3.2.3 Strengthening of beams for shear
Plates are used at side face of the beams for resist additional shear force.
The maximum force is taken among all the beams and from all the floors as 33.01 kN.
Take mild steel plate as Fe 250. Permissible stress for mild steel plate in shear is 140 N mm2
Area of steel plate = Force Permissible stress in plate
So As = 33010 = 235.79 mm2
140
Assume depth of the plate is 200 mm
So thickness of plate will be 235.79 = 1.179 mm 2 mm
200
But for the practical purpose take plate of size 200mm x 4mm.
3.2.4 Design of shear connector for shear
To transfer the shear stresses from existing shear reinforcement to outer plate, Shear connectors are used according to IS: 11384 1985.
As the maximum additional shear force among all the beams and from all the floors is 33.01 kN. So for this,
By table 1 of IS: 113841985 gives the Design strength of shear connectors for different concrete strengths.
Strength of shear connector for 12mm dia. and 62mm height used in M25 is 25.50 kN. So, 2 shear connectors are needed at a particular section to resist shear force of 33.01 kN.


CONCLUSION
The present study investigates the structural behaviour of an RC frame (G+2 Commercial building) under the additional load in the form of seismic forces. The structure is analyzed for two load cases. In first case (Gravity load case) structure is analyzed for only gravity forces and no seismic force is considered in this analysis while in second case (Seismic load case) structure is analyzed with consideration of seismic forces along with gravity forces. The seismic forces cause substantial change in beams forces in the structure.
4.1 Effects of additional seismic forces on beams
The results indicate that the significant increase is found in the shear force and bending moment in most of the beams. This increase of forces is more significant in plinth beams compared to roof beams. The comparison of critical value of shear force, hogging moments and sagging moments at each floor level is depicted in table 7.1.
Table 13 Effects of additional seismic forces on beams
Comparison of maximum shear force (kN) in beam 

Floor 
Max shear force 

STRGR 
STREQ 
% increase 

Plinth beam 
54.35 (LC 3) 
65.30 (LC 12) 
20.15 
First floor beam 
99.15 ( LC 3) 
99.15 (LC 7) 
0 
Second floor beam 
98.34 ( LC 3) 
98.34 (LC 7) 
0 
Third floor beam 
54.01 ( LC 3) 
54.01 (LC 7) 
0 
Comparison of maximum hogging moment (kNm) beam 

Floor 
Max hogging Moment 

STRGR 
STREQ 
% increase 

Plinth beam 
42.68 ( LC 3) 
68.54 (LC 14 & 15) 
60.59 
First floor beam 
86.00 ( LC 3) 
102.60 (LC 14 & 15) 
19.30 
Second floor beam 
85.77 ( LC 3) 
93.02 (LC 14 & 15) 
8.45 
Third floor beam 
46.49 ( LC 3) 
48.09 (LC 14 & 15) 
3.44 
Comparison of maximum sagging moment (kNm) in beam 

Floor 
Max sagging moment 

STRGR 
STREQ 
% increase 

Plinth beam 
26.20 ( LC 3) 
37.29 (LC 14 & 15) 
42.33 
First floor beam 
65.08 ( LC 3) 
65.08 (LC 14 & 15) 
0 
Second floor beam 
63.28 ( LC 3) 
63.28 (LC 14 & 15) 
0 
Third floor beam 
39.79 ( LC 3) 
39.79 (LC 14 & 15) 
0 
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