Ultimate Strength of Reinforced Concrete Beams in Combined ...
Retrofitting -Strength based design of Beams
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Transcript of Retrofitting -Strength based design of Beams
Job Information
Engineer Checked Approved
Name: Prakash R. Hada
Date: 28-Jan-16
RCC Frame
Structure Type SPACE FRAME
Number of Nodes 22
55
Highest Node 2255
Number of Elements 10
53
Highest Element 3069
Number of Plates 20
00
Highest Plate 2961
Number of Design Groups 1
Number of Design Slabs 0
Number of Load Cases 17
Number of Design Briefs 1
Included in this printout are data for:
Design Group Design Brief Design Code Members
G1: Design Group 1 B1: GFBeams IS456 Beam M3
Design Group Summary - Design Group 1
Member Design Span Type Main Bars Shear
Bars
Span
Depth Hog Sag
M3 Initial 1 Beam Ok Ok Ok Ok
2 Beam Ok Ok Ok Ok
Summary: the group is safe
Beam Spans Cover
Member Span Type Length
(m)
Top
(cm)
Btm
(cm)
Side
(cm) Link Size
M3 1 Beam 5.000 2.5 2.5 2.5 10
2 Beam 5.000 2.5 2.5 2.5 10
Beam Supports
Member Node Length
(m)
Support
Type
Col. Width
(cm)
M3 N9 8.000 Fixed 60.0
N27 8.000 Fixed 60.0
Member 3 - Main Steel Summary Distance
(m) Span
Moment
(kNm)
As Req.
(mm2)
As' Req.
(mm2)
Bottom Layers Top Layers
Bars Area Bars Area
0.000 1(s) 435.041 2178 244 3927 4825
-367.437 1849 0
0.300 1 374.235 1889 0 1963 2413
-332.614 1648 0
0.417 1 351.092 1753 0 1963 2413
-318.769 1571 0
0.833 1 270.920 1318 0 1963 2413
-267.835 1303 0
1.000 1 241.638 1171 0 1963 2413
-248.557 1205 0
1.250 1 198.629 895 0 1963 2413
-218.172 986 0
1.667 1 131.486 596 0 1963 2413
-166.473 749 0
2.000 1 79.403 440 0 1963 2413
-122.395 557 0
2.083 1 65.191 440 0 1963 2413
-109.483 452 0
2.500 1 3.358 440 0 1963 2413
-49.307 440 0
2.917 1 27.081 440 0 1963 2413
-66.600 440 0
3.333 1 92.385 440 0 1963 2413
-121.923 564 0
3.750 1 160.593 733 0 1963 2413
-172.116 784 0
4.000 1 204.969 998 0 1963 2413
-202.031 984 0
4.167 1 236.568 1150 0 1963 2413
-222.919 1084 0
4.583 1 318.210 1573 0 1963 2413
-273.552 1336 0
4.700 1 341.764 1704 0 1963 2413
-287.312 1407 0
5.000 1(e) 403.628 2051 111 3927 4825
-321.919 1593 0
5.000 2(s) 383.759 1954 10 3927 4825
-304.023 1478 0
5.300 2 326.987 1603 0 1963 2413
-273.557 1319 0
5.417 2 305.412 1486 0 1963 2413
-261.408 1257 0
5.833 2 230.841 1106 0 1963 2413
-216.526 1037 0
6.000 2 202.070 969 0 1963 2413
-197.939 950 0
6.250 2 161.637 721 0 1963 2413
-171.074 763 0
6.667 2 100.264 457 0 1963 2413
-126.359 568 0
7.000 2 52.797 440 0 1963 2413
-87.868 440 0
7.083 2 39.887 440 0 1963 2413
-76.591 440 0
7.500 2 0.817 440 0 1963 2413
-33.705 440 0
7.917 2 42.289 440 0 1963 2413
-79.123 440 0
8.000 2(e) 55.176 440 0 1963 2413
-90.401 440 0
Summary: the member is safe
Member 3 - Shear Results Summary Distance
(m) Span
Shear Force
(kN)
Shear Stress
(N/mm2)
Asv Required
(mm2)
0.000 1(s) 206.008 0.000 0
0.300 1 199.483 1.074 89
0.417 1 196.945 1.064 89
0.833 1 187.883 1.029 89
1.000 1 184.258 1.009 9
1.250 1 174.940 0.828 26
1.667 1 165.877 0.793 51
2.000 1 158.627 0.765 45
2.083 1 153.924 0.632 16
2.500 1 145.680 0.613 11
2.917 1 140.242 0.648 19
3.333 1 133.992 0.830 60
3.750 1 128.554 0.865 34
4.000 1 126.413 1.037 89
4.167 1 124.238 1.051 89
4.583 1 118.801 1.086 89
4.700 1 117.278 1.096 89
5.000 1(e) 113.363 0.000 0
5.000 2(s) 192.564 0.000 0
5.300 2 186.039 0.998 89
5.417 2 183.502 0.988 89
5.833 2 174.439 0.953 89
6.000 2 170.814 0.938 89
6.250 2 161.820 0.763 11
6.667 2 152.758 0.728 37
7.000 2 145.508 0.700 31
7.083 2 140.863 0.570 2
7.500 2 131.800 0.535 89
7.917 2 126.324 0.569 2
8.000 2 125.237 0.740 39
Summary: the member is safe
Member 3 - Shear Zones Summary Range
(m)
Asv Provided
(mm2)
Legs Spacing
(cm)
0.300 - 0.825 157 2 22.5
0.825 - 4.700 236 3 22.5
5.300 - 5.825 157 2 22.5
5.825 - 9.700 236 3 22.5
10.300 - 10.825 157 2 22.5
10.825 - 14.700 236 3 22.5
15.300 - 15.825 157 2 22.5
15.825 - 16.000 236 3 22.5
Summary: the member is safe
Span / Effective Depth
Member Span Length
(m) Type
Basic
Limit
Modified
Limit
Span
Depth
M9 1 5.000 Beam 26.0 64.2 8.3
2 5.000 Beam 26.0 64.2 8.3
3 5.000 Beam 26.0 64.2 8.3
4 5.000 Beam 26.0 64.2 8.3
5 5.000 Beam 26.0 64.2 8.3
Summary: the group is safe
Members
Member Element Node
A
Node
B Property
Emt Length
(m)
O. Length
(m)
M3 34 9 173 430 x 649 1.000 16.000
311 173 181 1.000
312 181 189 1.000
313 189 197 1.000
314 197 27 1.000
77 27 255 1.000
377 255 263 1.000
378 263 271 1.000
379 271 279 1.000
380 279 45 1.000
120 45 337 1.000
483 337 345 1.000
484 345 353 1.000
485 353 361 1.000
486 361 63 1.000
163 63 419 1.000
589 419 427 1.000
590 427 435 1.000
591 435 443 1.000
592 443 81 1.000
206 81 501 1.000
695 501 509 1.000
696 509 517 1.000
697 517 525 1.000
698 525 99 1.000
Member 3 - Main Reinforcing Bars Design Length
Bar Size Start
(m)
End
(m)
Anchorage
(cm)
1 25 0.001 24.999 141.5
2 25 0.001 24.999 141.5
3 25 0.001 24.999 141.5
4 32 0.001 24.999 181.2
5 32 0.001 24.999 181.2
6 32 0.001 24.999 181.2
7 25 0.001 24.999 141.5
Member 3 - Scheduled Bars Bar
Mark
Type and
size
No. of
bars
Bar Length
(mm)
Shape
code
A
(mm)
B
(mm)
C
(mm)
D
(mm)
E/R
(mm)
01 T25 4 18700 21 1145 16550
02 T25 5 20450 21 1540 16550
03 T10 105 2075 51 595 380
04 T10 90 650 13 30 595 60
The shape codes are based on Table B-2 of IS SP:34-1987
Member M3 Span 1
Detailed IS456 Design Requirements Section Property: 430 x 649
Beam Designed for : Vertical Bending and Shear
Span Length = 5.000 m Rectangular section
Width = 430 mm Depth = 650 mm
Covers: Top = 25 mm Bottom = 25 mm Side = 25 mm
Member M3 Span 1
Detailed IS456 Main Reinforcement Section at 0.000 m from start of member: Hogging
Moment applied to section = 465.67 kNm
Effective depth to tension reinforcement d = 599 mm
Depth to compression reinforcement d' = 48 mm
Compression steel required.
Asc' = 244.15 mm2 G-1.2
Stress in compression steel,fsc = 416.78 N/mm2
Asc = ((Mu-Mulim)/(fsc) (d - d')) = 244.15 mm2 G-1.2
Required tension steel area = 2178 mm2
Required compression steel area = 244 mm2
Tension bars provided = 3T32 ( 2413 mm2 )
Minimum area of tension reinforcement = 438 mm2 26.5.1.1(a)
Maximum area of tension reinforcement = 11180 mm2 26.5.1.1(b)
Compression bars provided = 4T25 (= 1963 mm2 )
Maximum area of compression reinforcement = 11180 mm2 26.5.1.2
Minimum horizontal bar spacing = 40 mm 26.3.2
Smallest actual horizontal space between bars = 87 mm
Maximum allowable spacing for tension bars (for 0% redistribution) = 150 mm 26.3.3
Largest actual space between tension bars = 132 mm
Beam Designed as a Doubly Reinforced Section
Actual neutral axis depth of section = 273.16 mm
Moment capacity of section = 521.97 KNm
OK
Section at 0.000 m from start of member: Hogging
Moment applied to section = 465.67 kNm
Effective depth to tension reinforcement d = 599 mm
Depth to compression reinforcement d' = 47 mm
Compression steel required.
Asc' = 244.15 mm2 G-1.2
Stress in compression steel,fsc = 416.78 N/mm2
Asc = ((Mu-Mulim)/(fsc) (d - d')) = 244.15 mm2 G-1.2
Required tension steel area = 2178 mm2
Required compression steel area = 244 mm2
Tension bars provided = 6T32 ( 4825 mm2 )
Minimum area of tension reinforcement = 438 mm2 26.5.1.1(a)
Maximum area of tension reinforcement = 11180 mm2 26.5.1.1(b)
Compression bars provided = 8T25 (= 3927 mm2 )
Maximum area of compression reinforcement = 11180 mm2 26.5.1.2
Minimum horizontal bar spacing = 40 mm 26.3.2
Smallest actual horizontal space between bars = -25 mm
Maximum allowable spacing for tension bars (for 0% redistribution) = 150 mm 26.3.3
Largest actual space between tension bars = 132 mm
Beam Designed as a Doubly Reinforced Section
Actual neutral axis depth of section = 273.16 mm
Moment capacity of section = 1100.79 KNm
OK
Section at 5.000 m from start of member: Hogging
Moment applied to section = 435.08 kNm
Effective depth to tension reinforcement d = 599 mm
Depth to compression reinforcement d' = 48 mm
Compression steel required.
Asc' = 111.07 mm2 G-1.2
Stress in compression steel,fsc = 416.78 N/mm2
Asc = ((Mu-Mulim)/(fsc) (d - d')) = 111.07 mm2 G-1.2
Required tension steel area = 2051 mm2
Required compression steel area = 111 mm2
Tension bars provided = 3T32 ( 2413 mm2 )
Minimum area of tension reinforcement = 438 mm2 26.5.1.1(a)
Maximum area of tension reinforcement = 11180 mm2 26.5.1.1(b)
Compression bars provided = 4T25 (= 1963 mm2 )
Maximum area of compression reinforcement = 11180 mm2 26.5.1.2
Minimum horizontal bar spacing = 40 mm 26.3.2
Smallest actual horizontal space between bars = 87 mm
Maximum allowable spacing for tension bars (for 0% redistribution) = 150 mm 26.3.3
Largest actual space between tension bars = 132 mm
Beam Designed as a Doubly Reinforced Section
Actual neutral axis depth of section = 273.16 mm
Moment capacity of section = 521.97 KNm
OK
Section at 5.000 m from start of member: Hogging
Moment applied to section = 435.08 kNm
Effective depth to tension reinforcement d = 599 mm
Depth to compression reinforcement d' = 47 mm
Compression steel required.
Asc' = 111.07 mm2 G-1.2
Stress in compression steel,fsc = 416.78 N/mm2
Asc = ((Mu-Mulim)/(fsc) (d - d')) = 111.07 mm2 G-1.2
Required tension steel area = 2051 mm2
Required compression steel area = 111 mm2
Tension bars provided = 6T32 ( 4825 mm2 )
Minimum area of tension reinforcement = 438 mm2 26.5.1.1(a)
Maximum area of tension reinforcement = 11180 mm2 26.5.1.1(b)
Compression bars provided = 8T25 (= 3927 mm2 )
Maximum area of compression reinforcement = 11180 mm2 26.5.1.2
Minimum horizontal bar spacing = 40 mm 26.3.2
Smallest actual horizontal space between bars = -25 mm
Maximum allowable spacing for tension bars (for 0% redistribution) = 150 mm 26.3.3
Largest actual space between tension bars = 132 mm
Beam Designed as a Doubly Reinforced Section
Actual neutral axis depth of section = 273.16 mm
Moment capacity of section = 1100.79 KNm
OK
Member M3 Span 1
Detailed IS456 Span / Effective Depth Check Basic span / effective depth ratio = 26.0 23.2.1 a
fs = 0.58 fy AsReqd / AsProv = 65.05 22.2.1 SP:24
Mod. factor for tension rft.= (1/0.225 + 0.00322 fs-0.625 log10(1/pt)) 2.0 = 2.00 23.2.1 c
Mod. factor for compression rft. = (1.6 pc/pc + 0.275) 1.5 = 1.24 23.2.2
Hence, modified span / effective depth ratio = 64.23
Actual span / effective depth ratio = 8.30 SAFE
Member M3 Span 1
Detailed IS456 Shear Reinforcement Minimum links zone: 0.300 m to 0.825 m
Maximum shear force within zone, Vu = 265.02 kN
v = (Vu/bd) = 1.03 N/mm2 40.1
cmax = 2.8 Hence dimensions adequate
c = (0.85 0.8fck((1 + 5) - 1)/6) where =0.8fck/6.89pt = 0.61 N/mm2 4.1 SP:16
Face of support is less than 2d away from section,
Hence enhancement of shear strength possible 40.5.2
distance to face of support, av = 533 mm
vc = 2d vc / av = 1.37 N/mm2
v < c, Hence provide nominal links 26.5.1.6
Spacing provided, sv = 225 mm
Minimum area of links = 0.4 b sv / 0.87 fy = 88.97 mm2
Area of links provided (2T10), Asv = 157.08 mm2
Shear Reinforcement provided = 2T10 @ 225 c/c
OK
High shear zone: 0.825 m to 4.700 m
Maximum shear force within zone, Vu = 214.98 kN
v = (Vu/bd) = 0.83 N/mm2 40.1
cmax = 2.8 Hence dimensions adequate
c = (0.85 0.8fck((1 + 5) - 1)/6) where =0.8fck/6.89pt = 0.56 N/mm2 4.1 SP:16
c < v < cmax 40.4
Spacing provided, sv = 225 mm
Minimum area of links = b sv (v - c) / 0.87 fy = 59.52 mm2
Area of links provided (3T10), Asv = 235.62 mm2
Shear Reinforcement provided = 3T10 @ 225 c/c
OK
Member M3 Span 2
Detailed IS456 Design Requirements Section Property: 430 x 649
Beam Designed for : Vertical Bending and Shear
Span Length = 5.000 m Rectangular section
Width = 430 mm Depth = 650 mm
Covers: Top = 25 mm Bottom = 25 mm Side = 25 mm
Member M3 Span 2
Detailed IS456 Main Reinforcement Section at 5.000 m from start of member: Hogging
Moment applied to section = 411.91 kNm
Effective depth to tension reinforcement d = 599 mm
Depth to compression reinforcement d' = 48 mm
Compression steel required.
Asc' = 10.28 mm2 G-1.2
Stress in compression steel,fsc = 416.78 N/mm2
Asc = ((Mu-Mulim)/(fsc) (d - d')) = 10.28 mm2 G-1.2
Required tension steel area = 1954 mm2
Required compression steel area = 10 mm2
Tension bars provided = 3T32 ( 2413 mm2 )
Minimum area of tension reinforcement = 438 mm2 26.5.1.1(a)
Maximum area of tension reinforcement = 11180 mm2 26.5.1.1(b)
Compression bars provided = 4T25 (= 1963 mm2 )
Maximum area of compression reinforcement = 11180 mm2 26.5.1.2
Minimum horizontal bar spacing = 40 mm 26.3.2
Smallest actual horizontal space between bars = 87 mm
Maximum allowable spacing for tension bars (for 0% redistribution) = 150 mm 26.3.3
Largest actual space between tension bars = 132 mm
Beam Designed as a Doubly Reinforced Section
Actual neutral axis depth of section = 273.16 mm
Moment capacity of section = 521.97 KNm
OK
Section at 5.000 m from start of member: Hogging
Moment applied to section = 411.91 kNm
Effective depth to tension reinforcement d = 599 mm
Depth to compression reinforcement d' = 47 mm
Compression steel required.
Asc' = 10.28 mm2 G-1.2
Stress in compression steel,fsc = 416.78 N/mm2
Asc = ((Mu-Mulim)/(fsc) (d - d')) = 10.28 mm2 G-1.2
Required tension steel area = 1954 mm2
Required compression steel area = 10 mm2
Tension bars provided = 6T32 ( 4825 mm2 )
Minimum area of tension reinforcement = 438 mm2 26.5.1.1(a)
Maximum area of tension reinforcement = 11180 mm2 26.5.1.1(b)
Compression bars provided = 8T25 (= 3927 mm2 )
Maximum area of compression reinforcement = 11180 mm2 26.5.1.2
Minimum horizontal bar spacing = 40 mm 26.3.2
Smallest actual horizontal space between bars = -25 mm
Maximum allowable spacing for tension bars (for 0% redistribution) = 150 mm 26.3.3
Largest actual space between tension bars = 132 mm
Beam Designed as a Doubly Reinforced Section
Actual neutral axis depth of section = 273.16 mm
Moment capacity of section = 1100.79 KNm
OK
Section at 10.000 m from start of member: Hogging
Moment applied to section = 417.43 kNm
Effective depth to tension reinforcement d = 599 mm
Depth to compression reinforcement d' = 48 mm
Compression steel required.
Asc' = 34.30 mm2 G-1.2
Stress in compression steel,fsc = 416.78 N/mm2
Asc = ((Mu-Mulim)/(fsc) (d - d')) = 34.30 mm2 G-1.2
Required tension steel area = 1977 mm2
Required compression steel area = 34 mm2
Tension bars provided = 3T32 ( 2413 mm2 )
Minimum area of tension reinforcement = 438 mm2 26.5.1.1(a)
Maximum area of tension reinforcement = 11180 mm2 26.5.1.1(b)
Compression bars provided = 4T25 (= 1963 mm2 )
Maximum area of compression reinforcement = 11180 mm2 26.5.1.2
Minimum horizontal bar spacing = 40 mm 26.3.2
Smallest actual horizontal space between bars = 87 mm
Maximum allowable spacing for tension bars (for 0% redistribution) = 150 mm 26.3.3
Largest actual space between tension bars = 132 mm
Beam Designed as a Doubly Reinforced Section
Actual neutral axis depth of section = 273.16 mm
Moment capacity of section = 521.97 KNm
OK
Section at 10.000 m from start of member: Hogging
Moment applied to section = 417.43 kNm
Effective depth to tension reinforcement d = 599 mm
Depth to compression reinforcement d' = 47 mm
Compression steel required.
Asc' = 34.30 mm2 G-1.2
Stress in compression steel,fsc = 416.78 N/mm2
Asc = ((Mu-Mulim)/(fsc) (d - d')) = 34.30 mm2 G-1.2
Required tension steel area = 1977 mm2
Required compression steel area = 34 mm2
Tension bars provided = 6T32 ( 4825 mm2 )
Minimum area of tension reinforcement = 438 mm2 26.5.1.1(a)
Maximum area of tension reinforcement = 11180 mm2 26.5.1.1(b)
Compression bars provided = 8T25 (= 3927 mm2 )
Maximum area of compression reinforcement = 11180 mm2 26.5.1.2
Minimum horizontal bar spacing = 40 mm 26.3.2
Smallest actual horizontal space between bars = -25 mm
Maximum allowable spacing for tension bars (for 0% redistribution) = 150 mm 26.3.3
Largest actual space between tension bars = 132 mm
Beam Designed as a Doubly Reinforced Section
Actual neutral axis depth of section = 273.16 mm
Moment capacity of section = 1100.79 KNm
OK
Member M3 Span 2
Detailed IS456 Span / Effective Depth Check Basic span / effective depth ratio = 26.0 23.2.1 a
fs = 0.58 fy AsReqd / AsProv = 65.05 22.2.1 SP:24
Mod. factor for tension rft.= (1/0.225 + 0.00322 fs-0.625 log10(1/pt)) 2.0 = 2.00 23.2.1 c
Mod. factor for compression rft. = (1.6 pc/pc + 0.275) 1.5 = 1.24 23.2.2
Hence, modified span / effective depth ratio = 64.23
Actual span / effective depth ratio = 8.30 SAFE
Member M3 Span 2
Detailed IS456 Shear Reinforcement Minimum links zone: 5.300 m to 5.825 m
Maximum shear force within zone, Vu = 245.35 kN
v = (Vu/bd) = 0.95 N/mm2 40.1
cmax = 2.8 Hence dimensions adequate
c = (0.85 0.8fck((1 + 5) - 1)/6) where =0.8fck/6.89pt = 0.61 N/mm2 4.1 SP:16
Face of support is less than 2d away from section,
Hence enhancement of shear strength possible 40.5.2
distance to face of support, av = 533 mm
vc = 2d vc / av = 1.37 N/mm2
v < c, Hence provide nominal links 26.5.1.6
Spacing provided, sv = 225 mm
Minimum area of links = 0.4 b sv / 0.87 fy = 88.97 mm2
Area of links provided (2T10), Asv = 157.08 mm2
Shear Reinforcement provided = 2T10 @ 225 c/c
OK
High shear zone: 5.825 m to 9.700 m Maximum shear force within zone, Vu = 198.87 kN
v = (Vu/bd) = 0.77 N/mm2 40.1
cmax = 2.8 Hence dimensions adequate
c = (0.85 0.8fck((1 + 5) - 1)/6) where =0.8fck/6.89pt = 0.56 N/mm2 4.1 SP:16
c < v < cmax 40.4
Spacing provided, sv = 225 mm
Minimum area of links = b sv (v - c) / 0.87 fy = 45.69 mm2
Area of links provided (3T10), Asv = 235.62 mm2
Shear Reinforcement provided = 3T10 @ 225 c/c
OK