1. Find Mn for the following T-beam: b = 48 in., bw = 12 in., h, = 4 in., d = 22 in., f = 4000 psi, and fy = 60,000 psi. The reinforcement is four No. 8 bars. As = 3.16 in² 2. Same as 1 with b = 36 in., bw = 12 in., h, = 4 in., d = 22 in., reinforcement of three No. 11 bars (3#11, A = 4.68 in²) TABLE A-10 Coefficient of Resistance (K) versus Reinforcement Ratio (p) (F = 4000 psi; fy 60,000 psi; units of kare ksi) R P R 0.0010 0.0595 0.0039 0.2259 0.0068 0.3835 0.0097 0.5322 0.0011 0.0654 0.0040 0.2315 0.0069 0.3888 0.0098 0.5372 0.0012 0.0712 0.0041 0.2371 0.0070 0.3941 0.0099 0.5421 0.0013 0.0771 0.0042 0.2427 0.0071 0.3993 0.0100 0.5471 0.0014 0.0830 0.0043 0.2482 0.0072 0.4046 0.0101 0.5520 The ACI Code, Section 21.2, 0.0015 0.0889 0.0044 0.2538 0.0073 0.4098 0.0102 0.5569 0.0016 0.0946 0.0045 0.2593 0.0074 0.4150 0.0103 0.5618 0.0017 0.1005 0.0046 0.2648 0.0075 0.4202 0.0104 0.5667 0.0018 0.1063 0.0047 0.2703 0.0076 0.4254 0.0105 0.0019 0.1121 0.0048 0.2758 0.0077 0.4306 0.0106 0.5716 0.5765 0.0020 0.1179 0.0049 0.2813 0.0078 0.4358 0.0107 0.5814 0.0021 0.1237 0.0050 0.2868 0.0079 0.4410 0.0108 0.5862 0.0022 0.1294 0.0051 0.2922 0.0080 0.4461 0.0109 0.5911 0.0023 0.1352 0.0052 0.2977 0.0081 0.4513 0.0110 0.5959 0.0024 0.1410 0.0053 0.3031 0.0082 0.4564 0.0111 0.6008 0.0025 0.1467 0.0054 0.3086 0.0083 0.4615 0.0112 0.6056 0.0026 0.1524 0.0055 0.3140 0.0084 0.4666 0.0113 0.6104 0.0027 0.1581 0.0056 0.3194 0.0085 0.4718 0.0114 0.6152 0.0028 0.1638 0.0057 0.3248 0.0086 0.4768 0.0115 0.0029 0.1695 0.0058 0.3302 0.0087 0.4819 0.0116 0.6200 0.6248 0.0030 0.1752 0.0059 0.3356 0.0088 0.4870 0.0117 0.0031 0.1809 0.0060 0.3409 0.0089 0.4921 0.0118 0.0032 0.1866 0.0061 0.3463 0.0090 0.4971 0.0119 0.6296 0.6343 0.6391 0.0033 0.1922 0.0062 0.3516 0.0091 0.5022 0.0120 0.0034 0.1979 0.0063 0.3570 0.0092 0.5072 0.0121 0.0035 0.2035 0.0064 0.3623 0.0093 0.5122 0.0122 0.6438 0.6485 0.6532 0.0036 0.2091 0.0065 0.3676 0.0094 0.5172 0.0123 0.6579 0.0037 0.2148 0.0066 0.3729 0.0095 0.5222 0.0124 0.0038 0.2204 0.0067 0.3782 0.0096 0.5272 0.0125 0.6626 0.6673 provides for these variables by using the following factors: Tension-controlled sections -0.90 Compression-controlled sections spirally reinforced-0.75 other reinforced members - 0.65 Shear and torsion - 0.75 Bearing on concrete-0.65 0.0126 0.6720 0.0154 0.7985 0.01806 0.9110 0.00500 0.0127 0.6766 0.0155 0.8029 0.0181 0.9126 0.00498 0.0128 0.6813 0.0156 0.8072 0.0182 0.9167 0.00494 0.0129 0.6859 0.0157 0.8116 0.0183 0.9208 0.00490 0.0130 0.6906 0.0158 0.8159 0.0184 0.9248 0.00485 0.0131 0.6952 0.0159 0.8202 0.0185 0.9289 0.00481 0.0132 0.6998 0.0160 0.8245 0.0186 0.9329 0.00477 0.0133 0.7044 0.0161 0.8288 0.0187 0.9369 0.00473 0.0134 0.7090 0.0162 0.8331 0.0188 0.9410 0.00469 0.0135 0.7136 0.0163 0.8374 0.0189 0.9450 0.00465 0.0136 0.7181 0.0164 0.8417 0.0190 0.9490 0.00461 0.0137 0.7227 0.0165 0.8459 0.0191 0.9529 0.00457 0.0138 0.7272 0.0166 0.8502 0.0192 0.9569 0.00453 0.0139 0.7318 0.0167 0.8544 0.0193 0.9609 0.00449 0.0140 0.7363 0.0168 0.8586 0.0194 0.9648 0.00445 0.0141 0.7408 0.0169 0.8629 0.0195 0.9688 0.00441 0.0142 0.7453 0.0170 0.8671 0.0196 0.9727 0.00437 0.0143 0.7498 0.0171 0.8713 0.0197 0.9766 0.00434 0.0144 0.7543 0.0172 0.8754 0.0198 0.9805 0.00430 0.0145 0.7587 0.0173 0.8796 0.0199 0.9844 0.00426 0.0146 0.7632 0.0174 0.8838 0.0200 0.9883 0.00422 0.0147 0.7676 0.0175 0.8879 0.0201 0.9922 0.00419 0.0148 0.7721 0.0176 0.8921 0.0202 0.9961 0.00415 0.0149 0.7765 0.0177 0.8962 0.0203 0.9999 0.00412 0.0150 0.7809 0.0178 0.9003 0.0204 1.0038 0.00408 0.0151 0.7853 0.0179 0.9044 0.0205 1.0076 0.00405 0.0152 0.7897 0.0180 0.9085 0.0206 1.0114 0.00401 0.0153 0.7941 0.02063 1.0126 0.00400 119
1. Find Mn for the following T-beam: b = 48 in., bw = 12 in., h, = 4 in., d = 22 in., f = 4000 psi, and fy = 60,000 psi. The reinforcement is four No. 8 bars. As = 3.16 in² 2. Same as 1 with b = 36 in., bw = 12 in., h, = 4 in., d = 22 in., reinforcement of three No. 11 bars (3#11, A = 4.68 in²) TABLE A-10 Coefficient of Resistance (K) versus Reinforcement Ratio (p) (F = 4000 psi; fy 60,000 psi; units of kare ksi) R P R 0.0010 0.0595 0.0039 0.2259 0.0068 0.3835 0.0097 0.5322 0.0011 0.0654 0.0040 0.2315 0.0069 0.3888 0.0098 0.5372 0.0012 0.0712 0.0041 0.2371 0.0070 0.3941 0.0099 0.5421 0.0013 0.0771 0.0042 0.2427 0.0071 0.3993 0.0100 0.5471 0.0014 0.0830 0.0043 0.2482 0.0072 0.4046 0.0101 0.5520 The ACI Code, Section 21.2, 0.0015 0.0889 0.0044 0.2538 0.0073 0.4098 0.0102 0.5569 0.0016 0.0946 0.0045 0.2593 0.0074 0.4150 0.0103 0.5618 0.0017 0.1005 0.0046 0.2648 0.0075 0.4202 0.0104 0.5667 0.0018 0.1063 0.0047 0.2703 0.0076 0.4254 0.0105 0.0019 0.1121 0.0048 0.2758 0.0077 0.4306 0.0106 0.5716 0.5765 0.0020 0.1179 0.0049 0.2813 0.0078 0.4358 0.0107 0.5814 0.0021 0.1237 0.0050 0.2868 0.0079 0.4410 0.0108 0.5862 0.0022 0.1294 0.0051 0.2922 0.0080 0.4461 0.0109 0.5911 0.0023 0.1352 0.0052 0.2977 0.0081 0.4513 0.0110 0.5959 0.0024 0.1410 0.0053 0.3031 0.0082 0.4564 0.0111 0.6008 0.0025 0.1467 0.0054 0.3086 0.0083 0.4615 0.0112 0.6056 0.0026 0.1524 0.0055 0.3140 0.0084 0.4666 0.0113 0.6104 0.0027 0.1581 0.0056 0.3194 0.0085 0.4718 0.0114 0.6152 0.0028 0.1638 0.0057 0.3248 0.0086 0.4768 0.0115 0.0029 0.1695 0.0058 0.3302 0.0087 0.4819 0.0116 0.6200 0.6248 0.0030 0.1752 0.0059 0.3356 0.0088 0.4870 0.0117 0.0031 0.1809 0.0060 0.3409 0.0089 0.4921 0.0118 0.0032 0.1866 0.0061 0.3463 0.0090 0.4971 0.0119 0.6296 0.6343 0.6391 0.0033 0.1922 0.0062 0.3516 0.0091 0.5022 0.0120 0.0034 0.1979 0.0063 0.3570 0.0092 0.5072 0.0121 0.0035 0.2035 0.0064 0.3623 0.0093 0.5122 0.0122 0.6438 0.6485 0.6532 0.0036 0.2091 0.0065 0.3676 0.0094 0.5172 0.0123 0.6579 0.0037 0.2148 0.0066 0.3729 0.0095 0.5222 0.0124 0.0038 0.2204 0.0067 0.3782 0.0096 0.5272 0.0125 0.6626 0.6673 provides for these variables by using the following factors: Tension-controlled sections -0.90 Compression-controlled sections spirally reinforced-0.75 other reinforced members - 0.65 Shear and torsion - 0.75 Bearing on concrete-0.65 0.0126 0.6720 0.0154 0.7985 0.01806 0.9110 0.00500 0.0127 0.6766 0.0155 0.8029 0.0181 0.9126 0.00498 0.0128 0.6813 0.0156 0.8072 0.0182 0.9167 0.00494 0.0129 0.6859 0.0157 0.8116 0.0183 0.9208 0.00490 0.0130 0.6906 0.0158 0.8159 0.0184 0.9248 0.00485 0.0131 0.6952 0.0159 0.8202 0.0185 0.9289 0.00481 0.0132 0.6998 0.0160 0.8245 0.0186 0.9329 0.00477 0.0133 0.7044 0.0161 0.8288 0.0187 0.9369 0.00473 0.0134 0.7090 0.0162 0.8331 0.0188 0.9410 0.00469 0.0135 0.7136 0.0163 0.8374 0.0189 0.9450 0.00465 0.0136 0.7181 0.0164 0.8417 0.0190 0.9490 0.00461 0.0137 0.7227 0.0165 0.8459 0.0191 0.9529 0.00457 0.0138 0.7272 0.0166 0.8502 0.0192 0.9569 0.00453 0.0139 0.7318 0.0167 0.8544 0.0193 0.9609 0.00449 0.0140 0.7363 0.0168 0.8586 0.0194 0.9648 0.00445 0.0141 0.7408 0.0169 0.8629 0.0195 0.9688 0.00441 0.0142 0.7453 0.0170 0.8671 0.0196 0.9727 0.00437 0.0143 0.7498 0.0171 0.8713 0.0197 0.9766 0.00434 0.0144 0.7543 0.0172 0.8754 0.0198 0.9805 0.00430 0.0145 0.7587 0.0173 0.8796 0.0199 0.9844 0.00426 0.0146 0.7632 0.0174 0.8838 0.0200 0.9883 0.00422 0.0147 0.7676 0.0175 0.8879 0.0201 0.9922 0.00419 0.0148 0.7721 0.0176 0.8921 0.0202 0.9961 0.00415 0.0149 0.7765 0.0177 0.8962 0.0203 0.9999 0.00412 0.0150 0.7809 0.0178 0.9003 0.0204 1.0038 0.00408 0.0151 0.7853 0.0179 0.9044 0.0205 1.0076 0.00405 0.0152 0.7897 0.0180 0.9085 0.0206 1.0114 0.00401 0.0153 0.7941 0.02063 1.0126 0.00400 119
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
Related questions
Question
100%
Transcribed Image Text:1. Find Mn for the following T-beam: b = 48 in., bw = 12 in., h, = 4 in., d = 22 in.,
f = 4000 psi, and fy = 60,000 psi. The reinforcement is four No. 8 bars. As = 3.16 in²
2. Same as 1 with b = 36 in., bw = 12 in., h, = 4 in., d = 22 in., reinforcement of three No. 11 bars (3#11, A = 4.68 in²)
TABLE A-10 Coefficient of Resistance (K) versus Reinforcement Ratio (p)
(F = 4000 psi; fy
60,000 psi; units of kare ksi)
R
P
R
0.0010
0.0595
0.0039
0.2259
0.0068
0.3835
0.0097
0.5322
0.0011
0.0654
0.0040
0.2315
0.0069
0.3888
0.0098
0.5372
0.0012
0.0712
0.0041
0.2371
0.0070
0.3941
0.0099
0.5421
0.0013
0.0771
0.0042
0.2427
0.0071
0.3993
0.0100
0.5471
0.0014
0.0830
0.0043
0.2482
0.0072
0.4046
0.0101
0.5520
The ACI Code, Section 21.2,
0.0015
0.0889
0.0044
0.2538
0.0073
0.4098
0.0102
0.5569
0.0016
0.0946
0.0045
0.2593
0.0074
0.4150
0.0103
0.5618
0.0017
0.1005
0.0046
0.2648
0.0075
0.4202
0.0104
0.5667
0.0018
0.1063
0.0047
0.2703
0.0076
0.4254
0.0105
0.0019
0.1121
0.0048
0.2758
0.0077
0.4306
0.0106
0.5716
0.5765
0.0020
0.1179
0.0049
0.2813
0.0078
0.4358
0.0107
0.5814
0.0021
0.1237
0.0050
0.2868
0.0079
0.4410
0.0108
0.5862
0.0022
0.1294
0.0051
0.2922
0.0080
0.4461
0.0109
0.5911
0.0023
0.1352
0.0052
0.2977
0.0081
0.4513
0.0110
0.5959
0.0024
0.1410
0.0053
0.3031
0.0082
0.4564
0.0111
0.6008
0.0025
0.1467
0.0054
0.3086
0.0083
0.4615
0.0112
0.6056
0.0026
0.1524
0.0055
0.3140
0.0084
0.4666
0.0113
0.6104
0.0027
0.1581
0.0056
0.3194
0.0085
0.4718
0.0114
0.6152
0.0028
0.1638
0.0057
0.3248
0.0086
0.4768
0.0115
0.0029
0.1695
0.0058
0.3302
0.0087
0.4819
0.0116
0.6200
0.6248
0.0030
0.1752
0.0059
0.3356
0.0088
0.4870
0.0117
0.0031
0.1809
0.0060
0.3409
0.0089
0.4921
0.0118
0.0032
0.1866
0.0061
0.3463
0.0090
0.4971
0.0119
0.6296
0.6343
0.6391
0.0033
0.1922
0.0062
0.3516
0.0091
0.5022
0.0120
0.0034
0.1979
0.0063
0.3570
0.0092
0.5072
0.0121
0.0035
0.2035
0.0064
0.3623
0.0093
0.5122
0.0122
0.6438
0.6485
0.6532
0.0036
0.2091
0.0065
0.3676
0.0094
0.5172
0.0123
0.6579
0.0037
0.2148
0.0066
0.3729
0.0095
0.5222
0.0124
0.0038
0.2204
0.0067
0.3782
0.0096
0.5272
0.0125
0.6626
0.6673
provides for these variables by
using the following factors:
Tension-controlled sections -0.90
Compression-controlled sections
spirally reinforced-0.75
other reinforced members - 0.65
Shear and torsion - 0.75
Bearing on concrete-0.65
0.0126
0.6720
0.0154
0.7985
0.01806
0.9110
0.00500
0.0127
0.6766
0.0155
0.8029
0.0181
0.9126
0.00498
0.0128
0.6813
0.0156
0.8072
0.0182
0.9167
0.00494
0.0129
0.6859
0.0157
0.8116
0.0183
0.9208
0.00490
0.0130
0.6906
0.0158
0.8159
0.0184
0.9248
0.00485
0.0131
0.6952
0.0159
0.8202
0.0185
0.9289
0.00481
0.0132
0.6998
0.0160
0.8245
0.0186
0.9329
0.00477
0.0133
0.7044
0.0161
0.8288
0.0187
0.9369
0.00473
0.0134
0.7090
0.0162
0.8331
0.0188
0.9410
0.00469
0.0135
0.7136
0.0163
0.8374
0.0189
0.9450
0.00465
0.0136
0.7181
0.0164
0.8417
0.0190
0.9490
0.00461
0.0137
0.7227
0.0165
0.8459
0.0191
0.9529
0.00457
0.0138
0.7272
0.0166
0.8502
0.0192
0.9569
0.00453
0.0139
0.7318
0.0167
0.8544
0.0193
0.9609
0.00449
0.0140
0.7363
0.0168
0.8586
0.0194
0.9648
0.00445
0.0141
0.7408
0.0169
0.8629
0.0195
0.9688
0.00441
0.0142
0.7453
0.0170
0.8671
0.0196
0.9727
0.00437
0.0143
0.7498
0.0171
0.8713
0.0197
0.9766
0.00434
0.0144
0.7543
0.0172
0.8754
0.0198
0.9805
0.00430
0.0145
0.7587
0.0173
0.8796
0.0199
0.9844
0.00426
0.0146
0.7632
0.0174
0.8838
0.0200
0.9883
0.00422
0.0147
0.7676
0.0175
0.8879
0.0201
0.9922
0.00419
0.0148
0.7721
0.0176
0.8921
0.0202
0.9961
0.00415
0.0149
0.7765
0.0177
0.8962
0.0203
0.9999
0.00412
0.0150
0.7809
0.0178
0.9003
0.0204
1.0038
0.00408
0.0151
0.7853
0.0179
0.9044
0.0205
1.0076
0.00405
0.0152
0.7897
0.0180
0.9085
0.0206
1.0114
0.00401
0.0153
0.7941
0.02063
1.0126
0.00400
119
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