A 3m diameter circular footing is transmitting a concentrated load of 1500 kN. a. Determine the bearing pressure exerted by this footing into the supporting soil b. Determine the increase in the vertical stress at a depth of 3m directly below the center of the footing c. Determine the increase in the vertical stress at a depth of 6m which is located at 2m radially from the center of the footing Table 1 Variation of A' with z/R and r/R r/R z/R 0 0.2 0.4 0.6 0.8 1 1.2 1.5 2 0 1.0 1.0 1.0 0.5 0 0 1.0 0.78797 0 0.00856 0.1 0.90050 0.88679 0.43015 0.09645 0.02787 0.89748 0.80388 0.79824 0.77884 0.2 0.63014 0.38269 0.15433 0.05251 0.01680 0.3 0.71265 0.70518 0.68316 0.52081 0.34375 0.17964 0.07199 0.02440 0.4 0.62861 0.62015 0.59241 0.44329 0.31048 0.18709 0.08593 0.03118 0.5 0.55279 0.54403 0.51622 0.38390 0.28156 0.18556 0.09499 0.03701 0.6 0.45078 0.33676 0.25588 0.17952 0.10010 0.48550 0.47691 0.42654 0.41874 0.39491 0.7 0.29833 0.21727 0.17124 0.10228 0.04558 0.8 0.37531 0.36832 0.34729 0.26581 0.21297 0.16206 0.10236 0.9 0.33104 0.32492 0.30669 0.23832 0.19488 0.15253 0.10094 1 0.29289 0.28763 0.27005 0.21468 0.17868 0.14329 0.09849 0.05185 1.2 0.23178 0.22795 0.21662 0.17626 0.15101 0.12570 0.09192 0.05260 1.5 0.16795 0.16552 0.15877 0.13436 0.11892 0.10296 0.08048 0.05116 2 0.10557 0.10453 0.10140 0.09011 0.08269 0.07471 0.06275 0.04496 2.5 0.07152 0.07098 0.06947 0.06373 0.05974 0.05555 0.04880 0.03787 3 0.05132 0.05101 0.05022 0.04707 0.04487 0.04241 0.03839 0.03150 4 0.02986 0.02976 0.02907 0.02832 0.02749 0.02651 0.02490 0.02193 5 0.01942 0.01938 0.01835 0.01573 6 0.01361 0.01307 0.01168 7 0.01005 0.00976 0.00894 8 0.00772 0.00755 0.00703 9 0.00612 0.00600 0.00566 0.00477 0.00465 10 1.0 0.86126 0.73483 0.62690 0.53767 0.46448 0.40427 0.35428 0.31243 0.27707 0.24697 0.19890 0.14804 0.09647 0.06698 0.04886 0.02802
A 3m diameter circular footing is transmitting a concentrated load of 1500 kN. a. Determine the bearing pressure exerted by this footing into the supporting soil b. Determine the increase in the vertical stress at a depth of 3m directly below the center of the footing c. Determine the increase in the vertical stress at a depth of 6m which is located at 2m radially from the center of the footing Table 1 Variation of A' with z/R and r/R r/R z/R 0 0.2 0.4 0.6 0.8 1 1.2 1.5 2 0 1.0 1.0 1.0 0.5 0 0 1.0 0.78797 0 0.00856 0.1 0.90050 0.88679 0.43015 0.09645 0.02787 0.89748 0.80388 0.79824 0.77884 0.2 0.63014 0.38269 0.15433 0.05251 0.01680 0.3 0.71265 0.70518 0.68316 0.52081 0.34375 0.17964 0.07199 0.02440 0.4 0.62861 0.62015 0.59241 0.44329 0.31048 0.18709 0.08593 0.03118 0.5 0.55279 0.54403 0.51622 0.38390 0.28156 0.18556 0.09499 0.03701 0.6 0.45078 0.33676 0.25588 0.17952 0.10010 0.48550 0.47691 0.42654 0.41874 0.39491 0.7 0.29833 0.21727 0.17124 0.10228 0.04558 0.8 0.37531 0.36832 0.34729 0.26581 0.21297 0.16206 0.10236 0.9 0.33104 0.32492 0.30669 0.23832 0.19488 0.15253 0.10094 1 0.29289 0.28763 0.27005 0.21468 0.17868 0.14329 0.09849 0.05185 1.2 0.23178 0.22795 0.21662 0.17626 0.15101 0.12570 0.09192 0.05260 1.5 0.16795 0.16552 0.15877 0.13436 0.11892 0.10296 0.08048 0.05116 2 0.10557 0.10453 0.10140 0.09011 0.08269 0.07471 0.06275 0.04496 2.5 0.07152 0.07098 0.06947 0.06373 0.05974 0.05555 0.04880 0.03787 3 0.05132 0.05101 0.05022 0.04707 0.04487 0.04241 0.03839 0.03150 4 0.02986 0.02976 0.02907 0.02832 0.02749 0.02651 0.02490 0.02193 5 0.01942 0.01938 0.01835 0.01573 6 0.01361 0.01307 0.01168 7 0.01005 0.00976 0.00894 8 0.00772 0.00755 0.00703 9 0.00612 0.00600 0.00566 0.00477 0.00465 10 1.0 0.86126 0.73483 0.62690 0.53767 0.46448 0.40427 0.35428 0.31243 0.27707 0.24697 0.19890 0.14804 0.09647 0.06698 0.04886 0.02802
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
Related questions
Question
Transcribed Image Text:A 3m diameter circular footing is transmitting a concentrated load of 1500 kN.
a. Determine the bearing pressure exerted by this footing into the supporting soil
b. Determine the increase in the vertical stress at a depth of 3m directly below the center of
the footing
c.
Determine the increase in the vertical stress at a depth of 6m which is located at 2m
radially from the center of the footing
Table 1 Variation of A' with z/R and r/R
r/R
z/R
0
0.2
0.4
0.6
0.8
1
1.2
1.5
2
0
1.0
1.0
1.0
1.0
1.0
0.5
0
0
0
0.1
0.90050
0.89748
0.88679
0.86126
0.78797
0.09645
0.02787
0.00856
0.43015
0.38269
0.2
0.80388
0.79824
0.77884
0.73483
0.63014
0.15433 0.05251
0.01680
0.3
0.71265
0.70518 0.68316
0.62690
0.52081
0.34375 0.17964 0.07199
0.02440
0.4
0.62861
0.62015
0.59241
0.53767
0.44329
0.31048
0.18709
0.08593
0.03118
0.5
0.55279 0.54403 0.51622
0.46448
0.38390
0.28156
0.18556
0.09499
0.03701
0.6
0.48550
0.47691
0.45078
0.40427
0.33676
0.25588
0.17952
0.10010
0.7
0.42654
0.41874
0.39491
0.35428
0.29833
0.21727
0.17124
0.10228
0.04558
0.8
0.37531
0.36832 0.34729
0.31243
0.26581
0.21297
0.16206
0.10236
0.9
0.33104
0.32492
0.30669
0.27707
0.23832
0.19488
0.15253
0.10094
1
0.29289
0.28763 0.27005
0.24697
0.21468
0.17868
0.14329
0.09849
0.05185
1.2
0.23178
0.22795
0.21662
0.19890
0.17626
0.15101
0.12570
0.09192
0.05260
1.5
0.16795
0.16552
0.15877
0.14804
0.13436
0.11892
0.10296
0.08048
0.05116
2
0.10557
0.10453
0.10140
0.09647
0.09011
0.08269
0.07471
0.06275
0.04496
2.5
0.07152
0.07098
0.06947
0.06698
0.06373
0.05974
0.05555
0.04880
0.03787
3
0.05132
0.05101
0.05022
0.04886
0.04707
0.04487
0.04241
0.03839
0.03150
4
0.02986
0.02976
0.02907
0.02802
0.02832
0.02749
0.02651
0.02490
0.02193
5
0.01942
0.01938
0.01835
0.01573
6
0.01361
0.01307
0.01168
7
0.01005
0.00976
0.00894
8
0.00772
0.00755
0.00703
9
0.00612
0.00600
0.00566
0.00477
0.00465
10
88
Transcribed Image Text:Table 1 (continued)
3
5
6
8
0
0
0
0
0
0
0
0
0
0.00211
0.00084
0.00042
0.00419
0.00167
0.00083
0.00048
0.00030
0.00020
0.00622
0.00250
0.01013
0.00407
0.00209
0.00118 0.00071
0.00053
0.00025
0.00014
0.00009
0.01742 0.00761 0.00393
0.00226
0.00143
0.00097
0.00050
0.00029
0.00018
0.00171
0.00115
0.01935 0.00871 0.00459 0.00269
0.02142 0.01013 0.00548
0.00325
0.00210
0.00141
0.00073
0.00043
0.00027
0.00659
0.00264
0.00180 0.00094
0.00056 0.00036
0.00214 0.00115
0.00068
0.00043
0.00308
0.00346 0.00242
0.00384
0.00394 0.00298 0.00179
0.00079
0.00051
0.00132
0.00282 0.00160 0.00099
0.00065
0.00113
0.00075
0.02221 0.01160
0.00399
0.02143 0.01221 0.00732 0.00463
0.01980 0.01220 0.00770 0.00505
0.01592 0.01109 0.00768 0.00536
0.01249 0.00949 0.00708 0.00527
0.00983 0.00795 0.00628 0.00492 0.00384
0.00784 0.00661 0.00548 0.00445 0.00360
0.00635 0.00554 0.00472 0.00398 0.00332
0.00520 0.00466 0.00409 0.00353 0.00301 0.00256
0.00438 0.00397 0.00352 0.00326
0.00299
0.00188
0.00124
0.00084
0.00291
0.00193
0.00130
0.00091
0.00276
0.00189
0.00134
0.00094
0.00184
0.00133
0.00096
0.00273
0.00241
Table 10.2 Variation of B' with z/R and r/R
r/R
z/R
0
0.2
0.4
0.6
0.8
1
1.2
1.5
2
0
0
0
0
0
0
0
0
0
0
0.1
0.09852
0.10140
0.11138
0.13424
0.18796
0.05388
-0.07899 -0.02672
0.2
0.18857
-0.00845
-0.01593
0.19306
0.20772
0.23524
0.25983
0.08513 -0.07759 -0.04448
0.3
0.26362 0.26787
0.28018 0,29483
0.27257
0.10757
-0.04316 -0.04999
-0.02166
0.4
0.32016
0.32748 0.32273
0.26925
0.12404
-0.00766 -0.04535
-0.02522
0.32259
0.35752
0.5
0.35777
0.35323
0.33106
0.26236
0.13591
0.02165 -0.03455
-0.02651
0.6 0.378311 0.37531
0.36308 0.32822
0.25411
0.14440
0.04457 -0.02101
0.7
0.38487 0.37962
0.36072
0.31929
0.24638
0.14986 0.06209 -0.00702 -0.02329
0.8
0.38091
0.37408
0.35133
0.30699
0.23779 0.15292
0.07530
0.00614
0.9
0.3
0.36275
0.33734
0.29299 0.22891
0.15404
0.08507
0.0179
1
0.35355
0.27819 0.21978
0.15355
0.09210
0.02814
-0.01005
1.2
0.14915 0.10002
0.04378
0.00023
1.5
0.13732 0.10193 0.05745
0.01385
2
0.34553 0.32075
0.31485 0.30730 0.28481 0.24836 0.20113
0,25602 0.25025 0.23338 0.20694 0.17368
0.17889 0.18144 0.16644 0.15198 0.13375
0.12807 0.12633 0.12126 0.11327 0.10298
0.09487 0.09394 0.09099 0.08635 0.08033
0.02836
2.5
0.03429
0.11331 0.09254 0.06371
0.09130 0.07869 0.06022
0.07325 0.06551
0.05145 0.04773 0.04532 0.03995
3
0.05354
0.03511
4
0.05707
0.05666
0.05562
0.05383
0.03066
5
0.03772
0.03760
0.03384
0.02474
6
0.02666
0.02468
0.01968
7
0.01980
0.01868
0.01577
8
0.01526
0.01459
0.01279
9
0.01212
0.01170
0.01054
10
0.00924
0.00879
Table 10.2 (continued)
3
4
5
6
12
14
0
0
0
0
0
0
0
0
0
-0.00210 -0.00084 -0.00042
-0.00412 -0.00166 -0.00083 -0.00024 -0.00015
-0.00599 -0.00245
-0.00010
-0.00991 -0.00388 -0.00199 -0.00116 -0.00073
-0.00049
-0.00025 -0.00014 -0.00009
-0.01115 -0.00608 -0.00344 -0.00210 -0.00135
-0.00092 -0.00048 -0.00028 -0.00018
-0.00179 -0.00151
-0.00995 -0.00632 -0.00378 -0.00236 -0.00156 -0.00107
-0.00669 -0.00600 -0.00401 -0.00265 -0.00181 -0.00126 -0.00068 -0.00040 -0.00026
0.00028 -0.00410 -0.00371 -0.00278 -0.00202 -0.00148 -0.00084 -0.00050 -0.00033
0.00661 -0.00130 -0.00271 -0.00250 -0.00201 -0.00156 -0.00094 -0.00059 -0.00039
0.01112 0.00157 -0.00134 -0.00192
-0.00099 -0.00065 -0.00046
0.01515 0.00595 0.00155 -0.00029 -0.00094 -0.00109 -0.00094 -0.00068 -0.00050
0.01522 0.00810 0.00371 0.00132
-0.00043 -0.00070 -0.00061 -0.00049
0.01380 0.00867 0.00496 0.00254
0.00028 -0.00037 -0.00047 -0.00045
0.01204 0.00842 0.00547 0.00332
0.00093 -0.00002 -0.00029 -0.00037
0.01034 0.00779 0.00554 0.00372
0.00141 0.00035 -0.00008 -0.00025
0.00888 0.00705 0.00533
0.00764 0.00631
0.00013
0.00110
0.00185
0.00236
0.00178
0.00066
0.00012
-0.00012
0.00386 0.00265
0.00382 0.00281
0.00501
0.00199
7
7
8
10
10
12
14
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