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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

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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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: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
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
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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