设在半空间体的平面边界上以[tex=0.571x0.786]c59+3vo0/Vn/FvNRhDRu5g==[/tex]为半径的圆面上作用有法向分布力 [tex=0.5x1.0]jedlXyMYwmfVwxRj2j9sSw==[/tex], 不计体力,求最大沉陷。[img=423x266]1795f21cc2d74d2.png[/img]

2022-06-27

设在半空间体的平面边界上以[tex=0.571x0.786]c59+3vo0/Vn/FvNRhDRu5g==[/tex]为半径的圆面上作用有法向分布力 [tex=0.5x1.0]jedlXyMYwmfVwxRj2j9sSw==[/tex], 不计体力,求最大沉陷。[img=423x266]1795f21cc2d74d2.png[/img]

答案：

[tex=0.857x1.0]NsK+Nsu4tMOJlOhgKxJo5Q==[/tex] 点在荷载作用面之外(见图8-13）,由图8-4 求出半空间体的边界上距圆心为 [tex=0.5x0.786]U5O66aolbR1y5vuKrQbXNA==[/tex]的一点 [tex=0.857x1.0]NsK+Nsu4tMOJlOhgKxJo5Q==[/tex]的沉陷。在荷载范围内取一微小面积(如阴影线所示)[tex=4.714x1.214]UvKdgVDks0I6hQAnhhvOysaMsSINkoAnLWw8qIAwpU4=[/tex]则由公式( 8 -94）得 [tex=0.857x1.0]NsK+Nsu4tMOJlOhgKxJo5Q==[/tex]点的沉陷为[tex=20.571x2.643]Hb9cg3lGfsGKuUqN4jUQ6wPnZhMs4vVnAtEoSgDi3MSC77Xyr3a8n5eI6fqMpB7F+E3vggune40eHyJgeACIVvuImNElayublijASCD4gI9SmP/7C09ZCrS7vaYWZX51K2eY6c2KMtDCj8OMsIeKrr9LeccFZJ49J4UlA3We6dBi/SYrEp2EpdllwCyRh8kd0Ipn/aD9j18WRMGjCboOZA==[/tex][tex=0.857x1.0]NsK+Nsu4tMOJlOhgKxJo5Q==[/tex] 点的总沉陷为[tex=10.071x2.857]ycokeHafisxsKgyGRLdj0yhU37Usm5Sh9G1Bl3Ln0jpeYGACQ9bvUgT8VTGXEnVoqRtFp8cSV5OG6FTfH/v3EQ==[/tex]弦 [tex=1.5x0.786]uDlrM/k6mXUKzRmRUTQRAw==[/tex] 的长度为[tex=7.0x2.214]TIywczC9wNVuLAafd7eyBn0C6dc+Q5gnVPq/GiuJ1kusHXYK3PqadEGOQ+yQVv4q[/tex]考虑到对称性,则[tex=16.571x2.857]9ipNfEpQ7ZU7gZro0w7pYrZp4KNDyBz3RCCYJ7kj4edTAkLXB05Y2ZYUx03zsTlG2q/u3i/YxAiJ7vKuGAHCa/SYX3KTw+chHPvUVyBTPsfcgASd+zwZBKSwGfro3GEZciEJ6rnxaZUlsj5/Szroew==[/tex]  （a）利用关系式 [tex=6.0x1.214]GHt9Uu2OBMCyporyD7UlbRyIYNwweR6KF9VWlMh3EtI=[/tex]。 于是得出[tex=13.643x3.5]OnRWjXlx60k4Gmg/ZNuQZHFVVd40Pvs+X7CnVqbelZIKjXnHqOmTxfbh4ARsK6hJCmu4DNBrtZ0TgMzdikg9QjJIKYqXzJtuc/L8rhKhjuOLtbpoPbrAS+6ihork0uqaRFaez+ZV1YyJMa5IPFWz1mQ5lkVjRvl8G6XTxgRYqMR4s1bNy1wN96jvonGKDeFs[/tex]将上式代人式(a),并注意当 [tex=0.714x1.214]hEHZwhVlHPnf9D4udzi0EA==[/tex] 由0 改变到 [tex=1.071x1.214]xI0cXAtFKe7W0IGrb45/2g==[/tex] 时,[tex=0.5x1.0]qm+hGi0qngLh1B7HsENMPg==[/tex]由0 改变到 [tex=0.857x2.143]N6eo2Jyw0qeC1xLZcnA39w==[/tex], 即得[tex=16.571x12.071]a0s3MH7cLIdmiBRR0YN06z1e5iNWLSQSKiKz+kEU58Vd6goF1IzVNzbm5fF5QETaJWlT9QxLISZ2BZ99oeWJ5q7/l4XGa5D1UbDpaS3WOlv6Zoi3v3hCcCnBvBf8TBN9rBHow55qteJAopd87kP7gOlasNLuTu7P6CjQkKB2a7kn3RSFuQrdUeF6MeVpsIv6leRZassZsud5QuN80SF/fbNdqaWFj9wDWS+JHPasi0UWuc2wtgQI/FWiHyPETAzZ695BLvvfCENiinwiO83PLoY/hc3v52fZaseq8UakBRMF2JRBBB3eczNbaw4M0+NIUlv/he3/jWaz1FSfkrMloj8HERRd4gGYkYS/r2gLlt3hLcWHXQuTJldVpXQ6X1Mpoqeh+1Kq2IcC00Ikezo0LE1YQYSRAfld63f7drulWk3TDGsfwnSqst6PyiLVT4+LuL4ADWLaBvFdnT3PHyd+YX3NXli7ZhEPmHFjVy8C9f8vdlAkIMgAcLEeJOnsuL9tDYX+e83IyrpmdRDdoBMu3rRNNwSHwNm8YyMhReOMly76L+lt7INYzYYwh4g4AvPf3Pkkg8ziHK1ojxum8Hd8fdl4CUx/GMuUsfSSABy2CDwjvRdMQp+dkaghf71G1tyh[/tex](8-99)这一方程右边的积分是所得椭圆积分,它们的数值可由函数表查得。当点位于荷载的边界上时, [tex=1.786x0.786]2TKX22AUFkZt6Nbahmd6dA==[/tex], 上式简化为[tex=12.0x5.929]a0s3MH7cLIdmiBRR0YN06z1e5iNWLSQSKiKz+kEU58Vd6goF1IzVNzbm5fF5QETa/qj5Exr3KOU+cjf2om+YHEJWELKX3RlmkI6JLvgHZyY/7saTH75iVDjr3Yvrvuz1jR/Z2tY/pD1xFS+38DMQ2ZhvRASwnM3SwHNxq7K7HdglpNAebc9vjp+f1Iw0wPpSHKwDk3jE6pDw8S/C15pSdPSB3sbExdV2rk73ffL7UxA=[/tex] (8-100)(2) [tex=1.0x1.0]0KCelhZna0R9EGhYF1VZHA==[/tex] 点在荷载作用面之内(见图 8-14）,则取微小面积(如阴影线所示 )[tex=4.714x1.214]7IqOdlbfJ2MZTzBmwZueUIdTsKv6U5RZo7rUUZGcL34=[/tex], 则 [tex=1.0x1.0]0KCelhZna0R9EGhYF1VZHA==[/tex] 点的沉陷仍为[tex=10.071x2.857]ycokeHafisxsKgyGRLdj0yhU37Usm5Sh9G1Bl3Ln0jpeYGACQ9bvUgT8VTGXEnVoI6ZQB832Ycj81iJsrLSHqA==[/tex]但弦 [tex=1.5x0.786]uDlrM/k6mXUKzRmRUTQRAw==[/tex] 的长度为[tex=3.214x1.0]jxFoBDSSgGBh68/0GRaU57Z5kOgX62WjnFKEgo/UM0k=[/tex],考虑到对称性,[tex=0.714x1.214]hEHZwhVlHPnf9D4udzi0EA==[/tex] 系由 0 改变到 [tex=0.857x2.143]N6eo2Jyw0qeC1xLZcnA39w==[/tex],所以有[tex=12.286x2.857]B7hXmBkLS27XtYsTYsN2bEyM0Tl5FK7BmQU37xCUQxLZLlfagBJTr0ZUDf/UuetP6d1arwMev5bLYrqfBZuZj1hD8f2GFujCB4lv8k5Ixgola8P8U5+NG2NFiKKtKVl5[/tex]利用关系式 [tex=6.0x1.214]GHt9Uu2OBMCyporyD7UlbZ3LhJ3NvvaGTzEo1mE6cr0=[/tex],于是上式可变换为[tex=16.429x2.929]B7hXmBkLS27XtYsTYsN2bEyM0Tl5FK7BmQU37xCUQxLpqforOxrxvV57tD7t1tGTjZbZb463OpHkJtVXJdQOzwEESFE90l7aVGnf50PwVgaZ5tNE1Ms7RYPHRmVRJ+/QZm3jhatovlugUEBM2WoAy//pbDo+tUxlG2t8UtGNvAQ=[/tex] (8-101)对于 [tex=0.786x2.143]1B7Dgf9GdXwIL9GmAXgRpg==[/tex]的任何数值,都可由函数表查得上式中椭圆积分的数值,从而求得沉陷 [tex=0.786x0.786]RaAINhYHT2QFWQ2tWIaawg==[/tex],最大沉陷将发生在圆心,将 [tex=1.786x1.0]PNpwEwaQkBq+PSYXc8Vnww==[/tex] 代入上式,可得[tex=8.214x2.643]knhR8hVLbjUbY+J5qYq3Zf59opfCNL+ubzLPUgjO88eS2rQiQwmoJ5L+fLvaEUu42J8ApFPwihSBbhkBlFVYfw==[/tex]（8-102）[img=298x297]1795f286726b5a9.png[/img]

举一反三

内容

0
静止型[tex=0.571x0.786]c59+3vo0/Vn/FvNRhDRu5g==[/tex]地中海贫血患者之间婚配，生出轻型[tex=0.571x0.786]c59+3vo0/Vn/FvNRhDRu5g==[/tex]地中海贫血患者的可能性是 A: 0 B: 1/8 C: 1/4 D: 1/2 E: 1
1
图所示电路中[tex=0.571x0.786]c59+3vo0/Vn/FvNRhDRu5g==[/tex]点电位为（）[tex=0.857x1.286]ZpwhzmyivskaH5M1X7ozaQ==[/tex]。[img=264x46]179eb475d70f256.png[/img] 未知类型：{'options': ['-10', '-1', '2'], 'type': 102}
2
图9-26所示，金属球[tex=0.571x0.786]c59+3vo0/Vn/FvNRhDRu5g==[/tex]和金属球壳[tex=0.429x1.0]JThLUuJ8WswSAPiYZWihWg==[/tex]同心放置，它们原先都不带电。设球为[tex=0.857x1.0]6WwbFXETRyeyXlvAruSoNg==[/tex]，球壳[tex=0.429x1.0]JThLUuJ8WswSAPiYZWihWg==[/tex]的内、外半径分别为[tex=0.857x1.0]BNzznGkXRFuGyw2vMy6rWw==[/tex]和[tex=0.857x1.0]Fz01PbYkU0SRGm3tB5KjiA==[/tex]。求在下列情况下[tex=0.571x0.786]c59+3vo0/Vn/FvNRhDRu5g==[/tex]、[tex=0.429x1.0]JThLUuJ8WswSAPiYZWihWg==[/tex]的电势差：使[tex=0.571x0.786]c59+3vo0/Vn/FvNRhDRu5g==[/tex]带[tex=1.286x1.143]HtShgpkNmCs66SDQIt6cYg==[/tex][img=191x199]17e1ac6b01d9ad2.png[/img]
3
图9-26所示，金属球[tex=0.571x0.786]c59+3vo0/Vn/FvNRhDRu5g==[/tex]和金属球壳[tex=0.429x1.0]JThLUuJ8WswSAPiYZWihWg==[/tex]同心放置，它们原先都不带电。设球为[tex=0.857x1.0]6WwbFXETRyeyXlvAruSoNg==[/tex]，球壳[tex=0.429x1.0]JThLUuJ8WswSAPiYZWihWg==[/tex]的内、外半径分别为[tex=0.857x1.0]BNzznGkXRFuGyw2vMy6rWw==[/tex]和[tex=0.857x1.0]Fz01PbYkU0SRGm3tB5KjiA==[/tex]。求在下列情况下[tex=0.571x0.786]c59+3vo0/Vn/FvNRhDRu5g==[/tex]、[tex=0.429x1.0]JThLUuJ8WswSAPiYZWihWg==[/tex]的电势差：使[tex=0.571x0.786]c59+3vo0/Vn/FvNRhDRu5g==[/tex]带[tex=1.286x1.143]HtShgpkNmCs66SDQIt6cYg==[/tex],使[tex=0.429x1.0]JThLUuJ8WswSAPiYZWihWg==[/tex]带[tex=1.286x1.143]NeILClIc8twxeO5vjYm8Dw==[/tex][img=203x220]17e1aa8f4234a38.png[/img]
4
图9-26所示，金属球[tex=0.571x0.786]c59+3vo0/Vn/FvNRhDRu5g==[/tex]和金属球壳[tex=0.429x1.0]JThLUuJ8WswSAPiYZWihWg==[/tex]同心放置，它们原先都不带电。设球为[tex=0.857x1.0]6WwbFXETRyeyXlvAruSoNg==[/tex]，球壳[tex=0.429x1.0]JThLUuJ8WswSAPiYZWihWg==[/tex]的内、外半径分别为[tex=0.857x1.0]BNzznGkXRFuGyw2vMy6rWw==[/tex]和[tex=0.857x1.0]Fz01PbYkU0SRGm3tB5KjiA==[/tex]。求在下列情况下[tex=0.571x0.786]c59+3vo0/Vn/FvNRhDRu5g==[/tex]、[tex=0.429x1.0]JThLUuJ8WswSAPiYZWihWg==[/tex]的电势差：使[tex=0.571x0.786]c59+3vo0/Vn/FvNRhDRu5g==[/tex]带[tex=1.286x1.143]NeILClIc8twxeO5vjYm8Dw==[/tex],将[tex=0.429x1.0]JThLUuJ8WswSAPiYZWihWg==[/tex]的外表面接地。[img=203x220]17e1aa8f4234a38.png[/img]