试用积分法求图 5-20 所示悬臂梁[tex=0.786x1.0]XUo+oVq0EXNG7rY4rJKp8w==[/tex] 端和跨中[tex=0.786x1.0]Wj2zFkrpqxe5CqhjLItV+A==[/tex]点的坚向位移和转角 (忽略剪切变形的影响)。[img=282x295]17cf49856748f2c.png[/img]

2022-07-02

试用积分法求图 5-20 所示悬臂梁[tex=0.786x1.0]XUo+oVq0EXNG7rY4rJKp8w==[/tex] 端和跨中[tex=0.786x1.0]Wj2zFkrpqxe5CqhjLItV+A==[/tex]点的坚向位移和转角 (忽略剪切变形的影响)。[img=282x295]17cf49856748f2c.png[/img]

答案：

解:（a）（1)A 端的坚向位移在[tex=0.786x1.0]XUo+oVq0EXNG7rY4rJKp8w==[/tex]段施加一个坚向虚设力, 则梁上产生的弯矩为: [tex=2.357x1.143]Zy2ULOliJUVpRF8G/KKDYw==[/tex]; 外力均布荷载产生的弯矩为: [tex=4.071x2.5]j8otBuDf+78lnU6O70ineI0QBtKm3r9xsbRLNf1NLP6g4As4HcFKz91Np2qjjfL1[/tex] 。 所以位移为: [tex=13.643x3.0]LGDrQGRpH+AgaHWiiwBHcYERYDeRhjnT+1VI0Cfjc7vlBaLwa5Sj60TsN6poBnlZF5jqWmZqzPYqJlNGk/+ExOzSGDgAeIGGPLsEFnfHyg6vlsdKAPOFtXsZapwxbw9tO0VwE30TIim4N0BwD1eqgHNEh4AEBme8E9+1SVvzIdQ=[/tex](2) A 端的转角在 [tex=0.786x1.0]XUo+oVq0EXNG7rY4rJKp8w==[/tex]段施加一个虚设弯矩, 则梁上产生的弯矩为: [tex=2.286x1.143]+DyBgzgk97LDygJ6u0zZMQ==[/tex]; 外力均布荷载产生的弯矩为: [tex=4.071x2.5]j8otBuDf+78lnU6O70ineI0QBtKm3r9xsbRLNf1NLP6g4As4HcFKz91Np2qjjfL1[/tex]。则位移为: [tex=10.571x3.0]3Mkb8IMLbNHv64XfLWEAHq6I45ik6RrDUP54DbkZRsEwPURd92V1iPJBiNKu9CyqrhpBs96p49ovcrw0onu+QjxcPQjMlYLNreSfhmppUNG4n4p7XExligSt/fsezmBY[/tex](逆时针)(3) C 点的坚向位移在[tex=0.786x1.0]Wj2zFkrpqxe5CqhjLItV+A==[/tex]点施加一个坚向虚设力, 则在梁上产生的弯矩: [tex=2.357x1.143]Zy2ULOliJUVpRF8G/KKDYw==[/tex](坐标原点放到 [tex=0.786x1.0]Wj2zFkrpqxe5CqhjLItV+A==[/tex] 点); 均布荷载产生的弯 矩为: [tex=9.286x2.5]VU1d/lr+DMORhKhZ/j/iuaRECVRIdpWmAC9z5qvZyyh2YXhljnqPs7YACFETEiWhUxwAEhTpV7hGFIDbX951OmEELVcRc7Yf2sYFkZFvPWI=[/tex] 。则位移为: [tex=21.143x3.429]egwUH80Oxs+ewXCfug8rBX8VceOAKUSB1B1/tkobR1w7w9wIuf3FkIv470FAU9gBLRqtTlhhEHklSoBNkehlPIeNG0OT6WOcNQR9/8uLF+rqoVMEDa8teS3BrxYr/ELHbKej6jXe7uD/sJ+LWR/Q/mFv3iqPDgVImFIAZtu+v1PJLSYewfoExl7CwEp6hQWqpR6RmCptxdKAQG5rzrM8Og0XkJi0RBz8U7e8IRuVbns=[/tex](4) [tex=0.786x1.0]Wj2zFkrpqxe5CqhjLItV+A==[/tex]点的转角在 [tex=0.786x1.0]Wj2zFkrpqxe5CqhjLItV+A==[/tex]点施加一个虚设弯矩, 则在梁上的产生的弯矩为: [tex=2.286x1.143]+DyBgzgk97LDygJ6u0zZMQ==[/tex] (坐标原点放到[tex=0.786x1.0]Wj2zFkrpqxe5CqhjLItV+A==[/tex]点); 均布荷载产生的弯矩 为: [tex=9.643x2.5]j8otBuDf+78lnU6O70ineGdovil4c/VYGOtgx9wgg/MSybC05GxL+cJIynfMt6wMFLn8btVPFLBXKin3RuQiEG7nW0t9Fy8nsWtBFGKOUF4=[/tex] 。则位移为: [tex=17.857x3.429]xM/oEdwDu9rQkIkBwEvYAFrfTOxtcrK3YsF6EAnaGPdMgUi21YwpsS3CKj/211OhV66+eT6/9XtyW3muzHPLuhqzzXQa5IzjXwhmsvhFwfgrnqUfSUPy2wBbECdYl7fH4jywLhPLZsb/bKO7g0ZRJoyZnCwmO7HZK2U3oertN6VZoDWRa684gOBgC7Hjhs7LeInHh7Zp/HjlKotiNA9j5g==[/tex] (逆时针)(b) 因为外力集中荷载在[tex=0.786x1.0]Wj2zFkrpqxe5CqhjLItV+A==[/tex]左边不产生作用, 因此为了方便起见, 把坐标原点放到 [tex=0.786x1.0]Wj2zFkrpqxe5CqhjLItV+A==[/tex]的位置。 (1)A 点的坚向位移[tex=8.571x2.429]3z/F8/Co4rFnardxRC00BwM+o2a2ti1J+7Pd5LkT5kG3I2dwxj3eHHh2XTxFLHmsC3MMT4UrqDP5J3LUNxK7eA==[/tex], 则位移为:[tex=16.643x2.929]Em2X0jj3ATbMeOhfzeRnHwAfypg6R+j4EuKNPjMtHAxt6i1V/jTzWDctpCiiv/ME2lKVJn8rw6xwFDXURT+mgNs3JSTZHZoB+Fq13sus6l06XVY+i2qOF1Qioku47/RrzuVqptXL12rKP1gIzg0sgwSG4+1M8yz9bzBKzqizwQ57IE9C6gYeEj3EyUacN2uxcwmiG45RDLFY1jy+FimHqpOrYUWoaulDS9bv4ZDPHKs=[/tex](2)A 点的转角[tex=4.143x1.357]cV7DZ5J3O8WrVUGFMwLryWe7qvAQIXlzCXYWgqO3P7I=[/tex] 同上, 则位移为:[tex=12.714x2.714]rqeNr8LwuTfGx5/gLy5J2Xnu6EmD9wAkW2Z6TyS4A7zx5R8WSHVk9KgrutV3pZ1ogz7OY0g+rlGoz3pSpFGxpw0BY6gOd0Xf890E8ng4iaNBkpiSZHjw2Yxj+fverDw1DcM1m3qNHAFQjADDO9rCV2BOd12F95O0QPswEUVGd60=[/tex](3) C 点的坚向位移[tex=1.429x1.286]yvE2bwdu/prx+4xEbin52XwnIpEDEXVSCyNDToI0Ahc=[/tex]同 (1),[tex=2.357x1.143]Zy2ULOliJUVpRF8G/KKDYw==[/tex], 则位移为: [tex=12.714x2.929]D9WbpzJJzgEQ7yfNiucHVzPdLB2pIvOgAkfUG8FnLZZLqRFHhavREQnbL0l35svvMRJkz0MH0NqwGmCoO2RrnO4lsLQ2OfR7Dt3+Z0FQU8OST92XW7A5VNnuOqGf8s43N/bqMG3DacFWyZowo+7fbtP6QuApuVAsnIPFqxH1TcAbFxmh3f1XC8vpheu00Lyt[/tex] )(4) C 点的转角[tex=1.5x1.214]6SShOxpmUiVM5bnQ1vavHPGq703d+ly3Irxa2sHejjo=[/tex]同 (1), [tex=2.286x1.143]+DyBgzgk97LDygJ6u0zZMQ==[/tex], 则位移为: [tex=12.0x2.929]c81Q0sNZe+eS91UhJ2OXtyk7ccIWAl4E+ndKPLZxISYYcWGuc8NwsN42IHXbasJxc6BAJ3IgBwUDzbrRIj8K/RsLEOOJv+LupzZGzNy1wu6koq+DxPdLT51oX6Bh47U3+y6cWEiE2o6mB7Wc8ul3zu1f2eX1gO0bm8vyKEGqpQIoePLn5rFbEF6+Xd6/VPdi[/tex] (逆时针)

举一反三

内容

0
简支梁的跨中作用一力偶[tex=1.0x1.0]0KCelhZna0R9EGhYF1VZHA==[/tex], 梁的弯曲刚度为[tex=1.214x1.0]s9Je1M5xVQ90RVSHJTCpMA==[/tex]试用积分法求[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]截面的转角和[tex=0.714x1.0]YiLkHgl7MlxE+QjUplQUKA==[/tex]截面的挠度。[img=193x116]179d6ed7a075ea4.png[/img]
1
求图示梁[tex=0.714x1.0]YiLkHgl7MlxE+QjUplQUKA==[/tex]点的s向位移和[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]截面的转角。设 [tex=2.0x1.0]C1eXktko86a0BBkBgiRJ8Q==[/tex]常数。[img=464x149]17a57fae41b326f.png[/img]
2
求图示曲梁 [tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex] 点的水平位移、竖向位移及 [tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex] 截面转角。设 [tex=2.0x1.0]hYBAALM+V4PV1D5W5pIDqA==[/tex]常数。[img=158x209]17a580ec58d178c.png[/img]
3
试求图 5-29 所示等截面圆弧曲杆[tex=0.786x1.0]XUo+oVq0EXNG7rY4rJKp8w==[/tex]点的坚向位移[tex=1.429x1.0]a3mBK50EUc4P09k1hLsQqpiVRdNLTICIRti3FERSDZE=[/tex] 和水平位移[tex=1.429x1.214]D9WbpzJJzgEQ7yfNiucHVzsIgKWblUalGXMhwAqm9HQ=[/tex]。设圆弧 [tex=1.5x1.0]osX852S+wV8CwpEm4xtoUQ==[/tex] 为 [tex=0.786x2.357]skQrMgG+4NxSwrl/6DdfjQ==[/tex]个圆周, 半径为[tex=2.286x1.214]XQG+skBaTp6rojgvx4xt+y6Q0a3h040NEmTsVndVDdg=[/tex]为常数。[img=196x274]17cf4ab5c670417.png[/img]
4
试求题[tex=3.643x1.357]C1Sgug4CieNvcehUx6WNyQ==[/tex]图所示三铰刚架[tex=0.786x1.0]XvHgf70VtK2FH5G93l0k3g==[/tex]点的水平位移和截面[tex=0.786x1.0]ri6gmnf1+J9dGqG5/1sV6A==[/tex]的转角,设各杆[tex=1.214x1.0]aXJNSgwe9sYfky/Vv9M4JQ==[/tex]为常数。[img=294x359]179d77e0e038dbf.png[/img][img=295x375]179d77e4585a105.png[/img]