从某铸铁构件内的危险点处取出的单元体，各面上的应力分量如图7—37所示。已知铸铁材料的泊松比[tex=3.643x1.286]RQB6FiJ5VOXQO9VDPs1o0A==[/tex]许用拉应力[tex=6.143x1.286]iMinYHOr/uNzLvQ8wq7bTS1vVfRtGmr97NVK1+79wUI=[/tex]，许用压应力[tex=6.143x1.286]uKE6SxFm6P2iOM7Q6/tEiX++yVbu0THnIDJfPrKM/5o=[/tex]。试按第一和第二强度理论校核其强度。[img=291x231]17d2370158ecfda.png[/img]

2022-07-02

从某铸铁构件内的危险点处取出的单元体，各面上的应力分量如图7—37所示。已知铸铁材料的泊松比[tex=3.643x1.286]RQB6FiJ5VOXQO9VDPs1o0A==[/tex]许用拉应力[tex=6.143x1.286]iMinYHOr/uNzLvQ8wq7bTS1vVfRtGmr97NVK1+79wUI=[/tex]，许用压应力[tex=6.143x1.286]uKE6SxFm6P2iOM7Q6/tEiX++yVbu0THnIDJfPrKM/5o=[/tex]。试按第一和第二强度理论校核其强度。[img=291x231]17d2370158ecfda.png[/img]

答案：

图7—37所示为平面应力状态，[tex=17.571x1.286]hFp/Sa9woh5GKHYmOezk4KOGMAttnwrW09kA4q6ZmjRoD8vUhQHZ8BDEJojtZ7BL3okCKj14OUl0fFvGUUC7BQ==[/tex]，则[tex=41.786x3.929]fnpmC2J6JmQBLyo5NmGAzzT/6QIQZjNVtS7cf7KOuhbOhPMO+6b6tdsSg7ndgDkrWz3dgtiQASrhiuZX66IHMDIuclnJSl59NJR4tCZdzkR/aax90oNZEIVgxKvNeyAHq1+zmQP91csfwdRsb0+FbXBidgjiG68Y/8VNwFbfDDWbGTQdgVDbwQ7LBOjJ72V9Wqbb2X7KJHUAVhb2LWzacd3OyAZXYcWQMxAtljh90PTeqEXZzZUHqOdQzYsz5Oc1xpwJXntirAx4LXtzQWVafYPKznp8pD6GkTLxkgyNMtqvMdtadD4M7dSSZ60QURr5EJvxPYhTnXuG/JGxoSYwUH+P9hAsj67/IZRPMGI0+c99U34FKgJa/CEssxJ6Rd3EgAozpiza1ygUVPEXvpTt88h3E+l0wepzyyaTAPXXFgontFdMn/9DznNH2KFPK2Zv[/tex] 因此，主应力为[tex=20.429x1.214]R9ppg7vp6/SfJLBGvKadwZGMHg70S2stFqrtwV3Zn7Y+ilBtIbivMzhevJIqykmE0GrWOZPkMYD3qNUfjeLj6WzvxXDbe0ahWxztdV1UJzo=[/tex]按第一强度理论有[tex=11.286x1.357]YlGBjfb83gDNIuzzJk0IavbuK+6Zw5RP4pyOJRNNShHe+9TMN2pg3vG7tkHT4iGx6vlPxkqXzxmfJ3M7lliE6A==[/tex]按第二强度理论有[tex=29.214x1.357]VUw0LFxqyjkKzLCpoGAAl8B3Ov6ca9zvNbVHwCH5/DPg9sGWCM56xsUniPyVpPyiNlbUSnxUj1PvjUHBvg5r3fbmDPY6tgE4036XjeuB1xtm3sdPLiqcbWgyeY7rVqLT/shaJjZ/jBVV/ZkGCxTf/E16miE0KXGTZY6iZuDwrPQ=[/tex]均满足强度要求。

举一反三

内容

0
材料为灰铸铁 [tex=4.214x1.143]+VaVck2TJ3J9avaGvFXn1A==[/tex] 的压力机框架如图所示。许用拉应力为 [tex=5.429x1.357]KGFn1ZdjVpyEhHpi76VFHVxj6hfjsnObpsLIvdXD+I0zDmaysDqNFru5NlkXYYBh[/tex], 许用压应力为 [tex=5.5x1.357]g7bsu9jPT94R5AsNOGiRbevcDbn98azY56Gq8MJjvMY2TM+6KlGqNnMxJHoOEKiySSE1IPaAOgeTD2yTJM9cuw==[/tex]。试校核该框架立柱的强度。[img=591x278]17979a5d64f3d9a.png[/img]
1
已知铝合金(塑性材料)零件中危险点应力状态如图所示(应力单位为[tex=2.143x1.0]i5fJyJssVoxx6TXz8ez6lg==[/tex])许用应力[tex=5.571x1.357]SPdg0BiqCUHDWsSvlnyHbsx6/vY1zcMzqvYrS1+ItBg=[/tex]，试校核其强度是否安全。[img=264x210]179c796b0ae1459.png[/img]
2
如图 3-12 所示, 拉杆用四个铆钉固定在格板上, 已知拉力[tex=3.714x1.0]mbYTyxXkfRnxjzp7/c1W7PHP6k0nyrtKBX04z1QhG0g=[/tex], 拉杆的案度 [tex=3.929x1.0]cae/f+weJAkilL+jhfA0gDjrJRp4sEDFwy/+Pnl7VMk=[/tex], 厚度[tex=3.929x1.0]twOcNwtuY59AnxdUz59VsxiU+dkT234/NtcGTScece8=[/tex], 铆钉直径 [tex=4.0x1.0]HWbXC28eq33KSfcaq8RnN+kuGTXUFxm8YUMLCUm1uyU=[/tex]; 材料的许用切应力 [tex=5.357x1.357]G0WVEpmkXOaCLIuFKm+WuybU47yx5x6dLS7KR6eFP/8=[/tex], 许用挤压应力[tex=6.357x1.357]g7bsu9jPT94R5AsNOGiRbX8fXW7hCb88ddd0W3In8TO23iGlMZLa3kCH32SDrfw4YjmRkW6b1lOVXLdVci3yKQ==[/tex], 许用拉应力[tex=5.5x1.357]2L55wb6Ie42hvgcbATi2GWJ89xebjM4iM9bOwcSYJU8=[/tex]。试校核铆钉与拉杆的强度。[img=565x199]17cf3f7f7dcf19e.png[/img]
3
横梁受力如图[tex=1.357x1.357]TWUgLpDrEXIKICMuiEQPjw==[/tex]所示。已知[tex=3.786x1.0]sfbz0KN/OuiVjbii4uTbzw==[/tex]，许用应力[tex=5.071x1.357]Rliai/lyLss5oN68j9T1x53HYih9/h69zqJpzeGx/XQ=[/tex]。校核其强度。[img=544x228]179d029477fc190.png[/img]
4
一矩形截面木梁, 其截面尺寸及荷载如习题图(a), [tex=5.214x1.357]fNVmOhoEUZqJlGoY2Oo2Ng==[/tex] 。已知许用弯曲正应力 [tex=5.357x1.357]P7zL+dpiV8bC9uKslCIT84dbsJynnStHybjyBJEWQoA=[/tex] 许用切应力[tex=4.714x1.357]LuG9XMEU9z/snypFKBqZ/A==[/tex]试校核梁的正应力和切应力强度。[img=492x181]17e0ea8294f60fd.png[/img]