材料力学 第三篇 扭 转.pptVIP

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * [例8]下图示椭圆形薄壁截面杆，横截面尺寸为：a=50 mm，b=75mm，厚度t =5mm，杆两端受扭转力偶 T=5000N·m，试求此杆的最大剪应力。 解：闭口薄壁杆自由扭转时的最大剪应力： b a t Chapter 3 Exercises 1. In a gear-box, why is the shaft with a slow speed thicker than that with a height speed？ 2. When the shearing stress and the normal stress coexist in an element, is the theorem of the conjugate shearing stress amenable? Why? 3. For a hollow circular tube of Al, the outside diameter is D＝100mm，the inside diameter is d＝80mm, and the length is L＝2.5m. The Shearing elastic modulus is G＝28GPa. ① If a force couple is acted on both ends of the circular tube and results in the pure torsion, try to determine the torsional angle when the maximum shearing stress is 50MPa. ② For the solid shaft of Al subjected to the same force couple and having the same maximum shearing stress, what is the diameter D2? ③ Determine the ratio of the weight of the hollow tube to that of the solid shaft. * 第三章 练习题 一、在变速箱中，为什么低速轴比高速轴粗？ 二、当单元体上同时存在剪应力和正应力时，剪应力互等定理是否成立？为什么？ 三、铝制空心圆管，外径D＝100mm，内径d＝80mm，长度L＝2.5m。铝的剪切弹性模量G＝28GPa。 ①若圆管两端受力偶矩作用产生纯扭转，试求当最大剪应力为50MPa时的扭转角。 ②对于承受相同力偶矩并产生相同最大剪应力的铝制实心轴，其直径 应为多大？ ③求空心管与实心轴的重量之比。 * Solution: ① ② ③ As the two have the same material and the same length, the ratio of weights is equal to the ratio of cross-section areas: * 解：① ② ③ 两者材料、长度相同，重量之比等于横截面面积之比： * * * * * * * * * * * * * * * * * * * * * * * * * * * * §3–7 等直圆杆在扭转时的应变能 一、 应变能与能密度 a c d dx b ? ? dy ?′ ?′ dz z ? x y 单元体微功： 应变比能： * 2、Calculation of the stress in cylindric close-coiled helical springs 1). Calculation of the stress = + t Q t T Q T Approximate value： P Q T * 二、圆柱形密圈螺旋弹簧的计算 1. 应力的计算 = + t Q t T Q T 近似值： P Q T * 2) Strength condition of the