简要回顾了国内扭转刚架内力计算方法的进展,对存在的问题作了说明。以摩擦压力机机架为例子,导出了求解半空间扭转刚架内力的另一表达式。同,外侧的剪应力大,二者方向相反并平行,其剪应力合力的作用点在横梁轴线延长线上的C点。设特征量r~*=(?)C,合力X_1用虚线力矢表示,由力的平移规则,在立柱端作用有力X_1和力偶距M_n。考虑到横梁对立柱弯曲的约束作用,在垂直立柱端截面平面内还应有集中力偶X_2。图示内力素间的关系为: 式(4)中特征量r~*等式右边的第二项是由剪力引起的。由力的平衡条件及式(4)得: x_1=M_k/(2(1_2/2+r~*)) (5) 式(4)、(5)的详细导出,可参看文献[3]。至此,立柱任意截面上的内力都已能求得。为了与文献(1,2)的结论相比较,将文献[3]中的力学计算模型统一到图1的计算模型上去。这时K值趋于无穷大,则η也趋于无穷大,X_2值趋于零(实际上K值并不为无穷大,X_2也不为零)。则式(5)变为: 文献[3]比文献[1,2]得出立柱上的扭矩M_n要大[3],故前者比较接近实测值。其原因很显然,式(1)的正则方程是一线性叠加方程,把各变形量看成是独立的。而实际半空间扭转刚架对立柱是一约束扭转,各变形量间并非是线性的关系,而文献[3]把立柱的弯曲变形与扭转变形看成是相互依存关系,较好地表达出约束扭转的特点,自然计算值就较好地逼近实测值。二、扭转刚架内力的进一步分析由式(6)得出立柱端部相应的受力情况如图3所示。从刚架整体看,立柱B截面并不绕自身轴线转动,而是绕刚架对称轴旋转。故在X_1力作用下,AB梁受弯曲变形的同时,还要引起附加扭矩M_n′、弯曲扭转双力矩B及弯曲扭转力矩M_w,各量的表达式为: 同理在M_n作用下,也要引起弯曲扭转双力矩B′及弯曲扭转力矩M_w′,其表达式为: 式(7)吸式(8)中,M_n′、M_w′的符号规定从座标原点沿x方向看,逆时针转向为正;而扭转双力矩B的符号规定从极点O看到的双力偶反时针转向为正。参数α为弹性弯曲扭转特性: α=GI_(n1)/(EJ_w)~(1/2) 式中J_w为扇形截面惯性矩,将立柱截面看成如图4a的相当工字形截面,而翼缘的厚度等于立柱两侧壁的厚,则求得: J_w=integral from s ω~2dA=integral sω~2tds 由图4b得: J_w=4×1/2×l_2h/4×h/2×2/3×l_2h/4 =(h~3l_2~2t)/24 (10) 由M_w导起的剪切应力很小,这里略去。由纯扭转引起的剪切应力近似采用等厚薄壁公式,则: τ_(n_(max))=M_n+M_n′/2Ωδ (11) 正应力为: σ=Mz/I_(?)+Bω/J_w+B′ω/J_w (12) 至于横梁的内力,只要把立柱端截面上的内力改变符号作用在横梁两端即可求得。从上述讨论可知,对半空间扭转闭式刚架进行简易计算时,必须注意约束扭转问题,否则计算值与实测值差距很大。 A brief review of the progress made in the domestic methods of reversing the calculation of internal forces of rigid frames is given, and the existing problems are described. Taking the friction press frame as an example, another expression for solving the internal force of torsional rigid frame in half space is derived. Same, the outside of the shear stress, the two opposite and parallel, the role of shear force together point C axis extension of the beam line. Let the characteristic force r * * = (?) C, the resultant force X_1 be represented by the dotted vector of force, and the force Xx and the force separation M_n act at the column end by the rule of force translation. Considering the restraint effect of the beam on the bending of the column, there should be a concentration couple X_2 in the plane of the vertical column end section. Diagram shows the relationship between the internal force as follows: Eq. (4) Characteristic quantity r ~ * The second term on the right side of the equation is caused by shear force. The equilibrium conditions of force and formula (4) are: x_1 = M_k / (2 (1_2 / 2 + r ~ *)) (5) The detailed derivation of equations (4) and (5) can be found in [3]. At this point, the column of internal forces on any cross section have been able to find. In order to compare with the conclusions of the literature (1, 2), the mechanical calculation model in [3] is unified into the calculation model in Fig.1. In this case, the value of K tends to infinity, then η also tends to infinity, and the value of X_2 tends to zero (in fact, the value of K is not infinite and X_2 is not zero). Then equation (5) becomes: Compared with the literature [1,2], literature [3] shows that the torque M_n on the column is larger [3], so the former is closer to the measured value. The reason is obvious, equation (1) of the normal equation is a linear superposition equation, the amount of deformation as independent. However, the actual half-space torsional rigid frame is a constrained column, and the deformations are not linear. However, the literature [3] considers the bending deformation and torsional deformation of the column as interdependent and well-constrained The characteristics of torsion, natural calculated value is better approximation of the measured value. Second, to reverse the internal force of the frame Further analysis of the formula (6) derived column end corresponding force situation shown in Figure 3. From the frame as a whole, the column B section does not rotate around its own axis, but around the frame axis of symmetry rotation. Therefore, under the action of X_1, the AB beam is subjected to the bending deformation, and at the same time, the additional torque M_n ’, the bending torsion double moment B and the bending torsional moment M_w are also caused, and the quantities are expressed as follows: Similarly, under the action of M_n, The bending torsion double moment B ’and the bending torsion moment M_w’ ​​are given as follows: Expression (7) In the suction type (8), the symbols of M_n ’and M_w’ ​​refer to the origin of the coordinate in the x direction and turn counterclockwise While the sign of twisting double torque B dictates that the dual force counterclockwise rotation seen from pole O is positive. Parameter α is elastic torsional torsional characteristics: α = GI_ (n1) / (EJ_w) ~ (1/2) where J_w is the moment of inertia of the sectorial cross section, which is taken as the equivalent I-shaped section of Figure 4a, Is equal to the thicknesses of the two side walls of the column, then it is obtained from Fig. 4b that: J_w = 4 × 1/2 × l_2h / 4 × h / 2 × 2 / 3 × l_2h / 4 = (h ~ 3l_2 ~ 2t) / 24 (10) The shear stress induced by M_w is small and is omitted here. The shear stress induced by the pure torsion is approximately the same as the thin-walled constant-thickness formula, then: τ_ (n_max) = M_n + M_n ’/ 2Ωδ The normal stress is: σ = Mz / I_ (?) + Bω / J_w + B’ω / J_w (12) As for the internal force beam, as long as the column end section of the internal force change sign on both ends of the beam can be obtained. It can be seen from the above discussion that when the simple calculation of a half-space closed-type rigid frame is to be performed, the problem of constrained torsion must be observed; otherwise, the calculated value is greatly different from the measured value.