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一、引言研究变截面梁的变位计算,对变截面梁进行刚度校核和解超静定变截面梁具有重要意义。由于变截面梁的轴线形状和截面变化往往比较复杂,得到的函数往往不能积分,或者不便积分,因此,过去对于较复杂的变截面梁的变位计算,不得不用总和法来代替定积分法。显然,用总和法计算变截面梁存在着一个缺点,即计算精度较低,如果要得到变截面梁精度很高的变位值,计算工作量无疑是很大的。但是,由于较复杂的变截面梁变位计算,迄今为止尚无较精确的计算方法,因此上述总和法仍沿用至今。本文根据虚梁法(国外有称为面积法或面积力矩法)原理,应用柯特斯(Cotes)数值积分法,推导出单跨变截面梁在荷载作用下变位值的较精确而简便的基本数值计算公式,以克服上述总和法的缺点。
I. INTRODUCTION It is of great significance to study the displacement calculation of variable cross-section beam and verify the stiffness of the variable cross-section beam and solve the statically determinate variable cross-section beam. Because the change of axis shape and cross-section of the variable cross-section beam is often complicated, the obtained function often cannot be integrated or inconvenient to integrate. Therefore, in the past, for the calculation of the displacement of the more complex variable cross-section beam, the summation method has to be used instead of the fixed integral method. Obviously, there is a disadvantage in calculating the variable cross-section beam by the summation method. That is, the calculation accuracy is low. If you want to get a high-precision displacement value of the variable cross-section beam, the calculation workload is undoubtedly great. However, due to the calculation of the displacement of the more complex variable cross-section beam, there is no more accurate calculation method so far, so the above summation method is still in use today. Based on the principle of the imaginary beam method (known as the area method or area torque method in foreign countries), this paper applies the Cotes numerical integration method to derive the accurate and simple displacement value of a single-span variable cross-section beam under load. Basic numerical formulas to overcome the shortcomings of the above summation method.