catenary length

简明释义

悬链线长

英英释义

例句

1.The artist used the concept of catenary length to create a visually appealing sculpture.

艺术家利用悬链线长度的概念创作了一件视觉上引人注目的雕塑。

2.The engineer calculated the catenary length to ensure the cable would have enough slack for movement.

工程师计算了悬链线长度以确保电缆有足够的松弛度以便移动。

3.The catenary length of the power line was measured to avoid excessive tension in the wires.

为了避免电线过度张紧，测量了电力线的悬链线长度。

4.To design the bridge effectively, we need to determine the catenary length of the suspension cables.

为了有效设计桥梁，我们需要确定悬挂电缆的悬链线长度。

5.In construction, understanding the catenary length helps in planning the layout of the cables.

在建筑中，理解悬链线长度有助于规划电缆的布局。

作文

Understanding the concept of catenary length is essential in various fields, especially in engineering and architecture. A catenary is the curve that a hanging flexible chain or cable assumes under its own weight when supported only at its ends. This curve is not a simple parabola; rather, it has unique mathematical properties that are crucial for designing structures such as bridges and arches. The catenary length refers to the actual length of the curve of the chain or cable, which is longer than the straight line distance between its endpoints.In practical applications, understanding the catenary length helps engineers calculate the forces acting on structures. For instance, when designing a suspension bridge, engineers must consider the catenary length of the cables that hold the bridge deck. If the cables are too short, they may not support the weight of the bridge adequately, leading to structural failure. Conversely, if the cables are too long, it could result in unnecessary material costs and increased weight on the supports.The mathematics behind the catenary length can be derived from calculus. The equation of a catenary can be expressed as y = a cosh(x/a), where 'a' is a constant that describes the steepness of the curve. To find the catenary length between two points on this curve, one must integrate the arc length formula. This involves calculating the integral of the square root of the sum of the squares of the derivatives of the function. Such calculations are vital for ensuring that structures can withstand various loads while maintaining safety and functionality.In addition to engineering, the concept of catenary length also finds its place in physics, particularly in the study of forces and tensions. When a cable or chain is suspended, the tension varies along its length, and understanding this variation is crucial for predicting how the structure will behave under different conditions. The catenary length provides insights into these tensions and helps in creating more efficient designs that minimize material use without compromising strength.Moreover, the aesthetic appeal of catenary curves cannot be overlooked. Many architects have employed the principles of the catenary length in their designs to create visually striking structures that also perform well structurally. The Gateway Arch in St. Louis, for example, is a perfect representation of a catenary curve, demonstrating how beauty and functionality can coexist in architectural design.In conclusion, the catenary length is a fundamental concept that intersects mathematics, engineering, and art. By grasping this concept, professionals in various fields can enhance their designs, ensuring both safety and aesthetic value. Whether it’s in the construction of a bridge or the design of a sculpture, the principles of the catenary length continue to play a pivotal role in shaping our built environment and understanding the physical world around us.

理解悬链线长度的概念在各个领域中至关重要，尤其是在工程和建筑领域。悬链线是指在仅由两端支撑的情况下，悬挂柔性链条或电缆在自身重力作用下所形成的曲线。这条曲线并不是简单的抛物线；相反，它具有独特的数学性质，这对于设计桥梁和拱门等结构至关重要。悬链线长度指的是链条或电缆曲线的实际长度，这个长度通常比其两个端点之间的直线距离要长。在实际应用中，理解悬链线长度有助于工程师计算结构上所承受的力量。例如，在设计悬索桥时，工程师必须考虑支撑桥面板的电缆的悬链线长度。如果电缆过短，可能无法充分支撑桥的重量，从而导致结构失效。相反，如果电缆过长，则可能导致不必要的材料成本，并增加对支撑的重量。悬链线长度背后的数学可以通过微积分推导出来。悬链线的方程可以表示为y = a cosh(x/a)，其中'a'是描述曲线陡峭程度的常数。要找出该曲线之间的悬链线长度，必须对弧长公式进行积分。这涉及到计算该函数导数平方和的平方根的积分。这些计算对于确保结构能够承受各种负荷，同时保持安全性和功能性至关重要。除了工程学，悬链线长度的概念还在物理学中占有一席之地，特别是在研究力量和张力方面。当电缆或链条悬挂时，沿其长度的张力会有所变化，理解这种变化对于预测结构在不同条件下的行为至关重要。悬链线长度提供了对这些张力的洞察，并有助于创造更高效的设计，最大限度地减少材料使用而不影响强度。此外，悬链线曲线的美学吸引力也不容忽视。许多建筑师在他们的设计中采用了悬链线长度的原理，以创造出视觉上引人注目的结构，同时在结构上表现良好。例如，圣路易斯的拱门就是悬链线曲线的完美体现，展示了美与功能如何在建筑设计中共存。总之，悬链线长度是一个基本概念，交织着数学、工程和艺术。通过掌握这一概念，各个领域的专业人士可以提升他们的设计，确保安全性和美学价值。无论是在桥梁的建设还是雕塑的设计中，悬链线长度的原理继续在塑造我们的建筑环境和理解周围物理世界中发挥关键作用。