Beam equations describe the behavior of beams under stress and are derived from beam theory. They are used to predict how much a beam will move or bend and to determine if it could be in danger of failure. The equations are complex and require knowledge of calculus. Beam theory was first developed in the mid-18th century and is sometimes referred to as Euler-Bernoulli beam theory. The Ferris wheel and Eiffel Tower were the first large structures to use the radius equation.
A beam equation is any mathematical equation used to describe the behavior of beams when placed under stress. The equations are derived from beam theory, first developed in the 1700s. Scientists and engineers use beam equations to predict how far a beam will move when a force is applied to a section of it. There are often many variables in the beam equations, and some knowledge of calculus is required to solve them.
Although notable Renaissance-era scientists Leonardo da Vinci and Galileo Galilei both attempted to describe the properties of rays mathematically using a radius equation, it was not until the mid-18th century that scientists first developed the beam theory. Once the equations were formulated, it took another hundred years for engineers to trust the mathematics of beam theory enough to put them into practice. Beam theory is sometimes referred to as Euler-Bernoulli beam theory, after 18th-century scientists, Leonhard Euler and Daniel Bernoulli. The Ferris wheel and the Eiffel Tower, both created in the 19th century, were the first large structures to use the radius equation.
Modern scientists and engineers use beam theory to predict the behavior of beams in many different situations. A beam equation can be used to predict how much a beam will move or bend when a section of the beam is subjected to a certain amount of force. These equations are especially useful for determining how much weight a beam can support without bending so much that the integrity of a structure is compromised. There are also beam equations to describe the stress on a beam, either from the force of another object acting on it or from any displacement in the beam itself. These equations are used to determine if a beam could be in danger of failure.
There are many different variables when working with a radius equation. Beams attached to one end behave differently than beams attached to both ends. The effect of a stress or weight is different depending on where it acts on the beam. Even large and small beams can react to stress in different ways. Given all these variables, and that many of them are expressed as coordinates, a sophisticated level of mathematical knowledge is required to solve a radius equation. The equations in beam theory are based on the principles of calculus.
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