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nucleargrab
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Hi. Does anyone have the x and y displacement formulas for a fixed cantilever beam of a given depth and length, under a UDL (uniform distributed load)? I can't find them anywhere!
nucleargrab said:Hi. Does anyone have the x and y displacement formulas for a fixed cantilever beam of a given depth and length, under a UDL (uniform distributed load)? I can't find them anywhere!
The Timoshenko Beam Problem is a mathematical model used to analyze the behavior of beams under various loading conditions. It was developed by Ukrainian scientist Stephen Timoshenko in the early 20th century and is widely used in engineering and physics.
A fixed cantilever refers to a beam that is fixed at one end and free to move at the other end. This type of beam is commonly used in structural engineering, such as in bridges and buildings.
The displacement formula for a fixed cantilever under uniform distributed load is given by: δ = (5qL^4)/(384EI), where q is the load per unit length, L is the length of the beam, E is the modulus of elasticity, and I is the moment of inertia of the beam cross-section.
The Timoshenko Beam Problem takes into account shear deformation and rotational inertia, while the Euler-Bernoulli Beam Problem assumes that the beam is rigid and does not consider these factors. The Timoshenko Beam Problem is more accurate for analyzing beams with relatively small cross-sections or high shear forces.
The Timoshenko Beam Problem is used in a variety of engineering and physics applications, such as in the design of bridges, buildings, and other structures. It is also used in the analysis of mechanical systems, such as in the design of drive shafts and other components. Additionally, the Timoshenko Beam Problem is used in research on the behavior of materials under stress and strain.