What is Beam theory: Definition and 15 Discussions

Euler–Bernoulli beam theory (also known as engineer's beam theory or classical beam theory) is a simplification of the linear theory of elasticity which provides a means of calculating the load-carrying and deflection characteristics of beams. It covers the case for small deflections of a beam that are subjected to lateral loads only. It is thus a special case of Timoshenko beam theory. It was first enunciated circa 1750, but was not applied on a large scale until the development of the Eiffel Tower and the Ferris wheel in the late 19th century. Following these successful demonstrations, it quickly became a cornerstone of engineering and an enabler of the Second Industrial Revolution.
Additional mathematical models have been developed such as plate theory, but the simplicity of beam theory makes it an important tool in the sciences, especially structural and mechanical engineering.

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  1. T

    Crane Arm Model using beam theory

    Can a Bernoulli or Timoshenko model be reasonable for a crane arm, on ships? Yes, the arm might have a truss element, yes there is a hydraulic force to lift the arm (or cables). But to some extent, can one model the crane arm as one of a simple beam (either Timoshenko or Bernoulli -- and...
  2. Srinath

    Timoshenko Beam Theory (Violin String Shape Functions)

    Homework Statement:: Violin String Shape Functions Homework Equations:: Violin String Shape Functions Hello, Is anyone working on violin string shape functions(Timoshenko Beam Theory)? It would be really helpful to my research if we share our knowledge on this topic. Thank you
  3. Teslosifone

    Irregular free-free beam, non-numerical solutions

    What are the simplest, even if not very accurate, non-numerical ways (for example a variation of Euler-Bernoulli) for describing the deflection relative to a given load of a free-free beam with irregular shape (variable second moment of area and/or lumped masses distributed at some points)? In...
  4. A

    Finite Element Model of Euler-Bernoulli Beam Theory

    In the formulation of Euler-Bernoulli Beam Theory, there are two degrees of freedom at a point, w and dw/dx. Typically, the finite element model of this theory uses cubic polynomial for interpolation of $w$ using a two noded element as given in Chapter 5 of this book [1]. This element is a...
  5. K

    Why Euler-Bernoulli beam theory does not work in this case?

    Hello, i would like to ask You a question about difference in results between Euler-Bernoulli method of analysis of stress in short slender beam and 3D FEA method mentioned in ansys aim tutorial here: https://confluence.cornell.edu/pages/viewpage.action?pageId=33636829 The problem looks like...
  6. H

    6D calculation of spring-forces/moments

    Hi, I'm a student in electrical engineering and I'm writing my master thesis at the moment. Ironically I'm now confronted with the deformation of springs. I'm not a physics (!) but I think and hope that you may can help me. Simple push and pull forces are not the problem. I need to calculate...
  7. W

    Axial eccentric loading on self-weight deflected cantileaver

    Homework Statement Hello, I am trying to model an arm mounted perpendicular to the straight mechanical column. An arm can be translated in horizontal direction by a gear which engages with the bottom of an arm such that it applies no force in vertical direction to the arm. And finally there is...
  8. K

    Need help with more indepth beam theory?

    I have a project for a class and our goal is to design a beam using 1018 steel to achieve a certain deflection under one load and not fail under an even larger load. The design I have come up with is very similar to a cantilever beam, but is has a variable cross section. I have used the...
  9. J

    Bending Waves, Plate and Beam theory?

    Hi, I am doing research on sound radiation of a plate due to bending waves. I have come across the Kirchhoff Plate theory, Euler beam theory and also the equations for the phase velocity of longitudinal, transverse shear and bending waves. What i am confused about is how these theories and...
  10. H

    Cantilever Beam Theory: Calculations & Analysis - hmk999

    https://skydrive.live.com/redir?resid=3B1281F72DB8729B!122&authkey=!AIkfRcYK6Grz0jw Can anyone please help? See link for sketch and calculations. I have a M30 x 150 long stainless steel stud fully welded to a base plate that is under a load of 12.5 ton = 122583 N. Using Cantilever...
  11. C

    Euler-Bernoulli Beam Theory and Nonlinear Differential Equations

    I've been reading through my mechanics of materials textbook recently, notably in regard to the section on the deflection of beams. The well regarded Euler-Bernoulli beam theory relates the radius of curvature for the beam to the internal bending moment and flexural rigidity. However the theory...
  12. T

    Beam Theory Constants Question

    From my understanding, the equation that models the transverse vibration of a beam is (Euler Bernoulli): u_{tt} = - \frac{EI}{A \rho} \cdot u_{xxxx} where E is Young's modulus, I is the 2nd moment of area, A is the cross-sectional area, and rho is the density of the beam. This equation...
  13. A

    Doubt regarding constants. Elastic Beam Theory.

    Hello. As a good mathematician, I'm having troubles reading some constants for a PDE. I'm modelling an elastic rod using the equation \rho A U_{tt} - N U_{xx} + E I U_{xxxx} = 0, where "\rho is the beam density, A and I are the area and moment of inertia of the beam cross section...
  14. L

    Beam theory or plate theory

    Can somebody provide some clarification: I am calculating the stress in a plate with the following dimensions: 41" long by 30" wide and the plate is 3/8" thick. The plate is simply supported along the 41" length sides, with the short lengths free. I have calculated the stress using beam theory...
  15. A

    (Beam theory) Deriving Virtual Work

    Homework Statement Derive the equation used for calculating the deflection of a beam at some arbitrary point. Because I haven't seen anything like this on the web or in textbooks, I am asking for some feedback. Homework Equations v_{k} = \int\frac{\delta M(x)M(x)}{EI} dx The Attempt...