What is Beam bending: Definition and 61 Discussions

In applied mechanics, bending (also known as flexure) characterizes the behavior of a slender structural element subjected to an external load applied perpendicularly to a longitudinal axis of the element.
The structural element is assumed to be such that at least one of its dimensions is a small fraction, typically 1/10 or less, of the other two. When the length is considerably longer than the width and the thickness, the element is called a beam. For example, a closet rod sagging under the weight of clothes on clothes hangers is an example of a beam experiencing bending. On the other hand, a shell is a structure of any geometric form where the length and the width are of the same order of magnitude but the thickness of the structure (known as the 'wall') is considerably smaller. A large diameter, but thin-walled, short tube supported at its ends and loaded laterally is an example of a shell experiencing bending.
In the absence of a qualifier, the term bending is ambiguous because bending can occur locally in all objects. Therefore, to make the usage of the term more precise, engineers refer to a specific object such as; the bending of rods, the bending of beams, the bending of plates, the bending of shells and so on.

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  1. J

    Cantilever beam bending moment and shear force

    Homework Statement im trying to write a program for a class but first i need the formulas for the bending moment and shear force. i have the displacement and angle of the cantilever beam under a point load: Y = -[(WX^2)/(6EI)][3a – x] for 0<x<a Y = -[(Wa^2)/(6EI)][3x – a] for a<x<L...
  2. T

    How can Castigliano's Method be used to solve for deflections in a cranked beam?

    Hello all I have a beam bending problem I need some help on. I need to calcuate the deflections at the load (and in the plane of the load) for a simply supported beam with equal point loads overhanging the supports. However my beam is cranked as shown in the attached diagram of the problem...
  3. J

    Uniaxial Plate Bending vs Beam Bending: What's the Difference?

    I would appreciate it if some one could help me with this. I read from Timoshenko's book Theory of Elasticity that for prismatical beam bending (uniaxial), the assumption is \sigma_x>>\sigma_z,\sigma_y=0 where \sigma_x is stress in the direction parallel to the deflection curve. And for...
  4. A

    Beam Bending and Moments of Inertia

    Homework Statement This is a two part question. In the first part you are asked to determine the mam moment that can be applied to the beam if it is bent about the z axis. They then ask you to redo the question bending about the y axis. This is probably a really simple question but what is the...
  5. J

    Analysis of beam bending against constraint

    I have been trying to analyze the deflection of the free end of a cantilevered beam with a point load P at the end. The trick is, the beam is supported underneath by a surface described by the arbitrary function g(x). So let's say that g(x)= 0.001*x^2, a very shallow parabola. As the beam...
  6. T

    Beam bending and moment of inertia

    If you have two beams, not attatched to each other, placed on top of each other in 3 point bending simply supported, what do you do to find the first moment of area and moment inertia of the two beams. Thanks
  7. Saladsamurai

    Calculating Maximum Stress in a Beam - where did I go wrong?

    !Help Please! Bending (stuck) Homework Statement Homework Equations \sigma_{max}=\frac{Mc}{I} The Attempt at a Solution I am not sure where I am messing this up. I am pretty I found I correctly to be 140.144. But I think I am using the wrong internal force. I am...
  8. P

    Beam Bending & Stress: Solve 2 Cantilever Problem

    I'm stuck on a beam bending problem I have. I have 2 cantilever beams one one top of the other applying a force. I need to know find the stress on the left hand beam and the deflection. I have the formulas (using Roark's formulas of stress and strain) but there's nothing about two cantilevers...
  9. C

    Why Does a Beam Bend Only About the Centroidal Axis?

    in beam bending the resistance of a cross section is measure by moment of inertia about centroidal why. How do we know that the bends only about the centroidal axis . Any detailed discussion on this?
  10. E

    Help Needed: Modeling Beam Bending with Electrostatic Forces

    Hey-- I'm trying to model the bending of a beam due to electrostatic forces. (Femlab does offer this model on their website, but the module I'd need to run it costs $600!) I have no problem modeling a beam bending, and I have no problem creating a parallel plate capacitor, but when I...
  11. C

    Beam Bending: Centroidal Axis Rotation

    how do we say that in a beam bending problem the bean cross section bends(rotates)around the centroidal axis. Why not about any other axis?
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