# Beam bending Definition and 22 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. ### I Base Motion and Vertical Beam - Basic Reaction Forces?

So I am trying to understand how to estimate the amount of deflection [D] the vertical beam shown above would experience if the base it is attached to is accelerating at a constant acceleration [a] of 9.81 m/s. I assume the Force [F] would be equal to weight of the vertical beam (mass x...
2. ### Confidence in FEA stress values?

Hi all, I’m trying to get a better understanding of ANSYS as I don’t have a lot of experience with it. My question is with respect to a static structural analysis of a solid part: “how can I be reasonably confident that FEA is giving me reasonably accurate stress values?” I’ll analyse a...

4. ### Deflection of a cantilever beam with applied tension at the free end

Not much to add since the question is fairly simple, but again I'm wondering if applying tension at the free end of a cantilever beam affects the deflection it would have if only itself weight is considered. Intuitively, tension should tend to straighten the beam, and if it does, how to...

6. ### 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...
7. ### Bending a beam from straight to an arc with axial force

Hi, If I have a straight beam and I start to push its ends towards each other with force F, the beam will obviously bend into an arc. What is the height/amplitude at the center of the arc when the beam length is l and the beam ends have been displaced by d. How much force (P) the center part...
8. ### Off-Axis Torque To A Cantilever Beam

I'm interested in understanding how to deal with a torque applied to an angled cantilever beam. The torque is being applied along a horizontal axis at the location of the end of a cylindrical beam. I am interested in how this torque will cause twist along the beam's axis, as well as any...
9. ### Beam Deflection Calculations

Hello, I am looking for some advice on calculating the beam deflection on a setup described below. There is an "I Beam" sitting across the back of two lorry trailers with a uniformly distributed load in the middle of the beam. I am slightly confused as to what type of support this would be if...
10. ### When does a cantilever beam fail in reality?

Hi, like the title says, how do we actually calculate when a cantilever beam fails in reality? We’ve been taught that these are absolutely fixed to the ground. However, in reality these would probably be bolted onto the ground, so how do we calculate the force trying to lift the fixed beam on...
11. ### Beam Fixed at Both Ends and subjected to nonuniform bending

If a beam is fixed at both end and subjected to nonuniform bending would the upper section of the beam still be in compression. My intuition and free body diagrams suggest it would but geometrically in this case, wouldn't all sections of the beam, even the upper section, have to elongate/curve...
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### Elastomer on top of a bending beam

I'm trying to understand differences between two setups. In one setup I put a thin metal layer on top of a rigid plastic film, which I then bend to a certain radius. The metal is not very prone to crack in itself but with very small bending radius you are able to crack the surface. If I have...
13. ### Inverting Shifted Laplace function

Homework Statement A beam is supported at one end, as shown in the diagram (PROBLEM 11 page 281 of Lea, 159 of the course pack). A block of mass M and length l is placed on the beam, as shown. Write down the known conditions at x = 0. Use the Laplace transform to solve for the beam...
14. ### Fixed-Fixed Beam with two UDL

I'm looking for the max bending moment and max deflection of the beam shown in the problem statement. I tried using the double integration method to find the deflection, but it does not look right. I did the model in ANSYS to evaluate the solution, and the result does not match with my...

Hi All, I'm trying to think through a problem and was hoping to ping the community for guidance. Suppose you have a beam that's symmetric about 2 axes (like a u channel or a triangular extrusion). Is it better to load the beam in compression on the side with material furthest away or should you...
16. ### Why does it keep getting harder to break a pencil in 2?

Consider a pencil. Now break it in 2. Do it again and it s obvious it gets harder to do it. Why is that? I thought of modeling the problems as a hinged beam with moments applied at both ends having opposite directions and same torque. So basically the length of the beam doesn't affect the moment...
17. ### Beam Deflection equation question

regarding this equation, δ=(PL^3 )/(48EI) For the calculation of maximum deflection, if my structure is not longer a full form beam (meaning the structure has 6 holes drilled to it), can this formula still be used?is...
18. ### Bending of beams: calculation of stresses

The cross-section of a cost-iron beam is shown in figure below, the loading being in the plane of the web, the upper portion of the section being in compression. If the maximum permissible stresses are 2000 kg/ cm2 in tension and 3000 kg/ cm2 in compression, find the moment of resistance of the...
19. ### Question about the location of max bending stress in a beam

Hello guys, I have a simple question about the max bending stress in a beam. We know that in a cantilever beam, the biggest moment occurs at the wall. This is also the location of the max stress with equation stress= M*y/I , However, in a simple supported beam, we have This time, the max...
20. ### Hamilton's principle

I want to obtain equation using Hamilton principle but I just couldn't figure it out; i have The kinetic energy : \begin{equation} E_{k}=\dfrac{1}{2}m_{z} \displaystyle\int\limits_{0}^{L}\ \left[ \left( \dfrac{\partial w(x,t)}{\partial t}\right)^{2}+\left( \dfrac{\partial v(x,t)}{\partial...
21. ### Shear and bending moment

Hi, I am designing a beam to replace a load bearing wall. I have produced 2 separate UDL diagrams which, one for floor load and one for wall load. I am trying to find shear force and bending moment as in one for the total of the two diagrams. I know how to do it if the loads are spread...
22. ### Stress in a hollow beam bent laterallly

I would like to calculate the maximum stress in a hollow beam being bent laterally. There has been some discussion in my office about the correct way to view the system in question, and so would like some other opinions on the matter. I will include pictures below. In simplified terms, the...