Beam bending Definition and 61 Threads

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. abayerle

    I Two beams joined after bending

    Thinking about Bernoulli Beam Theory and how to calculate the curvature of a beam, that you first bend and then glue to another beam. The latter is flat initially. How do I calculate the resulting curvature of the composite beam? How do I get the stress diagrams right - my first idea is in the...
  2. FEAnalyst

    Beam deflection and curvature radius formula doubts

    Hi, I am working with leaf springs and studying the derivation of the formula for the deflection of such a structure. The derivation is shown here: My only doubt is how to obtain the following formula: $$\delta=\frac{L^{2}}{8R}$$ where: ##\delta## - deflection, ##L## - length of the beam...
  3. S

    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...
  4. N

    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...
  5. K

    Difference Between FEA Result and Hand Calculation in Beam Bending?

    This is the analytical working out. I substituted the value of 306mm ( the maximum length of the beam) to find the maximum deflection along the Z-axis. Which came out to be -2.39mm. But according to Ansys the average deflection is 0.3mm and the maximum deflection is 0.8mm. This is the Ansys Values.
  6. goodOrBad

    Beam with a rope - type of problem (Statics)

  7. M

    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...
  8. D

    Engineering Do Axial Forces Affect Bending Moments in Beam Calculations?

  9. 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...
  10. kelvin scott

    Statics engineering: Beam bending problem

    Homework Statement a beam is 10 m long with point loads of 10kN at 3m from left and 20kN 10m from left. R1 and R2 these supports are 2m in from either end of the beam. The beam has a UDL of 5kN/m-1 along its length. Homework Equations (a) determine the vertical reaction at the support(b)...
  11. O

    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...
  12. A

    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...
  13. C

    How Do You Calculate Beam Deflection for an I Beam on Lorry Trailers?

    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...
  14. T

    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...
  15. UMath1

    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...
  16. N

    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...
  17. J

    Beam Bending of a Linearly Varying Beam with 2 point loads

    I'm trying to design something and rather than solve it using FEA guess and check, I'm trying to mathematically solve it. The part I'm getting stuck at is having 2 point loads on a linearly varying cantilever beam. https://imgur.com/LtHCvCB The closest example I could find to this that was...
  18. D

    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...
  19. H

    Does an electron beam bending lose energy by photon emission

    A beam of electron in vacuum with velocity v enter a region of spa e with a electric field E. The field is such the electrons circle with radius r. The electrons are now accelerating at constant tangential speed. Because this is not an atomic orbital then by classical physics the electrons...
  20. R

    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...
  21. S

    Preferential bending loading direction of a beam

    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...
  22. M

    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...
  23. A

    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...
  24. HorseRidingTic

    Solving Beam Bending Qs: Find Beam Dimensions with 25 MNm^2 Stiffness

    Bonjouro! Firstly, as this is my first post here, I would like to say thank you to everyone who is a part of the site and Hello! I've used this forum a number of times, but this is the first time I've posted here as this user! If the flexural stiffness of a beam is 25 MNm^2, and the beam is...
  25. A

    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...
  26. J

    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...
  27. Last-cloud

    Obtain Equation Using 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...
  28. S

    Simple Beam Bending - Where am I going wrong?

    I am trying to find the width of a square hollow structural member that can withstand the forces above. However, my calculations are showing me that a square hollow aluminum tube of 4 mm by 4 mm with a wall thickness of 1/16 of an inch would be adequate, which I don't believe. Is anyone able...
  29. J

    Piezoelectric Actuator Cantilever Beam bending

    I do not have much knowledge in piezoelectric, but all the piezoelectric I've read up on seems to only achieve maximum displacement in measurement values of microns. Is it even possible for some piezoelectric actuator to bend a 10 meter long cantilever beam up to 1 meter at its maximum...
  30. R

    Can I Calculate Shear Force and Bending Moment for Partially Loaded Beams?

    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...
  31. D

    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...
  32. L

    Beam bending of an angled flat plate

    Hello everyone, I am wondering how to properly go about calculating the stresses caused by bending on an angled flat plate. Two approaches seem valid but they give much different results: -Calculate the new area moments of inertia for the angled flat plate (new Ixx, ymax)...
  33. S

    Beam bending, overhang with 2 concentrated loads

    Homework Statement A beam supported at two locations is subjected to two equal loads at the end points Compute the central deflection W. Schematic: \downarrow........\downarrow ____________________________ <--->Δ<-------><------->Δ<---> ...a...L...L...a The delta's are the...
  34. R

    Maximizing Beam Design: Balancing Bending and Shear Forces

    Homework Statement This is not a homework problem but a general situation where I'd like to know which is better to do. Say for example I have a cantilever beam of length L and some moment of inertia I, first moment of area Q and thickness t with a force P applied at the free end...
  35. M

    Multi-Section Beam Bending Calculations

    Hello all, I have a shaft supported on both sides with a charge on each bearing, as shown on the following link: http://www.engineersedge.com/beam_bending/beam_bending4.htm I need to calculate the shaft deflection with the formula provided on the website, but my shaft often have different...
  36. D

    What is the required force to achieve constant radius beam bending?

    Hi All, I need to calculate how much force is required to bend a beam to a constant radius. The beam will be simply supported on both ends and the force will be applied much like a 3 point bend but with a curved face instead of a single point. For most of my application, the beams are...
  37. Saladsamurai

    Short Beam Bending: Roark's Formulas For Stress and Strain

    Is anyone familiar with the Roark's text that can clarify some terms for me? I am trying to clarify what Roark is referring to in the above mentioned text in the section on short beams (in the 5th edition 7.10 and in the 7th edition 8.10). Throughout the text, he uses the terms "span" and...
  38. L

    What are the elements of the strain tensor for a wide beam under bending?

    If I have a wide beam, parallel to the x axis, with its COM at the origin, then I want it to curve about the y axis, what would the elements of the strain tensor be? I have come to the conlusion that the beam would, for example,contract above x-axis and expand below it. But I don't know how...
  39. T

    Non-standard Beam Bending Question - Parallel to Neutral Axis

    Hi there, first post on these forums. I have a seemingly simply question about beam bending. We (mechanical engineers) are all very familiar with the standard beam bending scenario. The beams are always shown being loaded perpendicular to the neutral axis, regardless of the type of support...
  40. D

    Beam bending under a uniformly distributed load

    Homework Statement I have a bumper and I am trying to determine whether or not the rectangular tubing I am using to build it is strong enough to withstand a given load (rear end collision). The horizontal member is 4x3x.1875 tubing (4" base, 3" high, 95" long). Two 3x3x.1975 tubes are used as...
  41. J

    Beam Bending Theory compared to Real-world examples

    Does anyone know of any good articles, journals or books that discuss the difference between simplified theoretical analysis of a beam under load and the actual real life effects? Need to do some reading up for an assignment but I'm having trouble finding anything of any merit! Cheers in...
  42. O

    How finite element analysis differs from mathematic derivation in beam bending?

    So I just started learning to use the finite element package abaqus for modelling beam tip deflection under different loading conditions. I think I understand the theory behind it but was wondering if some one could answer a few questions about it to further my understanding. Firstly, how do...
  43. F

    Modeling bolt holes as stress concentrators in I beam bending

    curious as to the proper way to model this. beam is symmetric so centroid is in the middle (used to calculate distance from centroid d in bending moment of inertia equation) bending moment of inertia is I =\sum(I + Ad2) I=\frac{1}{12}bh b=base h=height d=distance of the area's...
  44. R

    Beam bending problem, calculate deflection of a beam

    Homework Statement The problem is to determine the maximum deflection when a person is standing on the beam in the attachment. E= 206.8 GPa, v=0.3 Homework Equations (although I am not completely sure if this one is relevant)The Attempt at a Solution I've thought a bit about the problem...
  45. W

    Calculating bolt size required to prevent beam bending

    The attachment shows a side section of a water tank.(lined with Marine Ply) The section will be bolted to a fixed bottom section with 4 bolts. I'm trying to determine the size and strength of bolts required to do this. My attempt at starting this problem is shown in the attachment...
  46. W

    Help calulating bolt strength to prevent beam bending

    Homework Statement The attachment shows a side section of a water tank.(lined with Marine Ply) The section will be bolted to a fixed bottom section with 4 bolts. I'm trying to determine the size and strength of bolts required to do this. Homework Equations Hydrostatic force? UDL...
  47. T

    Beam Bending of a Non-Straight Beam

    Hi all, I am designing a gear lever for a small race car, and am looking to validate my FEA of the lever through the use of hand calculations. The beam is not straight, and i have never tackled a problem like this before. I am using Roarks Formulas for Stresses and Strains, however am...
  48. T

    Singularity Functions for Beam Bending

    There is a beam of width 10cm, and vertical reaction loads on each end (x1 = 0cm, x2 = 10cm). Starting from the left end of the beam, we have a vertical distributed load of 2,000 N/m spanning from 0cm to 5cm. Finally, we have a 1,000 N point load located 7.5cm from the left end of the beam...
  49. T

    Solving Beam Bending Problem: 600N Load, 3.5mm Radius, 193GPa Young's Mod

    Homework Statement Hi there all, I am designing a pedal box for a vehicle, and its adjustment is does by removing some pit-pins and sliding the pedal box along a rail and reinserting the pins. I need to calculate the stresses in the pin given a 600N total load applied by the feet of the...
  50. M

    Beam Bending, beyond the basics, a little

    Ok, I am fairly comfortable with beam bending equations for simple rectangles. However, I am totally confused on how to approach other cross sections... like a channel can someone help? Or point me to a good online instructional resource? I have googled all I can think of... -Mark
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