What is Bending: Definition and 665 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

    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...
  2. Hadron

    Calculating truss shear and bending

    Is it known how to do this? If so, how?
  3. Gort

    I Gravitational Bending vs. Refraction

    I'd like to call attention to this paper: https://arxiv.org/ftp/physics/papers/0409/0409124.pdf I'm not trying to question the validity of GR in bending of light near a star (such as the sun), as this paper apparently does. But surely Newtonian refraction of light passing through the sun's upper...
  4. L

    I GR and its bending of space time

    Hello Maybe my question is dumb but is the bent of space time instant due to gravity? If a mass pops into existence will space time be bent instantly ? Intercations between forces are light speed but gravity is and is not a force depending on pov
  5. P

    I Bending of light - caused by gravity or relativity?

    The mainstream interpretation of GRT equations is, that additional double amount of angle of bending of light (Newton vs GRT) is caused by gravity (which is interpreted as curvature of spacetime). But when looking on the equations, it seems that this additional amount of bending is caused by...
  6. K

    A Gravitational Bending of Light: Equation for Photon Trajectory in Strong Fields

    I'm looking for an expression for the deflection of light in a static gravitational field. Referring to 'deflection of star light past the sun' in Sean Carroll's "Spacetime and Geometry" - equation 7.80 for the "transverse gradient": \nabla\perp\phi = \frac{GM}{(b^2 + x^2)^{3/2}}\vec b...
  7. C

    Calculating Bending Moments for a Round Bar: E=200x103 N/mm2, D=125mm

    Homework Statement a round bar,125mm in diameter , is to be used as a beam. if youngs modulus for the material E=200x103 N/mm2 Calculate: i)Maximum allowable bending moment(12marks) ii)The radius of curvature at the point of maximum bending moment(8marks) Homework Equations σ/y=m/I=E/R...
  8. alex4lp

    A Solve Bending of Light Formula Problem

    Good morning everybody. I have a problem with this wikipedia passage https://en.wikipedia.org/wiki/Schwarzschild_geodesics#Bending_of_light_by_gravity 'cause it says "Expanding in powers of rs/r, the leading order term in this formula gives the approximate angular deflection δφ for a massless...
  9. D

    Applying Bending Stress to a Model of Ship Section

    Good Afternoon. My name is Dimas M. Rachman, i am an undergraduate student majoring in Ocean Engineering/Naval Architecture. I am currently working on my final project. I need to model the effect of bending stress "inside" a plate of ship's deck with Ansys Workbench. Here is a review about...
  10. A

    I Simulating Plant Evolution: Branch Bending Physics

    I'm trying to simulate plant evolution to see if there's a genetic reason why fronds are so common in nature, and one problem I've come across is branch physics. Whenever a segment of a leaf or branch bends, not only does it affect the angle of all child segments (and thus how they'll bend), it...
  11. F

    Bending moment diagram equation method

    Homework Statement Draw the bending moment diagram the top part is the question, the bottom part is the answer. Homework EquationsThe Attempt at a Solution There is a force at the wall in x and y direction and a moment ##F_x, F_y, M_w## Sum of forces in x : ##F_x-1000=0, F_x=1000## Sum of...
  12. P

    Formula for bending a rod in the elastic range

    Is there a formula to calculate the radius that a rod of a given radius can be bent around while staying in the elastic range? For example, if I had a rod that was 1/4" in diameter and made of HDPE (which I think has a modulus of elasticity of 0.8 GPa), how would I calculate the minimum radius...
  13. P

    Formula for bending a rod in the elastic range

    Is there a formula to calculate the radius that a rod of a given radius can be bent around while staying in the elastic range? For example, if I had a rod that was 1/4" in diameter and made of HDPE (which I think has a modulus of elasticity of 0.8 GPa), how would I calculate the minimum radius...
  14. N

    How weight affects surface bending over time

    Very dumb classic mechanics question here: The other day I caught sight of a trivial objects arrangement: a basketball placed on top of a 6-sided cardboard box on the floor, and I wondered how the weight of the hollowed sphere could cause bending on the supported, flat top surface of the box...
  15. Liquito

    Heavy Duty Trolley Plastic Bending & Strain Energy

    Homework Statement http://imgur.com/a/RoKVR The link above have the full problem I mostly have issue with Part (b) of the problem where am not familiar with and don't know how to solve that part. I was wondering if someone can put some light in the tunnel or provide a link where I can study...
  16. DevonZA

    Draw the shear force and bending moment diagrams for beams

    Homework Statement Homework Equations [/B] Shear force is calculated at each point on the beam. Downward forces are negative, upward forces are positive. Moments about points are calculated as force multiplied by perpendicular distance. Clockwise moments are negative. Anti clockwise...
  17. E

    How do I calculate internal forces in a beam bending problem?

    Hello, I am having difficulties trying to work out one problem. I've attached a picture explaining the situation - the task is to determine internal forces in C but the bending moment M(x) doesn't seem to get me the correct results (I used equivalance and went from LHS). I would greatly...
  18. S

    Tube Bending Stress: Hand Calcs vs FEA Analysis

    I have ran an FEA simulation on a lever to work out the stress on the part. I have now started doing some hand calculations to validate the software results and am struggling to get the values to match up. I am unsure whether my calculations are wrong, or whether the software is incorrect. The...
  19. P

    Specifications for elephant-resistant steel poles

    This is probably simple for an engineer, but I’m a zoologist and analytical chemist and so I would rather ask those who know. I have camera traps out on the African bush, that are monitoring the responses of leopards to artificial scents. The cameras are in steel boxes to protect them from...
  20. W

    Simple bending moment calculation

    Hi, Really need some help with figuring out the max bending moment in the diagram shown below (I'm aware this is extremely simple but time and stress appear to have the better of me, so any help is appreciated) I think I've worked out the reactions at each support by doing m=wL as the...
  21. I

    Bending stiffness of circular bars

    Which of the two is stiffer in bending? 1. A circular rod of diameter D and length L. 2. A circular rod of diameter d and length L, surrounded by a tube of inner diameter d, outer diameter D, and length L. The tube is not bonded and can freely move. It seems like an easy solution in that we...
  22. U

    B Light Bending on Single Point: What Happens?

    Say you have two stars, star A and star B, separated by a distance of x, and the light from star A went directly from A to B but was heading directly for the centre point of star B. If the light passed near star B then due to the mass the will bend, yet if it was to pass through (or try to) the...
  23. saybrook1

    Analytical bending of a deformed beam

    Hi guys; I have an analytical solution for the deformation of a beam due to a couple with moments C_1 and C_2 with boundary conditions y=0 and x=±(L/2) where L≡length of the beam. The derivation from the Bernoulli-Euler equation is below: \begin{align*}...
  24. Strife_Cloud

    Stress analysis -- derive equations: bending & yielding

    Problem attached. I would appreciate anyone's help. I am an alloy chemist working on an MS degree in materials engineering and have come to the mechanical engineering part of the program and am feeling a bit behind. Deriving an equation for this case is proving to be difficult for me although...
  25. F

    B Bending of light in a gravitational field

    I have a few conceptual issues following a standard thought experiment to argue why light bends in a gravitational field and I'm hoping I can clear them up here. Consider an observer in a lift in free-fall in a uniform gravitational field and an observer at rest in the uniform gravitational...
  26. S

    Max Bending Stress: Find from Second Moment of Area

    Homework Statement The second moment of area of the beam shown about the neutral axis X X is 4x10^6mm^4 Find the maximum bending stresses, tensile and compressive, set up in a beam of this section 2.6m long and simply supported at its ends and carrying a concentrated load of 4.8kn at its mid...
  27. F

    Moment applied causing bending stress in beam

    Homework Statement From the solution , it's clear that the top part of the beam undergo tension , while the lower part undergo compression . Homework EquationsThe Attempt at a Solution But , i don't understand why it is so . When the moment is applied in the horizontal axis , the structure...
  28. U

    B Space Bending: Questions Answered

    please help me understand this, space is flat. space bends when its near matter. When matter moves from point A to point B, the space at point A returns to being flat. Where does the energy come from to bend the space back to flat come from? Why doesn't the space at point A stay bent?
  29. OrangeYogi

    Critical bending radius of optical fibres

    Hello, How do I calculate the critical bending radius of a single mode optical fibre? I'm using a polyimide coated fibre with coating diameter of 155μm. The wavelength is 1550nm. Let me know if you have any questions. Thank you
  30. C

    Shape of bending moment diagram

    Homework Statement in this question , I'm asked to draw the bending moment diagram and shear force diagram Homework EquationsThe Attempt at a Solution I don't have the ans for this question , can somoene check thruough my shape of graph . I'm not confident with it . [/B]
  31. C

    Graph of bending moment doesn't return to 0

    Homework Statement I gt VA and VB = 85 N and 65 N respectively ... but , my bending moment diagram doesn't return to 0 ... Is there something wrong with the question ? Homework EquationsThe Attempt at a Solution I found that if i didnt include both the moment of 75(0.05) = 3.75Nm , the...
  32. C

    Shear force diagram and bending moment diagram

    Homework Statement theoretically, bending moment should ends at bending moment = 0 , am i right ? Homework EquationsThe Attempt at a Solution Here's my sketch of SFD and BMD ,my bending moment doesn't return to 0 , which part of my working is wrong ... to find bending moment (M) , i get M...
  33. B

    Bending Moments and max deflection

    Please could some help me get around this problem I know the derived formulas are all over the internet, but I wanted to prove it out myself. Its for a supported beam 2 end beam, worked out the max bending moment is M=PL/4. However I just can't seem to get the max deflection equation of...
  34. kolleamm

    B Can We Warp Space Faster Than C? | IXS Enterprise | NASA

    I saw a NASA video on Facebook, about a warp drive proof of concept ship, The IXS Enterprise. It's supposed to travel to distant places at faster than light speed by warping the space around it, but that leads me to think if you can warp space faster than the speed of light. Is it possible? If...
  35. N

    Calculating Bending Stress for a Cantilever Beam

    Hi, I'm trying to calculate bending stress for a cylindrical beam. I'd like to have my result double checked because I got an answer that doesn't make sense to me. All of this is personal research, so I'm not very confident in my answer. It's a cantilever beam with a point mass of 347.4 oz. on...
  36. K

    Bending moments at equillibrium

    "Consider a prismatic member AB possessing a plane of symmetry and subjected to equal and opposite couples M and M0 acting in that plane . We observe that if a section is passed through the member AB at some arbitrary point C, the conditions of equilibrium of the portion AC of the member require...
  37. C

    Allowable shear stress in bending

    Homework Statement I think the notes is wrong . in the notes , it's given that σ allowable > Mmax / Ze Homework EquationsThe Attempt at a Solution i think it should be σ allowable > Mmax < Ze , am i right ? How could the σ allowable > Mmax / Ze ? If σ allowable > Mmax / Ze , the beam will...
  38. J

    Equivalent Bending Moment due to Impact Formula?

    Hi guys and girls, I've been working on this problem for a little while now but I'm not really getting the result that I want. This is what I have: I have what is essentially a big pair of vice grips controlled by a hydraulic cylinder. The cylinder opens and closes both arms of the vice grips...
  39. C

    Understanding the Difference Between Bending Stress and Normal Stress in Beams

    Homework Statement https://en.wikipedia.org/wiki/Bending [/B] form the link, we know that σ represent the bending stress, I'm wondering can I call the bending stress as normal stress act at the cross sectional area of beam?Homework EquationsThe Attempt at a Solution IMO, they are not the...
  40. C

    Understanding Reaction Forces in Pure Bending for Structural Resistance

    Homework Statement to resist the bending, there must be reaction force(blue) act against the applied force(red), the reaction force that resist bending is the longitidunal normal force , right? why the author stated it as longitidunal shear force, is it wrong? Homework EquationsThe Attempt at...
  41. SadPanda6022

    Bending of light concept help

    Homework Statement In this lab we used a half-circle container filled with water. Multiple angles are given to measure through the liquid in the container, calculating using snell's equation. However I don't understand why we do not have to calculate for the change in the angle from the plastic...
  42. T

    I Mind Bending Double-Slit Diffraction Thought Experiment

    Hi, I studied undergrad pure maths now post grad philosophy, not quantum physics, but please consider the following experiment: Suppose you set up a double slits experiment with a photon detector attached to each slit, and the photon detector attached to a photon transmitter, so the photon can...
  43. Guidestone

    Bending moment in an axis doesn´t match

    Hey guys, first of all, this isn't a homework question, I just want to know why the results are what they are. I've been trying t obtain the same numbers using moment equilibrium but they still don't match. This is the example: W are the forces applied by the gears in force-pounds. The gears...
  44. C

    Sign convention of shear force and bending moment

    Homework Statement http://nptel.ac.in/courses/112107146/22[/B] in the notes, the author define upward shear force as positive (LHS) , he take downward shear force as positive as positive (RHS)? Homework EquationsThe Attempt at a Solution why the author didnt fix downward shear force as...
  45. C

    Pure Bending: Understanding the Effects of Shear Force on Beam Behavior

    Homework Statement in the notes , i was told that when pure bending occur, there is no shear force acting... Homework EquationsThe Attempt at a Solution refer to diagram 3.11 , does it mean the center of beam (between 2 forces P) will break? since there's no shear force acting
  46. F

    Max Bending Moment: Calculation & Formula

    Homework Statement how the author found the maximum moment = 0.29MNm ? is there any formula ? how to find it in this question ? Homework EquationsThe Attempt at a Solution
  47. S

    I Light Beam Bending by Mass: Equation & Explanation

    What is the equation for how a light beam is bent by a mass? Say a mass M way out in space, and a light beam is aimed from VERY far away such that it should pass at a radius R from the mass.
  48. J

    Equations for bending steel in a car crash?

    I wanted to know what formula's do I need to figure how much force is required to make a dent in a car. I am then placing a bumper guard made up of carbon fiber, and wanted to know what equation do I need to use to figure out how much force is required to make a dent with the carbon fiber bumper...
  49. S

    Determine the absolute maximum bending stress of the beam.

    Homework Statement If w = 74 kN/m , determine the absolute maximum bending stress in the beam in MPa. Homework Equations I'm not too sure how to go about my calculations. Please help! The Attempt at a Solution I = [(1/12)*(200*256^3)] - [(1/12)*(192*250^3)] = 29.62*10^6 F = 74*24*1000? [/B]
  50. P

    Bending shear stress distribution

    I modeled a simple cantilever rectangular beam in Patran of (L,W,H = 100, 6, 4) with Hexa8 elements and applied a vertical shear load (upwards) of some magnitude at the free end. Ran in Nastran and plotted the vertical shear stress distribution on a cross-section in middle of length (in order...
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