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. P

    Understanding Bending Moments and Moment Equilibrium in Structural Analysis

    I have a quesrion about forming the eqaution of moment equilibrium. As shown in the picture at cut 1 there are 2 vertical forces and a bending moment. I expect V=A. If I apply moment equilibrium about the point where the bending moment is, we get that Ay*x = M(1). But how about if I take moment...
  2. C

    Engineering Where does the bending moment exerted by a wall on a beam come from?

    M = r x F r = 0 ∴ M = 0 But this is clearly wrong. For some reason, the "reaction moment" must exist. Why? Where does it come from? More specifically, which force(s) produces the bending moment, and at what distance(s)? Does it come from the reaction force form the wall on the left end of the...
  3. T

    Bending Moment & Bending Stress

    Hello all I was wondering if anyone could figure out the what the equation below means, specifically the W term? The equation to calculate bending stress for a cross section that i have used and i know is correct is:- Bending Stress = Moment (M) * Distance From Neutral Axis (Z) / Second...
  4. T

    Calculating the bending stress of a simply supported beam

    Hello all I am trying to calculate the bending stress of a simply supported beam with a load of 12kn at the middle of a 6m span, member depth of 0.016m I have drawn both the bending moment and shear force diagram. I want to know the following:- 1) When calculating the bending stress would...
  5. D

    Engineering Do Axial Forces Affect Bending Moments in Beam Calculations?

  6. Stephen Miller

    Max Deflection Hand Calculations: Find 1.734in Plate Bending

    Summary: Max Deflection Hand Calculations I have to do a project that involves FEA on a thin plate in NX NASTRAN 11, finding the max deflection, and then proving that answer with hand calculations. The max deflection is 1.734 in. I have absolutely no idea how to do the hand calculations...
  7. N

    Optimal beam geometry for 3-point bending

    Thinking of triangular pattern
  8. Phylosopher

    How does glue reinforce two sheets of paper joined together?

    I am no engineer, just a physicist. I usually do not work with such problems, so I basically do not know what to look for to begin with. My question/questions goes like this, take the following situation: Fetch a paper, such single paper is easy to bend. If one takes glue, and glue this...
  9. F

    Solving Shear Force and Bending Moment at Reaction Point R

    Hello Please see attached - trying to figure shear force and bending moment at reaction point R, with a horizontal force applied at top of Z. This is a veranda deck with balustrade. If F was vertical, then straightforward with SF = F and M = FX. But when F is horizontal as shown, I'm having...
  10. I

    How can I calculate the bending moment of a pin in double shear?

    I have attached an Excel-worksheet in which the problem should be clearified. The problem concerns the calculation of the bending moment acting in a pin in double shear, experiencing a certain load from a hydraulic cylinder. The plate thicknesses should be taken into account. Specifications and...
  11. dustball23

    Calculating bending stress on a pipe

    In both designs, a PVC pipe is being bent 90 degrees, fixed at each end. In both designs, the pipe is fixed at both ends. In both designs, the pipe is 1" (inner diameter) Schedule 40 PVC pipe, 450 PSI. Material code PVC 1120. NSF pw-G ASTM D1785 PPFA 02199101H6BX 0934. In design A, the length of...
  12. K

    Torsional moment vs bending moment

    The direction of x, y and a axes were shown in the highlighted part.. I think it is wrong. For red circled beam, i kinda agree that Moment about x-axis was defined as torsional moment.. While moment about z and y axes are bending moment... But for blue circled beam, I think that Moment about z...
  13. I

    Exploring the Relationship Between Photons and Vibration in Light Transmission

    Are photons vibration or is vibration the transport medium for light? In what kind of medium are photons more transferrable?
  14. Joe591

    Help with a Bending Stress Calculation

    I've attached a photo of a "problem". How would you calculate the stress at the area in question? I seriously doubt that the bending stress would vary linearly throughout the whole meter of total length of the section. I would expect it to become zero long before it reaches the opposite...
  15. S

    Stresses on a 3/16" fillet weld due to bending

    Hello, The resource I'm using is "Design of Machine Elements" by Spotts and, although they have examples of tensile and torsional stress, they don't show any examples with a load which causes a moment. What we have here is web of 3/16" thickness and 1.85" depth welded onto a rigid body from...
  16. J

    What are other names for bending stress?

    Hello, I need to input the bending stress from a database I am not sure what name it is, would it be yield strength or tensile strength? thanks
  17. 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)...
  18. A

    Cantilevered OSB Bending in the Wind

    Hope I am in the right subforum. I want to know how much a cantilevered sheet of OSB sheathing will deflect under wind load. I found the Moment of Inertia for OSB, but the units are in^4/ft. The bending equations I found use Moment of Inertia in units of in^4. The wind load will be uniform in...
  19. 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...
  20. pixel

    I Bending of light - Newton vs. Einstein

    Using Newton's equation for gravity and assuming a corpuscular theory of light, one can calculate the angle that light would bend in a gravitational field. General relativity predicts a bend that is twice as large. In the Newtonian limit of GR (which includes weak gravity), does the GR...
  21. R

    Find normal force, shear force, bending moment

    Hello. This is a basic statics/mechanics of materials problem. Here's an image of my work. I've taken a course in statics before, and this is supposed to be review, but I can't seem to get the correct answers which are V_c = 75 lb, M_c = 1125 lb*ft. I've chosen the right side, and it seems as...
  22. M

    Force Calculation for bending of TOR steel bars

    Hello everyone, I need some help to calculate the force required to bend a tor steel bar of dia 20mm and 12 m long from the centre. I want to bend it like a hair pin and need to know how much force is exactly required to do so. Any help or resource would be great. Regards, Mradul
  23. S

    Pure bending of a perfectly elastic cantilever beam

    Hi, My question is: If a constant load is applied at the free end of a perfectly elastic cantilever beam, would the beam oscillate about a mean position? Or would it eventually come to rest at the equilibrium position? There are no damping effects. Thank you.
  24. Jesse Niekamp

    Bending Stress on a Protective Cover

    Homework Statement A 30kg pallet falls from a height of 2m onto a protective cover. The cover has an area of 269m² and an overall thickness of 10.9mm. a. What is the force/pressure on the cover? b. What is the bending stress on the cover? Homework Equations F=ma bending stress =...
  25. K

    Optics: Huygens' principle and bending of light

    I know the technical details of why light bends towards "the normal" when meeting a more refractive medium must be complicated. But I was thinking about it in a more lay fashion. I was thinking if the bending can be explained using Christiaan Huygens' principle in that a light front is made of...
  26. H

    Bending and circumferential stress-Cylinder

    Homework Statement How do we combine bending stress on thick walled cylinder from external point load or moment to other longitudinal, radial and hop stresses which are from pressurized thick walled cylinder. Since bending stress and longitudinal stresses are in the same direction, do we just...
  27. M

    Stresses in the bending of a thin walled cylinder

    I am looking into the bending of a thin walled cylinder about it's neutral axis. Should be simple enough, it is just Mr/I. However, that is the maximum stress at the outer fibers of the cylinder and I want to find an approximate expression for the load per unit circumference on a small element...
  28. Al_Pa_Cone

    Determine the position and magnitude of the max bending moment

    Homework Statement For my question, I am following a previous method I used in my HNC where I had to determine the position and magnitude of the maximum bending moment. I am now working on my project and I have revisited this question but I am having some issues in my method. The above diagram...
  29. D

    Shear force and bending moment

    Homework Statement I was asked to find the shear force diagram and bending moment diagram for this load combination...But , i have problem of getting the BMD now . i am not sure which part is wrong , can anyone point out ? Homework EquationsThe Attempt at a Solution MA = 5(2)(1/2)(2/3 x 2) +...
  30. 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...
  31. S

    Bending light with temperature gradients

    A quick question about this type of apparatus. The apparatus itself is composed of 2 concentric hollow cylinders. The cylinder at center is cooled below -50C. The atmosphere around the outer cylinder is at room temperature. This creates a temperature gradient in the space between the cylinders...
  32. UMath1

    Is Shear Stress Vertical or Horizontal in I-Beam Webs?

    My mechanics of materials book states that in order for an element to be in equilibrium it must have equal horizontal and vertical shear stresses. However, it also states "The shear stresses in the web of a wide-flange beam act only in the vertical direction and are larger than the stresses in...
  33. physea

    I Shear force and bending moments graph

    Hello I am a bit confused how to calculate the shear force and bending moment graph for a beam under point loads, distributed loads and bending moments. Is the discontinuous functions the best method to solve such problems? Can anyone outline an approach? I don't understand for example how...
  34. Matthew Titus

    Calculating Elastic plastic bending moment

    1. The problem statement, all variables, and given/known data Good day I am preparing for a strength of materials exam and I can't seem to solve this problem. I am unsure if the section below the neutral axis is fully plastic before the edge of the flange experiences the yield stress. Could...
  35. K

    Parallel Axis Theorem / Bending Stress

    Homework Statement find bending stress in x and y dir Homework Equations I = bh^3/12 + ad^2 Stress = Mc/I The Attempt at a Solution I = bh^3/12 + ad^2 Stress = Mc/I see attached calculations My prof gave us a question where we have a motor (20" tall) sitting on a frame with a load of...
  36. Z

    What is the relationship between slope and bending moment in a penstock beam?

    << Mentor Note -- Thread moved from the technical forums, so no Template is shown >> Hi , Please I have to understand the solution of an exercice about calculating bending moment in penstock : It is assumed that maximum moment from penstock beam bending occurs at supports. The bending moment M...
  37. ZMacZ

    Bending light by use of a strong field...

    Like the title says, bending light by means of a strong field.. And before you say "it's electromagnetic field by itself and therefore can't be changed by such.." A strong gravitc field (also an electromagnetic field) can in fact change photons to never escape it (in effect bending the light...
  38. A

    Skew bending in a circular cross section (proof)

    Good day all I'm looking for the proof of stress generated in case of skew bending applied in acircular cross section ( I browsed internet the whole day without finding anything convincing) we use with many thanks in advance!
  39. A

    Stress generated by a bending moment

    Good day all, I have an issue regarding the theoretical concept regarding the stress generated by the skew bending in a rectangular cross section for example the formula used to calculated the stress is while when it is a circular cross section we have the following formula I really...
  40. J

    I Alcubierre Drive & Bending of Spacetime

    Hello, I've been wondering about this... If something like the Alcubierre drive is possible, that bends spacetime around it in order to reach great distances faster, why would this not affect other matter in its vicinity? If I'm understanding correctly, in order to move faster than light, a big...
  41. A

    Sign issue with the skew bending formula

    Good day ! I have an issue with the sign minus inside the skew bending (unsymmetric) formula First we all know that the stress generated by the bending moment is the following: and then after we have the formula I really don't understand why we don t have the sign minus in all the formula...
  42. M

    Bending Moment Statics Solving

    Homework Statement https://imgur.com/a/AGJaN It's a project so not a textbook question. The Attempt at a Solution Given in imgur picture. [/B] I'm looking to solve for C. The problem is actually a trailer with 3 axles but simplifying here as 3 fixed points where the wheels would be. The...
  43. C

    Calculating Maximum Bending Moment and Radius of Curvature for a Round Beam

    Homework Statement A round bar .125mm in diameter , is to be used as a beam. IF Youngs modulus For the material E=200x103N/mm2 and the stress due to bending is limited to 17.5N/mm2 A) Maximum allowable bending moment B) the radius of curvature at the point of Maximum bending moment Homework...
  44. K

    Boundary conditions of a bending plate

    Homework Statement I'm trying to find the boundary conditions for the following problem: A plate with length 2L is placed on supports at x = L/2 and x = - L/2. The plate is deforming elastically under its own weight (maximum displacement bowing up at x = 0). Both ends of the plate are free...
  45. Feodalherren

    First natural frequency for bending, axial and torsion modes

    Homework Statement We have a rod of length L fixed to a rigid support. At the end of the rod there is a mass, m. Assume that the rod has no mass. Find the first natural frequency for the bending, axial and torsion modes. Homework EquationsThe Attempt at a Solution So I'm reviewing some stuff...
  46. 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...
  47. F

    Sheer and bending moment diagrams

    ok so for concentrated loads the sheer diagram is constant meaning are straight horizontal lines and the bending moment diagram is linear. when there are evenly distributed loads sheer diagram is linear and bending moment diagram is quadratic. I am thinking that when there is a load distributed...
  48. H

    How do you find a curve pipe bending moment and shear force?

    1. Homework Statement I have problem solving the bending moment and shear force of a conduit with a curve end. The conduit is lifted in the mid-air with 2 slings and assume it is in equillibrum. I have attach a drawing for reference. Homework Equations What i know, there is a UDL somewhere...
  49. J

    What causes the bending of this rod?

    In this video, a man applies an angular acceleration to the base of a rod. While the rod rotates, it bends. Why? What force is there that causes the bending, aside from rod's own weight? It seems to me to be the work of a fictitious inertial force. I was always taught that those forces don't...
  50. Fraser MacDonald

    Finding Young’s modulus by bending a beam

    I have a question regarding finding the Young’s modulus of a rod by loading a weight to the end and measuring the change in displacement. The experiment is part of my advanced higher physics project on Young’s modulus however it is the only experiment that I’m doing that the book “Tyler” does...
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