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. S

    Finding shear force and bending moment in a beam

    Homework Statement I am attempting to calculate the shear force Vx, and bending moment Mx within the interval C - D of this beam. Homework Equations ƩFy = 0 ƩMx = 0 The Attempt at a Solution I have calculated the support reactions to be RA = 5kN and RB = 55kN ƩFy = 0...
  2. S

    Thin circular plate in pure bending

    Homework Statement Finding shear in terms of r My problem, is that i want t o find the shear force and if i want take a section , i need to know the reactions, but i can't find the value of reaction in terms of r I attached the problem (look at A) and my solution(in which i wasn't able to...
  3. schmiggy

    Optimising Support Location - Bending moments

    Homework Statement Firstly, I know posting images and asking for help is generally frowned upon, however in this case given the number of diagrams and equations involved I'm hoping it's warranted. So we're given a diagram as at the top of the attached image and we're asked, given most of the...
  4. N

    Why bending moment is constant on an end loaded beam

    Homework Statement For the same lab as I posted previously, I have been asked to prove a situation. I think I'm either over thinking it or it really is that complicated. I've been asked to prove why the bending moment is constant across an end loaded beam (inbetween the knife edges - the two...
  5. N

    Derivations for a Bending Moment and Angle from Koenig's Apparatus

    Homework Statement I'm having ALOT of trouble figuring out how to derive these equations. I'll post up photos and the equations as follows. C is the Bending Moment Y is the Young's Modulus of the material r is the Radius of Curvature of the neutral surface I is the geometrical moment...
  6. K

    Finding maximum bending moment when shear force equation is known

    Homework Statement Calculate the Maximum Bending Moment of the bridge section using the values given. Ra = 61837.91667 N Rb = 78304.5833 N (please refer to attached diagram) Homework Equations shear force is = 0 when x = 13.755998 m (I worked this distance and the shear force equation out...
  7. K

    Calculating the maximum bending moment on a bridge

    Homework Statement Calculate the maximum bending moment on the bridge section using the values given. (REFER TO DIAGRAM ATTACHED) mass of bridge = 9250 kg mass of car = 2250 kg length of bridge section = 26 m Homework Equations I worked out previously that: Reaction at A = reaction at B =...
  8. B

    Help. Shear force and bending moment problem makes no sense

    Homework Statement Homework Equations ƩFx=0 ƩFy=0 ƩMo=0 The Attempt at a Solution I have no clue. By cutting the pieces, it changes the length. By cutting the cable at c and removing the 2 supports, wouldn't it make all the forces and moments = 0?
  9. M

    Where is the Maximum Bending Stress Located in a Tapering Rod?

    A uniformly tapering cantilever of solid circular cross-section has a length L and carries a concentrated load at the free end. The diameter at the fixed end is D and at the free end d. Show that the position of maximum bending stress occurs at a section (d/(2(D-d))*L distance from the...
  10. Femme_physics

    How come there is no bending here? (Welding)

    http://img560.imageshack.us/img560/2662/nobending.jpg This exercise is from machine parts. In order to find the width of the weld, I calculate the shear force and bending moment for this exercise. However, according to my teacher, there is no bending here and I calculate this exercise for...
  11. M

    Validity of bending equations under different conditions

    Hi all, I want to ask you a question about the bending moment equation: σ= M * y / I Does this equation have the same form if we assume, -Plasticity instead of elasticity. -Viscoelasticity instead of elasticity. -Nonlinearity instead of linearity. -Anisotropy instead of isotropy...
  12. M

    Calculating Maximum Bending Stress of a Beam

    A uniform simply supported beam, 5 m long and having a cross-section as shown, is to support a load which varies linearly from zero at the left hand support to a magnitude of 20 kN/m at the right hand support. Determine the position and magnitude of the maximum bending stress. ANS : 140 MPa...
  13. 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...
  14. H

    Statics: Bending of a beam/evenly distributed force problem

    Hello, and sorry for my English, as I am Norwegian. I have a statics problem which I can not understand. I've taken a pic from my book: The problem asks me to find the largest bending stress, σb, in the incisions 1 and 2. I have the solution in front of me, I just don't understand...
  15. 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...
  16. L

    Designing a Beam from Shear Force & Bending Moment Diagram

    Homework Statement We need to design the cross section of a beam to make it suitable to carry a uniformly distributed load. The beam is held up by 4 ropes which are shown on my diagram as R. In the same attached picture I have the shear diagram and the bending moment diagram for this...
  17. A

    Bending Antenna: Benefits & Why it Matters

    why does the bending of antenna is important?why we can't just use two parallel wire to radiate energy? thanks.
  18. H

    Bending and Torsional stiffness of Hat/Omega stringer

    Hallo Engineers, I am a little bit confused here and i need some guidance. Can any of you educate me on how to calculate the Bending and Torsional stiffness of a Hat/Omega stringer attached on a plate to form a fuselage panel?..You can also recommend to me a book where it is clearly described...
  19. D

    To derive the bending moment of a simply supported beam

    Hi I am a new member and put illustrated diagram and my answer for Ra and Re but stuggling with how to calculate the other reactions of the beam, one other thing on the illustrated diagram it show w1, w2, w3 the weight is 0.2 kg on each load case, i think this needs to be converted 0.2 x 9.81 =...
  20. M

    Bending a Beam to Produce Uniform Tension

    Hello. I am attempting to build a fixture which will place uniform tension onto one surface of a rectangular beam. I know that I must force the beam to deflect along a set path, but I am having trouble determining what the equation for this path needs to be. Any guidance on this would be...
  21. S

    Length & Bending Stress: How Does Beam Length Impact Stresses?

    if you have a beam or something, anchored at one end and apply a moment at the other end, then the bending stress is given by M*y / I, where I is the moment of inertia of the beam. what affect does the length of the beam (i.e. the distance between the anchor and the end of the beam, where the...
  22. M

    Calculation of Bending Moments and beam deflection

    Homework Statement The picture of the beam below has a module of rigidity EI, determine the reactions at the supports and the equation of the deflection curve of the left half of the beam Homework Equations v*EI=((Ma*x2)/2)+((Ra*x3)/6) Ʃ of Forces in Y direction = Ra+Rb=0 Ʃ Moments...
  23. A

    Generating Shear and Bending Moment Diagrams for Beams with PDEs

    I'm trying to write a very simple program to generate shear and bending moment diagrams for beams. The thing is that I don't know what kind of loading that the beam may see so I want to be able to write it as generically as possible. I'm trying to find a web resource (not a book, unless...
  24. 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...
  25. W

    Bending Stresses on Male Component in Tapered/Interference Fits

    I'm looking for some help understanding bending stresses and stress concentrations in Morse Tapers (or any press-fit or interference-fit geometry). Specifically, I'm trying to understand the influence of a slot (and orientation of the slot) in the female component of a Morse Taper on the...
  26. H

    How to get the place of max bending moment ?

    what i know is the the max BM at zero shear but it is said that max BM in the cantileaver beam is at the fixation how? is the shear there )0) ?? there is reastion so how?
  27. N

    Find the Maximum (absolute) Vale of the Bending Moment

    Homework Statement Draw the shear and moment diagrams for the loaded beam. Then answer the questions. The distance x is measured from point A to the right. I have attached an image of the problem. Homework Equations The Attempt at a Solution I've managed to answer...
  28. C

    Bending moment of I section beam

    Homework Statement Hi everyone this is my first post. I am having a problem with the bending moments of the beam (see attached files). I cannot for the life of me seem to get the bending moment to finish at 0 so I can draw the bending moment diagram. I know this is generally quite a simple...
  29. M

    Calculating Bending Moments with UDL's

    Homework Statement The T-beam is loaded as shown in Figure attached Find the maximum transverse shear stress at the location of the maximum bending moment. Homework Equations Forces in Y direction = 0 for it to be in equilibrium Moments about a point = 0 for it to be in equilibrium...
  30. W

    Design ultimate bending moment one-way spanning slab

    Homework Statement Find the design ultimate sagging and hogging bending moments per metre width of slab. Load on slab- Imposed 32 kN/m - Permanent 39 kN/m Length: 5m Depth: 8m Thickness: 0.175m Not sure if relevant but it has 2 spans (i.e. two 5m lengths of slab) but...
  31. F

    Upward Band Bending in n-Type Si Contacted by Metal

    I am a little bit confused about the upward band bending in a n-type Si which is in contact with a metal. Suppose that electrons flow from Si to the metal to align the chemical potentials such that positive donor levels become depleted. In equilibrium one ends up with a negative charge density...
  32. S

    Moment for bending materials test

    Homework Statement I have to do the following practical, but I am unsure of how to calculate one of the variables. We are doing this test and we are given this information to calculate E. I have equations on how to calculate R and I, but I am not sure how to calculate M. It's...
  33. 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...
  34. 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...
  35. S

    Relationship between curvature of an arch and bending moment.

    Homework Statement A bridge has two arches, with one abutment in the center labeled A connecting the two arches, and a point b on the right. I have calculated that the maximum bending moment in the structure would be at point A, right on the abutment that is connecting the two arches. I am...
  36. M

    Electron Radius in a Bending Magnet

    Problem: 15 MeV electrons enter a bending magnet with a magnetic field of .7 tesla. What is the radius of the path of electrons? Equation: r = mV/Bq B = .7 tesla q = 1.6 x 10^-19 C My problem here is that I don't know how to find the velocity of the electron for this...
  37. N

    Shear Force Diagrams and Bending Moment Diagrams

    Homework Statement http://img189.imageshack.us/img189/9131/22465062cfdd4934b51d7f5.png Hopefully the image isn't too difficult to decipher... Basically a beam balanced on to pin jointed pivots with 6 metres in between each one. Homework Equations ƩFy = 0 ƩFx = 0 ƩMP = 0 The...
  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. B

    What Is the Force Threshold for Beam Bending?

    Hi Guys, Do you know of any short formula to calculate bending moment of the beam on the attached image? I need to know the force at which this beam will start bending.
  40. G

    Bending of Stainless steel pipe

    We have a design of stainless steel pipe with a bend radius of 1.5 The OD of the pipe is 47mm and the wall thickness is 3mm. Can anyone tell me if this is possible please? I am pretty sure the SS is austenitic. I thought that as a rule the minimum radius was 2. Thank you
  41. R

    Euler-Bernoulli bending moment equation, how do you know it's right?

    M=EI\frac{∂^2w}{∂x^2} 1. What exactly is this? Is it like a geometric constraint? This equation doesn't seem to depend explicitly on external loading or beam boundary conditions. 2. Can I derive this starting from the Euler-Bernoulli beam equation? I am dealing with a beam with...
  42. F

    Is it possible to have curvature without bending moment?

    The simple question is whether it is possible to have curvature in a beam with no bending moment (similar to how there can be strain without stress)?The main example I have to discuss what lead me to this question is a beam which has been prestressed concentrically and so is undergoing only...
  43. S

    Bending moment for curve and straight beam

    It’s clear that bending moment for a curve beam is less than straight one And you can attribute this to moment of inertia, but there is something i don’t understand Which is if i have straight beam with small moment of inertia or huge moment of inertia simple supported beam), the moment will...
  44. parazit

    COMSOL Multiphysics : Bending -Dipole- Magnet Design

    Hi friends. I am so new with Comsol software to design something but I wonder, if it is possible to desing a bending magnet (dipole) and simulate the motions of electrons ? I really would like to do this. Please give me a hand,help me to handle and try to do one together. Best.
  45. D

    Bending of a curved beam to protect a tank nozzle

    In the tank building industry some pressure vessels use curved pieces of flat bar, welded to the tank, to protect nozzles in the event that the tank rolls. I'm trying to determine how thick the flat bar should be for a given length so that it won't bend too much and allow a nozzle to be damaged...
  46. D

    Speed of light and bending time

    First, i want to state that i am very interested in physics, but i have not done any education on this subject, except for science class, which only covered the tip of the iceberg of information we now have. Second, i want to excuse myself for possible faults in data, I'm happy if you correct...
  47. A

    MATLAB Graph Bending Moment Equation in Excel/Matlab

    how can i graph the equation of the bending moment? The equation is: σ = MC / I and i want to graph in excel or matlab, , so i know that the graph is a straight line, and i have the values, but i don't know how draw the graph
  48. B

    Bending Titanium bar using appropriate press tonnage?

    Hi I am new to this site, but would be very grateful if someone could steer me in the right direction to calculate the following: Currently within my work area I have been asked to look into Titanium forming - I am just trying to approximate how much force or press tonnage would be sufficient...
  49. S

    Determine normal stresses for pure bending moments

    Homework Statement Hi I am having tough time figuring out how to determine normal stresses σx, σy, σz using the flexure formula. All that confuses me is which moment to take for which σ. My for σx or Mz for σx and so on.. I will post an example question. In the question below, find the...
  50. W

    Finding Magnetic Field for Bending Magnet - Help

    Hey everyone. I'm new here, but I figured I would jump right in. First of all, if this forum is anything like the forum I regularly participate in, then if this thread is in the wrong section, go ahead and move it to where it belongs, mods! I am a young (very young) researcher at FermiLab...
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