What is Bending moment: Definition and 202 Discussions

In solid mechanics, a bending moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend. The most common or simplest structural element subjected to bending moments is the beam. The diagram shows a beam which is simply supported (free to rotate and therefore lacking bending moments) at both ends; the ends can only react to the shear loads. Other beams can have both ends fixed; therefore each end support has both bending moments and shear reaction loads. Beams can also have one end fixed and one end simply supported. The simplest type of beam is the cantilever, which is fixed at one end and is free at the other end (neither simple or fixed). In reality, beam supports are usually neither absolutely fixed nor absolutely rotating freely.
The internal reaction loads in a cross-section of the structural element can be resolved into a resultant force and a resultant couple. For equilibrium, the moment created by external forces (and external moments) must be balanced by the couple induced by the internal loads. The resultant internal couple is called the bending moment while the resultant internal force is called the shear force (if it is transverse to the plane of element) or the normal force (if it is along the plane of the element).
The bending moment at a section through a structural element may be defined as the sum of the moments about that section of all external forces acting to one side of that section. The forces and moments on either side of the section must be equal in order to counteract each other and maintain a state of equilibrium so the same bending moment will result from summing the moments, regardless of which side of the section is selected. If clockwise bending moments are taken as negative, then a negative bending moment within an element will cause "hogging", and a positive moment will cause "sagging". It is therefore clear that a point of zero bending moment within a beam is a point of contraflexure—that is, the point of transition from hogging to sagging or vice versa.
Moments and torques are measured as a force multiplied by a distance so they have as unit newton-metres (N·m), or pound-foot (lbf·ft). The concept of bending moment is very important in engineering (particularly in civil and mechanical engineering) and physics.

View More On Wikipedia.org
1. Engineering Distance is a problem -- find shear force and bending moment diagram

This is our sample problem find shear force and bending moment diagram after calculations supports reactions and drawing shear force diagram we have a problem ..... Distance between F to O

Left side is fixed and right side is held together by a non deformable plate. There are two members with space inbetween. My question is when i want to calculate the stress due to bending moment at point A, which is shown in the crossection, where is the neutral axis? Is it at the middle of the...
3. I Calculating Combined Loading Stress: Neutral Axis and Bending Moment at Point A

Left side is fixed and right side is held together by a non deformable plate. There are two members with space inbetween. My question is when i want to calculate the stress due to bending moment at point A, which is shown in the crossection, where is the neutral axis? Is it at the middle of the...
4. What is bending moment? Is it a moment couple? Why?

In engineering statics I've learned the concept of bending moment, which in some way indicates an applied load that tends to bend the object, and it seems that it can move around freely in the reference frame. (I understand moment in engineering is not quite the same concept as torque in physics...
5. Loader Boom maximum bending moment

TL;DR Summary: Finding maximum bending moment on a boom I am trying to solve the problem stated in the picture below. The answers are given. I've manage to find the Normal and Shear Forces but I'm stuck at the bending moment. According to my analysis the maximum bending moment is +7208,1...
6. Maximum bending moment and maximum deflection of the spring?

How can I find the maximum bending moment and maximum deflection for a spring? It would be very helpful if you could explain the specific procedure and formula in an easy-to-understand manner. that's all, thank you very much.
7. Why do I have a bending moment and an axial displacement here?

Hello, I have an flexure where the force is applied asymmetrical, I just can't visualize why their should be a bending moment instead of an bending force? How can I distinguish those? Thanks!
8. Stuck on complex pipe system bending moment hand calcs

Some more details on the system are that L1 is very long (close to 100ft) and L2 is close to 30ft (the vertical pipes). The piping is all schedule 40 1/2" OD. Moment of inertia is roughly 10^-8. Components are about 2kg each. The distance of the pipes horizontally is small (around 2ft). Pressure...
9. Engineering Solving Stresses in Beams: Reactions at B & F

To determine the reactions at B and F, I don't know how to handle that L-shaped beam connected to the horizontal beam. My attempt is: $$\sum F_{y} \colon\;\;\; -200 + R_{B} - 75 + 32 + R_{F} - 1632 = 0$$ from which it follows that ##R_{B} + R_{F} = 1875##. \sum M_{B} \colon\;\;\; -5 \times...
10. Bending Moment for Bending Diagram

Hi Im a bit confused with the example Can somebody explain and show to me how they got the bending moment calculations for the diagram in the attached. i understand it up to there. I started course late and can't ask for help. Thanks
11. Sign convention of internal forces in vertical bars for bending moment

Hello: I was looking for a widespread convention (akin to Hibbeler's, Beer's, etc) that deals with the sign convention of a vertical bar for bending moments. For example, without knowing in advance, how do I draw the bending moment at a cut passing through point E in the figure attached? Beam...
12. Engineering Question about plotting a Bending Moment Diagram

I am confused why positive value of bending moment is plotted under the axis?
13. Engineering Cantilever and encastré beams: bending moment and shear force

I have to discuss the Bending moment and shear forces in cantilever and encastré beams. Does anybody know of good websites showing that is simple to understand showing. All i can find is how to calculate and bending moments and shear force digrams which don't really understand. Can...
14. Plate - bending moment equation

Hi, I'm trying to solve an exemplary case of a cantilever plate (one long edge fixed, all other edges free) subjected to pressure. I've already calculated this using approximation to beam of unit width and the results are good but I would like to use another method too. In a polish book I've...
15. Understanding Bending Moment Calculations in Mechanical Systems

But the correct solution is M= P* (b2+b1). I don't understand how b2+b1 is the perpendicular distance.

17. 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...
18. 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...
19. 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...

21. 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...
22. 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...
23. Deformation under eccentric shear stress

Hi, Starting with an example to clarify what I am looking for. Assume an extension force applied on a distance from the centroid/neutral axis of a body: see attached, please. As result, bending force besides the tensile force will be generated in that body as presented in section A-A in the...
24. 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...
25. 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...
26. 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) +...
27. 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...
28. 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...

Homework Statement The problem asks to find out whether the rod yields at points in section A according to the tresca and von mises criteria P is 120N Homework Equations Shear stress= VQ/It Stress= Mx/I shear stress= Tp/J The Attempt at a Solution I picked 2 points at section A. The...
30. 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...
31. 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...
32. 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...
33. 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...
34. 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...
35. 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...
36. G

Calculating Forces on an L-Bracket for Supporting Large Pipework

I am installing an L-shaped bracket into a brickwork chimney to support some large pipework. I am trying to work out the forces in each fixing to ensure that I won't be pulling the bracket off the wall once the pipes are filled with water. I've tried drawing the free body diagram and to resolve...
37. 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...
38. Determine the highest tension stress and the highest compression stress

Homework Statement Determine the highest tension stress and the highest compression stress along the top edge of the intel. Homework Equations stressx = Mx*y / Ix Ztop = Ix / ytop stress (max top) = Mx - Ztop The Attempt at a Solution
39. 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...
40. 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...
41. 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...
42. 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]

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...
44. 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...
45. 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...
46. 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...
47. 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...
48. 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
49. Calculating Shear Force and Bending Moment

hi all Basically I need to find the shear force and bending moment of a beam using octave. The length of the beam as well as forces and their distances are given. However the SF and BM must be calculated at every o.ooo5m. The forces can be Point Loads or Uniform Distributed Loads and there can...
50. Understanding Bending Moment Diagrams for Multiple Planes

can someone explain why this problem would involve two bending moment diagrams, one for the xy plane and another for the xz plane? Also, how are the reaction forces at B and C determined each time?