What is Bending moment diagram: Definition and 25 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.

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  1. A

    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...
  2. B

    Engineering Calculate shear force and bending moments with a UDL and a point load

    Hello, I am looking for some help. I have completed the question below. I will show my answers. My answer: I believe this to be correct. If it is not would appreciate someone letting me know so i can correct. Now i am attempting this question: Could anyone help, or point me in the...
  3. 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...
  4. 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...
  5. 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]
  6. kostoglotov

    Help with a BMD and deflection of beam problem

    Homework Statement I am given this beam: imgur link: http://i.imgur.com/tw6EEJz.jpg and asked to express the slope at A and the max deflection in terms of a, E, I, and Mo. I am being told that my answer has the wrong multiplier...so I assume that my overall approach is ok (??) but I've...
  7. 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...
  8. David Lewis

    Bending moment diagram for overhanging beam

    I've drawn the free-body diagram of an airplane wing spar. I know the magnitude and location of all forces. What is the procedure to construct the bending moment diagram?
  9. A

    Help with Bending Moment Diagram for Structure

    Homework Statement Hi I need help with drawing a bending moment diagram for this structure. All joints are rigid and it's fixed to the ground. I'm really struggling with this. I initially started with the horizontal beam (statically indeterminate) and found that the moments at the ends were...
  10. A

    Bending moment Diagram for fixed-fixed beam

    Homework Statement There is a beam, say length L, with a force F UP on the left built-in support and a CLOCKWISE moment. The right side has a force, F, DOWN and a COUNTERCLOCKWISE moment i.e F up, cw moment -------------------------------------------------------------F down, ccw moment...
  11. P

    Problem with values for a bending moment diagram

    Homework Statement I have a 5m long simply supported beam, with supports at points 0m and 5m. There's a UDL of 10kNm^-1 from 0m to 4m. It has downward forces acting at 2m (10kN) & 4m (15kN). I need to sketch a bending moment diagram to determine the position & value of the max bending...
  12. I

    What determines the starting point of a bending moment diagram?

    In the bottom left, why does the BM diagram start at -4kNm rather than 4kNm? I understand that if you make a cut you yield this result but if you don't make a cut how would you know whether it starts at -4kNm or 4kNm? Thanks
  13. F

    Shear and bending moment diagram problem

    Homework Statement I have attached a diagram Homework Equations 14 + Va -32 + Vb -15=0?? or Vb=-15? The Attempt at a Solution The reason why I cannot attempt this problem is that I'm not sure whether it is valid that there can be a point load at Support B or whether they are...
  14. M

    Shear Force and Bending Moment Diagram

    Homework Statement This is the question that I am struggling with. http://postimg.org/image/5kb0pur3z/ I need to plot shear force and bending moment diagram of it.Homework Equations The beam is in static equilibrium so algebraic sum of forces in x and y direction equal zero. Also, moment is...
  15. 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...
  16. F

    Relationship between funicular polygon and bending moment diagram

    Hello, I'm a civil engineering student. I learned how to contruct a funicular polygon and bending moment diagrams in two different subjects and I realized how close looking the two are, so I wondered if there was a good explanation to relate the two. I can feel it's kind of the same as the...
  17. S

    Calculating Re-acting Forces of 10m Beam w/ 3 Forces & Bending Moment Diagram

    Question : A beam 10 meters long, with 3 forces acting on it and 2 re-acting forces on it to keep it in equilibrium. The re-acting forces are at 2 meters from either end. The forces onto the beam are at 3 meters from the left end of 10kN, 10 meters from the left end of 20KN and a distributed...
  18. S

    Calculating Bending Moment of Pinned Beam: Is it Negative?

    I have just calculated the bending moment of a beam for every metre over a 10 metre length, the beam is pinned at both ends. Is it possible for the full diagram to be Negative?
  19. S

    Calculating Fixed End Moments with Uneven Beam Heights?

    Ok, so I have a problem as follows: A beam is simply supported at joints A, B, C D and E. there is a UDL acting on the BC member The member is 6m long with a UDL of 60kn/m However the tricky part is that this member is 1.2 times higher than the height of the members AB, CD, and DE. So BC =...
  20. L

    Shear force and bending moment diagram

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  21. K

    Statics- Bending Moment Diagram

    I'm trying to construct a bending moment diagram for the situation as below: [PLAIN]http://img42.imageshack.us/img42/633/bmdiag.jpg Where Ra and Rb are reaction forces, L1 and L2 are lengths between Ra and N and N and Rb respectively, N is a force acting perpendicular to the beam and P is...
  22. J

    Shear Force and Bending Moment Diagram

    Homework Statement I have to find the Shear Force and Bending Moment diagrams for this problem. The lengths in the picture are 1.2m each and the peak force is 4kN/m and I calculated the support reactions to be: Ay=4,8kN (up) Ma= 5.76kN.m (anticlockwise) Homework Equations These are what I'm...
  23. N

    Solve Bending Moment Diagram Problem: A=397.8kN, B=367.4kN, UDL=748.2kN

    i have the following problem and i have worked out the resultant forces that say A=397.8kN while B is 367.4 kN and the force of the UDL is 748.2kN. i have worked out the shear force diagram but am lost as to how to draw the bending moment for this problem any help would be appreicated. thank you
  24. V

    Shear Force and bending moment diagram

    Hi guys, For a Engineering Project, we will be suspending a bridge using a cantilever system. We have to draw the shear force diagram (SFD) and bending moment diagram (BMD) for the horizontal and vertical members. The arrows on the diagram represent the loading from the bridge itself. I...