Help with Bending Moment Diagram for Structure

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Discussion Overview

The discussion revolves around the challenges of drawing a bending moment diagram for a statically indeterminate structure with rigid joints fixed to the ground. Participants explore various methods and equations related to bending moments in beams, particularly focusing on the application of specific formulas and the implications of beam stiffness.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses difficulty in drawing the bending moment diagram and initially calculates moments at the ends of a horizontal beam as FL/8, but doubts the correctness of this result.
  • Another participant questions the completeness of the equation provided and requests clarification on how the FL/8 result was derived.
  • A different participant asserts that for a fixed-fixed beam, the bending moments are indeed FL/8, but challenges the application of this result to the current structure.
  • Another participant points out that the beam is not fixed-fixed and suggests that the equation presented is not quite correct.
  • One participant mentions a lack of knowledge about stiffness matrices and indicates that all beams are of equal length.
  • Another participant explains that the bending moment is influenced by the stiffness of the members in a statically indeterminate frame and suggests using either the stiffness method or moment distribution method.
  • A participant reiterates their reliance on the equation EI * d2v/dx2 = -M for a single statically indeterminate beam and expresses uncertainty about how to approach the current problem.
  • One participant proposes simplifying the problem using symmetry and suggests deriving equations based on two degrees of freedom, while also asking about specific formulas related to different beam conditions.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct approach to drawing the bending moment diagram, with multiple competing views on the applicability of the FL/8 result and the methods to be used for analysis.

Contextual Notes

There are unresolved assumptions regarding the structure's configuration and the applicability of certain formulas. The discussion highlights dependencies on definitions of beam types and stiffness, as well as the complexity of the problem at hand.

axe34
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Homework Statement


upload_2015-3-16_19-6-8.png

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 FL/8 (ccw on left, and cw on right) and that F/2 was applied up at each end of the beam. However, this is not the correct answer! Also this answer doesn't give the correct answer for the vertical beams. I really don't know how to do this.

Homework Equations


d2v/ dx2 = -M (helps with statically indeterminate beams but this is not the only way to deal with them but I like this method and this is how I calculated the FL/8's)

The Attempt at a Solution


as above
 
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Your equation isn't complete.

Can you show your work on how you derived FL/8?
 
Hi

For a fixed-fixed beam only, there are BMs of FL/8 - this is a standard result. It would take pages + pages to show this, but it starts from the fact that d2v/dx2 = -M. Fl/8 isn't correct here in this structure.
 
You are right the beam is not fixed-fixed but your equation is not quite correct.

Do you know the stiffness matrix for a beam element?
 
Hi
I know nothing about stiffness etc. - only each beam is L length and the same as the others.
 
Generally the bending moment will be a function of the members' stiffness for a statically indeterminate frame. If all the members have the same stiffness (EI) then the term simply cancels out.

So you can use this method or you could do a moment distribution method. Have you studied either of these methods?
 
Hi
The only method I've ever used for 1 statically indeterminate beam is to do EI * d2v/dx2 = -M. I just don't know where to start on this one. If I was given one horizontal beam, fixed at both ends, then using this method I'd get moments of F*L /8 at the ends
 
OK, this will be a long process starting from such a basic formula.

The first step I would recommend is to simplify the problem using the symmetry of the frame and leave just two degrees of freedom.

The 2nd step I would recommend is to derive two equations from these two degrees of freedom.

Do you happen to know any formulae that cover the following conditions:

1) for beam fixed-pinned with a moment M at the pinned end - formula for dv/dx at pinned end?
2) for beam fixed-fixed with a displacement v at one end - formula for M at ends?
 

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