Max Moment of resistance of a simply supported beam

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Discussion Overview

The discussion revolves around calculating the maximum moment of resistance for a simply supported beam subjected to a uniformly distributed load and a point load. Participants are addressing confusion between maximum bending moment and maximum moment of resistance, as well as the correct application of moment equations.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant expresses confusion between maximum bending moment and maximum moment of resistance, seeking clarification.
  • Another participant points out that the moment equations were written incorrectly, suggesting that the reaction at the right end of the beam should be greater due to the position of the point load.
  • A question is raised about whether bending moments should be calculated from the reference point to each acting force.
  • Participants discuss the correct formulation of moment equations, noting that the right-hand side of the equation should reference the correct reaction force.
  • There is a suggestion that correcting the moment equations would affect the calculation of the maximum moment of resistance.
  • One participant mentions that the maximum moment occurs at the point load, questioning the relationship between the shear curve and the maximum moment location.

Areas of Agreement / Disagreement

Participants are engaged in a technical discussion with some agreement on the need to correctly apply moment equations. However, there is no consensus on the implications of the corrections for the maximum moment of resistance, and the discussion remains unresolved regarding the final calculations.

Contextual Notes

There are limitations in the discussion regarding the assumptions made in the moment equations and the dependency on the correct identification of reaction forces. The scope of the problem is also restricted to the specific loading conditions described.

Michael V
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Homework Statement



A beam carries a uniformly distributed load, including its own weight, of 8 kN/m over its full length of 6 m. A point load of 300 kN is placed 2 metres from the one end of the beam which is simply supported.

Calculate the maximum moment of resistance for the beam if it occurs at the point load.

I'm getting confused with max bending moment and max moment of resistance, please my answer attached.
 

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Your moment equations are written backwards.

If you use the left end of the beam as your moment reference, you will find the reaction at the right end of the beam.

The reaction at RL should be greater than RR, since the point load is closer to the left end.
 
So for each bending moment, I must take the distance from the reference point to each acting force?
 
Well, yeah.

In your first moment equation, you wrote:

300 k * 2 + (8k * 6 * (6/2)) = RL * 6

The LHS is fine, but you are using the left end of the beam as the reference point. The RHS of the equation should be RR * 6, as RR, not RL, is located 6 meters from the left end.
 
Yeah, I see the mistake now. So that would also change the max moment of resistance then?
 
Once you have the beam statically determined, then you construct the shear curve. From the shear curve, you can construct the bending moment curve and find the maximum moment.
 
In the question they said that it occurs at the point load so isn't that where your shear curve (shear force diagram) cuts the axis?
 
yes.
 
So is this correct now?
 

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