Max Moment of resistance of a simply supported beam

In summary, the problem involves a beam carrying a uniformly distributed load of 8 kN/m and a point load of 300 kN at a distance of 2 meters from one end. The maximum moment of resistance for the beam occurs at the point load and can be found by constructing a shear curve and then a bending moment curve. The moment equations should be written with the reference point at the right end of the beam, as it is located 6 meters from the left end.
  • #1
Michael V
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0

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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  • #2
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.
 
  • #3
So for each bending moment, I must take the distance from the reference point to each acting force?
 
  • #4
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.
 
  • #5
Yeah, I see the mistake now. So that would also change the max moment of resistance then?
 
  • #6
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.
 
  • #7
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?
 
  • #8
yes.
 
  • #9
So is this correct now?
 

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Related to Max Moment of resistance of a simply supported beam

1. What is the "Max Moment of resistance" of a simply supported beam?

The "Max Moment of resistance" of a simply supported beam is the maximum amount of bending moment that a beam can withstand before it starts to permanently deform or fail. It is also known as the "Ultimate Moment of resistance" or "Capacity Moment".

2. How is the Max Moment of resistance calculated for a simply supported beam?

The Max Moment of resistance for a simply supported beam can be calculated using the formula M = WL/4, where M is the maximum moment, W is the load applied, and L is the length of the beam. This formula assumes a uniformly distributed load and assumes that the beam is made of a homogeneous material with a constant cross-section.

3. What factors affect the Max Moment of resistance of a simply supported beam?

The Max Moment of resistance of a simply supported beam is affected by several factors, including the material and cross-section of the beam, the type of load applied, the length of the beam, and the support conditions at each end of the beam. Other factors such as temperature, corrosion, and external forces can also affect the beam's resistance to bending.

4. How does the Max Moment of resistance relate to the safety of a simply supported beam?

The Max Moment of resistance is an important factor for determining the safety of a simply supported beam. If the applied moment exceeds the Max Moment of resistance, the beam may fail, leading to potential safety hazards. It is essential to calculate and design for a sufficient Max Moment of resistance to ensure the structural integrity and safety of the beam.

5. Can the Max Moment of resistance of a simply supported beam be increased?

Yes, the Max Moment of resistance of a simply supported beam can be increased by using stronger materials, changing the beam's cross-section, or increasing the beam's length. Proper reinforcement and bracing can also increase the beam's resistance to bending. However, it is crucial to follow engineering principles and safety standards when attempting to increase the Max Moment of resistance of a simply supported beam.

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