Max Moment of resistance of a simply supported beam

[Michael V]

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.

 

[SteamKing]

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.

 

[Michael V]

So for each bending moment, I must take the distance from the reference point to each acting force?

 

[SteamKing]

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.

 

[Michael V]

Yeah, I see the mistake now. So that would also change the max moment of resistance then?

 

[SteamKing]

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.

 

[Michael V]

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?

 

[SteamKing]

yes.

 

[Michael V]

So is this correct now?