Calculate Max Bending Moment for 10m Beam ABCD

[matthew_hanco]

Homework Statement

The beam ABCD in question is 10m long with supports at A and C. At B there is a 50KN point load and another 20Kn point load at D. The is a uniform load between A and c of 30KN/m.
A is 8m from C, A is also 2m from b and d is 2m from c.

I need to find the max bending moment but i also need a step by step guide on how to work it out?

I roughly know it should be around 280.

The reactions at A and C are 152.5 and 157.5 respectively.

If possible could you show me how to calculate the distance from support A that the max bending moment would occur?

I also need the point of contraflexure and the postion relative to A as well?

Homework Equations

The Attempt at a Solution

I have made numerous attempts but get know where near the answer i know it should be.

Thanks for the help.

 

[SteamKing]

Step 1: Draw a diagram of your beam, including the given loads, and show the location of points A B C D, using dimensions as necessary.

Step 2: Can you find the reactions at A and C using the equations of statics?

 

[matthew_hanco]

Ive drawn the beam and worked out the reactions, where do i go from there to calculate the max bending moment?

 

[matthew_hanco]

Is the max bending moment equal to the of moment about D i.e.

2x V2 -40 +m = 0

where V2 is the reaction at C i.e. 2 x 157.5

Giving me 275.

Is this correct?

 

[SteamKing]

No. Now that you have calculated your reactions, work out what the shear force diagram looks like along the length of the beam. And I calculate a different reaction at C. Please show your work for calculating the reactions.

 

[matthew_hanco]

reaction at C

8x V2 -(30x8x4) - 50x2 -20x10=0

8V2 = 1260
V2 = 157.5

Reaction at A

8V1 - (30x8x4) -50x6 +2 x 20
8V1= 1220

V1 = 152.5

Is that not right?

 

[SteamKing]

Your Reactions check out.
Now that you have the beam statically determined, you should start at A and construct the shear force diagram for the beam. This diagram will be 0 starting at A and should come back to 0 at D after accounting for all loads and reactions.

Once you have constructed the shear force diagram, the bending moment diagram for the beam can be constructed by calculating the area under the shear force diagram. Like the shear force diagram, the bending moment diagram will be 0 starting at A and it should also be 0 when you have reached D.

The shear and bending moment for this beam will be 0 at the ends of the beam. Why?