Solving a Bending Moment Question: R1 = 110kN & R2 = 141kN

[oli543]

Hi, I've got a little problem with a bending moment question.

Here it is (really sorry for the bad diagram!)

http://img474.imageshack.us/img474/7844/help15eu.jpg"

R1 and R2 are reactional forces, which using moments I have calcualted to be:

R1=110kN
R2=141kN

Section A of the beam is a mild steel beam, section B can be presumed to have infinite strength (i.e. all of the bending is taken by section A).

The value of 1000 x 9.81 is the weight of section A, do I take this into account in the bending moment diagrams?

How do I go about drawing the diagram for this, here are two possibilities:

http://img469.imageshack.us/img469/4135/help25cc.jpg"

In (b), I have said that section B can be treated as a wall, with a moment produced by the forces to the left of the wall.

I need to calculate the maximum bending stress in section A.

Any help would be amazing!

Hope I've made any sense, if you need any more info, just ask.

Thanks a lot, Oli.

 

[batman394]

so in the first part. up until the length of B ends. it will be a flat line at 0 on the bending moment diagram. it pretty much doesn't exist for all our purposes... i did double check your reaction forces and those are fine.

first you need to draw the sheer force diagram. i like option b since we are treating the section B like a wall. so we start with a 0 up until that point where B ends. then at 1.1m from the left.. youll have a force. since it is a wall. there will be a reaction sheer and moment force.. youll have to calculate those.. just pretend B doesn't exist and A is attached to a wall.. those are simple calculations.. then go through and map out the forces that go up/down like the reaction Y from the wall, 100*9.81, R2 and R1.. you SHOULD end up at 0 at the end of the beam. then just go through and calculate the area under the curve for each section of the Sheer diagram and thatll give you a moment diagram.. and the highest moment force you get throughout the beam. that's the force you use for the maximum bending stress calculations.

if that doesn't make sense send me a PM and ill show you more in depth

 

[piercas]

Dear Oli,

Thank you for reaching out with your question about bending moment. It seems like you have already made some progress in your analysis by calculating R1 and R2 using moments. Great job!

To answer your first question, yes, you should definitely take into account the weight of section A (1000 x 9.81) in your bending moment diagrams. The weight of the beam will create a bending moment that needs to be accounted for in your calculations.

As for drawing the diagram, both of your possibilities seem correct. In option (a), you are showing the weight of the beam as a distributed load, while in option (b) you are treating section B as a fixed wall. Both approaches are valid and will give you the same result.

To calculate the maximum bending stress in section A, you will need to use the bending moment equation: M = σ * I / y, where M is the bending moment, σ is the bending stress, I is the moment of inertia of the beam cross-section, and y is the distance from the neutral axis to the point where you want to calculate the stress.

Since you have already calculated the bending moment (using R1 and R2), you can rearrange the equation to solve for σ. Make sure to use the moment of inertia of section A, since that is the section experiencing the bending stress.

I hope this helps and good luck with your analysis! Let me know if you have any further questions.