Bending Moment and Force calculations two beams connected

[olski1]

Hello,

I need to find the bending moment and forces at the mid point cross-sections of two separate beams connected together. One is a horizontal beam connected to the top of a vertical beam that sort of look like this:

H========
H
H
H
H

There is a UDL of 10kn/m on the top member, with the bottom of the vertical beam is fixed to the ground.

I need to find the bending moment and Forces at the midpoint cross-section of both beams separately. How would I go about doing this?

So far in my course we have only dealt with single beams that are simply supported.

My first attempt at this question was to treat them as two separate beams and firstly find the reaction bending moment at the joining of the two beams using the udl. Then I would take that moment as a acting on the end of the vertical beam and work my way from there. Does that moment act at the very tip of the upright beam or half the width down of the horizontal beam?

But honestly I am quite confused with this one... any help on the method (not answer) would be greatly appreciated :)

 

[PhanthomJay]

Hello,

I need to find the bending moment and forces at the mid point cross-sections of two separate beams connected together. One is a horizontal beam connected to the top of a vertical beam that sort of look like this:

H========
H
H
H
H

There is a UDL of 10kn/m on the top member, with the bottom of the vertical beam is fixed to the ground.

I need to find the bending moment and Forces at the midpoint cross-section of both beams separately. How would I go about doing this?

So far in my course we have only dealt with single beams that are simply supported.

I assume you have also dealt with beams fixed at one support?

My first attempt at this question was to treat them as two separate beams and firstly find the reaction bending moment at the joining of the two beams using the udl.

you can do it this way, but don't forget the reaction force at that joint as well.

Then I would take that moment

..and force...

as a acting on the end of the vertical beam and work my way from there. Does that moment act at the very tip of the upright beam or half the width down of the horizontal beam?

For the purposes of this problem, you can use the beam centerlines for the analysis.

But honestly I am quite confused with this one... any help on the method (not answer) would be greatly appreciated :)

You should note that it it is not necessary to separate the beams when solving for the forces in the vertical beam. You can take a free body diagram at the mid point of the horiz beam to get it's internal moment and force at that point, and you can take a FBD at the midpoint of the vertical beam to get its internal force and moment

 

[olski1]

Okay thanks for your help,

For the top member which is 1m long I found:

ƩF_y=0=-10kN + R_AY => R_AY=10KN

ƩM_o=5<x>² + M_A => M_A= -5<x>²

when x = 1 => M_A=-5kNm

At the mid point section,

F=-5kN and M=-1.25KN

For the Vertical Memeber which is also 1 m long.

ƩF_x=0=-10kN + R_Bx => R_Bx=10KN

ƩM_o=-M_A + M_o => M_o= -5kNm

hence at x=0.5, M=-5knm and F=-10kN.

Just to check I ran this through F.E.A with a beam with cross section 80mm high and 40mm wide, which is the dimensions given in the problem. But I am getting slightly different results.

For example, the top member moment is 1.133kNm and the Force is 4.733kN compared to 1.25kNm and 5kN.

Why are they different? where did I go wrong?

 

[PhanthomJay]

You didn't go wrong, your calculation was excellent. When you do the computer analysis, the solution is dependent on the end connections...for example, whether the top beam frames into the vertical beam onto its top, or onto its side, will yield slightly different results, depending on how you input the member properties and lengths into the computer, and how you modeled the joint. Heck, the solution is only accurate to 1 significant figure anyway.

 

[DeeNos]

Hello,

First of all, it is important to note that when two beams are connected, they act as a single structural element and the forces and moments are distributed between them. In order to find the bending moment and forces at the midpoint cross-sections of both beams, you will need to use the principles of statics and structural analysis.

To start, you can treat the horizontal and vertical beams as separate beams and analyze them individually. This will allow you to find the reaction forces and moments at the connection point between the two beams. These forces and moments will then be distributed to each beam based on their relative stiffness.

To find the bending moment at the midpoint cross-section of each beam, you will need to use the equations for bending moment and shear force. These equations take into account the applied loads, support conditions, and the geometry of the beam. You can also use the principle of superposition to find the bending moment at any point along the beam.

As for the forces, you can use the equations for equilibrium to find the forces at the midpoint cross-section of each beam. These equations take into account the applied loads, the support conditions, and the geometry of the beam.

In order to accurately determine the bending moment and forces at the midpoint cross-sections, it is important to consider the type of connections between the beams. In your case, the bottom of the vertical beam is fixed to the ground, which means it is fully fixed and cannot rotate. This will have an effect on the distribution of forces and moments between the two beams.

In summary, to find the bending moment and forces at the midpoint cross-sections of two connected beams, you will need to analyze each beam individually and then distribute the forces and moments based on their relative stiffness. It is also important to consider the type of connections between the beams in order to accurately determine the forces and moments. I hope this helps guide you in your analysis.