SFD & BMD of beam with point force through distributed load

[miller123]

Hi Guys,
I'm having real difficulty trying to understand shear force and bending moment diagrams - both cantilever beams and supported ones like below. I've given it my best shot to solve the reactions at the points and would greatly appreciate any help on how to form the diagram and the equations after using method of sections.
Thanks

Homework Statement

Create SFD and BFD of following beam.

Homework Equations

Fy=0
Fx=0
M=0

The Attempt at a Solution

Ma=0
-Rb(6) +30(4.5)+[(10x4.5)/3.75]-20=0
Rb=21.2kN

Mb=0
(30)(1.5)+[(10X4.5)/2.25]-20-6Ra=0
Ra=7.5kN

http://imageshack.us/photo/my-images/710/unledosv.jpg/

 

[miller123]

Heres my attempt at using method of sections to write the equations:
I
0<x<a
v=-7.5kN
m=-20kNM

II
0<x<0
v=-7.5kN + 10x
m=-20kNm + (10x^2)/2

III
v=-7.5 kN + 10x + 30kN - 21.2kN
m=-20kN + (10x^2)/2 + 30kN.x -21.2kN(6)

As you can probably tell I'm struggling pretty bad on this lol. Any help is appreciated!

 

[SteamKing]

You have not written the correct equilibrium equations for this beam. The sum of the forces must equal zero, and the sum of the moments, taken about a single reference point, also must equal zero. You have written moment equations about two different points. The expression for the moment of the distributed load is also incorrect. Until you calculate the reactions, you will not be able to construct the SF and BM diagrams for this beam.

 

[miller123]

oh ok thanks. so you're not meant to take the moment of the two points? An example i saw did it that way i think so i thought i'd give it a go. oh well, back to the drawing board!

ps. you calculate the moment of the distributed load by multiplying the magnitude by its length and then placing a point force at the middle of the distributed load, don't you? Sorry I'm struggling big time

 

[DeeNos]

Hi there,

I can understand your difficulty in understanding shear force and bending moment diagrams. These diagrams are crucial in analyzing the behavior of beams under different loading conditions. Let me try to provide some guidance on how to approach this problem.

Firstly, it is important to understand the concept of shear force and bending moment. Shear force is the internal force that acts perpendicular to the longitudinal axis of the beam and causes it to shear or slide. Bending moment is the internal force that causes the beam to bend or deform.

To create the SFD and BMD, you need to follow a few steps:

1. Draw the free body diagram of the beam and identify all the external forces acting on it. In this case, we have a point force of 30kN and a distributed load of 10kN/m.

2. Calculate the reactions at the support points using the equations of equilibrium (Fx=0, Fy=0, and M=0). You have already done this in your attempt at a solution.

3. Choose a section on the beam where you want to draw the SFD and BMD. This section should be at a point where the loading changes (i.e. where there is a point force or a change in the distributed load).

4. Draw the SFD by starting from one end of the beam and moving towards the chosen section. The SFD will change whenever there is a point force or a change in the distributed load. At these points, the SFD will have a step or a jump, depending on the direction of the force.

5. After drawing the SFD, you can draw the BMD by starting from the same end of the beam and moving towards the chosen section. The BMD will change whenever there is a point force or a change in the distributed load. At these points, the BMD will have a discontinuity or a slope change, depending on the direction of the force.

6. To calculate the values of the SFD and BMD at any point, you can use the equations of equilibrium. For example, to calculate the value of the SFD at point A, you can take a section just before point A and apply the equation Fy=0. This will give you the value of the SFD at point A.

I hope this helps you in understanding how to create SFD and BMD. It may take some practice to get the hang of it, but once you understand the concept