Shear Force and Bending Moment Diagram

[jasonbot]

Homework Statement

I have to find the Shear Force and Bending Moment diagrams for this problem. The lengths in the picture are 1.2m each and the peak force is 4kN/m and I calculated the support reactions to be:

Ay=4,8kN (up)
Ma= 5.76kN.m (anticlockwise)

Homework Equations

These are what I'm looking for but failed to do...

The Attempt at a Solution

I first section the beam 0<x<4

Efy=0

+4.8 -.5x*3.33x-Vx=0

I got the 3.33x by using similar triangles; if triangle 1 is (1,2;4) then sectioned triangle should be (x;y) so therefore 4/1.2=y/x x=3.33xthis gave me Vx=-1.67x^3+4.8 which is wrong.

Then EMo=0

+Mx +.5x*3.33x*(x/3) -4.8x +5.76=0

which gets me Mx=-0.56x^3 +4.8x +5.76The correct answers for this question are:

Vx=4.8 -(x^3/6)
Mx=4.8x -(x^3/18) -5.76I have a feeling I'm not using the triangle force correctly. Please advise.

 

[PhanthomJay]

jasonbot, welcome to PF!

Homework Statement

I have to find the Shear Force and Bending Moment diagrams for this problem. The lengths in the picture are 1.2m each

Is it 12 m or 1.2 m?

and the peak force is 4kN/m and I calculated the support reactions to be:

Ay=4,8kN (up)
Ma= 5.76kN.m (anticlockwise)

yes, looks good

I first section the beam 0<x<4

0<x<12 m

Efy=0

+4.8 -.5x*3.33x-Vx=0

I got the 3.33x by using similar triangles; if triangle 1 is (1,2;4) then sectioned triangle should be (x;y) so therefore 4/1.2=y/x x=3.33x


this gave me Vx=-1.67x^3+4.8 which is wrong.

if you correct the 1.2 m to 12m , then Vx = -.167x^2 +4.8

Then EMo=0

+Mx +.5x*3.33x*(x/3) -4.8x +5.76=0

which gets me Mx=-0.56x^3 +4.8x +5.76

something is afoul between 1.2 m and 12 m, the decimal point is messed.., but you are still not quite right, don't let the plus and minus signs wear you down...

`
The correct answers for this question are:

Vx=4.8 -(x^2/6)

typo error

Mx=4.8x -(x^3/18) -5.76

taking clockwise moments as plus, I don't know about that decimal point, however

I have a feeling I'm not using the triangle force correctly. Please advise.

Looks like you did well, but check out your plus and minus signs, they'll bite you every time...

 

[Mene]

I would first like to commend you on your attempt at solving this problem. It is clear that you have a good understanding of the basic principles involved in finding the Shear Force and Bending Moment diagrams for a beam.

However, I would suggest that you take a step back and review your approach. It seems that you are using the method of sections to find the Shear Force and Bending Moment at a particular point on the beam. While this method can be effective in some cases, it may not be the best approach for this problem.

Instead, I would recommend using the equations for Shear Force and Bending Moment at a point on a beam in terms of the applied loads and reactions. These equations can be derived from the equilibrium equations and are much simpler to use in this case. You can then use these equations to find the Shear Force and Bending Moment at any point along the beam.

In addition, it is important to carefully consider the signs of the forces and moments. In your attempt, you have not taken into account the direction of the forces and moments, which has resulted in incorrect solutions.

I hope this helps and good luck with your future calculations!