Have i done this right? Simply Supported Beams

[Vancurt]

ƩƩ

Homework Statement

I am having issues finding Ra and Rb using the Sum of the momemnts, it's ƩMCW = MACW.

I need to find the position of the maximum and minimum bending moments.

The Supported beams in question is 3.5m long. Starting from the left and moving towards the right: 1m in and then a 2KN load, then 1.5m further in and then another load of 3KN hits down and then an extra 1m when it meets the end.

Like this: 1m, 2KN, 1.5m, 3KN, 1m.
Ra Rb

Looking at my notes for some example i did (didn't finish the notes, must of forgot and now paying the price), example i did:

3m, 4KN, 4m, 3KN.
Ra Rb

And here are the notes:

ƩMCW = MACW

(4x3) + (3X7) = Rb x 12

12 + 21 =Rb x 12

33/12 = Rb =2.75KN

ƩFup = ƩFdown

Ra + Rb = 4+3

Ra + 2.75 = 7

Ra = 7 - 2.75

Ra = 4.25KN

In the Engineering book i brought: Engineering Science by Mike Tooley and Lloyd Dingle, there is a beam example:

2m, 20KN, 3m, 5KN, 2m, 30KN, 2m, 15KN.
Ra Rb

He did this: 2x20 + 5x5 + 7x30 + 9x15 = 8xRb

Using this example and my own, i attempted to answer the question to find Ra and Rb. The very first and poorly drawn supported beam at the top.

Homework Equations

Direct Stress σ = F/A = Force/Area n/m squared

Sheer stress ζ = F/A = Force/Area n/m squared

Strain ε = Δ x L/L = Change in length/Original length.

Modulus of elasticity E = σ/ε = stress/strain N/M squared.

The Attempt at a Solution

Here is my attempt at the very first diagram (the 3.5 over all length)

(2x1) + (2.5x3) = 9.5

Rb x 3.5 = 9.5 x 3.5 = 33.25

2+7 = Rb x 3.5

9.5/3.5 = 2.71KN

Rb = 2.71KN

ƩFup = ƩFdown

Ra + Rb = 2 + 3 = 5

Ra + 2.71 = 5 - 2.71 = 2.5 KN

Ra = 2.5KN

So Rb = 2.71 KN and Ra = 2.5KN

What i don't undertand is on my previous attempt, Ra = 2.286 KN and Rb = 2.714KN

Where have i gone wrong? And what do i need to do after finding Ra and Rb?

 

[Vancurt]

Found Ra. How did i miss that.

My first notes were correct. Rb = 2.714kn and Ra = 2.286kn

I did the calculations wrong.

 

[Vancurt]

Ok, i need help, how do i plot the sheer force diagram?

I did a rough example:

+

+2.28 for 1m then with the 2KN i come down to .28 for 2.5m and with the 3KN i come down to -2.72 for 3.5m and then back up to 0 inbetween the plus and minus.
-

Is this rough version ok?

 

[pongo38]

You can always check your own reactions by taking moments about ANY point you haven't used to get the initial result. Your SFD seems ok to me, But people use various sign conventions.

 

[rezeew]

As a scientist, it is important to double check your calculations and make sure that your approach is correct. It seems like you have made some errors in your calculations, resulting in different values for Ra and Rb in your previous attempt.

To find Ra and Rb, you can use the equations ƩMCW = MACW and ƩFup = ƩFdown. Make sure that you are considering all the forces and moments acting on the beam and using the correct sign conventions.

Once you have found the values for Ra and Rb, you can use them to determine the position of the maximum and minimum bending moments. This can be done by setting up an equation for the bending moment at a specific point on the beam and solving for that point. Alternatively, you can draw a shear and moment diagram to visualize the distribution of bending moments along the beam.

If you are still having trouble, it might be helpful to review some examples in your textbook or seek assistance from a tutor or classmate. Remember to always double check your work and make sure your approach is correct before moving on to the next step. Good luck!