ƩƩ(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant 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.

3. 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?

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# Homework Help: Have i done this right? Simply Supported Beams

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