Aerstz said:
That's the problem; I am unable to follow the steps in the examples. The steps are too big; I need smaller steps to bridge the gaps.
To me, the examples seem to go from A straight to Z in one giant leap. I need to know B,C,D...etc., in between. Currently I am completely blind to what these intermediate steps are.
For example, and as I asked above in the first post: Why does A = - (wL^3)/24? What I mean to ask is, how was the (wL^3)/24 arrived at? I am extremely challenged with this 'simple' mathematics and I really need a kind soul to guide me through it very gently and slowly!
I hear you. Looking at part of the first problem, step by step, inch by inch:
1. EI(y) = wLx^3/12 -wx^4/24 + Ax + B
Now since at the left end, at x = 0, we know there is no deflection at that point; thus, y = 0 when x =0, so substitute these zero values into Step 1 to obtain
2. 0 = 0 - 0 + 0 + B, which yields
3. B = 0, thus Eq. 1 becomes
4. EI(y) = wLx^3/12 - wx^4/24 + Ax
Now since at the right end, at x = L, we also know that y = 0 , substitute X=L and y=0 into Eq. 4 to yield
5. 0 = wL(L^3)/12 - wL^4/24 + AL or
6. 0 = w(L^4)/12 - wL^4/24 + AL .
Now since the first term in Eq. 6 above, wL^4/12, can be rewritten as 2wL^4/24, then
7. 0 = (2wL^4/24 - wL^4/24) +AL, or
8. 0 = wL^4/24 + AL. Now divide both sides of the equation by L, and thus
9. 0 = wL^3/24 + A = 0,
and now solve for A by subtracting (wL^3/24) from both sides of the equation to get
10. 0 -wL^3/24 = (wL^3/24 -wL^3/24) + A, or
11. -wL^3/24 = 0 + A
12.
A = -wL^3/24
