Linearly varying force and bending moment problem.

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ajayguhan
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I have attached both the question and my attempt at solution.

My problem is reducing the equation further to get the value of a/L
 
Attachments
  • Beam ABCD with overhanging ends a on each side and a central span L, supports at B and C, carrying a downward linearly varying distributed load of intensity q1 at the left end A and q1 at the right end D, with the load increasing from A to D; dimensions a and L labelled below.
    1411051609751.jpg
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  • Handwritten engineering solution on lined paper: a beam with a trapezoidal distributed load diagram at top left, then equations for shear at point M, q_x = q_1 + x(q_2 - q_1)/(a+L+a), and moment equations solving for R_B.
    1411051694307.jpg
    23.8 KB · Views: 481
  • Handwritten derivation on lined paper, rotated sideways, with several equations involving a1, a2, a3, a, b, L and a^2 in brackets over multiple lines, showing algebraic reduction of a bending moment expression.
    1411051731932.jpg
    26.6 KB · Views: 473
  • Handwritten algebra working on lined paper, rotated sideways, showing a series of equations with terms in a1, a2, a, L and square brackets, ending in a line with P_B x L^2 and a fraction over 6.
    1411051751432.jpg
    24.1 KB · Views: 481
Have mercy on us. Rotate your phone when you take images of your work. It's very difficult to rotate the thumbnails and get a legible image. Good luck with your problem.
 
You can rotate it easily nah ...? What's the problem in rotating the image. If my work is not legible then just say, I'll repost it better than now.
 
Sorry, I tried downloading and viewing the thumbnails attached to the OP. Things just got worse after that. I'd like to help, but not at the cost of a sore neck.