Beam Deflection In Exercises 61 and 62, forces w1, w2, and w3 (in pounds) act on a

Chapter 2, Problem 62

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Exercises 61 and 62, forces \(w_{1}, w_{2},\) and \(w_{3}\) (in pounds) act on a simply supported elastic beam, resulting in deflections \(d_{1}, d_{2}\), and \(d_{3}\) (in inches) in the beam (see figure).

Use the matrix equation d = Fw, where

\(\mathbf{d}=\left[\begin{array}{l} d_{1} \\ d_{2} \\ d_{3} \end{array}\right], \quad \mathbf{w}=\left[\begin{array}{l} w_{1} \\ w_{2} \\ w_{3} \end{array}\right] \)

and F is the 3  3 flexibility matrix for the beam, to find the stiffness matrix \(F^{-1}\) and the force matrix w. The entries of F are measured in inches per pound.

\(F=\left[\begin{array}{lll} 0.017 & 0.010 & 0.008 \\ 0.010 & 0.012 & 0.010 \\ 0.008 & 0.010 & 0.017 \end{array}\right], \quad \mathbf{d}=\left[\begin{array}{r} 0 \\ 0.15 \\ 0 \end{array}\right] \)

Text Transcription:

w_1, w_2

w_3

d_1, d_2

d_3

d = [_d_3 ^d_2 ^d_1], w = [_w_3 ^w_2 ^w_1]

F^-1

F = [_0.008 ^0.010 ^ 0.017 _0.010 ^0.012 ^0.010 _0.017 ^0.010 ^0.008], d = [_0 ^0.15 ^0]