Ch3sol - 3.1 Obtain expressions for the maximum deflection...

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3.1 Obtain expressions for the maximum deflection and the maximum moment of a beam- column subjected to a uniformly distributed load as shown in Fig. P3- 1. Fig. P3-1 Solution Both ends fixed beam-column subjected to a uniformly distributed load The 4th order beam-column governing differential equation is or The homogeneous solution of the above equation is Let the particular solution to be in the form, . Then 1
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by observation 2
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3.2 Determine the expression for the maximum deflection and maximum moment of a both ends clamped column that is subjected to a concentrated load at midspan as shown in Fig. P3-2. 3
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Fig. P3-2 Solution Summing moments at the left support gives , let Assume, then and, Hence, the total solution is , , let, then 4
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5
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know Hence, know Let, 3.3 Determine the maximum moment for a beam-column shown in Fig. 3-3 that is bent in (a) single curvature and (b) reverse curvature when . Fig. P3-3 Discuss the problem. (a) For the single curvature case: 6
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by observation (or ) 7
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(b) For the reverse curvature case: Assume to be of . Then 8
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x becomes negative Alternately, the solution of the 4th order equation of (a) can be used with the following boundary conditions: The rest of the procedure is identical to that shown above. 3.4 A simply supported beam-column is subjected to an axial load P and a linearly varying load as shown in Fig. P3-4. Fig. P3-4 (a) Determine the equations for the deflection and moment at any point along the length by solving the governing differential equation.
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