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Unformatted text preview: f - - 9 'Ig ' - - + - - - - -~ 16 kIDirect Displacement Method, Part 2Example Problem:Two-Span Indeterminate BeamproblemstatementUsing the direct displacement method, determine the final member end forces in the two-span indeterminatebeam below. The modulus of elasticity (E) is constant for the entirebeam, the moment of inertia (I) for each member varies as indicated in the figure.Note: The colors of the loads and momentsare used to help indicatethe contributionof each force to the deflectionor rotationbeing calculated.The momentdiagramsshow the momentsinducedby a load using the same color as the load.1.51cAdeterminethe kinematicdegreesof freedomThe kinematic degrees of freedom are the number of independent joint displacements,inthis structure there is only one:11.5 Ideterminethe fixed end momentsdue to the applied loadsRestrain all degrees of freedom of the structure. From this restrained structure, determinethe fixed end moments due to the applied loads (positive moments are in the clockwisedirection).For a point load, located at the center of a span, the fixed end moments are equal to PU8...
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- Fall '10