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Unformatted text preview: Direct Disptecemetv: Method (3) ThreeSpan Indeterminate Beam problem statement Using the direct displacement method, determine the final member end forces in the threespan indeterminate beam below. The modulus of elasticity (E) and the moment of inertia (1)are constant for the entire beam. Note: The colors of the loads and moments are used to help indicate the contribution of each force to the deflection or rotation being calculated. The moment diagrams show the moments induced by a load using the same color as the load. A I 3 ~ I mmTffimm + + 1 5 '  +  1 0 '  1 ~O~ f  1 0 ' l  1 5 ' 30 k D determine the kinematic degrees of freedom The kinematic degrees of freedom are the number of independent joint displacements, in this structure there are two: A B determine the fixed end moments due to the applied loads Restrain all degrees of freedom of the structure. From this restrained structure, determine the fixed end moments due to the applied loads (positive moments are in the clockwise direction). A UlUt RotallC.lfl 121/25 41/2514EI/30 , C 21/3010 o 01 For a distributed load, the fixed end moments are equal to wL'/12=2x(30)'/12~150 For a point load, located at a distance a from one end and b from the other end of a span, the fixed end moments are equal to Pab'IL 2 ~ 30xlOx(l5)2/(25)2~ 108 and Pa'bIL 2 ~ 30x( 10)'x 15/(25)' ~ 72 I 10'+15' 15' 10'1 ~ 30 k { y A 8 C fEM 108 +72150 +150 I n ln~ 1 I" nl t r ,, ( I) calculate stiffness coefficients due to applied unit displacements Apply a unit displacement in the direction of, and at the same location as each unknown degree of freedom.degree of freedom....
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 Fall '10
 Hosteng

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