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765_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

765_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 9.7 Nonprismatic Beams 759 Problem 9.7-4 A simple beam ABCD has moment of inertia I near the supports and moment of inertia 2 I in the middle region, as shown in the figure. A uniform load of intensity q acts over the entire length of the beam. Determine the equations of the deflection curve for the left-hand half of the beam. Also, find the angle of rotation u A at the left-hand support and the deflection d max at the midpoint. q A L 2 I I I B C D L 4 L 4 Solution 9.7-4 Simple beam (nonprismatic) Use the bending-moment equation (Eq. 9-12a). R EACTIONS , BENDING MOMENT , AND DEFLECTION CURVE B . C . 1 Symmetry: (5) S LOPE AT POINT B ( FROM THE RIGHT ) Substitute (6) B . C . 2 C ONTINUITY OF SLOPES AT POINT B ( ) Left ( ) Right From Eqs. (3) and (6): S LOPE OF THE BEAM ( FROM E QS . 3 AND 5) (7) (8) A NGLE OF ROTATION u A ( FROM EQ . 7) u A v ¿ (0) 7 qL 3 256 EI
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