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719_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

719_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 9.3 Deflection Formulas 713 Problem 9.3-7 Obtain a formula for the ratio d C / d max of the deflection at the midpoint to the maximum deflection for a simple beam supporting a concen- trated load P (see figure). From the formula, plot a graph of d C / d max versus the ratio a/L that defines the position of the load (0.5 a/L 1). What conclusion do you draw from the graph? (Use the formulas of Example 9-3.) Solution 9.3-7 Simple beam (concentrated load) Replace the distance b by the distance a by substituting L a for b : Divide numerator and denominator by L 2 : A LTERNATIVE FORM OF THE RATIO d c d max (3 1 3 )( 1 + 8 b 4 b 2 ) 16(2 b b 2 ) 3/2 ; Let b a L d c d max (3 1 3 L ) a 1 + 8 a L 4 a 2 L 2 b 16 a 2 a L a 2 L 2 b 3/2 ; d c d max (3 1 3 L ) a 1 + 8 a L 4 a 2 L 2 b 16 L a 2 a L a 2 L 2 b 3/2 d c d max (3 1 3 L )( L 2 + 8 aL 4 a 2 ) 16(2 aL a 2 ) 3/2 d c d max (3
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