09-01ChapGere.0007

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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 concentrated 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) SECTION 9.3 Deflection Formulas 553 ab L AB P Eq. (9-35): Eq. (9-34): Replace the distance b by the distance a by substituting L 2 a for b : Divide numerator and denominator by L 2 : A LTERNATIVE FORM OF THE RATIO Let d c d max 5 (3 Ï 3 )( 2 1 1 8 b 2 4 b 2 ) 16(2 b 2 b 2 ) 3 / 2 b 5 a L d c d max 5 Ï 3 ) ¢ 2 1 1 8 a L 2 4 a 2 L 2 16 ¢ 2 a L 2 a 2 L 2 3 / 2 d c d max 5 Ï 3 L ) ¢ 2 1 1 8 a L 2 4 a 2 L 2 16 L ¢ 2 a L 2 a 2 L 2 3 / 2 d c d max 5 Ï 3 L 2 L 2 1 8 ab 2 4 a 2 ) aL 2 a 2 ) 3 / 2 d c d max 5 Ï 3 L )(3 L 2 2 4 b 2 ) 16( L 2 2 b 2 ) 3 / 2 Ê ( a $ b ) d max 5
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This note was uploaded on 09/20/2009 for the course COE 3001 taught by Professor Armanios during the Spring '08 term at Georgia Tech.

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