Explanation Given information: The force applied at the center of the shaft is P . The deflection at the center C of the shaft ( υ C ) is 0 . The flexural rigidity of the shaft is E I . The length of the shaft ( L ) is a . The distance of the ( x ) is a 2 Calculation: Show the deflected shape of the shaft as in Figure 1. Refer to Figure 1. The deflection at C ( υ C ) 1 due to point load ( P ) is, ( υ C ) 1 = − P a 3 48 E I = P a 3 48 E I ↓ Calculate the deflection at C ( υ C ) 2 due to moment ( M 0 ) using the formula: ( υ C ) 2 = M 0 x 6 E I L ( x 2 − 3 L x + 2 L 2 ) (1) Substitute a for L and a 2 for x in Equation (1). ( υ C ) 2 = M 0 × a 2 6 E I × a [ ( a 2 ) 2 − ( 3 × a × a 2 ) + ( 2 × a 2 ) ] = M 0 12 E I ( a 2 4 − 3 2 a 2 + 2 a 2 ) = M 0 12 E I × 3 a 2 4 = M 0 a 2 16 E I Calculate the deflection at C ( υ C ) 3 due to moment ( M 0 ) using the formula: ( υ C ) 3 = ( υ C ) 2 (2) Substitute M 0 a 2 16 E I for ( υ C ) 2 in Equation (2)

10th Edition

ISBN: 9780134319650

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 12.5, Problem 12.98P

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The moment of the shaft (M0).

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The moment of the shaft ( M 0 ) .

Solution Summary: The author explains the moment of the shaft (M_0) and the deflection at the center C.

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