Explanation Given information : The given force function w is ( 5 x + ( 16 + x 2 ) 1 2 ) kN / m . Determine the resultant force using the equation of equilibrium. F R = ∫ d F = ∫ 0 L w d x (I) Here, the total span of the beam is L . Determine the location of the resultant force by taking moment of force about point A . F R ( x ¯ ) = ∫ 0 L x d F ( x ¯ ) = ∫ 0 L x d F F R (II) Conclusion : Substitute ( 5 x + ( 16 + x 2 ) 1 2 ) kN / m for w and 4 m for L in Equation (I). F R = − ∫ 0 4 ( 5 x + ( 16 + x 2 ) 1 2 ) d x (III) Write the Simpson’s rule formula to calculate the given integral. ∫ x 1 x 2 f ( x ) d x ≈ { 1 3 h [ f ( x 1 ) + 2 Σ n = 1 20 − 1 f ( 2 h n + x 1 ) + 4 Σ n = 1 20 f ( h ( − 1 + 2 n ) + x 1 ) + f ( x 2 ) ] } Here, the lower limit is x 1 and the upper limit is x 2 . Determine the h value. h = ( x 2 − x 1 2 n ) Here, the number of interval is n . Substitute 4 m for x 2 , 0 m for x 1 , and 20 for n . h = ( 4 − 0 2 × 20 ) = 1 10 Write the symbolic form of the Simpson’s rule for the given integral. ∫ 0 4 ( 5 x + ( 16 + x 2 ) 1 2 ) d x ≈ { 1 30 [ 2 + 2 Σ n = 1 20 − 1 n + 400 + n 2 5 + 4 Σ n = 1 20 n + 1 10 ( − 5 + 1 , 601 − 4 n + 4 n 2 ) + 20 + 4 2 ] } Solve the Equation (III) using the Simpson’s rule calculator

13th Edition

ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Question

Chapter 4.9, Problem 162P

To determine

The equivalent resultant force and location of the resultant force on the beam measured from point A using the Simpsons rule.

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Chapter 4.9, Problem 161P

Chapter 4.9, Problem 163RP

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Chapter 4 Solutions

Engineering Mechanics: Statics

Ch. 4.4 - F41. Determine the moment of the force about point...Ch. 4.4 - F42. Determine the moment of the force about point...Ch. 4.4 - F43. Determine the moment of the force about point...Ch. 4.4 - Neglect the thickness of the member.Ch. 4.4 - F45. Determine the moment of the force about point...Ch. 4.4 - F46. Determine the moment of the force about point...Ch. 4.4 - F47. Determine the resultant moment produced by...Ch. 4.4 - F48. Determine the resultant moment produced by...Ch. 4.4 - F49. Determine the resultant moment produced by...Ch. 4.4 - Express the result as a Cartesian vector.

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