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

See similar textbooks

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.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.9, Problem 161P

Chapter 4.9, Problem 163RP

Students have asked these similar questions

First monthly exam Gas dynamics Third stage Q1/Water at 15° C flow through a 300 mm diameter riveted steel pipe, E-3 mm with a head loss of 6 m in 300 m length. Determine the flow rate in pipe. Use moody chart. Q2/ Assume a car's exhaust system can be approximated as 14 ft long and 0.125 ft-diameter cast-iron pipe ( = 0.00085 ft) with the equivalent of (6) regular 90° flanged elbows (KL = 0.3) and a muffler. The muffler acts as a resistor with a loss coefficient of KL= 8.5. Determine the pressure at the beginning of the exhaust system (pl) if the flowrate is 0.10 cfs, and the exhaust has the same properties as air.(p = 1.74 × 10-3 slug/ft³, u= 4.7 x 10-7 lb.s/ft²) Use moody chart (1) MIDAS Kel=0.3 Q3/Liquid ammonia at -20°C is flowing through a 30 m long section of a 5 mm diameter copper tube(e = 1.5 × 10-6 m) at a rate of 0.15 kg/s. Determine the pressure drop and the head losses. .μ= 2.36 × 10-4 kg/m.s)p = 665.1 kg/m³

2/Y Y+1 2Cp Q1/ Show that Cda Az x P1 mactual Cdf Af R/T₁ 2pf(P1-P2-zxgxpf) Q2/ A simple jet carburetor has to supply 5 Kg of air per minute. The air is at a pressure of 1.013 bar and a temperature of 27 °C. Calculate the throat diameter of the choke for air flow velocity of 90 m/sec. Take velocity coefficient to be 0.8. Assume isentropic flow and the flow to be compressible. Quiz/ Determine the air-fuel ratio supplied at 5000 m altitude by a carburetor which is adjusted to give an air-fuel ratio of 14:1 at sea level where air temperature is 27 °C and pressure is 1.013 bar. The temperature of air decreases with altitude as given by the expression The air pressure decreases with altitude as per relation h = 19200 log10 (1.013), where P is in bar. State any assumptions made. t = ts P 0.0065h

36 2) Use the method of MEMBERS to determine the true magnitude and direction of the forces in members1 and 2 of the frame shown below in Fig 3.2. 300lbs/ft member-1 member-2 30° Fig 3.2. https://brightspace.cuny.edu/d21/le/content/433117/viewContent/29873977/View

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.

Knowledge Booster