CONTROL SYSTEMS ENGINEERING
7th Edition
ISBN: 2819770197050
Author: NISE
Publisher: WILEY
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Chapter 5, Problem 8RQ
How are summing junctions shown on a signal-flow graph?
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1. The beam shown carries the following loads:Total dead load, wDL = 36 kN/mConcentrated live load, PLL = 240 kNThe beam section is HSS16X12X3/8 with properties:Span, L = 6 mArea, A = 12,100 mm2Moment of inertia about x-axis, Ix = 292 x 106 mm4Fy = 345 MPa
1. Calculate the location of the live load, from the left support, for maximum moment to occur at the fixed support.Answer: 2.536 m2. Calculate the maximum moment. Answer: 439.128 kN-m
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2. The space truss shown is supported by ball-and-socket joints at A, B and C. Factored loads P1 and P2 areacting on joints D and E, respectively, towards the negative y-direction.
1. Calculate the stress of member CE, indicate tension or compression. Answer: 23.61 MPa Tension2. Calculate the stress of member AD, indicate tension or compression. Answer: 21.01 MPa Compression3. Calculate the stress of member CD, indicate tension or compression. Answer: 11.03 MPa Tension
CORRECT ANSWER AND COMPLETE FBD ONLY. I PREFER HANDWRITTEN BUT ITS OKAY IF NOT. I WILL UPVOTE
3. The frame has pin supports at A and E, subject to a wind load. Treat joint C to be an internal hinge.
Given:Dimensions, H1 = 3.0 m; H2 = 4.5 m; L = 10.0 mWind loads, wWL (AB) = 4.8 kN/m; wWL (BC) = 3.9 kN/m; wWL (CD) = 1.5 kN/m; wWL (DE) = 1.2 kN/mMembers are made of A36 steel Wide Flange Section with the following properties:Area, A = 64000 mm2Depth, d = 762 mmFlange width, bf = 371 mmThickness of web, tw = 32 mmThickness of flange, tf = 57.9 mmMoment of inertia about x-axis, Ix = 6080 x 106 mm4The wide flange is oriented so that the bending is about the x-axis1. Calculate the stress in member AB, due to the axial load it carries, indicate if tension or compression.Answer: 0.0476 MPa Tension2. Calculate the stress in member DE, due to the axial load it carries, indicate if tension or compression.Answer: 0.2351 MPa Compression3. Calculate the maximum bending stress at B. Answer: 4.282 MPa
Chapter 5 Solutions
CONTROL SYSTEMS ENGINEERING
Ch. 5 - Prob. 1RQCh. 5 - Name three basic forms for interconnecting...Ch. 5 - For each of the forms in Question 2, state...Ch. 5 - Besides knowing the basic forms as discussed in...Ch. 5 - For a simple, second-order feedback control system...Ch. 5 - Prob. 6RQCh. 5 - Prob. 7RQCh. 5 - How are summing junctions shown on a signal-flow...Ch. 5 - If a forward path touched all closed loops, what...Ch. 5 - Name five representations of systems in state...
Ch. 5 - Prob. 11RQCh. 5 - Which form of the state-space representation leads...Ch. 5 - When the system matrix is diagonal, what...Ch. 5 - What terms lie along the diagonal for a system...Ch. 5 - Prob. 15RQCh. 5 - Prob. 16RQCh. 5 - For what kind of system would you use the observer...Ch. 5 - Describe state-vector transformations from the...Ch. 5 - Prob. 19RQCh. 5 - Prob. 20RQCh. 5 - Prob. 21RQCh. 5 - Find the closed-loop transfer function, T(s) =...Ch. 5 - Find the equivalent transfer function, T(s) =...Ch. 5 - Reduce the system shown in Figure P5.4 to a single...Ch. 5 - Reduce the block diagram shown in Figure P5.6 to a...Ch. 5 - Find the unity feedback system that is equivalent...Ch. 5 - 8. Given the block diagram of a system shown in...Ch. 5 - 9. Reduce the block diagram shown in Figure P5.9...Ch. 5 - Reduce the block diagram shown in Figure P5.10 to...Ch. 5 - 11. For the system shown in Figure P5.11, find the...Ch. 5 - 12. For the system shown in Figure P5.12, find the...Ch. 5 - Prob. 13PCh. 5 - For the system of Figure P5.14, find the value of...Ch. 5 - 15. For the system shown in Figure P5.15, find K...Ch. 5 - For the system of Figure P5.16, find the values of...Ch. 5 - Find the following for the system shown in Figure...Ch. 5 - 18. For the system shown in Figure P5.18, find ,...Ch. 5 - Prob. 19PCh. 5 - Prob. 20PCh. 5 - Find the transfer function G(s) = Eo(s)/T(s) for...Ch. 5 - Prob. 22PCh. 5 - Prob. 23PCh. 5 - State Space SS
24. Given the system below, draw a...Ch. 5 - Prob. 25PCh. 5 - Using Mason’s rule, find the transfer function,...Ch. 5 - Using Mason’s rule, find the transfer function,...Ch. 5 - Prob. 28PCh. 5 - Use block diagram reduction to find the transfer...Ch. 5 - State Space SS 30. Represent the following systems...Ch. 5 - Prob. 31PCh. 5 - State Space SS 32. Repeat Problem 31 and represent...Ch. 5 - Prob. 33PCh. 5 - Prob. 34PCh. 5 - Repeat Problem 34 for the system shown in Figure...Ch. 5 - Prob. 37PCh. 5 - State Space SS 38. Consider the rotational...Ch. 5 - Prob. 40PCh. 5 - Prob. 41PCh. 5 - State Space SS
42. Consider the subsystems shown...Ch. 5 - Prob. 43PCh. 5 - Prob. 44PCh. 5 - State Space SS
45. Diagonalize the following...Ch. 5 - Prob. 46PCh. 5 - Prob. 48PCh. 5 - Prob. 51PCh. 5 - Figure P5.33 shows a noninverting operational...Ch. 5 - Figure P5.34 shows the diagram of au inverting...Ch. 5 - Prob. 54PCh. 5 - A car active suspension system adds an active...Ch. 5 - Prob. 58PCh. 5 - Prob. 60PCh. 5 - Some medical procedures require the insertion of a...Ch. 5 - Prob. 62PCh. 5 - Prob. 64PCh. 5 - Prob. 65PCh. 5 - The purpose of an Automatic Voltage Regulator is...Ch. 5 - 68. Integrated circuits are manufactured through a...Ch. 5 - Prob. 69PCh. 5 - Prob. 72PCh. 5 - Prob. 73PCh. 5 - Assume ideal operational amplifiers in the circuit...Ch. 5 - Parabolic trough collector. Effective controller...
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- 32 mm 32 mm b' c' C 32 mm 32 mm b PROBLEM 6.41 a The extruded beam shown has a uniform wall thickness of 3 mm. Knowing that the vertical shear in the beam is 9 kN, determine the shearing stress at each of the five points indicated.arrow_forwardIn a structural reliability problem, the resistance (capacity) R and load effect (demand) S random variables associated with a failure mode of the structure of interest are normally distributed and statistically independent with the following probability distribution parameters (or statistics) in consistent units: MR = 12, σR = 3 μs = 5, σs = 2 (a) Determine the exact probability of failure pF ·arrow_forwardThe resistance R and load effect S for a given failure mode are statistically independent random variables with marginal PDF's 1 fR (r) = 0≤r≤100 100' fs(s)=0.05e-0.05s (a) Determine the probability of failure by computing the probability content of the failure domain defined as {rarrow_forwardPlease solve this problem as soon as possible My ID# 016948724arrow_forwardThe gears shown in the figure have a diametral pitch of 2 teeth per inch and a 20° pressure angle. The pinion rotates at 1800 rev/min clockwise and transmits 200 hp through the idler pair to gear 5 on shaft c. What forces do gears 3 and 4 transmit to the idler shaft? TS I y 18T 32T This a 12 x 18T C 48T 5arrow_forwardQuestion 1. Draw 3 teeth for the following pinion and gear respectively. The teeth should be drawn near the pressure line so that the teeth from the pinion should mesh those of the gear. Drawing scale (1:1). Either a precise hand drawing or CAD drawing is acceptable. Draw all the trajectories of the involute lines and the circles. Specification: 18tooth pinion and 30tooth gear. Diameter pitch=P=6 teeth /inch. Pressure angle:20°, 1/P for addendum (a) and 1.25/P for dedendum (b). For fillet, c=b-a.arrow_forward5. The figure shows a gear train. There is no friction at the bearings except for the gear tooth forces. The material of the milled gears is steel having a Brinell hardness of 170. The input shaft speed (n2) is 800 rpm. The face width and the contact angle for all gears are 1 in and 20° respectively. In this gear set, the endurance limit (Se) is 15 kpsi and nd (design factor) is 2. (a) Find the revolution speed of gear 5. (b) Determine whether each gear satisfies the design factor of 2.0 for bending fatigue. (c) Determine whether each gear satisfies the design factor of 2.0 for surface fatigue (contact stress). (d) According to the computation results of the questions (b) and (c), explain the possible failure mechanisms for each gear. N4=28 800rpm N₁=43 N5=34 N₂=14 P(diameteral pitch)=8 for all gears Coupled to 2.5hp motorarrow_forward1. The rotating steel shaft is simply supported by bearings at points of B and C, and is driven by a spur gear at D, which has a 6-in pitch diameter. The force F from the drive gear acts at a pressure angle of 20°. The shaft transmits a torque to point A of TA =3000 lbĘ in. The shaft is machined from steel with Sy=60kpsi and Sut=80 kpsi. (1) Draw a shear force diagram and a bending moment diagram by F. According to your analysis, where is the point of interest to evaluate the safety factor among A, B, C, and D? Describe the reason. (Hint: To find F, the torque Tд is generated by the tangential force of F (i.e. Ftangential-Fcos20°) When n=2.5, K=1.8, and K₁ =1.3, determine the diameter of the shaft based on (2) static analysis using DE theory (note that fatigue stress concentration factors need to be used for this question because the loading condition is fatigue) and (3) a fatigue analysis using modified Goodman. Note) A standard diameter is not required for the questions. 10 in Darrow_forward3 N2=28 P(diametral pitch)=8 for all gears Coupled to 25 hp motor N3=34 Full depth spur gears with pressure angle=20° N₂=2000 rpm (1) Compute the circular pitch, the center-to-center distance, and base circle radii. (2) Draw the free body diagram of gear 3 and show all the forces and the torque. (3) In mounting gears, the center-to-center distance was reduced by 0.1 inch. Calculate the new values of center-to-center distance, pressure angle, base circle radii, and pitch circle diameters. (4)What is the new tangential and radial forces for gear 3? (5) Under the new center to center distance, is the contact ratio (mc) increasing or decreasing?arrow_forward2. A flat belt drive consists of two 4-ft diameter cast-iron pulleys spaced 16 ft apart. A power of 60 hp is transmitted by a pulley whose speed is 380 rev/min. Use a service factor (Ks) pf 1.1 and a design factor 1.0. The width of the polyamide A-3 belt is 6 in. Use CD=1. Answer the following questions. (1) What is the total length of the belt according to the given geometry? (2) Find the centrifugal force (Fc) applied to the belt. (3) What is the transmitted torque through the pulley system given 60hp? (4) Using the allowable tension, find the force (F₁) on the tight side. What is the tension at the loose side (F2) and the initial tension (F.)? (5) Using the forces, estimate the developed friction coefficient (f) (6) Based on the forces and the given rotational speed, rate the pulley set. In other words, what is the horse power that can be transmitted by the pulley system? (7) To reduce the applied tension on the tight side, the friction coefficient is increased to 0.75. Find out the…arrow_forwardThe tooth numbers for the gear train illustrated are N₂ = 24, N3 = 18, №4 = 30, №6 = 36, and N₁ = 54. Gear 7 is fixed. If shaft b is turned through 5 revolutions, how many turns will shaft a make? a 5 [6] barrow_forwardCE-112 please solve this problem step by step and give me the correct answerarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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