Engineering Mechanics: Dynamics (14th Edition)
14th Edition
ISBN: 9780133915389
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 22.1, Problem 18P
To determine
The stiffness of each spring and the mass of the beam.
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This problem studies the response of two single degree of freedom bridge systems shown in Figure 1 under three loading cases. The problem has two parts. Part A and Part B use the same loading cases but the system is modified. Assume the following three loading cases in both Part A and Part B: (a) Harmonic wind load acting on the bridge deck pw(t) = powsin(ωwt) with amplitude pow and forcing circular frequency ωw. (b) Harmonic displacement base excitation acting at the base of the bridge pier ug(t) = ugosin(ωgt) with amplitude ugo and displacement circular frequency ωg. (c) Rectangular pulse load acting on the bridge deck with amplitude pop and pulse duration td.
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Chapter 22 Solutions
Engineering Mechanics: Dynamics (14th Edition)
Ch. 22.1 - A spring is stretched 175 mm by an 8-kg block. If...Ch. 22.1 - Prob. 2PCh. 22.1 - A spring is stretched 200 mm by a 15-kg block. If...Ch. 22.1 - When a 20-lb weight is suspended from a spring,...Ch. 22.1 - Prob. 5PCh. 22.1 - Prob. 6PCh. 22.1 - Prob. 7PCh. 22.1 - Prob. 8PCh. 22.1 - A 3-kg block is suspended from a spring having a...Ch. 22.1 - Prob. 10P
Ch. 22.1 - Prob. 11PCh. 22.1 - 22-12. Determine the natural period of vibration...Ch. 22.1 - The body of arbitrary shape has a mass m, mass...Ch. 22.1 - Determine the torsional stiffness k, measured in...Ch. 22.1 - Prob. 15PCh. 22.1 - Prob. 16PCh. 22.1 - If the natural periods of oscillation of the...Ch. 22.1 - Prob. 18PCh. 22.1 - Prob. 19PCh. 22.1 - A uniform board is supported on two wheels which...Ch. 22.1 - If the wire AB is subjected to a tension of 20 lb,...Ch. 22.1 - The bar has a length l and mass m. It is supported...Ch. 22.1 - The 20-kg disk, is pinned at its mass center O and...Ch. 22.1 - Prob. 24PCh. 22.1 - If the disk in Prob. 22-24 has a mass of 10 kg,...Ch. 22.1 - Prob. 26PCh. 22.1 - Prob. 27PCh. 22.1 - Prob. 28PCh. 22.1 - Prob. 29PCh. 22.2 - Determine the differential equation of motion of...Ch. 22.2 - Determine the natural period of vibration of the...Ch. 22.2 - Determine the natural period of vibration of the...Ch. 22.2 - Prob. 33PCh. 22.2 - Determine the differential equation of motion of...Ch. 22.2 - Prob. 35PCh. 22.2 - Prob. 36PCh. 22.2 - Prob. 37PCh. 22.2 - Prob. 38PCh. 22.2 - Prob. 39PCh. 22.2 - If the slender rod has a weight of 5 lb, determine...Ch. 22.6 - If the block-and-spring model is subjected to the...Ch. 22.6 - Prob. 42PCh. 22.6 - A 4-lb weight is attached to a spring having a...Ch. 22.6 - Prob. 44PCh. 22.6 - Prob. 45PCh. 22.6 - Prob. 46PCh. 22.6 - Prob. 47PCh. 22.6 - Prob. 48PCh. 22.6 - Prob. 49PCh. 22.6 - Prob. 50PCh. 22.6 - The 40-kg block is attached to a spring having a...Ch. 22.6 - The 5kg circular disk is mounted off center on a...Ch. 22.6 - Prob. 53PCh. 22.6 - Prob. 54PCh. 22.6 - Prob. 55PCh. 22.6 - Prob. 56PCh. 22.6 - Prob. 57PCh. 22.6 - Prob. 58PCh. 22.6 - Prob. 59PCh. 22.6 - The 450-kg trailer is pulled with a constant speed...Ch. 22.6 - Prob. 61PCh. 22.6 - Prob. 62PCh. 22.6 - Prob. 63PCh. 22.6 - The spring system is connected to a crosshead that...Ch. 22.6 - Prob. 65PCh. 22.6 - Prob. 66PCh. 22.6 - Prob. 67PCh. 22.6 - The 200-lb electric motor is fastened to the...Ch. 22.6 - Prob. 69PCh. 22.6 - If two of these maximum displacements can be...Ch. 22.6 - Prob. 71PCh. 22.6 - Prob. 72PCh. 22.6 - Prob. 73PCh. 22.6 - Prob. 74PCh. 22.6 - Prob. 75PCh. 22.6 - Prob. 76PCh. 22.6 - Prob. 77PCh. 22.6 - Prob. 78PCh. 22.6 - Prob. 79P
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- d Q.2. A Pelton wheel has a mean bucket speed of 15 m/s. The jet of water issued from a nozzle of 12 cm in diameter impinges the bucket with a velocity of 40 m/s. If the buckets deflect the jet through an angle of 165°, find the head and power generated by the turbine. Assume the hydraulic efficiency is 90% and the mechanical efficiency is 85%. [50 Marks] Po 7n = 90%arrow_forwardAt its optimum point of caines. operation, a given centrifugal pump with an impeller diameter of 50 cm delivers 3.2 m³/s of water at a 2 head of 25 m when rotating at 1450 rpm and power of 955 kW. If a homologous pump with an impeller diameter of 80 cm rotates at 1200 rpm, what would be the discharge, head, shaft break power and P H₂arrow_forward(read image)arrow_forward
- Hi, can you please assist with the attached question please. Please do not use Ai software. Many thanks.arrow_forwarddetermine the allowable bending and contact stresses for a grade 1 steel through-hardened to 250 HB. Assume the desired reliability is 50% and that the pinion and gear have the same hardness and the gear encounters hydrodynamic lubrication and is to last ten million cyclesarrow_forwardUsing the four-point bending tool, detail the influence of both applied load and notch size on the transverse strain. Cover the following points in your answer. a. A detailed description of the methodology you have used to create a set of results suitable to answer this question. Include details on the placement of line scans, the loads used, etc. (there is no need to describe the process of extracting the data from the interactive or the fundamental principles behind DIC). (5 marks) b. A description of the results you have found, including a written description, images, and both vertical and horizontal line scans from the four-point bending tool. Include a minimum of three loads and three notch sizes in your results. (20 marks) c. The conclusions you can make regarding the influence of load and notch size on the strain experienced by the beam based on the data you collect. (5 marks) To achieve full marks, you will need to include the following in your work: • properly labelled graphs…arrow_forward
- Using the four-point bending tool, discuss how measurements of transverse strain using DIC and compare with those from the strain gauge attached at the centre top of the specimen. In your answer, include the following: a. A short explanation of how each of the strain measurement techniques works. (4 marks) b. A description of the methodology you have used to make the data that you discussed from each technique as comparable as possible. (6 marks) c. A set of figures (images, graphs and/or tables as necessary) with appropriate captions demonstrating the comparability of data extracted from the two strain measurement methods. This should include at least three different applied loads. (10 marks) d. A brief description of the findings. (5 marks)arrow_forwardAn undamped single-degree-of-freedom system consists of a spring with stiffness k = 10 kip/in and a mass weighing W = 10 kips. The system is at rest and it is suddenly subjected to a half-cycle sine pulse force. The pulse force has an amplitude po = 1 kips and time duration td = 0.1 seconds. Calculate the maximum restoring force in the spring due to the pulse force.arrow_forwardm=400mm n=300mm q=28mm r=20mm P=0.9kNarrow_forward
- determine the allowable bending and contact stresses for a Grade 1 steel through-hardened to 250 HB. Assume the desired reliability is 50 %and that the pinion and gear have the same hardness and it is expected that the gear will encounter 100,000 load cyclesarrow_forwardPlease can you plot the Mohr's strain circle using the above informarrow_forwardA gearbox has permanent shaft positions defined by the bearing mounting positions, but the gear ratio can be changed by changing the number of teeth in the pinion and gear. To achieve similar power transmission ability for different gear ratios, a manufacturer chooses to have the same module for two different gearboxes. One of the gaerboxes has a pinion with 22 teeth, a gear with 68 teeth, and a center distance of 225mm. How large is the gear module and which gear ratios are possible for a pinion with 22 or more teeth using the same module?arrow_forward
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