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# Mechanical Engineering

### Stress Due to Axial Force and Bending Moment

A circular cross section solid steel shaft 3" in diameter and 4 feet long is fixed at one end and free at the other. As shown in the figure below, the shaft is subjected to an axial tensile load of 50,000 lbs. If the force P = 390 lbs, what is the combined stress at point A and point B. Indicate whether they are compressive o

### Strength of material using the Paris Law

(See attached file for full problem description with equations and diagram) --- Practice problem for Fracture and Fatigue. Adapted from S. Suresh, Fatigue of Materials, second edition, Cambridge University Press Publishing. Consider an aircraft fuselage, existing like a cylindrical pressure vessel. Every day, this aircr

### Solving for the equation of a cubic b-spline curve

Find the equation of a cubic B-Spline curve defined by these control points. See separate file attached with problem set up. Coordinates of four control points given here: P0 = [ 2 1 0 ] P1 = [ 2 3 0 ] P2 = [ 3 2 0 ] P3 = [ 3 4 0 ]

### Maximum Horizontal Shear and Bending Stress

See the attached file. 3. A 4 inch diameter solid circular shaft has a V-belt pulley attached to one end and is supported as shown below. The combined pulley weight and belt pull is 1000 lbs. Determine the magnitude and location of the: (a) maximum horizontal shear stress (b) maximum bending stress Neglect the shaft wei

### Vertical Columb & Compressive Strength

A vertical column has the cross-sectional area shown in Fig1. (dimensions mm). The column carries a vertical compressive point-load of 300kN at C. Calculate the following: 1. The second moments of area, Izz, and Ixx. 2. The maximum values of the compressive and tensile stresses. 3. The position of the cross section where

### Vibration and Time Response

Plot the response x of the 20kg body ( see figure 1, attached) over the time interval 0<t>/1 second. Determine the maximum and minimum values of x and their respective times. The initial conditions are X0=0 and dx/dt=2m/s.

### Flow and Momentum

A hot gas stream enters a uniform diameter return bend as shown. The entrance velocity is 100 f/s, the gas density is .02lbm/cubic ft. and the mass flow rate is 1 lbm/cubic ft. The gas is cooled before exiting the bend and exits the bend at a density of .06 lbm/cubic ft. The pressures at the entrance and exit of the bend are equ

### Linear Equations and Outputs

An AC sine wave is applied to the input of a full wave rectifier. The output of the full wave rectifier is then applied to a half wave rectifier. The output of the half wave rectifier will most closely resemble: A) the original sine wave. B) an inverted form of the original sine wave. C) the output of the full wave rectifier.

### Shear Force and Bending

The beam shown below is simply supported at its ends A and E. It carries a load that is uniformly distributed over part of the beam together with two concentrated loads: (See attached file for full problem description with diagram) Using convenient scales, construct the Shear Force and Bending Moment diagrams for the beam and

### Altimeter Reading at Sea Level

Please provide some help with this problem, the answer is 5186m, 16.6m below sea level but I need to understand why: An aeroplane is fitted with an altimeter calibrated assuming the atmosphere meets the ISA specification. On a day when sea level pressure and temperature are 101,500 N/m2 and 25 degrees the altimeter reads 5000

### What is the output horsepower? Efficiency?

If a fully loaded 440V, three-phase motor draws 12.4 A at 86% power factor (pf). It's speed is 1730 rpm and its torque output to a mechanical load is 29.1 lb-ft x 1.356 = 39.5 Nm. What is the output horsepower? Efficiency?

### Cavitation Problem in a Sphere

A sphere 1 foot in diameter is moving at a depth of 10 feet below a water surface where the water temp is 50 degrees F. At what speed will cavitation first appear? Please show work and any assumptions.

### Aircraft acceleration and time

An aircraft accelerates uniformly from rest down a runway. After a distance of 800m, the aircraft reaches its take-off speed of 288 km/h. (a) What is the acceleration of the aircraft (in m/s2)? (b) How long does it take the aircraft to reach its take-off speed? Please provide equations and solutions.

### Hoist drum questions

A hoist drum consists of a uniform cylinder of diameter 1.2m, radius of gyration 0.45m and mass 200kg. It is being used to lower a crate of mass of 60 kg which is attached to the hoist by a light, inextensible rope. Initially, the crate is at rest 3.0 m above the ground. A brake on the drum is accidentally partially released

### Stiffness matrices and displacements in spring systems

For the spring system shown in the attached diagram, find: a) The stiffness matrix for each element b) The unconstrained global stiffness matrix c) The constrained (reduced) stiffness matrix d) The displacements of node 2 and node 3 e) The reaction forces at node 1 and node 4 For the given spring system in the second at

### Maximum flow around a circular cylinder

The maximum flow past a circular cylinder is 2 X the Up stream velocity. The max velocity occurs at the center line of the top of the cylinder. Assume std pressure and Temp for air and irrational flow. What is the difference between the lowest and highest pressures? The cylinder is suspended in a 40/m wind.

### Carbon Content of Steel

A steel contains 55% alpha-ferrite and 45% gamma-ferrite or austenite at 750 degrees Celsius. What is the carbon content of steel? a) 0.25% b) 0.5% c) 0.28% ****This is how the problem was written however I'm not sure if it makes sense that 55% and 45% are supposed to be 0.55% and 0.45%**** My guess at the answer is (

### Diffusion Coeffiecient, Calculate Constant

The diffusion coefficient for Cr^+3 in Cr2O3 is 6x10^-15 cm2/s at 727 degrees Celcius and is 1x10^-9 cm2/s at 1400 degrees Celcius. Calculate the constant D0. Use the value of the Gas constant R+1.987 cal/mole.K a) 0.015 cm2/s b) 0.055 cm2/s c) 0.25 cm2/s

### Applied Loads, Young's Modulus, Poisson's Ratio

The Young's modulus and the Poisson's ratio for copper are 124.8 GPA and 0.36 respectively. When a tensile load is applied to a 1.5cm diameter copper rod, the diameter is reduced to 1.498cm. What is the correct applied load? a) 81,640N b) 73,500N c) 82,550N

### Tension and Force Exerted

A 1 kg collar C slides without friction along the rod OA and is attached to rod BC by a frictionless pn. The rods rotate in the horizontal plane. At the instant shown BC is rotating counterclockwise and the speed of C is 1m/s, increasing at a rate of 1.2m/s^2. Determine at this instant, a) the tension n rod BC, b) the force exer

### Newton Laws, conveyer belt

1. A package is at rest on a conveyer belt which is initially at rest. The belt is started and moves to the right for 1.5s with a constant acceleration of 3.2m/s^2. The belt then moves with a constant deceleration a_2 and comes to a stop after a total displacement of 4.6m. Knowing that the coefficients of friction between the pa

### Working Speed in RPM

A transmission shaft is fitted with a coupling that is secured by eight 20 mm diameter bolts pitched on a circle with a diameter of 225 mm. The bolt material has an ultimate shear stress of 280 MN/m2 and a factor of safety of 4.0 is to be used. If the power being transmitted is 1.8 MW, determine the working speed of the shaft in

### Shear Stress Calculations

Aluminium alloy blanks are produced from sheet metal by a punching machine that generates a punching force of 30 kN. For sheet metal with a thickness of 3 mm the maximum diameter of the blanks is 13.0 mm. Determine. (a) The ultimate shear stress of the aluminium alloy. (b) The stress on the punch face. Please show work

### Shear stress calculation

The butt riveted joint shown below consists of two cover plates and three 8 mm diameter rivets in each main plate. (a) During testing, a tensile load is applied to the main plates. The load is increased until the joint fails at a load of 57.3 kN. Determine the ultimate shear stress of the rivet material. (see attachment fo

### Stress and Strain Calculations

A mild steel shaft (modulus of elasticity = 210 GN/m2) has a stepped circular cross-section. Part A has a diameter of 75 mm and a length of 425 mm. Part B has a diameter of 60 mm and has a length of 375 mm. The shaft carries an axial tensile load of 65.0 kN. Determine: (a) The stress in Part A (b) The stress in Part B (c

### Process Design - Assembly Line

#1.) An assembly line is to operate 8 hours per day with a desired output of 240 units pr day. The following table contains information on this product's task, task time, and precedence relationship. (see attachment) a.) Design an assembly line that is capable of achieving the desired output rate with the fewest number

### Francis turbine rotation

1. Water flows at a rate of 19.8m^3/s through a Francis turbine rotating at 228rpm. At the inlet to the runner, the runner diameter is 1.8m, the blade length is 30cm, and the relative flow angle is 29 degrees, measured from the radial direction. The fluid leaves the runner without swirl, and the hub and tip diameters at runner e

### Stress and Rotation Angle of Two Steel Shafts

Two solid steel shafts (G = 11.2 x 106 psi) are connected by the gears shown. Ends B and D are fixed. Assume points A and C are where the gears meets the shafts. What is the maximum shear stress in shaft CD under the loading shown? Choose One: 7.832ksi 6.987ksi 6.443ksi 5.844ksi What is the angle through which end C r

### Direct Stress and Strain on Steel Rod

A steel rod having a cross-sectional area of 0.005m2 and length 3m is attached to supports. Find (a) the force exerted by the rod on the supports if the temperature falls 60 degrees and the supports are unyielding. and (b) the force exerted by the rod on the supports if they yield 0.0002m while the temperature raises 50 degrees.

### Equation of an Elastic Curve

Given the equation of the elastic curve for a simply supported beam, how would you obtain the slope in the beam, since the equations are related? I was confident that I had to differentiate the elastic curve twice however that answer was wrong!!! My other options are... a) Differentiate the elastic curve b) Integrate the