Photo via : Les Chatfield  In the NCEES "Sample Questions + Solutions" book, the problems for the afternoon section are numbered 501 through 540. This post is about Problem 513 of the Machine Design and Materials exam. 
Description of Problem 513: The problem statement shows a sketch of a cantilever beam. The beam is subject to a distributed load of constant magnitude in a section of its length. You are asked to obtain the internal shear force at a certain location within the beam. Analysis of Problem 513: This kind of problem is most easily handled with the method of sections: You make a "cut" of the beam at the location of interest  thus "splitting" the beam into two sections. Then apply the equations of equilibrium to one of the two sections. Problem 513 is easier than most solved examples found on this topic in any Strength of Materials textbook. Here's a similar problem inspired by a solved example we find in Mechanics of Materials by R.C. Hibbeler 
The magnitude of the internal shear force (kip) at point A (10 ft from the fixed support) is nearest: (A) 17 (B) 38 (C) 54 (D) 108 You may download the solution from the link below. Have any questions? Need help? Leave a comment below!

Photo via : John Donges  In this "dissecting" series of posts we discuss every problem in the NCEES "Sample Questions + Solutions" book. The afternoon section problems in this book are numbered 501 through 540. This post is about problem 514 for the Machine Design and Materials exam. 
Description of Problem 514: The problem statement shows a sketch of a simply supported beam. The beam is subject to some external loads. You are asked to obtain the maximum bending moment within the beam. Analysis of Problem 514: Here you just have to draw the shear force diagram and then the bending moment diagram for the beam. Once you have these diagrams you locate where the maximum bending moment occurs. The most efficient way to do this is with the graphical approach you learned back in the day in engineering school. This approach is reviewed well in the Mechanical Engineering Review Manual by M. Lindeburg, and also in any Strength of Materials textbook (e.g., Mechanics of Materials by R.C. Hibbeler). Here's a similar problem that is a little more challenging than Problem 514, yet it is not harder than anything you did in school: Mechanical Systems and Materials Depth (PM) Exam Sample Problem #3 Post CD is fixed to beam AB as shown. The length d of post CD is such that the system is in static equilibrium. 
The maximum bending moment within the beam is most nearly: (A) P (L/3) (B) P (2L/3) (C) PL (D) 3PL You may download the solution via the link below. Have any questions? Need help? Leave a comment!

Photo via : Upupa4me  The problems for the afternoon section in the NCEES "Sample Questions + Solutions" book are numbered 501 through 540. This post is about Problem 506 of the Thermal and Fluid Systems sample exam. Description & Analysis of Problem 506: This is a relatively straightforward Utube manometer problem. The configuration is very simple and is similar to what is found as a solved example in any Fluid Mechanics or Thermodynamics textbook. The following problem is inspired by a solved example in "Fundamentals of Fluid Mechanics" 6th edition, by Munson, et al. and is only slightly more complicated than Problem 506. 
The pressure reading (psi) of the gage is nearest: (A) 1.0 (B) 2.0 (C) 3.0 (D) 4.0 Have any questions? Need help? Leave a comment below! You may download the solution here: 

Yielding of ductile member. Photo via : Sean Hagen  In the NCEES "Sample Questions + Solutions" book, the problems for the afternoon section are numbered 501 through 540. Today we are looking at Problem 504 of the Mechanical Systems section. Description of Problem 504: A figure showing a 3D, statically indeterminate machine element is shown. The element is subject to combined loading. Several geometric dimensions (lengths, radii, height, etc) are provided. You are asked to list the dimensions that are needed to calculate the support reactions. 
Analysis of Problem 504: At first, this problem might be somewhat intimidating because it is statically indeterminate and the geometry is threedimensional. Nevertheless, you do not need to actually find the support reactions  only list the geometric dimensions that would need to be specified in order to find the support reactions. As always, this is actually easier than many strength of materials problems you had to do as undergraduate engineering student. Here is a similar problem we have created to test the same concept: 
The post shown in the figure is fixed to to the floor at its base and has a diameter d. External loads P1 and P2 are acting in the x and y directions, respectively. Point A is located on the surface of the post within cross section a – a, which is at a distance h below the line of action of P1 . Distance b is from the axis of the vertical part of the post to the end of the horizontal part of the post. 
Of the following statements, select the one that is true: 
(A) The bending moment due to P1 causes a normal stress distribution at the cross section. At point A, the magnitude of this normal stress is independent of h. (B) The shear force due to P1 causes a shear stress distribution at the cross section. At point A, this shear stress is highest. (C) The load P2 causes a torsional stress at the cross section. At point A, this torsional stress is lowest. (D) The bending moment due to P2 causes a normal stress distribution at the cross section. At point A, the magnitude of this normal stress is independent of h. Have any questions? Need help? Leave a comment below! You may download the solution by clicking on the button: 
Copyright: klotz / 123RF Stock Photo  In this "dissecting" series of posts we will closely look at every problem in the NCEES "Sample Questions + Solutions" book. Today we start with the HVAC and Refrigeration sample questions. In the NCEES "Sample Questions + Solutions" book, the problems for the afternoon section are numbered 501 through 540. We begin our analysis with Problem 501. 
Description of Problem 505: You are given the flow rate through an orifice plate flow meter and are asked to calculate the corresponding pressure drop. Analysis of Problem 505: The relationship between pressure drop and flow rate for an orifice meter is a simple equation available in any Fluid Mechanics textbook. There is a solved example in the ME Review Manual by Lindeburg that is virtually the same as this problem. Here is a problem we've crafted dealing with a venturi flow meter to test your understanding of the equations that apply to these flow metering devices. 
Thermal and Fluid Systems Depth (PM) Exam Sample Problem #5 A venturi meter is installed in a 2in diameter, schedule 40 steel pipe (ID = 2.067 in). The fluid in the pipe is ambient temperature No. 4 fuel oil with a specific gravity SG=0.85. The meter is provided with a Utube manometer. From past experience with this meter, it is known that for a manometer fluid height, h, of 8 inches, the oil flow rate is 400 gallons per minute. 
The average fluid velocity (ft/min) in the pipe just upstream of the meter when the height h=4 inches, is most nearly: (A) 27 (B) 200 (C) 1,225 (D) 1,623 Have questions? Need help? Then leave a comment below. You may download the solution here:

Photo via : United States Dept. of Agriculture  In this "dissecting" series of posts we discuss every problem in the NCEES "Sample Questions + Solutions" book. The afternoon section problems in this book are numbered 501 through 540. This post is about problem 505 for the HVAC&R Depth (PM) exam. 
Description of Problem 505: The problem gives some data for a liquid desiccant dehumidifier. (e.g., incoming air dry and wet bulb temperatures, CFMs, desiccant solution incoming temperature, etc). You are asked to determine the dry bulb temperature of the air leaving the dehumidifier. In case you didn't know, liquiddesiccant conditioners (absorbers) contact the air with a liquid desiccant, such as lithium chloride or glycol solution. Desiccant solutions work by moisture transfer caused by a difference between water vapor pressures at their surface and of the surrounding air. When the vapor pressure at the desiccant surface is lower than that of the air, the desiccant attracts moisture, so the air is dehumidified. Analysis of Problem 505: There are a few features that make this problem confusing, and quite frankly a "bad" problem. There is the usual superfluous information (this time in the form of a large chart giving you performance data for a liquid absorbent conditioner as well as the misleading statement that a "psychrometric chart is provided on page 83 for your possible use"). But the problem statement provides a value for a "bypass factor". This is a source of confusion because unlike the superfluous/unnecessary stuff previously mentioned, this "bypass factor" is crucial to arrive at NCEES' answer. The issue we have, is that for liquiddesiccant conditioners the concept of "bypass factor" is not typically used or even defined in the relevant literature. Chapter 24, DESICCANT DEHUMIDIFICATION AND PRESSUREDRYING EQUIPMENT of ASHRAE's 2012 HVAC Systems and Equipment Handbook makes no mention of a "bypass factor" in the entire section dedicated to liquid desiccant equipment. This is also the case for other authoritative references (e.g, the textbook by Sauer et al., and the book by Kavanaugh). Once you see the solution to the problem, you realize that NCEES meant something analogous to the bypass factor used in cooling coil analysis (defined as the equivalent fraction of air that bypasses the cooling coil while the remaining portion of the air is completely cooled to the apparatus dewpoint temperature) So, according to NCEES definition of "bypass factor" for a liquid desiccant conditioner, the incoming desiccant solution temperature is analogous to the apparatus dew point  the temperature that the air would reach if there were no bypass. Hence: BF = (Tair,out  Tsolution)/(Tair,in  Tsolution) Once you realize what they mean by "bypass factor" then the problem is straightforward. You use the equation above to solve for the temperature of the air leaving the unit, Tair,out. Customarily in these blog posts we would follow the analysis of NCEES' problem with a problem of our own to give you extra practice with the topic being evaluated. However, for this one, we're not quite sure what the topic is, or what the point of this problem is. Nevertheless, here is a problem dealing with a dehumidifier using a continuously rotating desiccant wheel: HVAC&R Depth (PM) Exam Sample Problem #5 The sketch shows a packaged unit dedicated to conditioning the air in a natatorium (an indoor swimming pool room). The unit uses a silica gel desiccant dehumidification wheel. The unit's heating coil provides the reactivation energy for the desiccant dehumidification process. The unit's cooling coil cools and dehumidifies the air prior to entering the desiccant wheel. The table below provides the known information for the summer design condition: Assume all the water removed by the wheel from the air at state 2 is transferred to the air exhausted to the atmosphere. 
Under the conditions described above, the dew point temperature (°F) at state 6 is most nearly: (A) 51 (B) 67 (C) 72 (D) 75 Have questions? Need help? Then leave a comment below. You may download the solution here:

Photo via : Prayitno  The problems for the afternoon section in the NCEES "Sample Questions + Solutions" book are numbered 501 through 540. In this post we provide an analysis of Problem 504 of the Thermal and Fluid Systems depth (PM) section. 
Problem 504 is virtually the same as Problem 502: You are given a flow velocity and mass flow rate, and are asked to calculate the flow crosssectional area. In Problem 502 the substance was steam and you had to use the property tables to obtain the density. Here in Problem 504, however, the fluid is air so you use the ideal gas equation of state to find the density. Here is a problem that can be found as a solved example in the Thermodynamics textbook by Cengel and Boles. It is slightly more challenging than problem 504 and gives you additional insight/practice with the ideal gas equation. Thermal and Fluid Systems Depth (PM) Exam Sample Problem #4 Air at 10°C and 80 kPa enters the diffuser of a jet engine steadily with a velocity of 200 m/s. The inlet area of the diffuser is 0.4 squared meters. The air leaves the diffuser with a velocity that is very small compared with the inlet velocity... 
The mass flow rate of the air (kg/min) is nearest: (A) 79 (B) 245 (C) 2230 (D) 4728 Have questions? Need help? Then leave a comment below. You may download the solution here:

Photo via : fourthandfifteen  In this "dissecting" series of posts we discuss every problem in the NCEES "Sample Questions + Solutions" book. The afternoon section problems in this book are numbered 501 through 540. This post is about problem 504 for the Mechanical Systems Depth (PM) exam. Description of Problem 504: The problem statement shows a sketch of a rope wrapped around a cylindrical surface. You are asked to calculate the minimum force to be applied on one end of the rope in order to lift a body of known weight at the other end of the rope. 
Analysis of Problem 504 This kind of problem is straightforward as long as you are aware of the relationship describing the variation of the tension in a cord or rope wrapped around a cylindrical surface due to friction. What makes this problem complicated is that, chances are, the last time you saw this relationship was in your sophomore year in engineering school when taking engineering statics. Here's a similar problem dealing with friction that is a little more challenging than Problem 504, yet it is not harder than anything you did in school: Mechanical Systems and Materials Depth (PM) Exam Sample Problem #4 The following experiment has been devised to determine the coefficient of friction between a cord and a steel cylinder of 0.2 m in diameter: The steel cylinder is fixed and does not rotate. A small force is applied at end of the cord. This force is slowly increased until the block is set in motion (sliding horizontally). The experiment was performed maintaining a constant angle of contact, ϕ=90°, between the cord and the cylinder. The force required to initiate movement of the block was measured to be 65 N. The mass of the block is 20 kg, and the static coefficient of friction between the block and the horizontal surface on which it slides is 0.25... 
The coefficient of friction between the rope and the cylinder is nearest: (A) 0.003 (B) 0.180 (C) 0.750 (D) Cannot be calculated with the information provided. You may download the solution via the link below. Have any questions? Need help? Leave a comment!
