Timken rates its bearings for 3000 hours at 500 rev/min. Determine the catalog rating for a ball bearing running for 10000 hours at 1800 rev/min with a load of 2.75 kN with a reliability of 90 percent.

Answers

Answer 1

Answer:

C₁₀ = 6.3 KN

Explanation:

The catalog rating of a bearing can be found by using the following formula:

C₁₀ = F [Ln/L₀n₀]^1/3

where,

C₁₀ = Catalog Rating = ?

F = Design Load = 2.75 KN

L = Design Life = 1800 rev/min

n = No. of Hours Desired = 10000 h

L₀ = Rating Life = 500 rev/min

n₀ = No. of Hours Rated = 3000 h

Therefore,

C₁₀ = [2.75 KN][(1800 rev/min)(10000 h)/(500 rev/min)(3000 h)]^1/3

C₁₀ = (2.75 KN)(2.289)

C₁₀ = 6.3 KN


Related Questions

The point at 0°, 0° is

Answers

x because it’s at the origin x and y

calculate the magnitude of the force acting on the pin at D. Pin C is fixed in DE and bears against the smooth slot in the triangular plate.

Answers

Answer:

hello your question lacks the required diagram attached below is the diagram

answer : 58.47 N

Explanation:

The magnitude of the force acting on the Pin D

Fd = [tex]\sqrt{Dx^2 + Dy^2}[/tex]

    = [tex]\sqrt{16.80^2 + 56^2}[/tex]

    = 58.465 N

Dx = 16.80 N

Dy = 56 N

hello attached below is the detailed solution

An engineer is trying to build a new measurement tool. Which step should the engineer complete first? A. Design a model of the tool to be tested. B. Precisely define the problem that is to be solved. Selected:c. Write a list of the criteria and constraints for the tool.This answer is incorrect. D. Conduct research on how similar problems were solved in the past.

Answers

Answer:

B. Precisely define the problem that is to be solved.

Explanation:

Engineering can be defined as the scientific and technological principles that is used for the design, development, operation and control of tools, machines or equipments, structures and systems. These machines, tools, systems and structures are typically designed and developed for the purpose of solving peculiar problems relating to human life. Simply stated, engineering is focused on proffering solutions to real life problems through a design process.

Generally, the design process comprises of series of steps used for the development of various tools, machines, structures and systems. In a chronological order, the basic steps of a design process are;

1. Define the problem: to proffer a solution to any problem, you have to precisely define the problem that is to be solved. Therefore, this is the first step of the design process.

2. Conduct a research: the engineer should collect or gather data (informations) relating to the project.

3. Brainstorming and analysis of data: this is the stage where the engineer conceptualize his or her ideas.

4. Create a prototype or simulated model of the product.

5. Product analytics and test: this is where the product is being used and tested for any flaw, error or defects. Thus, troubleshooting is also required at this stage.

Hence, if an engineer is trying to build a new measurement tool; the first step the engineer should complete is to precisely define the problem that is to be solved so as to have a good clear-cut understanding of the problem.

What are the two most important things to remember when at the end of your interview?

Answers

Answer:1. Ask questions2. Thank the interviewer for their time Explanation:

1. When the interviewer asked if you have any questions at the end of the interview don't say no. You should always say yes your interviewer is expecting you to ask a few good questions before ending the interview.

2. Always thank the interviewer for their time and effort to interview you. This would look very good for you and its a nice way to help wrap up the interview.

Seth wants to build a wall of bricks. Which equipment will help him in the process?
OA masonry pump
OB. hacksaw
OC. mortar mixer
OD. pressurized cleaning equipment

Answers

Answer:

it's B I think

Explanation:

hopefully that helps you

Answer: C

Explanation: A mortar mixer is the equipment that would help Seth in the process of building a wall of bricks. A mortar mixer is used to mix the mortar, which is the binding material used to hold the bricks together. It ensures the mortar is properly mixed to the right consistency for laying the bricks.

Explain why the scenario below fails to illustrate an understanding of the importance of metrology. Situation: Natalie is a calibration technician at a food production plant. Natalie: "The oven is just a couple of degrees off. I will just wait a few hours to see if it will level out on its own"

Answers

Answer:

Explanation:

The situation being described completely fails in regard to the importance of metrology. This is because the main importance of metrology is making sure that all of the measurements in a process are as accurate as possible. This accuracy allows an entire process to function efficiently and without errors. In a food production plant, each individual department of the plant relies on the previous function to have completed their job with the correct and accurate instructions so that they can fulfill their functions correctly and end up with a perfect product. If the oven (like in this scenario) is a couple of degrees off it can cause the product to come out burned or undercooked, which will then get transferred to the next part of production which will also fail due to the failed input (burned or undercooked product). This will ultimately lead to an unusable product at the end of the process and money wasted. Which in a large production plant means thousands of products in a single batch are thrown away.

In terms of the necessity of metrology, the situation stated absolutely fails. This is because metrology's primary goal is to ensure that all measurements in a process are as precise as feasible. This precision allows a whole process to run smoothly and error-free. If the oven temperature is wrong by a few degrees, the product will come out charred or undercooked, and the product will be sent to the next step of the process, which will also fail owing to the failed input. This will result in a useless product and a waste of money at the end of the procedure. In a big manufacturing facility, this means thousands of goods are discarded in a single batch.

The insulator is the connection between the grounded circuit conductor and the equipment grounding conductor at the service.

Answers

The answer to your question is correct/ true

What are the differences between separately and shunt DC motor?

Answers

A separately excited DC motor and a DC shunt motor are similar in construction and in all aspects except the way in which the field winding is excited in both the machines.
In a separately excited DC motors, field winding is excited from a separate source, and the armature is excited from another supply. But in a DC shunt motor the armature and field windings connected in parallel across a supply.
In separately excited motors the flux in the filed winding is independent on the load, but in the case of a shunt motor it depends on the load on the motor.

Hope this helps!

Determine the greatest pressure drop allowed over the 10-m-long pipe caused by viscous friction, so the flow remains laminar.

Answers

This question is incomplete, the complete question is;

Determine the greatest pressure drop allowed over the 10-m-long pipe caused by viscous friction, so the flow remains laminar.

The 125-mm-diameter smooth pipe is transporting SAE 10W-30 oil with ρ=920 kg/m3 and µ=0.2 N.s/m2 .

Answer: the greatest pressure drop allowed is 14247 Pascals

Explanation:

LAMINAR FLOW INF PIPE

greatest pressure drop

(P1 - P2) = pressure drop

(P1 - P2) = 32uvl / D²

so (P1 - P2) ∝ V

greatest pressure drop is only at very high velocity

now Re (Reynold Number = svd / u

Re ∝ V

so velocity is high when Re is high

Re = 2000 ( Highest for LAMINAR)

Re = 2000 = svd / u

now in the question we were given that

s = 920 kg/m³, u = 0.2 NS/m², d = 125mm = 0.125m, l = 10m

so we substitute;

2000 = (920 × v × 0.125) / 0.2

v = 3.48 m/s

now pressure drop = (P1 - P2) = 32UVL / d²

we substitute

(P1 - P2)  = (32(0.2) (3.48)(10)) / (0.125)²

(P1 - P2) = 14247 Pascals

therefore the greatest pressure drop allowed is 14247 Pascals

A spherical ball has 3cm internal diameter and its inner surface temperature is 250˚C and the outer surface temperature is 30˚C. Calculate the outer diameter of the ball if the heat loss from the ball is 1600W and has 2.75W/m.˚C thermal conductivity.

Answers

Answer:

The outer diameter of the ball is 6.2138 cm

Explanation:

The formula to apply is ;

Heat loss ,

[tex]Q/t=kA*\frac{( T_1-T_2)}{d}[/tex]

where ;

Q/t=total heat loss from the ball = 1600 w

k=coefficient of heat transmission through the ball= 2.75 W/m.˚C

A=area in m² of the ball with the coefficient of heat transmission

T₁=Hot temperature

T₂=Cold temperatures

d=thickness of the ball

Area of spherical ball using internal diameter, 3cm= 0.03 m will be

Radius = half the diameter = 0.03/2 = 0.015

Area = 4 *π*r²

Area = 4*π*0.015² = 0.002827 m²

Apply the formula for heat loss to get the thickness as:

1600 = {2.75 * 0.002827 *(250-30 ) }/d

1600 =1.711/d

1600d = 1.711

d=1.711/1600 = 0.001069 m

d= 0.1069

Using internal radius and the thickness to get outer radius as;

3 + 0.1069 = 3.1069 cm

Outer diameter will be twice the outer radius

2*3.1069 = 6.2138 cm

Assume you have a steel beam that is 20 feet long and carries a concentrated load of 500 pounds at a distance of 15 feet from Reaction (R ). Reaction (R ) is pinned 5 feet from the load. What are the values in lbs for R and R ? A. 475 and 25 B. 500 and 00 C. 375 and 125 D. 125 and 375

Answers

Answer:

The answer is "Option D".

Explanation:

[tex]\to \epsilon_T= 0\\\\\to R+R_1=500 \ lb \\\\\to \epsilon \ M_{pin} > 0\\\\\to -R \times 20 +(500 \times 5) =0\\\\\to 2500 =20R\\\\\to 20R= 2500\\\\\to R= \frac{2500}{20}\\\\\to R= \frac{250}{2}\\\\\to R= 125 \ lb \\\\\to R_1 =500-125\\[/tex]

         [tex]=375 \ lb \\[/tex]

Using a roof calculator or rafter length guidebook, calculate the theoretical length of the common rafters for a gable roof on a building which is 12’ wide by 36’ long, with a slope of 5/12.

Answers

Answer:

35 feet

Explanation:

Suppose an underground storage tank has been leaking for many years, contaminating a groundwater and causing a contaminant concentration directly beneath the site of 0.30 mg/L. The contamination is flowing at the rate of 0.5 ft/day toward a public drinking water well 1 mile away. The contaminant degrades with a rate constant of 1.94 x 10^-4 1/day. Draw a picture of the system. Estimate the steady-state pollutant concentration expected at the well. If the slope factor is 0.02 (mg/kg-day)^-1.

Required:
Estimate the cancer risk for an adult male drinking the water for 10 years.

Answers

Answer: the cancer risk for an adult male drinking the water for 10 years is 2.88 × 10⁻⁶

Explanation:

firstly, we find the time t required to travel for the contaminant to the well;

Given that, contamination flowing rate = 0.5 ft/day

Distance of well from the site = 1 mile =  5280 ft

so t = 5280 / 0.5 = 10560 days

k is given as 1.94 x 10⁻⁴ 1/day

next we find the Pollutant concentration Ct in the well

Ct = C₀ × e^-( 1.94 x 10⁻⁴ × 10560)

Ct = 0.3 x e^-(kt)  

Ct= 0.0386 mg/L

next we determine the chronic daily intake, CDI

CDI =  (C x CR x EF x ED) / (BW x AT)

where C is average concentration of the contaminant(0.0368mg/L), CR is contact rate (2L/day), EF is exposure frequency (350days/Year), ED is exposure duration (10 years), BW is average body weight (70kg).

now we substitute  

CDI = (0.0368 x 2 x 350 x 10) / ((70x 365) x 70)

= 257.7 / 1788500

= 0.000144 mg/Kg.day

CDI = 1.44 x 10⁻⁴ mg/kg.day  

Finally we calculate the cancer risk, R

Slope factor SF is given as 0.02 Kg.day/mg

Risk, R = I x SF

= 1.44 x 10⁻⁴ mg/kg.day  x 0.02Kg.day/mg    

R = 2.88 × 10⁻⁶

therefore the cancer risk for an adult male drinking the water for 10 years is 2.88 × 10⁻⁶

Why do the changes to the mass of the planet NOT AFFECT the orbital path of the Planet?

Answers

Answer:

changes of Mass affect the planet because... I'm sorry If this didn't help.

The orbital path of the planet is determined by the balance of the gravitational pull of that planet and the larger body it orbits. Mass does not change the orbital path because the mass that determines this “balance” is the mass of the body the planet is orbiting, not the mass of the planet itself

Match each titration term with its definition.
Process of slowly adding a solution to react with another solution and determine the Choose... concentration of one of the solutions tased on the reaction between them
Solution of an unknown concentration that has another solution slowly added to it Choose...
When the required amount of one solution has been added to the second solution to Choose... complete the reaction
Solution of known concentration that is slowly added to a solution of unknown Choose... concentration
Glassware that allows a solution to be precisely and slowly added to another solution Choose...
A reagent added to the analyte solution that changes color when the reaction is Choose... complete

Answers

Answer:

1) titration

2) titrand

3) equivalence point

4) titrant

5) Burette

6) Indicator

Explanation:

The process in which a known volume of a standard solution is added to another solution so that the standard solution can react with the solution of unknown concentration such that its concentration is determined  can be referred to as titration.

The solution which is added to another solution  is called the titrant.  The titrand is the solution of unknown concentration

A burette is a glassware used to slowly add a known volume of the titrant to the titrand.

The indicator used signals the point when the reaction is complete by a color change. At this point, a stoichiometric amount of titrant has been added to the titrand. This is also referred to as the equivalence point.

Don't break or crush mercury-containing lamps because mercury powder may be released.
A) TrueB) False

Answers

A.

It would be released without a doubt so be careful!

Hope this helps :)

Describe the blade design for a wind turbine that you would choose. Why did you choose this design?

Answers

Answer: aerofoil type blades

Explanation: they are more difficult to make but offer better performance and higher rotational speeds making them ideal for electrical energy generation.

.
Describe a ways car manufacturers try to reduce drag and why.

Answers

Answer:

Aerodynamic drag can be reduced by altering the density of the air and the vehicle speed, but these factors are not easily controlled. Instead, to reduce drag, car manufacturers can make the height and width of the front of the car smaller. ... This shape reduces drag and the forces that try to propel the car backwards.

Answer:

Car manufacturers can make the height and width of the front of the car smaller.

Explanation:

The shape reduces drag and the forces it to propel the car backwards.

Which of the following is considered a bated standard

Answers

Answer:

is it multiple choice or....

Under a subsection for geological hazards the buyer is encouraged to obtain an read the booklet

Answers

Answer:

Buyer is encouraged to obtain and read the booklet entitled "The Homeowners Guide to Earthquake Safety." In most cases a questionnaire within the booklet must be completed by Seller and the entire booklet given to the Buyer if the Property was built prior to 1960.

Common car loan duration

Answers

Answer:

In 2019, the average term length was 69 months for new cars and 65 months for used vehicles. Most car loans are available in 12 month increments, lasting between two and eight years. The most common loan terms are 24, 36, 48, 60, 72, and 84 months, according to Autotrader

Explanation:

Read the following paragraph as quickly as you can, and see if you encounter any diculties.
Aoccdrnig to rscheearch at an Elingsh uinervtisy, it deosn't mttaer in waht oredr the ltteers in a wrod are, the olny iprmoetnt tihng is taht the frist and lsat ltteer is at the rghit pclae. The rset can be a toatl mses and you can sitll raed it wouthit a porbelm. Tihs is bcuseae we do not raed ervey lteter by itslef but the wrod as a wlohe.
This has been presented as an example of a principle of human reading compre-hension. If you keep the rst letter and the last letter of a word in their correct positions, then scramble the letters in between, the word is still quite readable in the context of an accompanying paragraph. However, it seems that this is a bit of a myth and not truly based on solid research.1 In short, for longer words the task is much more dicult. Nonetheless, we are going to imitate the process on some English text.
The task will be to read in a paragraph from a le, scramble the internal letters of each word, and then write the result to a le. Handling punctuation is tricky. You are required to deal with punctuation that comes at the end of a word (period, question mark, exclamation, etc.)|that is, punctuation is left untouched and does not count as the nal unscrambled letter. Optionally, one can deal with the more dicult task of handling all punctuation, such as apostrophes for possessives or hyphenated words. Truly randomizing the order of letters is a task for later in the text, but we can do some reasonable approximations now. Attacking this problem in a divide-and-conquer way should begin by writing code to scramble the letters in a word.
Create a dierent solution by dening scrambling functions for each of the following approaches: (Each approach counts as a dierent problem)
(a) For each letter choose a random number and rotate that letter by the random amount. Import random and use the random.randint(a,b) function where `a' and `b' dene the range of random numbers returned.
(b) Implement a dierent method to scrambling the letters. You must clearly describe in the comments the process to scramble the letters in place.It must be dierent than the process from part a.

Answers

Answer:

a

Explanation:

just took the quiz

A steam pipe passes through a chemical plant, where wind passes in cross-flow over the outside of the pipe. The steam is saturated at 17.90 bar and you can assume that the resistances to heat transfer inside the pipe and of the pipe itself are minimal, so that the outside surface temperature of the pipe is equal to the saturation temperature of the steam. The pipe is stainless steel and has an outside diameter of 6.75 cm and a length of 34.7 m. The air flows over the pipe at 7.6 m/s and has a bulk fluid temperature of 27 °C.
A. What is the rate of heat transfer from the pipe to the air?
B. would your answer change if the air flow direction changes to parallel flow? If so, calculate that q as well.

Answers

Answer:

a) the rate of heat transfer from the pipe to the air is 23.866 watts

b) YES, the rate of heat transfer changes to 3518.61 watt

Explanation:

Given that:

steam is saturated at 17.90 bar.

the pipe is stainless steel and has an outside diameter of 6.75 cm

length = 34.7 m

Air flows over the pipe at 7.6 m/s

Bulk fluid temperature of 27°C

we know that

hD/k = 0.028 (Re)^0.8 (Pr)^0.33

Outside diameter of pipe = 6.75 cm

length of the pipe = 34.7 m

velocity of air = 7.6 m/s

Cp of air = 1.005 kJ/Kgk

viscosity of air = 1.81 × 10⁻⁵ kg/(m.sec)

thermal conductivity of air = 2.624 × 10⁻⁵ kw/m.k

so as

hD/k = 0.028 (Re)^0.8 (Pr)^0.33

hD/k = 0.028 (Dvp / u)^0.8 (Cpu / k)^0.33

(h × 0.0675 / 2.624 × 10⁻⁵) = (0.028 ([0.0675 × 7.6 × 1.225] / [1.81 ×10⁻⁵])^0.8) (((1.005 × 1.81 × 10⁻⁵) / (2.624 × 10⁻⁵))^0.33))

h = 0.0414 w/m².k

a)

Now to find the rate of heat transfer Q

Q = hAΔT

Q = 0.0414 × (2π × 0.03375 × 34.7) × (105.383 - 27)

Q = 23.866 watts

therefore the rate of heat transfer from the pipe to the air is 23.866 watts

b)

Now the flow direction changes to parallel flow, then

(h × 0.0675 / 2.624 × 10⁻⁵) = (0.028 ([34.7 × 7.6 × 1.225] / [1.81 ×10⁻⁵])^0.8) (((1.005 × 1.81 × 10⁻⁵) / (2.624 × 10⁻⁵))^0.33))

h = 6.1036 w/m².k

so from the steam table, saturated steam at 17.70 bar, temperature of steam will be 105.383°C

so to find the rate of heat transfer Q

Q = hAΔT

Q = 6.1036 × (2π × 0.03375 × 34.7) × (105.383 - 27)

Q = 3518.61 watt

Therefore the rate of heat transfer changes to 3518.61 watt

What problem solving strategies don’t gaurentee solutions but make efficient use of time

Answers

The strategy is Heuristics

Tech A says that most electric fuel pumps are now mounted inside of the fuel tank. Tech B says that fuel flows through the center of the electric pump and is used to cool the pump. Who is correct?

Answers

Answer:

both

Explanation:

Tech A says that most electric fuel pumps are now mounted inside of the fuel tank. Tech B says that fuel flows through the center of the electric pump and is used to cool the pump. Who is correct? quizlet said so  

In this case, both Technicians are right.

The electric fuel pump is a device that powers a vehicle's engine system by providing fuel.

There are two classes of electric fuel pumps: external fuel pumps and in-tank fuel pumps.

In modern vehicles (also in motorcycles) the electric fuel pump is now located inside the fuel tank.

In conclusion, both Technicians are right.

Learn more in:

https://brainly.com/question/10889330

Which color of white light bends the most when it is refracted by a prism? red green yellow orange

Answers

The color of white light bends the most when it is refracted by a prism is green after the violet.

Why green bents towards the light?

The shorter the wavelength of the mild, the greater its miles refracted. As a result, crimson mild is refracted the least, and violet mild is refracted the most - inflicting the colored mild to unfold out to shape a spectrum.

The hues of white mild withinside the order of lowering wavelength are crimson orange-yellow inexperienced blue indigo violet. Fro the listing we are given withinside the alternatives inexperienced has the shortest wavelength than others. Therefore inexperienced will bend the most.

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Which type of design does not need special care for the placement of dimensions?

Answers

Answer:

cubes

Explanation:

Design for software engineering does not need special care for the placement of dimensions. Software engineering generally deals with arranging lines of coding.

What is Software Engineering Design?

In order to achieve a software's goal by using lower-level, machine-understandable algorithms and a set of parameters based on project requirements or environmental constraints, software design is the process of outlining solutions, planning, and specifying a method of implementation based on the needs of the user.

Software engineering is the application of engineering principles, which are often employed in the design, development, testing, deployment, and management of physical systems to the design.

Therefore, the main focus of software engineering is organizing coded lines that are kept in a device's or computer's memory rather than in actual physical space.

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Help!!
Which of the following describes the first and foremost guideline in dimensioning?
A. Legibility
B. Measurement
C. Accuracy
D. Sketching

Answers

Answer:

it should be accuracy

Explanation:

Answer:

option C

Explanation:

6. You are an electrician working in an industrial plant. You are building a motor control cabinet that contains six motor starters and six pilot lamps. All control components operate on 120 volts AC. Two of the motor starters have coil currents of 0.1 amperes each and four have coil currents of 0.18 amperes each. The six pilot lamps are rated at 5 watts each. The supply room has control transformers with the following rating (in volt-amperes):

75, 100, 150, 250, 300, and 500.

Which of the available control transformers should you choose to supply the power for all the control components in the cabinet?

Answers

Answer:

It's indeed safer to suggest a 150 VA transformer. Following table however is the clarification given.

Explanation:

For 2 motors with 0.1 A, the Power will be:

P = [tex]2\times 120\times 0.1[/tex]

  = [tex]24 \ W[/tex]

For 4 motors with 0.18 A, the Power will be:

P = [tex]4\times 120\times 0.18[/tex]

  = [tex]86.4 \ W[/tex]

As we know, for 6 pilot lamps, the power is "5 W".

So,

The total power will be:

⇒ P = [tex]24+86.4+5[/tex]

       = [tex]115.4 \ W[/tex]

Now,

Consider the power factor to be "0.95"

VA of transformer is:

= [tex]PF\times Power[/tex]

= [tex]115.4\times 0.9[/tex]

= [tex]109.63 \ VA[/tex]

5-81 The shaft is made of A-36 steel and is fixed at end D, while end A is allowed to rotate 0.005 rad when the torque is applied. Determine the torsional reactions at these supports.

Answers

Answer:

The answer is "7.73 kip-ft".

Explanation:

Using this equation, calculate the polar moment of shaft inertia:

[tex]J= \frac{\pi }{32} d^4\\\\[/tex]

  [tex]= \frac{\pi}{ 32} \times 6^4\\\\= 127.234 \ \ in^4[/tex]

Equate the number of moments in x:

[tex]\sum M_x =0[/tex]

[tex]\to T_A-T_B +T_C+T_D =0\\\\\to T_A-40 +20+T_D =0[/tex]

Calculate the torsional response at A using the superposition method:

[tex]\to \phi_A =(\phi_A)_{T} - (\phi_A)_{T_A}\\\\[/tex]

         [tex]= \frac{T_B L_{BC}}{JG}+ \frac{T_C L_{CD}}{JG} - \frac{T_A L_{AD}}{JG}\\\\[/tex]

[tex]0.05= \frac{40 \times 12 \times 2 \times 12}{127.234 \times 11 \times 10^3}+ \frac{20 \times 12 \times 1.5 \times 12 }{127.234 \times 11 \times 10^3} - \frac{T_A \times 12 \times 5 \times 12}{127.234 \times 11 \times 10^3}[/tex]

[tex]0.05= (8.22 \times 10^{-3})+ (3.086 \times 10^{-3})- (5.14 \times 10^{-4} \ T_A)\\\\[/tex]

[tex]\to T_A =12.27 kip \ ft \\\\[/tex]

The torsional answer in help A is  12.27 kip- ft.  It replace the necessary equation values:

[tex]\to T_A-40 +20+T_D =0 \\\\\to 12.27-40+20+T_D=0\\\\T_D=7.73 kip \ ft[/tex]

The torsional reactions at the given supports are;

T_a = 12.3 Kip.ft and T_d = 7.7 Kip.ft

What are Torsional Reactions from Torque?

From the image of the shaft attached, if we take a free body diagram and torsion about x, we will have;

∑Mₓ = 0;

T_a + T_d + 20 - 40 = 0     -----(1)

Using the method of superposition, we have;

Φ_a = (Φ_a)_T - (Φ_a)_T_a

Formula for rotation Φ is;

Φ = TL/(JG)

Thus;

0.005 = [tex][\frac{40 * 12 * 2 * 12}{(\pi/2) *3^{4} * 11 * 10^{3}} + \frac{20 * 12 * 1.5 * 12}{(\pi/2) *3^{4} * 11 * 10^{3}}] - \frac{T_{A} * 12 * 5 * 12}{(\pi/2) *3^{4} * 11 * 10^{3}}[/tex]

Solving for T_a in this gives;

T_a = 12.3 Kip.ft

Thus, from eq 1;

12.3 + T_d + 20 - 40 = 0

T_d = 20 - 12.3

T_d = 7.7 Kip.ft

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