A cross beam in a highway bridge experiences a stress of 14 ksi due to the dead weight of the bridge structure. When a fully loaded tractor-trailer crosses over the bridge, however, the stress in the beam increases to 45 ksi. The beam is fabricated from steel with an ultimate tensile strength of 76 ksi, a yield strength of 50 ksi, and an endurance limit of 38 ksi. Find the safety factor for an infinite fatigue life:

a. if the effect of mean stress on fatigue strength is ignored
b. when the effect of mean stress on fatigue strength is considered.

Answers

Answer 1

Answer:

a) 2.452

b) 1.256

Explanation:

Stress due to dead weight. = 14 Ksi

Stress due to fully loaded tractor-trailer = 45Ksi

ultimate tensile strength of beam = 76 Ksi

yield strength = 50 Ksi

endurance limit = 38 Ksi

Determine the safety factor for an infinite fatigue life

a) If mean stress on fatigue strength is ignored

β = ( 45 - 14 ) / 2

  = 15.5 Ksi

hence FOS ( factor of safety ) = endurance limit / β

                                                 = 38 / 15.5 = 2.452

b) When mean stress on fatigue strength is considered

β2 = 45 + 14 / 2

    = 29.5 Ksi

Ratio  = β / β2 = 15.5 / 29.5 = 0.5254

Next step: applying Goodman method

Sa =  [ ( 0.5254 * 38 *76 ) / ( 0.5254*76 + 38 ) ]

     = 19.47 Ksi

hence the FOS ( factor of safety ) = Sa / β

                                                      = 19.47 / 15.5 = 1.256

Answer 2
(a) The safety factor "2.452".(b) The safety factor "1.256".

Given:

Stress due to dead weight = 14 KsiDue to loaded tractor = 45 KsiTensile strength of beam = 76 KsiYield strength = 50 KsiEndurance limit = 38 Ksi

(a)

According to the question,

→ [tex]\beta = \frac{45-14}{2}[/tex]

      [tex]= \frac{31}{2}[/tex]

      [tex]= 15.5 \ Ksi[/tex]

hence,

The safety factor will be:

= [tex]\frac{Endurance \ limit}{\beta}[/tex]

= [tex]\frac{38}{15.5}[/tex]

= [tex]2.452[/tex]

(b)

→ [tex]\beta_2 = \frac{45+14}{2}[/tex]

       [tex]= \frac{59}{2}[/tex]

       [tex]= 29.5 \ Ksi[/tex]

Ration will be:

= [tex]\frac{\beta}{\beta_2}[/tex]

= [tex]\frac{15.5}{29.5}[/tex]

= [tex]0.5254[/tex]

By applying Goodman method,

→ [tex]Sa = \frac{0.5254\times 38\times 76}{0.5254\times 76+38}[/tex]

       [tex]= 19.47 \ Ksi[/tex]

hence,

The safety factor will be:

= [tex]\frac{Sa}{\beta}[/tex]

= [tex]\frac{19.47}{15.5}[/tex]

= [tex]1.256[/tex]

Thus the above response is correct.

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Related Questions

2 Select the correct answer from each drop-down menu. Identify the jobs with the type of risks they include. Michael is a/n engineer with the risk of inhaling very small crystalline particles that can cause silicosis, pulmonary diseases, or lung cancer. Tommy is a/n engineer with the risk of exposure to poisonous pollutants in production units when a certain reaction does not follow h. textile Reset Next chemical automobile​

Answers

Answer:

2nd option is correct

Explanation:

as Tommy is an engineer only exposed to poisonous pollutants while Michael is an engineer exposed to small crystalline particles that can cause lung cancer and other diseases

I Hope You Got Your Answer

A steel wire is suspended vertically from its upper end. The wire is 400 ft long and has a diameter of 3/16 in. The unit weight of steel is 490 pcf. Compute:

a. the maximum tensile stress due to the weight of the wire
b. the maximum load P that could be supported at the lower end of the wire. Allowable tensile stress is 24,000 psi.

Answers

Answer:

a) the maximum tensile stress due to the weight of the wire is 1361.23 psi

b) the maximum load P that could be supported at the lower end of the wire is 624.83 lb

Explanation:

Given the data in the question;

Length of wire L = 400 ft = ( 400 × 12 )in = 4800 in

Diameter d = 3/16 in

Unit weight w = 490 pcf

First we determine the area of the wire;

A = π/4 × d²

we substitute

A = π/4 × (3/16)²

A = 0.0276 in²

Next we get the Volume

V = Area × Length of wire

we substitute

V = 0.0276 × 4800

V = 132.48 in³

Weight of the steel wire will be;

W = Unit weight × Volume

we substitute

W = 490 × ( 132.48 / 12³ )

W = 490 × 0.076666

W = 37.57 lb

a) the maximum tensile stress due to the weight of the wire;

σ[tex]_w[/tex] = W / A

we substitute

σ[tex]_w[/tex] = 37.57 / 0.0276

= 1361.23 psi

Therefore, the maximum tensile stress due to the weight of the wire is 1361.23 psi

b) the maximum load P that could be supported at the lower end of the wire. Allowable tensile stress is 24,000 psi

Maximum load P that the wire can safely support its lower end will be;

P = ( σ[tex]_{all[/tex] - σ[tex]_w[/tex] )A

we substitute

P = ( 24000 - 1361.23  )0.0276

P = 22638.77 × 0.0276

P = 624.83 lb

Therefore, the maximum load P that could be supported at the lower end of the wire is 624.83 lb

What type of sensor is a crankshaft position sensor?

Answers

Answer: Generally, there are four types of crankshaft magnetic pick-up coils, Hall-effect sensors, magneto-resistive element sensors, and optical sensors.

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Suppose you have two arrays: Arr1 and Arr2. Arr1 will be sorted values. For each element v in Arr2, you need to write a pseudo code that will print the number of elements in Arr1 that is less than or equal to v. For example: suppose you are given two arrays of size 5 and 3 respectively. 5 3 [size of the arrays] Arr1 = 1 3 5 7 9 Arr2 = 6 4 8 The output should be 3 2 4 Explanation: Firstly, you should search how many numbers are there in Arr1 which are less than 6. There are 1, 3, 5 which are less than 6 (total 3 numbers). Therefore, the answer for 6 will be 3. After that, you will do the same thing for 4 and 8 and output the corresponding answers which are 2 and 4. Your searching method should not take more than O (log n) time. Sample Input Sample Output 5 5 1 1 2 2 5 3 1 4 1 5 4 2 4 2 5

Answers

Answer:

The algorithm is as follows:

1. Declare Arr1 and Arr2

2. Get Input for Arr1 and Arr2

3. Initialize count to 0

4. For i in Arr2

4.1 For j in Arr1:

4.1.1 If i > j Then

4.1.1.1 count = count + 1

4.2 End j loop

4.3 Print count

4.4 count = 0

4.5 End i loop

5. End

Explanation:

This declares both arrays

1. Declare Arr1 and Arr2

This gets input for both arrays

2. Get Input for Arr1 and Arr2

This initializes count to 0

3. Initialize count to 0

This iterates through Arr2

4. For i in Arr2

This iterates through Arr1 (An inner loop)

4.1 For j in Arr1:

This checks if current element is greater than current element in Arr1

4.1.1 If i > j Then

If yes, count is incremented by 1

4.1.1.1 count = count + 1

This ends the inner loop

4.2 End j loop

Print count and set count to 0

4.3 Print count

4.4 count = 0

End the outer loop

4.5 End i loop

End the algorithm

5. End

This determines whether two different String objects contain the same string.
a. the == operator
b. the = operator
c. the equals method
d. the stringCompare method

Answers

Answer: c. the equals method

Explanation:

There are more than one comparison that could be made about string objects. Hence, depending on the comparison we want to make, we could be in need of the == operator, equal() or the Stringcompare method. For the question posed above, we want to kno of two string objects containa the same string, hence we are concerned about comparing the content of each string. For this purpose, we make use of the equal(). In the case of making comparison about string reference, we use the == method while the StringCompare method comes in handy while making alphabetical or lexicographic comparison.

List down 10 items made from plastic in your home. Describe why each item is made from plastic.

Answers

Answer:

each item is made from plastic are:

water bottlebucketjuggallonplastic bags as poly thin bagto cover wirehandle of knife,pressure cooker,etc plastic roofdustbinplastic plates ,cups

Explanation:

Items made from plastic in our home are

water bottlesjugbucketfood wrappersdisposable plastic cupshand sanitizer bottlesplastic grocery bagsstraws fruit basket Dustbin

items and their uses

Water bottles are used to drink waterfood wrappers are used to wrap the different types of food itemsplastic grocery bags are used to carry grocery itemshand sanitizer bottles are used to store sanitizerfruit basket is used to store and carry fruits .

hope it is helpful to you

The 5-lb cylinder is falling from A with a speed vA = 10 ft/sonto the platform. Determine the maximum displacementof the platform, caused by the collision. The spring has anunstretched length of 1.75 ft and is originally kept incompression by the 1-ft long cables attached to the platform. Neglect the mass of the platform and spring and any energy lost during the collision.

Answers

Answer:  hello some pictorial details related to your question is missing attached below is the missing detail

answer : 0.0735  ft

Explanation:

weight of cylinder = 5 IB

speed  ( v ) = 10 ft/s

Calculate the maximum displacement of platform

Express the initial energy of the system as

potential energy of cylinder + potential energy of spring + Kinetic energy of cylinder

=  mgh + 1/2 ky^2 + 1/2 mv^2

y = initial spring compression = 1.75 - 1 = 0.75

hence the initial energy can be expressed as

= 5 ( 3 + x ) + 1/2 (400)(0.75)^2 + 1/2 ( 5/32.2) (10)^2 ------------ ( 1 )

Next : determine the Final energy of the system

Final energy of the system = potential energy of the system

= 1/2 k ( x + 0.75 )^2  ----- ( 2 )

Equating  equations ( 1 ) and ( 2 )  to determine the value of x

5 ( 3 + x ) + 1/2 (400)(0.75)^2 + 1/2 ( 5/32.2) (10)^2  = 1/2 k ( x + 0.75 )^2

solve for x

x ( max displace of platform )  = 0.0735  ft

When you see a school bus stop with its stop sign extended or its lights flashing, you must stop, except for cases when:

Answers

Answer:

Whenever you approach a school bus from any direction, which has stopped to pick up or let off passengers while operating its flashing red lights, you must stop your vehicle at least 25 feet from the school bus. The only time you do not have to stop is when you are on the other side of a divided highway. You must stay stopped until the bus has started again or the bus driver stops operating the flashing red lights.

4. Which of the following requires an endorsement on your CDL?
A. Air brakes
B. Double/triple trailers
C. Manual transmission
D. All of the above

Answers

All of the above is the answer

The components which requires an endorsement on your Commercial Driver License (CDL) are: D. all of the above.

What is CDL?

CDL is an acronym for Commercial Driver License and it can be defined as a category of driver's license that is issued to an individual, in order to  indicate that he or she is qualified to operate and drive certain types of automobile vehicles or to use them in specific ways.

In the United States of America, the components which requires an endorsement on your Commercial Driver License (CDL) are:

Air brakesDouble/triple trailersManual transmission

Read more on CDL here: https://brainly.com/question/14326814

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Three single-phase, 10 kVA, 460/120 V, 60 Hz transformers are connected to form a three-phase 460/208 V transformer bank. The equivalent impedance of each transformer referred to HV side is 1.0 +j2.0 Ω. The transformer delivers 20 kW at 0.8 pf leading. Answer the following questions:
(a) Draw a schematic diagram showing the transformer connection.
(b) Determine the magnitude of transformer primary and secondary winding currents.
(c) Determine the primary voltage magnitude for this operating condition. Determine the voltage regulation

Answers

Answer:

A) attached below

B) I₁ = 18.1 A ,  I₂ = 69.39 A

C)  V( magnitude) = 454.5 ∠ 5.04° V ,  Voltage regulation = ≈  -1.2%

Explanation:

A) Schematic diagram attached below

attached below

B) magnitude of primary and secondary winding currents

I₂ ( secondary current ) = P / √3 * VL * cos∅ ---------- ( 1 )

VL = Line voltage = 208

cos∅  ( power factor ) = 0.8

P = 20 * 10^3 watts

insert values into equation 1

I₂ = 69.39 A

I₁ ( primary current ) = I₂V2 / V1

                               I₁ = ( 69.39 * 120 ) / 460  = 18.1 A

C ) Calculate the Primary voltage magnitude and the Voltage regulation

V(magnitude ) = Vp + ( I₁ ∠∅ ) Req                            ( 1 + j2 = 2.24 ∠63.43° )

                       = 460 + ( 18.1 * cos^-1 (0.8) ) ( 1 + j2 )

                       = 460 + 40.544 ∠ 100.3°

V( magnitude) = 454.5 ∠ 5.04° V

Voltage regulation

= ((Vmag - V1) / V1 )) * 100

= (( 454.5 - 460 / 460 )) * 100

= -1.195 % ≈  -1.2%

Which federal agency issues the model food code?

Answers

The FDA! (food and drug administration)

The federal agency issues the model food code is FDA

How to determine the agency

The U. S. Food and Drug Administration (FDA) publishes the Food Code, a model that assists food control jurisdictions at all levels of government by providing them with a scientifically sound technical and legal basis for regulating the retail and food service segment of the industry (restaurants and grocery stores.

The Food Code is a model for safeguarding public health and ensuring food is unadulterated and honestly presented when offered to the consumer. It represents FDA's best advice for a uniform system of provisions that address the safety and protection of food offered at retail and in food service.

Learn more about FDA at: https://brainly.com/question/939216

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*Avoid waiting in long drive-thru lines, for example, at fast-food restaurants or banks. Park your car and go in. *When possible, use public transportation, walk, or ride a bike. *Get regular engine tune ups and car maintenance checks. *Join a carpool or vanpool to get to work or school. *Keep tires properly inflated and aligned. Conservation. The choices in the list above help to regulate important biogeochemical cycles as well as conserve important natural resources. Making these good choices impacts several cycles on Earth.

Required:
Which set of answers - biogeochemical cycle; natural resource; consequence - is not affected by the list above?

Answers

Answer:

When possible, use public transportation, walk, or ride a bike

Explanation:

Answer:

water; water; Oxygen enters the waterways and causes an imbalance of plant life to animal life.

Explanation:

Blood pressure is conventionally measured in the dimensions of millimeters in a column of mercury, and the readings are expressed as two numbers, for example, 120 and 80. The first number is called the systolic value, and it is the maximum pressure developed as the heart contracts. The second number (called the diastolic reading) is the pressure when the heart is at rest. In the units of kPa and psi, what is the difference in pressure between the given systolic and diastolic readings? The density of mercury is 13.54 Mg/m3.

Answers

Answer:

- the difference in pressure between the given systolic and diastolic readings in KPa is 5.313 KPa

- the difference in pressure between the given systolic and diastolic readings in psi is 0.77 psi

Explanation:

Given the data in the question;

blood pressure reading = 120 and 80 { systolic and diastolic }

To determine the difference in pressure between the two readings, we use the equation as follows;

change in pressure ΔP = p × g × h

where p is mercury density, g is acceleration due to gravity and h is difference of height in mercury column.

Frist,  

difference of height in mercury column h = 120 - 80 = 40 mm = 0.04 m

given that; The density of mercury is 13.54 Mg/m³ = 13.54 × 10³ kg/m³

Not that Mg is Megagrams not Milligrams }

we know that g = 9.81 m/s²

so we substitute into our equation;

change in pressure ΔP = (13.54 × 10³) × 9.81 × 0.04

ΔP = 5313.096 kg/m-s² ≈ 5313.096 N/m²

ΔP = 5.313 KPa

Therefore, the difference in pressure between the given systolic and diastolic readings in KPa is 5.313 KPa.

In psi,

ΔP = 5.313 KPa

ΔP = 5313 Pa

ΔP = 5313 pa × ( 1.45 × 10⁻⁴ psi / 1 Pa )

ΔP = 0.770385 psi ≈ 0.77 psi

Therefore, the difference in pressure between the given systolic and diastolic readings in psi is 0.77 psi

In addition to passing an ASE certification test, automotive technicians must have __________ year(s) of on the job training or __________ year(s) of on the job training and a two-year degree in automotive repair to qualify for certification.

Answers

Two years or one year
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