Engineering, 15.07.2020 01:01 geraldmorgan5580

A ductile hot-rolled steel bar has a minimum yield strength in tension and compression of 350 MPa. Using the distortion-energy and maximum-shear-stress theories, determine the factors of safety for the following plane stress states. a. σx = 94 MPa, and τxy = -75 MPa
b. σx = 110 MPa, σy = 100 MPa
c. σx = 90 MPa, σy = 20 MPa, τxy =−20 MPa

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Answer from: SupremeDiaz17

Explanation:

From the given question:

Using the distortion energy theory to determine the factors of safety FOS can be expressed by the relation:

$\dfrac{Syt}{FOS}= \sqrt{ \sigma x^2+\sigma y^2-\sigma x \sigma y+3 \tau_{xy^2}}$

where; syt = strength in tension and compression = 350 MPa

The maximum shear stress theory can be expressed as:

$\tau_{max} = \dfrac{Syt}{2FOS}$

where;

$\tau_{max} =\sqrt{ (\dfrac{\sigma x-\sigma y}{2})^2+ \tau _{xy^2$

a. Using distortion - energy theory formula:

$\dfrac{350}{FOS}= \sqrt{94^2+0^2-94*0+3 (-75)^2}}$

$\dfrac{350}{FOS}=160.35$

${FOS}=\dfrac{350}{160.35}$

FOS = 2.183

USing the maximum-shear stress theory;

$\dfrac{350}{2 FOS} =\sqrt{ (\dfrac{94-0}{2})^2+ (-75)^2$

$\dfrac{350}{2 FOS} =88.51$

$\dfrac{350}{ FOS} =2 \times 88.51$

${ FOS} =\dfrac{350}{2 \times 88.51}$

FOS = 1.977

b. σx = 110 MPa, σy = 100 MPa

Using distortion - energy theory formula:

$\dfrac{350}{FOS}= \sqrt{ 110^2+100^2-110*100+3(0)^2}$

$\dfrac{350}{FOS}= \sqrt{ 12100+10000-11000$

$\dfrac{350}{FOS}=105.3565$

$FOS=\dfrac{350}{105.3565}$

FOS =3.322

USing the maximum-shear stress theory;

$\dfrac{350}{2 FOS} =\sqrt{ (\dfrac{110-100}{2})^2+ (0)^2$

$\dfrac{350}{2 FOS} ={ (\dfrac{110-100}{2})^2$

$\dfrac{350}{2 FOS} =25$

FOS = 350/2×25

FOS = 350/50

FOS = 70

c. σx = 90 MPa, σy = 20 MPa, τxy =−20 MPa

Using distortion- energy theory formula:

$\dfrac{350}{FOS}= \sqrt{ 90^2+20^2-90*20+3(-20)^2}$

$\dfrac{350}{FOS}= \sqrt{ 8100+400-1800+1200}$

$\dfrac{350}{FOS}= 88.88$

FOS = 350/88.88

FOS = 3.939

USing the maximum-shear stress theory;

$\dfrac{350}{2 FOS} =\sqrt{ (\dfrac{90-20}{2})^2+ (-20)^2$

$\dfrac{350}{2 FOS} =\sqrt{ (35)^2+ (-20)^2$

$\dfrac{350}{2 FOS} =\sqrt{ 1225+ 400$

$\dfrac{350}{2 FOS} =40.31$

$FOS} =\dfrac{350}{2*40.31}$

FOS = 4.341

Answer from: Quest

answer: 500 wph.

explanation:

Answer from: Quest

Infrared sensor is most used sensor in wireless technology where remote controlling functions and detection of surrounding objects/ obstacles are involved. this post will discuss about what is infrared sensor, its working principle, how it works, types, applications, advantages and disadvantages. what is infrared sensor

ir sensor is a simple electronic device which emits and detects ir radiation in order to find out certain objects/obstacles in its range. some of its features are heat and motion sensing.

ir sensors use infrared radiation of wavelength between 0.75 to 1000µm which falls between visible and microwave regions of electromagnetic spectrum. ir region is not visible to human eyes. infrared spectrum is categorized into three regions based on its wavelength i.e. near infrared, mid infrared, far infrared.

wavelength regions of infrared spectrum

near ir – 0.75µm to 3 µm
mid ir – 3 µm to 6 µm
far ir – > 6 µm
1 introduction to infrared sensor

fig. 1 – introduction to infrared sensor

working principle of infrared sensor

infrared sensors works on three fundamental physics laws:

planck’s radiation law: any object whose temperature is not equal to absolute zero (0 kelvin) emits radiation.
stephan boltzmann law: the total energy emitted at all wavelengths by a black body is related to the absolute temperature.
wein’s displacement law: objects of different temperature emit spectra that peak at different wavelengths that is inversely proportional to temperature.
key elements of infrared detection system

the key elements of infrared detection system are:

ir transmitter

ir transmitter acts as source for ir radiation. according to plank’s radiation law, every object is a source of ir radiation at temp t above 0 kelvin. in most cases black body radiators, tungsten lamps, silicon carbide, infrared lasers, leds of infrared wavelength are used as sources.

transmission medium

as the name suggests, transmission medium provides passage for the radiation to reach from ir transmitter to ir receiver. vacuum, atmosphere and optical fibers are used as medium.

ir receiver

generally ir receivers are photo diode and photo transistors. they are capable of detecting infrared radiation. hence ir receiver is also called as ir detector. variety of receivers are available based on wavelength, voltage and package.

ir transmitter and receivers are selected with matching parameters. some of deciding specifications of receivers are photosensitivity or responsivity, noise equivalent power and detectivity.

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A ductile hot-rolled steel bar has a minimum yield strength in tension and compression of 350 MPa. U...

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