We Started Looking At Fluctuating Loads Last Time - That Is, Loads That Feature Some Combination Of Non-zero

We Started Looking At Fluctuating Loads Last Time - That Is, Loads That Feature Some Combination Of Non-zero

We started looking at fluctuating loads last time - that is, loads that feature some combination of non-zero mean and alternating stresses - and how to account for them using a Goodman diagram. Let’s re-examine the bracket design problem we did earlier. This time, instead of a fully-reversed load, we’ll assume a fluctuating load with a mean force of 200 lbs, a minimum force of 50 lbs, and a maximum force of 350 lbs. We’ll say the dimensions of the bracket are those we calculated earlier that could handle the fully reversed load. (Problem adapted from Machine Design: An Integrated Approach, 4th Ed., by Robert L. Norton.)

Most of the calculations we did earlier will still hold. We won’t need to recalculate the endurance limit or stress concentration factors. The only new things we need to do are calculate the mean and alternating stresses and the new safety factors.

First step is to calculate the mean and alternating force.

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From here, we get the mean and alternating moment.

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We’re dealing with a situation of simple bending, so we can calculate mean and alternating stress using the basic bending stress equation.

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The geometry of the part hasn’t changed, so we’ll apply the same stress concentration factors that we used before.

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Great. We’ve got our new stresses. Now we need to figure out safety factors. As we mentioned earlier, this is now a slightly more complicated proposition. Which safety factor is appropriate will depend on how the alternating and mean stress behave in relation to each other. The possible failure states are shown as points A, B, C, and D on the Goodman diagram for this situation.

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We’ll step through all the possible situations one by one using the new stresses we calculated and the endurance limit we got earlier.

Case 1: Constant alternating stress, variable mean stress.

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Case 2: Variable alternating stress, constant mean stress.

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Case 3: Alternating and mean stress are proportional to each other.

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Case 4: Alternating and mean stress vary independently.

We take the worse case, with the failure state F being as close as possible to the current stress situation.

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Our design will survive all four cases. Note that Case 4 is always the most conservative case - if you don’t know what your stresses are going to do, this is the one to go with.

More Posts from T-sci-eng and Others

7 years ago
Overwhelming Cloaking Devices And False Peace Highlights Star Trek: Discovery, Season 1 Episode 8
Overwhelming Cloaking Devices And False Peace Highlights Star Trek: Discovery, Season 1 Episode 8
Overwhelming Cloaking Devices And False Peace Highlights Star Trek: Discovery, Season 1 Episode 8
Overwhelming Cloaking Devices And False Peace Highlights Star Trek: Discovery, Season 1 Episode 8
Overwhelming Cloaking Devices And False Peace Highlights Star Trek: Discovery, Season 1 Episode 8
Overwhelming Cloaking Devices And False Peace Highlights Star Trek: Discovery, Season 1 Episode 8
Overwhelming Cloaking Devices And False Peace Highlights Star Trek: Discovery, Season 1 Episode 8
Overwhelming Cloaking Devices And False Peace Highlights Star Trek: Discovery, Season 1 Episode 8
Overwhelming Cloaking Devices And False Peace Highlights Star Trek: Discovery, Season 1 Episode 8
Overwhelming Cloaking Devices And False Peace Highlights Star Trek: Discovery, Season 1 Episode 8

Overwhelming Cloaking Devices And False Peace Highlights Star Trek: Discovery, Season 1 Episode 8

“Can you please make it stop, even for a moment? We were biologically determined for one purpose and one purpose alone: to sense the coming of death. I sense it coming now. We have come to Pahvo for your help. We have come to end this war. I am so afraid. So. Afraid.”

You’re in a time of war, and your enemy has a technological advantage that makes you unable to fight them on equal footing. This has happened so often throughout history: with iron vs. bronze weapons; with the invention and application of gunpowder; with the rise of nuclear capabilities. In space, the augmentation of a cloaking device makes the Klingons virtually invincible, and the Federation is losing this war, badly. What are they to do? What comes next? The ability to see an invisible ship is what’s needed, and this latest episode highlights an attempt to do so, by exploiting an uncontacted alien world. The aliens there are sentient, however, so using this technology would be a violation of both the Prime Directive and First Contact protocols. But what’s the ethical thing to do? Is it better to not interfere and face certain defeat? Or to exploit their technology, violate your principles, and gain the advantage?

Star Trek: Discovery is a show where right-and-wrong isn’t so cut-and-dry. Despite its flaws, it’s an interesting development that makes you think, without providing easy answers. Those, fortunately, will come next episode!


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7 years ago
On The Transpose Of A Matrix
On The Transpose Of A Matrix
On The Transpose Of A Matrix

On the transpose of a matrix

In this post, I would just like to highlight the fact an image can be represented in a matrix form and matrix transformations such as transpose, shearing, scaling, etc, from an image processing point of view are purely physical !

Check out this article from the klein project if this post interested you.

Have a great day!

* Interactive Felix the cat and matrix

7 years ago

Solar System: Things to Know This Week

Reaching out into space yields benefits on Earth. Many of these have practical applications — but there’s something more than that. Call it inspiration, perhaps, what photographer Ansel Adams referred to as nature’s “endless prospect of magic and wonder.“ 

Our ongoing exploration of the solar system has yielded more than a few magical images. Why not keep some of them close by to inspire your own explorations? This week, we offer 10 planetary photos suitable for wallpapers on your desktop or phone. Find many more in our galleries. These images were the result of audacious expeditions into deep space; as author Edward Abbey said, "May your trails be crooked, winding, lonesome, dangerous, leading to the most amazing view.”

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1. Martian Selfie

This self-portrait of NASA’s Curiosity Mars rover shows the robotic geologist in the “Murray Buttes” area on lower Mount Sharp. Key features on the skyline of this panorama are the dark mesa called “M12” to the left of the rover’s mast and pale, upper Mount Sharp to the right of the mast. The top of M12 stands about 23 feet (7 meters) above the base of the sloping piles of rocks just behind Curiosity. The scene combines approximately 60 images taken by the Mars Hand Lens Imager, or MAHLI, camera at the end of the rover’s robotic arm. Most of the component images were taken on September 17, 2016.

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2. The Colors of Pluto

NASA’s New Horizons spacecraft captured this high-resolution, enhanced color view of Pluto on July 14, 2015. The image combines blue, red and infrared images taken by the Ralph/Multispectral Visual Imaging Camera (MVIC). Pluto’s surface sports a remarkable range of subtle colors, enhanced in this view to a rainbow of pale blues, yellows, oranges, and deep reds. Many landforms have their own distinct colors, telling a complex geological and climatological story that scientists have only just begun to decode.

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3. The Day the Earth Smiled

On July 19, 2013, in an event celebrated the world over, our Cassini spacecraft slipped into Saturn’s shadow and turned to image the planet, seven of its moons, its inner rings — and, in the background, our home planet, Earth. This mosaic is special as it marks the third time our home planet was imaged from the outer solar system; the second time it was imaged by Cassini from Saturn’s orbit, the first time ever that inhabitants of Earth were made aware in advance that their photo would be taken from such a great distance.

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4. Looking Back

Before leaving the Pluto system forever, New Horizons turned back to see Pluto backlit by the sun. The small world’s haze layer shows its blue color in this picture. The high-altitude haze is thought to be similar in nature to that seen at Saturn’s moon Titan. The source of both hazes likely involves sunlight-initiated chemical reactions of nitrogen and methane, leading to relatively small, soot-like particles called tholins. This image was generated by combining information from blue, red and near-infrared images to closely replicate the color a human eye would perceive.

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5. Catching Its Own Tail

A huge storm churning through the atmosphere in Saturn’s northern hemisphere overtakes itself as it encircles the planet in this true-color view from Cassini. This picture, captured on February 25, 2011, was taken about 12 weeks after the storm began, and the clouds by this time had formed a tail that wrapped around the planet. The storm is a prodigious source of radio noise, which comes from lightning deep within the planet’s atmosphere.

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6. The Great Red Spot

Another massive storm, this time on Jupiter, as seen in this dramatic close-up by Voyager 1 in 1979. The Great Red Spot is much larger than the entire Earth.

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7. More Stormy Weather

Jupiter is still just as stormy today, as seen in this recent view from NASA’s Juno spacecraft, when it soared directly over Jupiter’s south pole on February 2, 2017, from an altitude of about 62,800 miles (101,000 kilometers) above the cloud tops. From this unique vantage point we see the terminator (where day meets night) cutting across the Jovian south polar region’s restless, marbled atmosphere with the south pole itself approximately in the center of that border. This image was processed by citizen scientist John Landino. This enhanced color version highlights the bright high clouds and numerous meandering oval storms.

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8. X-Ray Vision

X-rays stream off the sun in this image showing observations from by our Nuclear Spectroscopic Telescope Array, or NuSTAR, overlaid on a picture taken by our Solar Dynamics Observatory (SDO). The NuSTAR data, seen in green and blue, reveal solar high-energy emission. The high-energy X-rays come from gas heated to above 3 million degrees. The red channel represents ultraviolet light captured by SDO, and shows the presence of lower-temperature material in the solar atmosphere at 1 million degrees.

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9. One Space Robot Photographs Another

This image from NASA’s Mars Reconnaissance Orbiter shows Victoria crater, near the equator of Mars. The crater is approximately half a mile (800 meters) in diameter. It has a distinctive scalloped shape to its rim, caused by erosion and downhill movement of crater wall material. Since January 2004, the Mars Exploration Rover Opportunity has been operating in the region where Victoria crater is found. Five days before this image was taken in October 2006, Opportunity arrived at the rim of the crater after a drive of more than over 5 miles (9 kilometers). The rover can be seen in this image, as a dot at roughly the “ten o'clock” position along the rim of the crater. (You can zoom in on the full-resolution version here.)

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10. Night Lights

Last, but far from least, is this remarkable new view of our home planet. Last week, we released new global maps of Earth at night, providing the clearest yet composite view of the patterns of human settlement across our planet. This composite image, one of three new full-hemisphere views, provides a view of the Americas at night from the NASA-NOAA Suomi-NPP satellite. The clouds and sun glint — added here for aesthetic effect — are derived from MODIS instrument land surface and cloud cover products.

Full Earth at night map

Americas at night

Discover more lists of 10 things to know about our solar system HERE.

Make sure to follow us on Tumblr for your regular dose of space: http://nasa.tumblr.com

5 years ago
Thought This Was Important To Post.
Thought This Was Important To Post.
Thought This Was Important To Post.

Thought this was important to post.

7 years ago
Students Fortify Concrete By Adding Recycled Plastic

Students fortify concrete by adding recycled plastic

Adding bits of irradiated plastic water bottles could cut cement industry’s carbon emissions

Discarded plastic bottles could one day be used to build stronger, more flexible concrete structures, from sidewalks and street barriers, to buildings and bridges, according to a new study.

MIT undergraduate students have found that, by exposing plastic flakes to small, harmless doses of gamma radiation, then pulverizing the flakes into a fine powder, they can mix the plastic with cement paste to produce concrete that is up to 20 percent stronger than conventional concrete.

Concrete is, after water, the second most widely used material on the planet. The manufacturing of concrete generates about 4.5 percent of the world’s human-induced carbon dioxide emissions. Replacing even a small portion of concrete with irradiated plastic could thus help reduce the cement industry’s global carbon footprint.

Reusing plastics as concrete additives could also redirect old water and soda bottles, the bulk of which would otherwise end up in a landfill.

Read more.

7 years ago
Are Cloaking Devices Coming? Metalens-Shaped Light May Lead The Way
Are Cloaking Devices Coming? Metalens-Shaped Light May Lead The Way
Are Cloaking Devices Coming? Metalens-Shaped Light May Lead The Way
Are Cloaking Devices Coming? Metalens-Shaped Light May Lead The Way
Are Cloaking Devices Coming? Metalens-Shaped Light May Lead The Way
Are Cloaking Devices Coming? Metalens-Shaped Light May Lead The Way
Are Cloaking Devices Coming? Metalens-Shaped Light May Lead The Way
Are Cloaking Devices Coming? Metalens-Shaped Light May Lead The Way

Are Cloaking Devices Coming? Metalens-Shaped Light May Lead The Way

“The biggest challenge facing a real-life cloak has been the incorporation of a large variety of wavelengths, as the cloak’s material must vary from point-to-point to bend (and then unbend) the light by the proper amount. Based on the materials discovered so far, we haven’t yet managed to penetrate the visible light portion of the spectrum with a cloak. This new advance in metalenses, however, seems to indicate that if you can do it for a single, narrow wavelength, you can apply this nanofin technology to extend the wavelength covered tremendously. This first application to achromatic lenses covered nearly the full visible-light spectrum (from 470 to 670 nm), and fusing this with advances in metamaterials would make visible-light cloaking devices a reality.”

What would it take to have a true cloaking device? You’d need some way to bend the light coming from all across the electromagnetic spectrum around your cloaked object, and have it propagate off in the same direction once it moved past you. To an outside observer, it would simply seem like the cloaked object wasn’t there, and they’d only view the world in front of and behind them. Even with the recent advances that have been made in metamaterials, we have not yet been able to realize this dream in three dimensions, covering the entire electromagnetic spectrum, and from all directions. But a new advance in metalens technology might get you the full electromagnetic spectrum after all, as they appear to have solved the problem of chromatic aberration with a light, small, and inexpensive solution. If we can combine these two technologies, metalenses and metamaterials, we just might realize the dream of a true invisibility cloak.

Whether you’re a Star Trek or Harry Potter fan, the ability to turn yourself invisible would be Earth-shattering. Come see how transformation optics might transform the world!


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7 years ago
A Portal To Another Universe ?
A Portal To Another Universe ?

A portal to another universe ?

That my dear friends is a CT scan machine. Stripped off all the body parts, you can see clearly see what goes on inside.

A computerized tomography (CT) or computerized axial tomography (CAT) scan combines data from several X-rays to produce a detailed image of structures inside the body.

A Portal To Another Universe ?

                                            CT scan of Brain

Pretty cool, don’t you think ?

Extras

Difference between MRI and CT scan

Why dont you spin the patient instead ? - Awesome reddit thread

Better quality gifs : here

Source Video: Micheal Jonnson

7 years ago

coolest physics thing that u know??

The coolest physics thing that I know keeps changing over time. But here is one that is extremely fascinating ( and also exaggerated for the effect ; but true! ):

Person living at the top of a skyscraper experiences time faster than one at the bottom

It is a known fact that the higher you are in the earth’s ** atmosphere, the lesser the effect of gravity is.

But the lesser the effect of gravity is, the faster the time ticks.

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By how much you ask? Even if you live on the top floor of the Burj Khalifa  your entire life, you would have aged more only by a few milliseconds than your friends at the bottom. 

( Sure, doesn’t seem like much, but hell would break loose if we don’t consider this on the bigger scale of things )

This is known as Gravitational time dilation and is at the foundations of General Theory of Relativity. (More about this in an upcoming post)

Have a great day and thanks for asking!

EDIT: ** Lets just say hypothetically the earth is not spinning( just to ignore special relativistic effects) and we are looking at only the effects of height.

7 years ago
Sound waves could take a tsunami down a few notches
A tsunami’s ferocious force could be taken down a few notches with a pair of counter waves.

Fight waves with more waves!

A tsunami’s immense wall of water may not be stoppable. But there may be a way to take the ferocious force of nature down a few notches, using a pair of counterwaves.

If released at the right moment, a type of sound wave known as an acoustic-gravity wave could subdue a tsunami, applied mathematician Usama Kadri of Cardiff University in Wales reports January 23 in Heliyon. These acoustic-gravity waves, which reach deep below the ocean’s surface, can stretch tens or hundreds of kilometers and easily travel long distances at high speeds.

7 years ago
Alloys: Steel
Alloys: Steel
Alloys: Steel
Alloys: Steel

Alloys: Steel

According to Dictionary.com, steel is “any of various modified forms of iron, artificially produced, having a carbon content less than that of pig iron and more than that of wrought iron, and having qualities of hardness, elasticity, and strength varying according to composition and heat treatment: generally categorized as having a high, medium, or low-carbon content”. 

Perhaps the most well known alloy around, as well as one of the most common materials in the world, steel is essentially iron with a small percentage of carbon (and, on occasion, one or more other elements). Not enough carbon and you’re stuck with wrought iron, too much carbon and you get cast iron. The graph above is a binary iron-carbon phase diagram that goes from zero percent carbon to about 6.5 percent, illustrating the various phases that can form.

Steel has been known about since ancient times, some pieces dating back to 1800 BC, but it was the invention of the Bessemer process during the industrial revolution that really popularized the alloy. (Technically, similar methods had been used before, particularly in China and Japan, but Henry Bessemer invented the modern method, industrializing it and obtaining a patent in 1856.)

Mainly used in construction, the alloy has been used for almost every possible application: from office furniture to steel wool, from bulldozers to washing machines, and from wires to watches, the possibilities are pretty much endless. Steel is also one of the world’s most-recycled materials, able to be used more than once, with a recycling rate of over 60% globally.

The addition of carbon allows the steel to be stronger than the iron it’s made from. Adding nickel and manganese increases its tensile strength, chromium increases hardness and melting temperature, and vanadium also increases hardness while making it less prone to metal fatigue. Stainless steel has at least eleven percent chromium, whereas Hadfield steel (which resists wearing) contains twelve to fourteen percent manganese. Check out these links for more information on the effects of adding certain elements.  

Sources: 1 (top images), 2 (bottom images)

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