# Mohr’s Circle Solution For The Strain Gauge Rosette Essay Sample For College

### Quick and Dirty

Mohr’s Circle Solution for the Strain Gauge Rosette A 3 gauge rosette is attached to a simple tension bar. The three gauges of the rosette are at 45 degrees in relation to each other but the rosette is not aligned with the strap. The strap is 1. 00 inches wide and 0. 25 inches thick and is loaded with 3000 lbs tension with the force aligned with the long axis of the bar. The material is steel with: E = 29E6 psi and ? = 0. 3

### Theory

The theory is that the stress in the bar is uniaxial with the principal stresses being equal to P/A and zero.

The strains are biaxial with the maximum being P/AE and the minimum being – ? P/AE. The first principal stress and strain will be aligned with the force and the long axis of the bar. ?1 = P/A = 3000/(1. 00×0. 25) = 12,000 psi ? 2 = 0 psi ? 1 = P/AE = ? 1/E = 12,000/29E6 = 0. 000414 in/in = 414 µ? ?2 = – ? P/AE = – ? ?1/E = – ? ?1 = -0. 3×414 = 124 µ? Test Data: When loaded with 3000 lbs tension the three strain readings were: ? A = 310 µ? ?B = -20 µ? ?C = 26 µ? 10/27/2008

### Solution

Gauges A and C are perpendicular and since angles are doubled on Mohr’s circle, they will plot 180 degrees apart on the circle and define a diameter. A and C form a diameter of the circle, the center of the circle will be halfway between them. Center at (310 + 26)/2 = 168 µ? Find the offset from the center to gauges A and B 310 – 168 = 142 µ? -20 – 168 = -188 µ?

These can be used to find the radius Radius = [ 1422 + (-188)2 ]1/2 = 235 µ? Now we can find the principal strains ? 1 = center + radius = 168 + 235 = 404 µ? ?2 = center – radius = 168 – 235 = -67 µ?

Using the center and the radius, draw Mohr’s circle and draw three lines to represent the gauge readings. Consider a diameter of the circle connecting A and C. This diameter will have a perpendicular extending to B. There is only one way that this can be arraigned such that the counter-clockwise sense, ABC, of the rosette is preserved. In our case, the diameter connecting A and B must slope upward to the right (not downward to the right). We can now locate the exact three points on the circle that represent the directions of A, B, and C.

Remember that a point on the circle quantifies the normal and shear strains associated with a particular direction. Any location on the circle represents the same point on the structure and the same condition of strain or stress – just a different orientation for the coordinate system used to quantify the strains or stresses. Note that the shear coordinates of points A, B, and C are the offsets determined above and used to calculate the radius. This is because the vertical and horizontal projections of the 3 radii associated with points A, B, and C form equal triangles.

The completed Mohr’s circle of strain looks like this: Mohr’s Circle of strain -300 -200 20-100 310 Now we can calculate the principal stresses from the biaxial form of Hooke’s law.

?x = E (? x + v ? y ) 1? v2 E ? y = (? y + v ? x ) 1? v2 -100 68- 0 0 100 200 168 300 400 404 500 And 100 200 26 ?1 = 12,100 psi ? 2 = 2100 psi

We have some error in the magnitude of principal stresses. The direction of the first 300 principal stress can be found from Mohr’s circle of strain above. The angle from gauge A (@ +310 µ? ) to ? is clockwise and the cosine of the angle is:

Horizontal component/radius = (310 – 168) / 235 = 0. 604 Since the angle on the circle is double the physical angle, we want ? the angle to locate the direction of the first principal stress ? 1 in reference to gauge A. ?P =? arcos (0. 604) = 26. 4o

Our solution shows the first principal stress 0. 4 degrees clockwise from the theory. The first principal stress is 100 psi in magnitude off from the theoretical value and the second is 2100 psi off.

## Arauco(a): Forward Integration Or Horizontal Expansion.

Summary: Arauco(A): Forward Integration or Horizontal Expansion. Conclusion There is an obvious need for transformation in this company to protect its debt holders, shareholders, and employees. Concentrating on products that will have a growing demand such as toilet paper, tissue paper, and magazine paper would aid in stabilizing the company’s earnings. Having over 50% of revenues derive from pulp sales increases risk of instability. Attempting to first reduce costs and pay outstanding debts should be Celulosa-Arauco’s primary goals.

Eventually there will be restrictions placed on these companies causing them to rely solely on their plantations. The slow inventory production and turnover could cause significant problems for Celulosa-Arauco. Celulosa-Arauco should seek to limit risks that they have incurred by operating in a better planned and more organized manner. Arauco should consider greater positioning in China as it will be the world’s largest paper consumer. This is evident from the increase in educational spending but lack of functional computer software for students.

The immense amount of Chinese characters creates great constraints on using non-paper educational tools. The fact that Chinese characters are not standardized across the different provinces should also add to a long-term consumption of paper. Cutting the current dividend and transforming the company into lean, efficient, well-managed segments with appropriate oversight is crucial at this point. Here are possible transformations that Arauco could proceed with: ? Change the product / services portfolio ? Change operations

With a threat on Celulosa-Arauco’s core competence, pursuing a transformation on the first option could result in a transformation that is more drastic than Celulosa-Arauco can sustain. Second, Celulosa-Arauco can proceed by changing operations. One alternative to proceed with this transformation would be to migrate out of the political and legal pressures. Celulosa-Arauco can explore diversifying their operations to other countries, possibly those with more stable political policy. Such a migration requires logistical concerns and expenses.

In order for Celulosa Arauco to sustain success or even thrive in this changing market, it would have to undergo a transformation. Forestry operations, although still a sustainable market, is undergoing greater scrutiny due to raising environmental concerns. In the last few years, Celulosa Arauco underwent great scrutiny over a few of the company’s sawmills. In the last few years, the Chilean government increased political and legal pressure on Arauco due to great environmental concerns with Arauco’s operations.

This increased pressure forced Arauco to close saw mills in Chile, resulting in millions of US\$ in profits (~ US\$250,000 per day) ii. The increased political/legal pressure and uncertainty results in the third trigger of industry transformation: “a change in regulation can alter the mix of buyer value and cost that companies are permitted to offer”. However, there’s no indication of an urgent matter with the environmental concerns. Celulosa-Arauco would not be able to sustain success if they continue to just suspend or close saw mills as that results in loss of profits and investment.

If the concerns grow and political / legal pressures escalate, this could prove fatal to Celulosa-Arauco. Resources I “Celulosa Arauco: Forward Integration or Horizontal Expansion? ” ii Celulosa Arauco Annual Report 2006; http://www. arauco. cl/pdf/Arauco20-F_2006. pdf iii “Industry Transformation”; Michael E. Porter and Jan W. Rivkin; 2000; Harvard Business School Reprint 9-701-008 iv “Leading Change: Why Transformation Efforts Fail”; John P. Kotter; 2006; Harvard Business School Reprint R0701

## Battle Of Kamalpur

BATTLE OF KAMALPUR INTRODUCTION 1. 1971 a new country was born in the earth named “ Bangladesh ” through a nine month bloody war . Thousands of golden sons of this soil had to embrace martyrdom . Though this historical event took place in the year of 1971 but this was a long charted dream of all the Bangles since the fall freedom in the “ Battle of Palashi ” in 1957 . Bangles thought that their dream was going to be materialized during the partition in 1947 . But it appeared in more frustrating way for the negligence of the Pakistan government in all aspects.

This latent desire was exposed as a volcanic eruption in 25 march 1971 when Pakistan Army carried a plan genocide all over the country . They attacked the innocent people of the Bangladesh like hungry Hayna and killed thousand of people in one single night . They thought they would be able to smash the dream of freedom of Bangles to the ground . But they were certainly wrong . Instead of bowing down to the evil force people of Bangladesh turn around and stood against it with what so ever they could get as weapon .

Which ultimately force the “ Mukti Bahini ” composed of people from all walks of life . Unlike many countries Bangladesh was not given freedom rather we have earned it through many fighting and many battle against the well equipped regular force of Pakistan . Among those the Battle of Kamalpur occupied a very important place in the history of liberation war of Bangladesh . Till that time liberation forces kept themselves restricted within the limit of defensive role and minor guerilla operation .

After raising , first regular “ Brigade ” the Z Force , it carried out first major offensive morale and confidence of Mukti Bahini , Which ultimately contributed to take on number of offensive action against a regular force and earn the victory . 44. Kamalpur was only a small battle in the war of liberation . But in this small battle Mukti Bahini demonstrated its ability to fight . There was no dearth of brave man to shed their blood for their shonar Bangla .

The young leader of Bangladesh demonstrated that they could stomach the hard realities of war , they had the will to lead their inexperienced , ill-equipped and hurriedly trained people forward into battle . In the final reckoning they had the ultimate courage to show their men how to die for their country . Anx : A. Location of Kamalpur . BIBLIOGRAPHY 1. The Documents of the Liberation War of Bangladesh part 10. 2. AGAROTY SECTOR BIJOY KHAHINI by Major Rafiqul Islam, psc 3. Witness to Surrender by Siddique Salik. 4. Military History precis of BMA.

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