The Pantheon Essay Example For Students

The Pantheon Essay IntroductionI chose to report on the pantheon because Ive seen pictures and I am also very fascinated by all the Roman monuments. I looked all around the internet and libraries. The Pantheon was very hard to find information about. It was very challenging but I found enough information to complete this report. This famous building stands in the business district of Romemuch as it was built some 18 centuries ago. Amazingly, it has withstood the ravages of both the elements and war permitting a firsthand view of a unique product constructed by Roman hands. Now, it is exposed to acid rain and fumes from passing automobiles and overshadowed by buildings of inferior taste; but, with trust in the future, the Pantheon will survive. We will write a custom essay on The Pantheon specifically for you for only $16.38 $13.9/page Order now Unrecognized, the design of this ancient concrete building reveals unparalleled features not encountered in modern designstandards. Recent studies reveal several major cracks in the dome, but it still functions unimpaired. This condition will surely excitethe curiosity of our structural engineers. The building was built entirely without steel reinforcing rods to resist tensile cracking, sonecessary in concrete members, and for this concrete dome with a long span to last centuries is incredible. Today, no engineerwould dare build this structure without steel rods! Modern codes of engineering practice would not permit such mischief. Noinvestor with knowledge of concrete design would provide the funding. Additional constraints when attempting to build a structure as large as the Pantheon will be discussed later, but briefly they include the use of inadequate hand tools and unsafe lifting devices. I believe we can learn from this activity. Workers can build from a plan and can successful ly use their proven practices only if construction quality controls are maintained. History tells us that the Pantheon is a Greek word meaning to honor all Gods (particularly the Olympian divinities). It is ironic that our building has existed throughout many wars while being dedicated to all Gods; one can readily perceive this to be a temple for our one God. And, the Church has claimed this holy structure as a resting place for its most famous Popes, so we continue tohonor its magnificent divinity. The first incarnation of this ancient temple was built by Agrippa, the son-in-law of the Roman Emperor Augustus, about 27 B.C. Today, above the entrance carved in stone are the words M. AGRIPPA L. F. COS. TERTIUM FECIT which is translated,Marcus Agrippa, son of Lucius, in his third consulate, made it. Indeed, it is worth mentioning that Agrippas engineering talentswere used in building the famous Pont de Gard aqueduct in France. As with many cities, tragedy in the form of large fires such as those of 60, 64, 79, 100 and 110 A.D. seemed to strike Rome. Originally, many Roman buildings contained travertine (limestone rock) which easily cracked in fires. The first Pantheon wasseverely damaged and required replacement except for some parts of the lower porch section and foundation. The Pantheon was rebuilt by the Emperor Hadrian during the period 118 to 128 A.D. (a time given by Ward-Perkins).2 But theWard-Perkinss period is disputed by, Lugli who said the building was started sometime after 123 A.D. and was finished byEmperor Pius about 140 A.D.3 However, most of the bricks were made and placed in the Pantheon in 123 A.D., a date that themaker stamped on his bricks. This was discovered in 1892 by the French archaeologist, George Chedanne. It appears theconstruction of the rotunda walls took a period of 4 to 5 years, and the dome required a like period because of its height and themeager tools the Romans used. This long construction period was fortunate as it gave this pozzolan concrete ample time to cureand gain strength. Was the second temple like the first? Yes, the fundamental principle of the old Roman religion required that the temples be rebuilt without changes in original form. Tradition required that the main entrance face north, and thus the whole building was oriented on the north-south axis of the building. A description of its structural features is separated into the configuration, foundation ring, circular walls, and dome to more clearly define various components. How these pieces are unique in view of todays design requirements will be discussed shortly. .u3d21db72b76ae454e111ae537f589b3c , .u3d21db72b76ae454e111ae537f589b3c .postImageUrl , .u3d21db72b76ae454e111ae537f589b3c .centered-text-area { min-height: 80px; position: relative; } .u3d21db72b76ae454e111ae537f589b3c , .u3d21db72b76ae454e111ae537f589b3c:hover , .u3d21db72b76ae454e111ae537f589b3c:visited , .u3d21db72b76ae454e111ae537f589b3c:active { border:0!important; } .u3d21db72b76ae454e111ae537f589b3c .clearfix:after { content: ""; display: table; clear: both; } .u3d21db72b76ae454e111ae537f589b3c { display: block; transition: background-color 250ms; webkit-transition: background-color 250ms; width: 100%; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #95A5A6; } .u3d21db72b76ae454e111ae537f589b3c:active , .u3d21db72b76ae454e111ae537f589b3c:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .u3d21db72b76ae454e111ae537f589b3c .centered-text-area { width: 100%; position: relative ; } .u3d21db72b76ae454e111ae537f589b3c .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .u3d21db72b76ae454e111ae537f589b3c .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .u3d21db72b76ae454e111ae537f589b3c .ctaButton { background-color: #7F8C8D!important; color: #2980B9; border: none; border-radius: 3px; box-shadow: none; font-size: 14px; font-weight: bold; line-height: 26px; moz-border-radius: 3px; text-align: center; text-decoration: none; text-shadow: none; width: 80px; min-height: 80px; background: url(https://artscolumbia.org/wp-content/plugins/intelly-related-posts/assets/images/simple-arrow.png)no-repeat; position: absolute; right: 0; top: 0; } .u3d21db72b76ae454e111ae537f589b3c:hover .ctaButton { background-color: #34495E!important; } .u3d21db72b76ae454e111ae537f589b3c .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .u3d21db72b76ae454e111ae537f589b3c .u3d21db72b76ae454e111ae537f589b3c-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .u3d21db72b76ae454e111ae537f589b3c:after { content: ""; display: block; clear: both; } READ: Economic Globalization EssayBodyThe Pantheon is one of the great spiritual buildings of the world. It was built as a Roman temple and later consecrated as a Catholic Church. Its monumental porch originally faced a rectangular colonnaded temple courtyard and now enfronts the smaller Piazza della Rotonda. Through great bronze doors, one enters one great circular room. The interior volume is a cylinder above which rises the hemispherical dome. Opposite the door is a recessed semicircular apse, and on each side re three additional recesses, alternately rectangular and semicircular, separated from the space under the dome by paired monolithic columns. The only natural light ent ers through an unglazed oculus at the center ofthe dome and through the bronze doors to the portico. As the sun moves, striking patterns of light illuminate the walls and floors of porphyry, granite and yellow marbles. Inside the PantheonThe building design is one of a large round shape very much like a large barrel with a dome covering the top. There is a light-well in the center of the dome. Layers of beautiful thin brickwork cover the outside, round walls. Small access holes appear occasionally in the wall which were used during construction to frame interior voids. The main entrance is thoroughly impressive:double bronze doors 21 feet high (6.4 meters), a lasting and fitting contribution from their metal smiths. These doors are protectedby a high, broad porch, made with 16 well arranged granite columns supporting a gable styled roof. The beams in the roofstructure of the porch are wooden. They were substituted for bronze members stripped-out by those in later years needing metal for their canons. Professional Roman surveyors located the inlaid marble floor to conform with a convex contour which drainedaway the rain from the oculus for these hundreds of years. In the following descriptions, some general dimensions are given to indicate the magnitude of this undertaking by the Romans. The rotunda has a rather awesome inner diameter of 142.4 feet (43.4 m), made mostly of concrete. Comparatively speaking, this distance represents about one half the length of our football field. And from the floor to the top of the opening in the dome is the same distance. As a matter of fact, we could think of the design of this building as one that could contain a theoretical ball some 143 feet in diameter. The design is not entirely unusual because there are other Roman buildings which have a similar configuration, but the size is unusual. Other buildings such as the Temple of Mercury (71 feet/21.5 m diameter) at Baiae and Domitian Nympheaum at Albano (51 feet/15.6 m diameter) have domes of this type. The Pantheon still has the longest span constructed before the 19th Century. To provide details on this complex configuration, the following figures show the building with its two-ring foundation, voids in the walls, and the step-ring and coffer arrangement in the dome. FoundationThe Pantheon was built on marshy, unstable earth which gave a serious supporting problem to its builders. The Jutland Archaeological Society described in detail various aspects of the ring foundation; they found it rested on a bed of bluish colored river clay.8 This condition invited disaster, and in the final construction phase, the foundation cracked at the two ends of the North-South axis. If one section of a building settles slightly faster and lower than an adjacent section, very large bending stresses are initiated at a point between these two sections which can crack the concrete. And uneven settling was the problem given to the builders. The present-day engineering solution to this type of foundation problem is to drive piles through the clay to bedrock so the building will be firmly supported all the way around. The Roman builders chose a different approach. They built a second ring to hold the first ring from cracking further and to give the clay more area to support the structure. It worked becausethe building has lasted over 1800 years. .u48ec6d0362e82b71bb10e6e698c7826b , .u48ec6d0362e82b71bb10e6e698c7826b .postImageUrl , .u48ec6d0362e82b71bb10e6e698c7826b .centered-text-area { min-height: 80px; position: relative; } .u48ec6d0362e82b71bb10e6e698c7826b , .u48ec6d0362e82b71bb10e6e698c7826b:hover , .u48ec6d0362e82b71bb10e6e698c7826b:visited , .u48ec6d0362e82b71bb10e6e698c7826b:active { border:0!important; } .u48ec6d0362e82b71bb10e6e698c7826b .clearfix:after { content: ""; display: table; clear: both; } .u48ec6d0362e82b71bb10e6e698c7826b { display: block; transition: background-color 250ms; webkit-transition: background-color 250ms; width: 100%; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #95A5A6; } .u48ec6d0362e82b71bb10e6e698c7826b:active , .u48ec6d0362e82b71bb10e6e698c7826b:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .u48ec6d0362e82b71bb10e6e698c7826b .centered-text-area { width: 100%; position: relative ; } .u48ec6d0362e82b71bb10e6e698c7826b .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .u48ec6d0362e82b71bb10e6e698c7826b .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .u48ec6d0362e82b71bb10e6e698c7826b .ctaButton { background-color: #7F8C8D!important; color: #2980B9; border: none; border-radius: 3px; box-shadow: none; font-size: 14px; font-weight: bold; line-height: 26px; moz-border-radius: 3px; text-align: center; text-decoration: none; text-shadow: none; width: 80px; min-height: 80px; background: url(https://artscolumbia.org/wp-content/plugins/intelly-related-posts/assets/images/simple-arrow.png)no-repeat; position: absolute; right: 0; top: 0; } .u48ec6d0362e82b71bb10e6e698c7826b:hover .ctaButton { background-color: #34495E!important; } .u48ec6d0362e82b71bb10e6e698c7826b .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .u48ec6d0362e82b71bb10e6e698c7826b .u48ec6d0362e82b71bb10e6e698c7826b-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .u48ec6d0362e82b71bb10e6e698c7826b:after { content: ""; display: block; clear: both; } READ: Helping Others: Ian in "Shattered" by Eric Walters EssayIn addition to keeping the crack from extending, the builders placed buttress walls on the south side opposite the massive porch. This acted as a clampng device; and although the structural projection appears to be an additional room, it only serves the purpose of being part of the clamp. These rings are made of pozzolan concrete consisting of travertine pieces in layers held together by a mortar of lime and pozzolan. This will be discussed later in this work. Interestingly enough, the Jutland Societys investigation showed the foundation material had become rock hard,11 a case we might expect when we study the chemistry of pozzolanic reaction under these conditions. How It Stands upThe challenge of determining stresses within various sections of the Pantheon has always excited both architects and engineers who are interested in the building. Technical design people recognized that the long 143 foot span of the ancient dome could have critical stress concentrations leading to a catastrophic failure of the structure, but this has not happened. Nothing in life seems perfect, and this is the case with the Pantheon. The dome and walls have cracked. Concrete cracks under excessive tensile stress as viewed in a hoop condition. A. Terenzio, an Italian superintendent of monuments, documented cracking in the walls and dome duringhis inspection of the Pantheon in 1930. Terenzio identifies fractures `reaching from the base of the rotunda to the summit of the dome that he thought were brought about by differential settlement from uneven loading of the wall, particularly near the entrance of the rotunda in the principal niche. Rather than finding vertical differential settlement, we have observed only traces of lateral opening across the cracks corresponding to the effect of hoop tension. Terenzio believed cracking occurred shortly after construction because of dated brick repairs. The Mark and Hutchinson study showed that meridional cracking in the dome was in the lower half extending up to about 57 degrees from the horizontal on the spring line. An earlier stress analysis of this dome by Cowan theoretically placed this point at 37 degrees 36. This is the point where hoop stresses in the dome change from tension to compression presenting a point of weakness within the unreinforced concrete dome. This theoretical point is in reasonable agreement with the actual end of meridional cracking. The Mark and Hutchinson study located the cracks as occurring generally at the openings within the upper cylindrical wall which increased local tensile hoop stresses. In addition to dome, Terenzio mentioned that cracks in the walls extended upward from 24.6 feet (7.5 m) above the floor. The cracking pattern of the concrete in the Pantheon provides an unique stress configuration acting in the dome and walls. Mark and Hutchinson describe this picture as one in which the major internal forces in the cracked dome are only in the meridional direction, and this region serves as a series of arches which bears a common compression keystone in the form of the uncracked upper dome. The cracked walls serve as a series of independent piers to support these arches. Perhaps as insurance against som future dislocation, should we add a steel band around a step-ring? Although the building has survived centuries, this valuable, cracked landmark of Roman history should be protected against future earthquakes at a small cost. ConclusionAs you can tell the Pantheon was a great structure created by the Romans. I believe it has played a great role in Greek history. Even though this building is unpopular to many people, but this report proves that it is one of the greatest and most historical man made creation. BibliographyEncarta 95 EncyclopediaH. W. Cowan, The Master Builders. John Wiley and Son, New York, 1977Http://www.broyan/sor/index.pa-pr/Pantheon.html- Programmer: Jack M. Loudel

Lab Report Operational Amplifier Application Essays

Lab Report Operational Amplifier Application Essays Lab Report Operational Amplifier Application Paper Lab Report Operational Amplifier Application Paper In this report, we Will go through two experiments, Which are the fundamental circuits of operational amplifiers: non-inverting and inverting amplifier circuits, to analyze the difference between ideal and real pop-amps. For the following section, the relevant theory will be introduced, and then the detail and results of the experiments Will be discussed before proceeding to conclusion. Theory Figure 1 The pop amp and its ideal attributes As the Figurer shown, operational amplifier has two inputs labeled (+) and (-) with positive and negative power supply, and a single output. It is primarily a sigh gain differential amplifier which amplifies the difference tot voltages been two inputs. The output voltage of the amplifier Bout is given by the following formula: Bout = A (VT V-) Where A is the open loop voltages gain of the amplifier, which typically is very large about ISO at low frequency. And V- are the non-inverting and inverting input voltage respectively. From the equation, output voltage is entirely governed by the difference between the two input voltages. However for real pop-amps inputs do draw a small amount of current and the output voltage is affected by the output current drawn. Poor the analysis, both inverting and non-inverting amplifiers are applying negative feedback. It cause the V- to increase, hence voltages Of the two input terminals Will be much closed together. And the input draw current is assumed to be zero. Therefore Kerchiefs first (current) Law and Kerchiefs second (voltage) Law could be applied. Experiment The main apparatus for this experiment are the test board with TLS power supply, Kingwood ACCESS oscilloscope, Homage DVDs, and the input signal function generator is Homage HM80030-2. Inverting amplifier: Bout=-RFC Vein Inverting amplifier: Figure 2 Inverting Amplifier Constructing the circuit of an inverting amplifier as shown in figure 2 on the test board. In order to make an amplifier with a gain of . 10, setting RI 2. 7 k and RFC = 27 aquaplaning a Homage signal generator, a KHz sine wave was supply into the amplifier input, the amplitude should be adjusted to low values to prevent waveform distortion occur. Moreover, connecting the input and output of amplifier to X-Y channels of the Oscilloscope, to check the waveform and verity the amplification, If both inputs are held at a common zero, the offset voltage will not be zero as deadly owing to a small amount of bias currents and internal imbalances of a real amplifier. Setting the oscilloscope to X-Y mode, a graph like Figure 3 will be display in the screen. The output offset voltage which is the sum of two independent variables, one is Input offset voltage (Vein offal the other one is input bias current (In bias ). The equation of the Bout off is given below: Bout off=Vein offal+RFC+line bias RFC For the experimental purpose, the values of RI and RFC should be varied to form simultaneous equations, as a result, Vein Off and In bias could be derived separately. When applying RI = 2. Non and RFC = kick , the value of offset voltages Obtained was urn: furthermore, the value Of Bout Off increased to I Iron While RI = 0. Aka and RFC = Aka. Hence the simultaneous equation could be solved: offshoot 2. K*line bias ask Vein off= 0. 916 NV offal bias ask In bias 06. 92 an Figure 3 WY mode trace of Bout against Vein With the respect to Figure 3, the values foeman and Vein acquired from experiment are and -1 IV, therefore the real output voltage range is from -IV to +13. IV when  ±IV supply rails are being used. Additionally, two horizontal nines reveal that maximum and minimum output voltages will less than the supply rail voltages due to the energy losses in the internal resistors. Figure 4 Measurement of the output impedance Measure the output impedance of the inverting amplifier by setting input voltage to ground, and injecting a load current to output side by adding a signal generator which drives a 10 kHz sine wave via a 2200 resistor. Compare the difference between V out and V load shown in figure 4 by applying the oscilloscope, so that the output impedance could be derived by following equation Output impedance: V outlet here lout=(V load- V out)220 As the result, the value Of output impedance obtained from experiment is I . Q, which is quite small but still not equal to zero as ideal situation. In addition to this, V out Will rise when the frequency Of the signal is increasing; Meanwhile, the closed loop output impedance Will tend to zero. Because the deviation between the V out and V load is getting smaller. Inverting amplifier: Bout=1+Riving Non-inverting amplifier: Bout= 1 Vein Figure S: Nan-inverting amplifier Converting the circuit in to non-inverti ng amplifier and using the same values of RFC and RI ,Moreover, applying the signal to the positive input of pop-amps, thus a positive gain can be acquired Much more interesting, the output offset voltage and output impedance will stay the same as values obtained from inverting amplifier. The reason is the resistors for both circuits are consistent. Discussion Prom the investigation Of the experiments, the gain Of non-ideal amplifiers is finite and it could be affected by the changing in frequency and existence of input Offset voltages. Experiments have shown that there is error input voltage due to the non-zero bias currents flowing in the input terminals. Also they have proved that the maximum gain Of real pop-amps is finite and limited by maximum and minimum supply voltages. During the experiment, it is vital to be aware of the error that may occur. Generally, errors can be divided into tuft categories which are the systematic errors and random errors. Unfortunately, systematic errors are unavoidable because of the existing error in the equipment used in the experiments. For instance, homage DVDs can accurate about 0. 1% for DC voltages and 0. 2% for resistance; the accuracy of AC signals is around 1% while the frequency is within angel from GHz to kHz. However,the random error could be minimized to the best extent by taking several measurements and using the average values. Conclusion The results acquired from the experiments reveal the properties of both inverting and non-inverting amplifiers, and describe the differences between real and ideal pop-amp Further, the phase relationships of input and output voltage for the inverting amplifier are 180 degrees out of phase; as opposed to this, they are in phase with each other for Nan-inverting amplifier.