Definisi Satuan untuk Pengonversi Pressure, Stress, Young's Modulus Converter.
Figure 1: Rectangular specimen subject to compression, with Poisson’s ratio circa 0.5Poisson’s ratio ( ν), named after, is the ratio, when a sample object is stretched, of the contraction or transverse (perpendicular to the applied load), to the extension or axial strain (in the direction of the applied load).When a sample cube of a is stretched in one direction, it tends to contract (or occasionally, expand) in the other two directions perpendicular to the direction of stretch. Conversely, when a sample of is compressed in one direction, it tends to expand (or rarely, contract) in the other two directions. This phenomenon is called the Poisson effect.
Poisson’s ratio ν is a measure of the Poisson effect.The Poisson’s ratio of a stable, linear material cannot be less than −1.0 nor greater than 0.5 due to the requirement that the, the and have positive values. Most materials have Poisson’s ratio values ranging between 0.0 and 0.5.
A perfectly incompressible material deformed elastically at small strains would have a Poisson’s ratio of exactly 0.5. Most steels and rigid polymers when used within their design limits (before ) exhibit values of about 0.3, increasing to 0.5 for post-yield deformation (which occurs largely at constant volume.) Rubber has a Poisson ratio of nearly 0.5. Cork’s Poisson ratio is close to 0: showing very little lateral expansion when compressed. Some materials, mostly polymer foams, have a negative Poisson’s ratio; if these are stretched in one direction, they become thicker in perpendicular directions.
While anisotropic materials can as well have Poisson ratios in some directions above 0.5.Assuming that the material is compressed along the axial direction:where ν is the resulting Poisson’s ratio, is transverse strain (negative for axial tension, positive for axial compression) is axial strain (positive for axial tension, negative for axial compression). Cause of Poisson’s effectOn the molecular level, Poisson’s effect is caused by slight movements between molecules and the stretching of molecular bonds within the material lattice to accommodate the. When the bonds elongate in the stress direction, they shorten in the other directions. This behavior multiplied millions of times throughout the material lattice is what drives the phenomenon.
Volumetric changeThe relative change of volume ΔV/ V due to the stretch of the material can be calculated using a simplified formula (only for small deformations):where V is material volume Δ V is material volume change L is original length, before stretch Δ L is the change of length: Δ L = L new − L old. Influences of selected component additions on Poisson’s ratio of a specific base glass. Materialpoisson’s ratio 0.500.42saturated clay0.40-0.500.350.340.33–0.330.30-0.450.30-0.310.27-0.300.21-0.260.20-0.450.200.18-0.30.10 to 0.40 0.00negativematerialplane of symmetryν xyν yxν yzν zyν zxν xzx − y, x=ribbon direction0.490.690.012.753.880.01–x − y0.290.290.320.060.060.32Negative Poisson’s ratio materialsSome materials known as materials display a negative Poisson’s ratio.
When subjected to positive strain in a longitudinal axis, the transverse strain in the material will actually be positive (i.e. It would increase the cross sectional area).
For these materials, it is usually due to uniquely oriented, hinged molecular bonds. In order for these bonds to stretch in the longitudinal direction, the hinges must ‘open’ in the transverse direction, effectively exhibiting a positive strain. Applications of Poisson’s effectOne area in which Poisson’s effect has a considerable influence is in pressurized pipe flow. When the air or liquid inside a pipe is highly pressurized it exerts a uniform force on the inside of the pipe, resulting in a radial stress within the pipe material.
Due to Poisson’s effect, this radial stress will cause the pipe to slightly increase in diameter and decrease in length. The decrease in length, in particular, can have a noticeable effect upon the pipe joints, as the effect will accumulate for each section of pipe joined in series. A restrained joint may be pulled apart or otherwise prone to failure.Another area of application for Poisson’s effect is in the realm of.
Rocks, just as most materials, are subject to Poisson’s effect while under stress and strain. In a geological timescale, excessive erosion or sedimentation of Earth’s crust can either create or remove large vertical stresses upon the underlying rock. This rock will expand or contract in the vertical direction as a direct result of the applied stress, and it will also deform in the horizontal direction as a result of Poisson’s effect.
This change in strain in the horizontal direction can affect or form joints and dormant stresses in the rock. Jump to: navigation, searchIn solid mechanics, Young’s modulus (E) is a measure of the stiffness of an isotropic elastic material. It is also known as the Young modulus, modulus of elasticity, elastic modulus (though Young’s modulus is actually one of several elastic moduli such as the bulk modulus and the shear modulus) or tensile modulus. It is defined as the ratio of the uniaxial stress over the uniaxial strain in the range of stress in which Hooke’s Law holds. 1 This can be experimentally determined from the slope of a stress-strain curve created during tensile tests conducted on a sample of the material.Young’s modulus is named after Thomas Young, the 19th century British scientist.
However, the concept was developed in 1727 by Leonhard Euler, and the first experiments that used the concept of Young’s modulus in its current form were performed by the Italian scientist Giordano Riccati in 1782 — predating Young’s work by 25 years. 2 UnitsYoung’s modulus is the ratio of stress, which has units of pressure, to strain, which is dimensionless; therefore Young’s modulus itself has units of pressure.The SI unit of modulus of elasticity (E, or less commonly Y) is the pascal (Pa or N/m²); the practical units are megapascals (MPa or N/mm²) or gigapascals (GPa or kN/mm²). In United States customary units, it is expressed as pounds (force) per square inch (psi). UsageThe Young’s modulus allows the behavior of a bar made of an isotropic elastic material to be calculated under tensile or compressive loads. For instance, it can be used to predict the amount a wire will extend under tension or buckle under compression. Some calculations also require the use of other material properties, such as the shear modulus, density, or Poisson’s ratio.
Linear versus non-linearFor many materials, Young’s modulus is essentially constant over a range of strains. Such materials are called linear, and are said to obey Hooke’s law. Examples of linear materials include steel, carbon fiber, and glass.
Rubber and soils (except at very small strains) are non-linear materials. Directional materialsYoung’s modulus is not always the same in all orientations of a material. Most metals and ceramics, along with many other materials, are isotropic: Their mechanical properties are the same in all orientations.
However, metals and ceramics can be treated with certain impurities, and metals can be mechanically worked to make their grain structures directional. These materials then become anisotropic, and Young’s modulus will change depending on the direction from which the force is applied. Anisotropy can be seen in many composites as well.
For example, carbon fiber has a much higher Young’s modulus (is much stiffer) when force is loaded parallel to the fibers (along the grain). Other such materials include wood and reinforced concrete. Engineers can use this directional phenomenon to their advantage in creating structures. CalculationYoung’s modulus, E, can be calculated by dividing the tensile stress by the tensile strain:where E is the Young’s modulus (modulus of elasticity) F is the force applied to the object; A 0 is the original cross-sectional area through which the force is applied; ΔL is the amount by which the length of the object changes; L 0 is the original length of the object.
Influences of selected glass component additions on Young’s modulus of a specific base glassYoung’s modulus can vary somewhat due to differences in sample composition and test method. The rate of deformation has the greatest impact on the data collected, especially in polymers. The values here are approximate and only meant for relative comparisons. 2.1 Teori Stabilitas Struktur2.1.1 Konsep StabilitasInstabilitas merupakan keadaan dimana perubahan geometri pada struktur atau komponen struktur di bawah gaya tekan mengakibatkan kehilangan kemampuan untuk menahan beban (Chen, W.F. Dan Lui, E.M., 1987). Konsep stabilitas struktur dapat digambarkan dengan tiga cara, yaitu sebagai berikut:1). Stabilitas berdasarkan posisi keseimbangan.Sebuah bola dalam posisi keseimbangan di atas permukaan cekung bila diberi gangguan beban yang dapat mengakibatkan sedikit perpindahan struktur akan kembali pada semula (Gambar 2.1a).
Posisi ini disebut posisi keseimbangan stabil ( stable equilibrium). Jika gangguan beban diberikan terhadap bola pada posisi permukaan cembung (Gambar 2.1c), bola akan berpindah seterusnya dan tidak kembali ke posisi semula.
Posisi bola ini disebut keseimbangan tidak stabil ( unstable equilibrium). Jika gangguan beban diberikan terhadap bola pada posisi permukaan rata (Gambar 2.1b), bola akan berada pada keadaan keseimbangan pada posisi baru. Posisi ini disebut keseimbangan netral ( neutral equilibrium).2). Stabilitas berdasarkan sistem kekakuan.Sistem struktur berderajat kebebasan tertentu, hubungam gaya dan perpindahan sistem dinyatakan dalam fungsi matriks kekakuan.
Jika fungsi matriks kekakuan positive definite, sistem dikatakan stabil. Transisi antara sistem dari keadaan keseimbangan stabil ke netral maupun tidak stabil ditandai oleh titik batas stabilitas ( stability limit point), dimana kekakuan tangen pada titik ini hilang atau sangat kecil mendekati nol.3). Stabilitas berdasarkan prinsip energi potensial total nol.Pada sistem elastis selalu menunjukkan tendensi keadaan dimana energi potensial total pada keadaan minimum.
Sistem dalam keseimbangan stabil jika deviasi dari keseimbangan keadaan semula meningkatkan total energi potensial, dan sebaliknya keadaan tidak stabil jika deviasi dari keseimbangan semula mengurangi total energi potensial sistem. Sistem dalam kondisi netral jika deviasi dari keseimbangan semula tidak menghasilkan peningkatan atau pengurangan energi potensial total sistem. Gambar 2.1 Konsep stabilitas digambarkan bola di atas bidang lengkung: (a)Keseimbangan stabil, (b)Keseimbangan netral, dan (c)Keseimbangan tidak stabil.Energi potensial ∏ terdiri atas energi regangan (elastis) U dan kerja dari beban W yang dapat didefinisikan:∏ = U – W. 2.1Berdasarkan teori Lagrange-Dirichlet, meminimumkan energi potensial ∏ akan mendapatkan kriteria fundamental untuk stabilitas keseimbangan struktur.Jika perubahan beban adalah fungsi dari parameter λ dan δq1, δq2, δqn adalah variasi perpindahan, maka fungsi ∏ dapat dijabarkan dengan deret Tailor untuk keadaan keseimbangan sebagai: 2.2dimana: adalah variasi pertama, kedua, ketiga dan seterusnya energi potensial. Kondisi sistem struktur dalam keadaan keseimbangan adalah:Jika: δ∏ = 0 untuk setiap δqiatau ∂∏ /∂qi =0 untuk setip harga i 2.4Mengikuti teori Lagrange-Dirichlet, keadaan keseimbangan adalah:Jika: δ 2∏ 0 sistem dalam keadaan stabil.Jika: δ 2∏ = 0 sistem dalam keadaan kritis.Jika: d 2P.
Gambar 2.2 Konsep stabilitas digambarkan dengan bola di atas bidang lengkung dengan berbagai keadaan: (a-f, h) Posisi keseimbangan stabil dan tidak stabil, (g)Variasi energi potensial yang merepresentasikan keadaan stabil. (Bazant, 1991).2.1.2 Analisis Stabilitas Metode EnergiUntuk menjelaskan Analisis stabilitas dengan Metode Variasi kedua Energi Potensial digunakan contoh struktur rangka batang ( truss) dua batang seperti Gambar 2.3. Setiap batang bersifat elastis, kekakuan aksial setiap batang adalah k=EA/(L/cosa) dengan anggapan stiap batang tidak mengalami buckling lokal. Regangan batang e=(Lcosa/cosq-L)/L. Panjang batang mula-mula adalah L/cosa dimana L adalah panjang setelah bentang struktur dan a adalah sudut kemiringan batang mula-mula.Energi potensial.
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(persamaan 2.6)Dengan mendiferensialkan, kita dapatkan kondisi keseimbangan. (persamaan 2.7)Sehingga diperoleh. (persamaan 2.8). Gambar 2.5: Kurva Variasi kedua energi potensial (∂2∏ /∂q2) dibandingkan dengan kurva P(q). Kondisi: kritis terjadi pada (∂2∏ /∂q2)=0, stabil pada (∂2∏ /∂q2)0 dan tidak stabil pada (∂2∏ /∂q2). Gambar 2.6: Fenomena buckling pada struktur: (a)kolom langsing, (b)lateral buckling balok, (c)pelat tipis, (d)cangkang silindris dibebani aksial sumbu, dan (e)cangkang silindris dibebani tegak lurus sumbu.Perilaku buckling beberapa jenis struktur dapat dilihat dari kurva hubungan beban-perpindahan.
Perbedaan perilaku kurva beban-lendutan struktur kolom, pelat dan cangkang dapat diilustrasikan pada Gambar 2.7. Pada pelat, jika mekanisme pasca beban kritis dapat dipenuhi maka peningkatan beban di atas beban kritis dapat dicapai dengan meningkatnya perpindahan. Sedangkan pada cangkang beban maksimum terjadi pada beban kritis, setelah itu terjadi penurunan kekakuan secara signifikan, (Kuleuven, 2005).
A kip per square inch (ksi, kip/in²) is a unit of pressure, stress, Young’s modulus and ultimate tensile strength in the US Customary Units and British Imperial Units. It is a measure of force per unit area.A kip or kip-force, or kilopound (kip, klb, kipf) is a non-SI non-metric unit of force. It is equal to 1,000 pounds-force and used primarily by American architects and engineers to measure engineering loads. 1 kip = 4448.22 newtons (N) = 4.44822 kilonewtons (kN). The name kip comes from combining two words: “kilo” and “pound”. It is also called kilopound-force.
A kip per square inch (ksi, kip/in²) is a unit of pressure, stress, Young’s modulus and ultimate tensile strength in the US Customary Units and British Imperial Units. It is a measure of force per unit area.A kip or kip-force, or kilopound (kip, klb, kipf) is a non-SI non-metric unit of force. It is equal to 1,000 pounds-force and used primarily by American architects and engineers to measure engineering loads.
1 kip = 4448.22 newtons (N) = 4.44822 kilonewtons (kN). The name kip comes from combining two words: “kilo” and “pound”. It is also called kilopound-force. Pengonversi Satuan UmumPanjang, massa, volume, luas, suhu, tekanan, energi, daya, kecepatan dan pengonversi satuan pengukuran populer lainnya. Pressure, Stress, Young’s Modulus ConverterPressure is the ratio of force to the area over which that force is distributed. In other words, pressure is force per unit area applied in a direction perpendicular to the surface of an object.Pressure may be measured in any unit of force divided by any unit of area.
The SI unit of pressure is the pascal (Pa). One pascal is defined as one newton per square meter.
A pressure of 1 Pa is small, therefore everyday pressures are often stated in kilopascals (1 kPa = 1000 Pa). The pressure in car tires can be in the range of 180 to 250 kPa.In continuum mechanics, stress is a measure of the internal forces acting within a deformable body, which either reversibly or irreversibly changes its shape. It is a measure of the average force per unit area of a surface within the body on which internal forces act. These internal forces arise as a reaction to external forces applied to the body. These internal forces are distributed continuously within the volume of the material body, and result in deformation of the body shape.
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Beyond limits of material strength, this can lead to a permanent shape change or structural failure.The dimension of stress is the same as that of pressure, and therefore the SI unit for stress is the pascal (Pa), which is equivalent to one newton per square meter (N/m²). In Imperial units, stress can be measured in pound-force per square inch, which is abbreviated as psi. Menggunakan Pengonversi Pressure, Stress, Young’s Modulus ConverterPengonversi satuan online ini memungkinkan konversi yang cepat dan akurat antar banyak satuan pengukuran, dari satu sistem ke sistem lainnya. Laman Konversi Satuan menyediakan solusi bagi para insinyur, penerjemah, dan untuk siapa pun yang kegiatannya mengharuskan bekerja dengan kuantitas yang diukur dalam satuan berbeda.