What Does Hoop Stress Mean? Water can flow uphill when driven by the hydraulic pressure of the reservoir at a higher elevation, but without a pressure-containing pipe an aqueduct must be constructed so the water can run downhill all the way from the reservoir to the destination. compression and expansion depends on the stiffness (elasticity and geometry) of the two pieces. If you would like to change your settings or withdraw consent at any time, the link to do so is in our privacy policy accessible from our home page.. If the material is subjected to both stresses \(\sigma_x\) and \(\sigma_y\) at once, the effects can be superimposed (since the governing equations are linear) to give: \[\epsilon_x = \dfrac{\sigma_x}{E} - \dfrac{\nu \sigma_y}{E} = \dfrac{1}{E} (\sigma_x - \nu \sigma_y)\]. Yes, hoop stress is the principal stresses. Therefore, by definition,there exist no shear stresses on the transverse, tangential, or radial planes. Hoop stress is caused by Internal pressure. Thick walled portions of a tube and cylinder where only internal pressure acted can be express as. Structures such as pipes or bottles capable of holding internal pressure have been very important in the history of science and technology. When a shell is subjected to a large amount of internal pressure, tensile stresses act along both directions. What is the contact pressure generated between the two cylinders if the temperature is increased by 10\(^{\circ} C\)? The hoop stress formula for a spherical shell is: where \eta is the efficiency of joints. y = Pointing a level of a cone and unit is in. In the case of a thick cylinder, the stresses acting are mainly Hoop's Stress or circumferential stress and Radial Stress. | Civil Engineer. For a sphere, the hoop stress of a thin walled pressure vessel is also calculated using similar principle; however, the stress acting on the shell is only of one type, i.e., the hoop stress. Similarly, the left vertical and lower horizontal planes are \(-y\) and \(-x\), respectively. unit for the internal pressure of the pressure vessel express as Pascal, and unit for Mean diameter of the pressure vessel is meter, unit for thickness of the wall of the pressure vessel meter. From the .eqn (1) and eqn (2) we can write, Force produce for the internal fluid pressure = Resulting force for the reason of hoop stress or circumferential stress. 57). The radial and hoop stresses induced by flux pinning in a type-II bulk superconductor shaped as a long circular cylinder are discussed during an applied magnetic field increases after zero-field cooling. Therefore, the hoop stress acting on the wall thickness, = pid2t. that is developed perpendicular to the surface and may be estimated in thin walled cylinders as: In the thin-walled assumption the ratio Google use cookies for serving our ads and handling visitor statistics. Airplane cabins are another familiar example of pressure-containing structures. = 20 Another distinction is a brittle material's compression strength is usually significantly larger than its tensile strength. This occurs commonly in thin sheets loaded in their plane. Only emails and answers are saved in our archive. A method to measure hoop tensile strength of 1-mm-diameter brittle ceramic spheres was demonstrated through the use of a "C-sphere" flexure strength specimen. Pin-jointed wrought iron hoops (stronger in tension than cast iron) resist the hoop stresses; Image Credit Wikipedia. The hoop stress can be explain as, the stress which is produce for the pressure gradient around the bounds of a tube. Knowledge of these stresses is helpful in designing the riveted or welded joints on the body. The relations governing leakage, in addition to the above expressions for \(\delta_b\) and \(F_b\) are therefore: \[\delta_b + \delta_c = \dfrac{1}{2} \times \dfrac{1}{15}\nonumber\]. r Mathematically can written for hoop stress in pressure vessel is, P = Internal pressure of the pressure vessel, t = Thickness of the wall of the pressure vessel. Since this strain is the change in circumference \(\delta C\) divided by the original circumference \(C = 2\pi r\) we can write: \[\delta_C = C_{\epsilon_{\theta}} = 2\pi r \dfrac{pr}{bE}\nonumber\]. The internal pressure generates a force of \(pA = p(\pi r^2)\) acting on the fluid, which is balanced by the force obtained by multiplying the wall stress times its area, \(\sigma_{\phi} (2\pi rb)\). Hoop stress formula for conical cylinder can be express for two conditions. r The \(z\) components of stress vanish at the surfaces because there are no forces acting externally in that direction to balance them, and these components do not have sufficient specimen distance in the thin through-thickness dimension to build up to appreciable levels. What if the copper cylinder is on the outside? It can be shown that for isotropic materials the bulk modulus is related to the elastic modulus and the Poissons ratio as. This page titled 2.2: Pressure Vessels is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Roylance (MIT OpenCourseWare) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. The large cylindrical shells are manufactured with joints, and when the efficiency of the joints is taken into consideration, the circumferential stress equation becomes: where t\eta_\mathrm{t}t is the efficiency of longitudinal joints because the forces are acting along the longitudinal section. What is the radial displacement \(\delta_r\)? The hoop stressincreases the pipes diameter, whereas the longitudinal stress increases with the pipes length. unit, P (the internal pressure of pipe) expresses as Pascal, and unit for D (diameter of the pipe) is meter, unit for t (thickness of the wall of the pipe) is meter. In a tube the joints of longitudinal produced stress is two times more than the circumferential joints. When a thick-walled tube or cylinder is subjected to internal and external pressure a hoop and longitudinal stress are produced in the wall. Of course, these are not two separate stresses, but simply indicate the stress state is one of uniaxial tension. Hoop stresses are generally tensile. Different grades and diameter to thickness (D/t . The radial expansion by itself doesnt cause leakage, but it is accompanied by a Poisson contraction \(\delta_c\) in the axial direction. When a pressure vessel has open ends, such as with a pipe connecting one chamber with another, there will be no axial stress since there are no end caps for the fluid to push against. When the pressure is put inside the inner cylinder, it will naturally try to expand. How do I calculate hoop stress of a sphere? EQ 7 Note that if there is no torque, the shear stress term drops out of the equa-tion. The Poissons ratio is a dimensionless parameter that provides a good deal of insight into the nature of the material. As the thickness of weld metal increases further, the bending effect of newly deposited weld metal forms extra tensile axial stress and compressive hoop stress on inner cylindrical surface, which enhances with deposition of weld metal corresponding to passes from 76 to 124. The hoop stress is appearing for resist the effect of the bursting from the application of pressure. Fig. The hoop stress in a pressure vessel is acted perpendicular to the direction to the axis. 2.1. Some of our partners may process your data as a part of their legitimate business interest without asking for consent. In the system of the Inch pound second unit, P (the internal pressure of pipe) expresses as ponds force per square inch, and unit for D (diameter of the pipe) is inches, unit for t (thickness of the wall of the pipe) is inches. In the pathology of vascular or gastrointestinal walls, the wall tension represents the muscular tension on the wall of the vessel. Inch-pound-second system (IPS) units for P are pounds-force per square inch (psi). But for the stress square to be in equilibrium, this arrow must be balanced by another acting on the \(-x\) face and pointed in the \(-x\) direction. For the thin-walled assumption to be valid, the vessel must have a wall thickness of no more than about one-tenth (often cited as Diameter / t > 20) of its radius. Cylindrical vessels of this nature are generally constructed from concentric cylinders shrunk over (or expanded into) one another, i.e., built-up shrink-fit cylinders, but can also be performed to singular cylinders though autofrettage of thick cylinders.[2]. In a cylinder with inside diameter 200 mm (radius 100 mm) and outside diameter 400 mm (radius 200 mm) there is a pressure 100 MPa relative to the outside pressure. is less than 10, the radial stress, in proportion to the other stresses, becomes non-negligible (i.e. . . The accuracy of this result depends on the vessel being thin-walled, i.e. Let consider the terms which explaining the expression for hoop stress or circumferential stress which is produce in the cylindrical tubes wall. These three principal stresses- hoop, longitudinal, and radial can be calculated analytically using a mutually perpendicular tri-axial stress system.[1]. An object being pushed together, such as a crumpled sponge, is subject to compressive stress and may undergo shortening. Analysis of hoop and other stresses also increases the pipe's longevity and is warranted when there are sensitive equipment connections, the presence of external pressure, and elevated temperatures. po = External pressure for the cylinder or tube and unit is MPa, psi. The ZDBC condition results in larger stress change in comparison to the constant stress condition at the outer boundary. To find the hoop stress in the spherical tank: Enter the diameter of the shell, d=3md = 3\ \mathrm{m}d=3m. Input the thickness of the shell, t=16.667mmt = 16.667\ \mathrm{mm}t=16.667mm. Due to high internal pressure, the parameters like hoop stress and longitudinal stress become crucial when designing these containers. Hoop stresses separate the top and bottom halves of the cylinder. Thick walled portions of a spherical tube and cylinder where both internal pressure and external pressure acted can be express as. {\displaystyle {\dfrac {r}{t}}\ } Discount calculator uses a product's original price and discount percentage to find the final price and the amount you save. To estimate the longitudinal stress need to create a cut across the cylinder similar to analyzing the spherical pressure vessel. In the outer radius or inner radius portion of a tube hoop stress is remains maximum. The formula for the hoop stress can be written as. Scope (3.91). Failure due to hoop stress can result in the pipe splitting into two halves or rupturing perpendicular to maximum stress. \(r \gg b\). Cylindrical shell bursting will take place if force due to internal fluid pressure will be more than the resisting force due to circumferential stress or hoop stress developed in the wall of the cylindrical shell. . In the theory of pressure vessel, any given element of the wall is evaluated in a tri-axial stress system, with the three principal stresses being hoop, longitudinal, and radial. Terms of Use - Now the deformations are somewhat subtle, since a positive (tensile) strain in one direction will also contribute a negative (compressive) strain in the other direction, just as stretching a rubber band to make it longer in one direction makes it thinner in the other directions (see Figure 8). Consider a shell of made a material whose Young's modulus is EEE and Poisson's ratio, (any doubts on those concepts? Similarly for a strain in the \(y\) direction: \[\epsilon_y = \dfrac{\sigma_y}{E} - \dfrac{\nu \sigma_x}{E} = \dfrac{1}{E} (\sigma_y - \nu \sigma_x)\]. In health sciences, we use it to refer to other things, for example, anxiety: you can even use it to diagnose disorders. Thin walled portions of a spherical tube or cylinder where both internal pressure and external pressure acted can be express as. The modulus of the graphite layer in the circumferential direction is 15.5 GPa. By how much should the temperature of the aluminum cylinder be lowered in order to fit it inside the steel cylinder? Please read AddThis Privacy for more information. We now take the next step, and consider those structures in which the loading is still simple, but where the stresses and strains now require a second dimension for their description. Inspections, hand calculations, or computer modeling are methods of analyzing pipe stresses. But of course the real world is three-dimensional, and we need to extend these concepts accordingly. The hoop stress usually much larger for pressure vessels, and so for thin-walled instances, radial stress is usually neglected.The radial stress for a thick-walled cylinder isequal and opposite of the gauge pressure on the inside surface, and zero on the outside surface. Equating these: \[p(\pi r^2) = \sigma_{\phi} (2\pi rb)\nonumber\]. The sign convention in common use regards tensile stresses as positive and compressive stresses as negative. Considering an axial section of unit length, the force balance for Figure 5 gives, \[2 \sigma_{\theta} (b \cdot 1) = p(2r \cdot 1)\nonumber\]. What are the hoop and axial stresses \(\sigma_{\theta}, \sigma_z\) when the cylinder carries an internal pressure of 1500 psi? The formula of the Barlows is used for estimate the hoop stress for the wall section of the pipe. Figure 1: Hoop Stress & Longitudinal Stress in a Pipe under Pressure. Enter the internal pressure on the walls of the shell, p=1.5MPap = 1.5\ \mathrm{MPa}p=1.5MPa. In a vertical well, breakouts are centered at the azimuth of minimum horizontal stress SHmin because this is where the compressive hoop stress is greatest. This result different stresses in different directions occurs more often than not in engineering structures, and shows one of the compelling advantages for engineered materials that can be made stronger in one direction than another (the property of anisotropy). Let's go through the steps to calculate the stresses using this hoop stress calculator. These applications will - due to browser restrictions - send data between your browser and our server. Similarly, the longitudinal stress, considering circumferential joint efficiency, c\eta_\mathrm{c}c is: Now that we know the hoop stress, one can also estimate the ratio of longitudinal stress to hoop stress, which is 0.50.50.5. It is common to build pressure vessels by using bolts to hold end plates on an open-ended cylinder, as shown in Figure 9. Then only the hoop stress \(\sigma_{\theta} = pr/b\) exists, and the corresponding hoop strain is given by Hookes Law as: \[\epsilon_{\theta} = \dfrac{\sigma_{\theta}}{E} = \dfrac{pr}{bE}\nonumber\]. axial stress, a normal stress parallel to the axis of cylindrical symmetry. - that in addition stress caused by pressure -stress can be induced in the pipe or cylinder wall by restricted temperature expansion. They illustrate very dramatically the importance of proper design, since the atmosphere in the cabin has enough energy associated with its relative pressurization compared to the thin air outside that catastrophic crack growth is a real possibility. The consent submitted will only be used for data processing originating from this website. where the \(a\) and \(s\) subscripts refer to the brass and steel cylinders respectively. Consider a cylindrical pressure vessel to be constructed by filament winding, in which fibers are laid down at a prescribed helical angle \(\alpha\) (see Figure 6). = Hoop stress in the direction of the both and unit is MPa, psi. 0 When the e/h value is equal to 0.3, the load capacity is found to be mostly dependent on the concrete compressive strength and tensile steel bars (e.g., Daugeviius et al. The hoop stress formula for a spherical shell with diameter d and thickness t under pressure p is: (h) = p d / (4 t ) where is joint efficiency. t Dm = Mean Diameter . Pressure vessels are specially designed containers used to hold fluids at a different pressure than ambient ones. Note: Loads beyond 180 not support in load terms equations. Yup, stress: physicists and engineers use this word when talking about materials, as you can see in our stress calculator. Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications! Bursting of the pipe occurs if the force created by the internal pressure exceeds the hoop stress's resisting force. P = Internal fluid pressure of the cylindrical tube, d = Internal diameter for the thin cylindrical tube, H = Hoop stress or circumferential stress which is produce in the cylindrical tubes wall, Force produce for the internal fluid pressure = Area where the fluid pressure is working * Internal fluid pressure of the cylindrical tube, Force produce for the internal fluid pressure = (d x L) x P, Force produce for the internal fluid pressure = P x d x L .eqn (1), Resulting force for the reason of hoop stress or circumferential stress = H x 2Lt .eqn (2). Various pressure vessels include boilers, water tanks, petrol tanks, gas cylinders, spray cans, fire extinguishers, pipes, etc. Hub Shaft Mathematically hoop stress can be written as. / The stress in axial direction at a point in the tube or cylinder wall can be expressed as: a = (pi ri2 - po ro2 )/(ro2 - ri2) (1), a = stress in axial direction (MPa, psi), pi = internal pressure in the tube or cylinder (MPa, psi), po = external pressure in the tube or cylinder (MPa, psi), ri = internal radius of tube or cylinder (mm, in), ro = external radius of tube or cylinder (mm, in). What pressure is needed to expand a balloon, initially \(3''\) in diameter and with a wall thickness of \(0.1''\), to a diameter of \(30''\)? {\displaystyle B=0} r = The hoop stress in the direction of the radial circumferential and unit is MPa, psi. Their first interest was in studying the design and failures of steam boilers. But the inner-surface radial stress is equal to \(p\), while the circumferential stresses are \(p\) times the ratio (\(r/2b\)). This innovative specimen geometry was chosen because a simple, monotonically increasing uniaxial compressive force produces a hoop tensile stress at the C-sphere's outer surface . The greater the force and the smaller the cross . The steps are listed below. Consider a thin-walled pressure vessel. pi = Internal pressure for the cylinder or tube and unit is MPa, psi. ri = Internal radius for the cylinder or tube and unit is mm, in. 1 Introduction Note! The hoop stress in the direction of the axial at a particular point in the wall of the cylinder or tube can be written as. Hoop stress is the stress that occurs along the pipe's circumference when pressure is applied. The fluid itself is assumed to have negligible weight. Circumferential or Hoop Stress: This is the stress which is set up in resisting the bursting effect of the applied internal pressure and can be most conveniently treated by considering the equilibrium of the cylinder. Stress in Thick-Walled Cylinders or Tubes, stress can be induced in the pipe or cylinder wall by restricted temperature expansion. Due to the internal pressure acting inside the vessel, some stresses are developed in the inner wall of the vessel along the radius of the vessel which is known as the Radial Stresses. In order to fit the two cylinders together initially, the inner cylinder is shrunk by cooling. Trenchlesspedia is a part of Janalta Interactive. An internal pressure \(p\) induces equal biaxial tangential tensile stresses in the walls, which can be denoted using spherical \(r\theta \phi\) coordinates as \(\sigma_{\theta}\) and \(\sigma_{\phi}\). Hoop stress formula in the case of thick cylinder three sections. This technique helps to reduce absolute value of hoop residual stresses by 58%, and decrease radial stresses by 75%. Hoop stress in pipelines can be explain as, the stress in a wall of a pipe operable circumferentially in a profile perpendicular to the axis of the longitudinal of the tube and rose by the tension of the fluid substance in the pipe. Plot this function and determine its critical values. The Benefits of Trenchless Technology to the Utility Industry in Asia, The Key Principles of Effective Solids Control, Why Reamers Are Important to Trenchless Boring, Plus Available Types of Reamers, Planning a Bore For a Trenchless Project? You can target the Engineering ToolBox by using AdWords Managed Placements. Yielding is governed by an equivalent stress that includes hoop stress and the longitudinal or radial stress when absent. Hoop stress that is zero During a pressure test, the hoop stress is twice that of the axial stress, so a pressure test is used to determine the axial strength under "biaxial" loading. Consider a compound cylinder, one having a cylinder of brass fitted snugly inside another of steel as shown in Figure 7 and subjected to an internal pressure of \(p = 2\) Mpa. Hoop stresses are tensile and generated to resist the bursting effect that results from the application of pressure. Subscribe to our newsletter to get expert advice and top insights into every aspect of trenchless construction and rehabilitation. Note that a hoop experiences the greatest stress at its inside (the outside and inside experience the same total strain, which is distributed over different circumferences); hence cracks in pipes should theoretically start from inside the pipe. {\displaystyle R_{i}=0} thickness Here lets say for example the cylinder is made of copper alloy, with radius \(R = 5''\), length \(L = 10''\) and wall thickness \(b_c = 0.1''\). The hoop stress calculator determines the stresses acting on a thin-walled pressure vessel. In a properly supported round pipe containing a fluid under pressure the largest tensile stress is the hoop stress. A stress state with both positive and negative components is shown in Figure 2. In the sections to follow, we will outline the means of determining stresses and deformations in structures such as these, since this is a vital first step in designing against failure. SI units for P are pascals (Pa), while t and d=2r are in meters (m). The Poissons ratio is also related to the compressibility of the material. The hoop stress is tensile, and so wrought iron, a material with better tensile strength than cast iron, is added. In mechanics, a cylinder stress is a stress distribution with rotational symmetry; that is, which remains unchanged if the stressed object is rotated about some fixed axis. The hoop stress calculator then uses the circumference stress equation: You can follow similar steps if you wonder how to calculate hoop stress in a pipe by setting the shape to Cylinder, or for any other pressure vessel calculations. < Three cylinders are fitted together to make a compound pressure vessel. For calculating the hoop stress just need to multiply the internal diameter (mm) of the pipe with internal pressure (MPa) of the pipe and then the value need to divided with the thickness (mm) of the pipe with 2. A cylinder has two main dimensions length and diameter, which would change due to internal pressure. Therefore, by definition, there exist no shear stresses on the transverse, tangential, or radial planes.[1]. {\displaystyle A=P_{o}} However, a state of plane stress is not a state of plane strain. Formula for estimate the hoop stress of a cylinder is. Note that this is a statically determined result, with no dependence on the material properties. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. V = - N A z + V A u + LT v. LT M LT N, and LT V are load terms for several types of load. Legal. (ri < r < ro), Maximum hoop stress for the cylinder or tube is, ri = r. The hoop stress in the direction of the radial at a particular point in the wall of the cylinder or tube can be written as. The bolts have 18 threads per inch, and the retaining nuts have been tightened 1/4 turn beyond their just-snug point before pressure is applied. Hoop stress acts perpendicular to the axial direction. Check out 34 similar materials and continuum mechanics calculators . hoop stress b) radial stress Figure 12.6 Stress distributions of hoop and radial stresses. Dont Miss the Latest From Trenchlesspedia! P The hoop stress generated when a cylinder is under internal pressure is twice that of the longitudinal stress. [9] Fairbairn realized that the hoop stress was twice the longitudinal stress, an important factor in the assembly of boiler shells from rolled sheets joined by riveting. unit, P (the internal pressure of pipe) expresses as Pascal, and unit for D (diameter of the pipe) is meter, unit for t (thickness of the wall of the pipe) is meter. Similarly, if this pipe has flat end caps, any force applied to them by static pressure will induce a perpendicular axial stress on the same pipe wall. Enter the internal pressure on the walls of the shell, ppp. This means that the inward force on the vessel decreases, and therefore the aneurysm will continue to expand until it ruptures. When the vessel has closed ends, the internal pressure acts on them to develop a force along the axis of the cylinder. We and our partners use data for Personalised ads and content, ad and content measurement, audience insights and product development. In thick-walled pressure vessels, construction techniques allowing for favorable initial stress patterns can be utilized. The maximum hoop stress always occurs at the inner radius or the outer radius depending on the direction of the pressure gradient.Axial stress describesthe amount of force per unit of cross-sectional area that acts in the lengthwise direction of a beam or axle. Paradoxically, the tightly bonded ceramics have lower bulk moduli than the very mobile elastomers. Figure 26.2. These stresses are vital parameters when it comes to pressure vessel design. Continue with Recommended Cookies. The hoop stress increases the pipe's diameter, whereas the longitudinal stress increases with the pipe's length. For instance, the hoop stress in the inner brass cylinder is, \[\sigma_{\theta, b} = \dfrac{(p - p_c) r_b}{b_b} = 62.5 \text{ MPa} (= 906 \text{ psi})\nonumber\], Note that the stress is no longer independent of the material properties (\(E_b\) and \(E_s\)), depending as it does on the contact pressure pc which in turn depends on the material stiffnesses. Hoop tensile strength and longitudinal tensile strengths and modulus were considered during the study and the development of a computer program was performed for design and analysis purposes. No, hoop stress or circumference stress is not a shear stress. The results are averaged, with a typical hoop tensile strength for filament wound vinylester pipe being 40,000 psi (276 MPa). radial stress, a normal stress in directions coplanar with but perpendicular to the symmetry axis. Where: P = is the internal pressure t = is the wall thickness r = is the inside radius of the cylinder. Formula for estimate the hoop stress in a pipe is, Hoop stress = Internal diameter x Internal pressure/2 x Thickness. t = Thickness of the pipe and unit is mm, in. r = Radius for the cylinder or tube and unit is mm, in. As shown in Figure 4, both hoop stress and hoop strain at more than 10 m distant from the crack tip in the adhesive layer of 0.1 mm thickness is much higher . M = M A - N A R ( 1 - u) + V A R z + LT M. Hoop Stress. The bolts then stretch by an amount \(\delta_b\) given by: \[\delta_b = \dfrac{F_b L}{A_b E_b}\nonumber\], Its tempting to say that the vessel will start to leak when the bolts have stretched by an amount equal to the original tightening; i.e. The change in circumference and the corresponding change in radius \(\delta_r\) are related by \(delta_r = \delta_C /2\pi, so the radial expansion is: This is analogous to the expression \(\delta = PL/AE\) for the elongation of a uniaxial tensile specimen. | Civil Engineer, Technical Content Writer, By: Della Anggabrata where the minus sign accounts for the sign change between the lateral and longitudinal strains. The hoop stress actually is a function which is go about to tension the pipe separately in a direction of the circumferential with the tension being created on the wall of the pipe by the internal pressure of the pipe by natural gas or other fluid. When this ratio is large, the radial stresses can be neglected in comparison with the circumferential stresses. The calculations show that . The resisting force resulting from the hoop stress is a product of the resisting area and the hoop stress. The purpose of this study is to analyze the thermal degradation of filament wound glass fiber/epoxy resin tubular . The vertical plane on the right is a \(+x\) plane. Hoop Stress or Circumferential Stress in a Piping System: The Normal Stress that acts perpendicular to the axial direction or circumferential direction is known as Hoop Stress. Stress in Axial Direction The stress in axial direction at a point in the tube or cylinder wall can be expressed as: a = (pi ri2 - po ro2 )/ (ro2 - ri2) (1) where a = stress in axial direction (MPa, psi) The Boltzmann factor calculator computes a relative probability of two states of a system at thermal equilibrium. n. Stress applied along the length of a body. {\displaystyle {\text{diameter}}/{\text{thickness}}<20}