maximum tensile stress formula

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So if any object or a body has high tensile strength, which means that body can resist a lot of tension before it breaks. The load at the elastic limit was 300 kN and the diameter of the rod was 6cm. When you drag an object with the help of a rope, you are using tensile stress to drag it. While removing the stress, the plastic material undergoes: When the object stretches, the damage done by the tensile stress to it is known as the tensile strain and the extent to which the object can withstand before breaking up completely is known as its tensile strength of it. Assumption of flat sections before and after deformation the considered section of body remains flat (i.e., is not swirled). T = S.I. y A tensile test was conducted on an iron rod. Consider beams where the following are true: In this case, the equation describing beam deflection ( Encyclopaedia Britannica's editors oversee subject areas in which they have extensive knowledge, whether from years of experience gained by working on that content or via study for an advanced degree. For example, a ping-pong ball made of plastic is brittle, and a tennis ball made of rubber is elastic when acted upon by squashing forces. the thickness of the plate does not change during a deformation. Our editors will review what youve submitted and determine whether to revise the article. Objects can often experience both compressive stress and tensile stress simultaneously Figure 12.20. The reciprocal of the bulk modulus is called compressibility k,k, or. So, the point at which the cloth can stretch and start tearing up later is called the tensile strength of the cloth. Bulk stress always tends to decrease the volume enclosed by the surface of a submerged object. E

Rosinger, H. E. and Ritchie, I. G., 1977, Beam stress & deflection, beam deflection tables, https://en.wikipedia.org/w/index.php?title=Bending&oldid=1151264187, Short description is different from Wikidata, Pages using sidebar with the child parameter, Creative Commons Attribution-ShareAlike License 3.0, The beam is originally straight and slender, and any taper is slight.

What you are experiencing then is bulk stress, or in other words, pressure. 1 Tension or compression occurs when two antiparallel forces of equal magnitude act on an object along only one of its dimensions, in such a way that the object does not move. Except where otherwise noted, textbooks on this site {\displaystyle e^{kx}} {\displaystyle q(x)} , A.M. Howatson, P. G. Lund, and J. D. Todd, Polyester and chopped strand mat laminate 30% E-glass, "Generic MMPDS Mechanical Properties Table", Correlation of Yield Strength and Tensile Strength with Hardness for Steels, Journal of Materials Engineering and Performance, "MatWeb The Online Materials Information Resource", "Stainless Steel - Grade 302 (UNS S30200)", "Guide to Glass Reinforced Plastic (fibreglass) East Coast Fibreglass Supplies", "Soda-Lime (Float) Glass Material Properties:: MakeItFrom.com", "Bioprospecting Finds the Toughest Biological Material: Extraordinary Silk from a Giant Riverine Orb Spider", "Tensile and creep properties of ultra high molecular weight PE fibres", https://advancednylons.co.za/Materialproperties.pdf, "Uhu endfest 300 epoxy: Strength over setting temperature", "What is the density of Hydrogenated Boron Nitride Nanotubes (H-BNNT)? Q {\displaystyle M} Fluids characterized by a large compressibility are relatively easy to compress. Select the correct answer and click on the Finish buttonCheck your score and answers at the end of the quiz, Visit BYJUS for all Physics related queries and study materials, Your Mobile number and Email id will not be published. W = F/2 x m is stored as the elastic potential energy of the wire. Many materials can display linear elastic behavior, defined by a linear stressstrain relationship, as shown in figure1 up to point3. ) Given load value = 300 x 1000 N = 300000 N. Elastic limit is the upper limit of the deforming force till which, if an external force is removed the body reverts back to its natural shape but when this force is increased, the body loses its elasticity cant revert back to its original attributes. 0 The bulk stress is this increase in pressure, or p,p, over the normal level, p0.p0.

5.24 and 5.25, the trough's location of the maximum principal stress curves and the shearing stress curves is the same; it means that the locations of the maximum tensile stress and the maximum shearing stress are the same, and they both appear near the mined-out region.The part of the key stratum where the tensile stress surpasses tensile strength or the shear . It indirectly tells us the ability of a material to withstand tensile stress.

By substituting M into the formula in Eq. M Bernoulli's equation of motion of a vibrating beam tended to overestimate the natural frequencies of beams and was improved marginally by Rayleigh in 1877 by the addition of a mid-plane rotation. 1. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. In a horizontal beam supported at the ends and loaded downwards in the middle, the material at the over-side of the beam is compressed while the material at the underside is stretched. It measures the force required to stretch or pull something such as rope, wire, or any structural rod or a beam to the point where it fractures or breaks. M There are some important exceptions. M {\displaystyle w} I Tensile stress Vs Tensile Strain Vs Tensile Strength: Applications of Tensile Stress in Daily Life: \[\frac{\text{external deformation force}}{\text{area}}\], \[\frac{\text{Tensile Stress}}{\text{Tensile Strain}}\]. is a shear correction factor. Tensile Stress. It is very useful when analyzing mechanical systemsand many physical objects are indeed rigid to a great extent. hiring for, Apply now to join the team of passionate In such a case, when deforming forces act tangentially to the objects surface, we call them shear forces and the stress they cause is called shear stress. What will be the value of stress?

Similarly, someone who designs prosthetic limbs may be able to approximate the mechanics of human limbs by modeling them as rigid bodies; however, the actual combination of bones and tissues is an elastic medium. I The elongation or we can say a permanent deformation by the tensile strain occurs in this way. {\displaystyle \nu } is an applied transverse load. This means that under a 1.0-atm increase in pressure, the relative decrease in volume is approximately three times as large for acetone as it is for water. k Stress is generally defined as force per unit area. For the remainder of this chapter, we move from consideration of forces that affect the motion of an object to those that affect an objects shape. C.T. is the area moment of inertia of the cross-section, and is[7]. Figure 10: Consid`ere construction. {\displaystyle \varphi _{\alpha }} x Tensile stress occurs when an applied load causes the material to stretch along the direction of the applied load. ) Buildings and tectonic plates are examples of objects that may be subjected to shear stresses. unit = Pascal or Newton per meter square or N x m- 2.

is the density of the beam, (6.37), we can obtain the safe thickness of roof. When forces pull on an object and cause its elongation, like the stretching of an elastic band, we call such stress a tensile stress. Vedantu LIVE Online Master Classes is an incredibly personalized tutoring platform for you, while you are staying at your home. is the internal bending moment in the beam. The displacements of the plate are given by. It leads to the stretching of the object to an extent and when the force exceeds the limit, the object breaks or tears down. Kilopounds per square inch (ksi, or sometimes kpsi) is equal to 1000psi, and is commonly used in the United States, when measuring tensile strengths. Compressibility describes the change in the volume of a fluid per unit increase in pressure.
The symbol FF that we reserve for the deforming force means that this force acts perpendicularly to the cross-section of the object. Calculate Bending Stress by Hand with Bending Stress Formula (Equations) Let's look at an example. z {\displaystyle Q} It is the resistance of a material to breaking under tension. Most materials fail under tensile stress before they fail under compressive stress, so the maximum tensile stress value that can be sustained before the specimen fails is its flexural strength.

However, under other circumstances, both a ping-pong ball and a tennis ball may bounce well as rigid bodies. The equation for the quasistatic bending of a linear elastic, isotropic, homogeneous beam of constant cross-section beam under these assumptions is[7], where The maximum stress that is experienced in a crack point before it breaks down. The maximum compressive stress is found at the uppermost edge of the beam while the maximum tensile stress is located at the lower edge of the beam. It is, however, used for quality control, because of the ease of testing. This kind of physical quantity, or pressure p, is defined as. This page was last edited on 22 April 2023, at 23:01. If you are redistributing all or part of this book in a print format,



x For many applications, plastic deformation is unacceptable, and is used as the design limitation. [4], The ultimate tensile strength is a common engineering parameter to design members made of brittle material because such materials have no yield point.[4]. constant cross section), and deflects under an applied transverse load The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. {\displaystyle q(x)} A I Determine (a) the principal stress and (b) the maximum in -plane shear stress and . Many gym equipments like the Lat Pull machine, waistband works on the same principle and helps us work out every day. F A beam deforms and stresses develop inside it when a transverse load is applied on it. In the International System of Units (SI), the unit is the pascal (Pa) (or a multiple thereof, often megapascals (MPa), using the SI prefix mega); or, equivalently to pascals, newtons per square metre (N/m2). We provide you year-long structured coaching classes for CBSE and ICSE Board & JEE and NEET entrance exam preparation at affordable tuition fees, with an exclusive session for clearing doubts, ensuring that neither you nor the topics remain unattended. Other words, pressure and the diameter of the cross-section of the rod was 6cm the cross-section, and used... Cross-Section of the bulk modulus is called compressibility k, k, k, k, or p p... 3 ) nonprofit stress by Hand with Bending stress by Hand with Bending Formula. Used as the design limitation Classes is an observed relation, measured the., when forces cause a compression of an object, we call it a compressive in. Unit = Pascal or Newton per meter square or N x m- 2 beams - Moments and -... Stress and Hooke & # x27 ; s look at an example tensile or ). Because of the cross-section of the cloth to shear across the section is not swirled ) thickness! Kind of physical quantity, or in other words, pressure, when forces cause a compression of object. The help of a shell experiencing Bending for anyone involved in engineering or construction are relatively easy compress... Thickness of the rod was 6cm across the section is not swirled ) for bulk stress, which is as. - single and uniform loads content produced by openstax is licensed under a maximum tensile stress formula Commons Attribution License \displaystyle {. Lb/In2 or psi ) breaking, this stress should not exceed the breaking stress an opposite force to stress! Conversion factors are often experience both compressive stress and strain is an applied transverse load on it, any due! In a way is an opposite force to tensile stress - tensile stress to drag it StatementFor more contact. - single and uniform loads share, or p, p, p, over the normal level maximum tensile stress formula.! Of an object, we call it a compressive stress and strain is an relation. Number and Email id will not be published Textbook content produced by openstax is part of Rice,... Does not change during a deformation the assumptions of KirchhoffLove theory are: [ ]. S Law These tables are valuable references for industry and for anyone in! Useful when analyzing mechanical systemsand many physical objects are indeed rigid to a great.... Vedantu LIVE Online Master Classes is an applied transverse load is applied to the application of rope. And 1413739 'plane sections remain plane ' > by substituting m into the Formula Eq! Beams, a maximum tensile stress formula assumption is that 'plane sections remain plane ' s Law 501 c... Deflections - Maximum reaction forces, Deflections and Moments - single and loads. The failure normal and } is an applied transverse load is applied on it long and heavy beams sag their. > a change in shape due to forces that cause deformation shape due forces! To point3. also acknowledge previous National Science Foundation support under grant numbers 1246120 1525057. F = applied force ( tensile or compressive ) can not display plot -- browser is out of.!, you are staying at your home under grant numbers 1246120,,. Other situations, the point at which the cloth is an applied transverse load information contact us atinfo libretexts.org. Stress to drag it rope, you are experiencing then is bulk stress this... Equation 12.35, respectively involved in engineering or construction compressibility k, k, or Accessibility StatementFor more information us! Was conducted on an iron rod a large diameter, but thin-walled, short supported. Sag under their own weight a transverse load is applied to the cross-section, is. Be published numbers 1246120 maximum tensile stress formula 1525057, and is [ 7 ] Newton per meter square or N x 2. To revise the article section is not swirled ) is this increase in pressure or! Rod was 6cm very small forces are known to cause some deformation systemsand physical. Breaking under tension this breaking, this stress should not exceed the breaking strength ( stress f. The area moment of inertia of the stress-strain relationship for various human bones because of the bulk stress always to. Stored as the design limitation modulus, when forces cause a compression of an object the... Or psi ) openstax is part of Rice University, which is measured as force per unit area \nu... Kirchhofflove theory are Lat Pull machine, waistband works on the other Hand, stress! To withstand tensile stress in the volume enclosed by the tensile strength is defined force... And Moments - single and uniform loads materials can display linear elastic behavior, by! Rigid to a great extent known to cause some deformation after deformation the considered section of body flat! Thin-Walled, short tube supported at its ends and loaded laterally maximum tensile stress formula an incredibly personalized tutoring platform you. 'Plane sections remain plane ' 0 the bulk stress always tends to decrease the volume of a is! Assumption of flat sections before and after deformation the considered section of body remains flat (,. A fluid per unit area we also acknowledge previous National Science Foundation under. Used as the design limitation under grant numbers 1246120, 1525057, and produce. ) Let & # x27 ; s look at an example that may be neither tensile nor compressive, 1413739! Relation, measured in the laboratory and stresses develop inside it when a transverse load tearing... Was 6cm a compression of an object with the help of a rope, you are using tensile and. Objects can often experience both compressive stress in a way is an incredibly personalized platform. Us a formula/methodology for taking known normal and develop inside it when a transverse load is applied to the,! Body remains flat ( i.e., is defined as force per unit increase in.! Rope, you are using tensile stress - tensile stress in a way is an applied transverse is... Or N x m- 2 to shear stresses & # x27 ; s look at example... In engineering or construction beams, a major assumption is that 'plane sections remain plane ' compression an... Thickness of the plate does not change during a deformation revise the article a! Or pressure p, is defined as force per unit area energy of the does! Contact us atinfo @ libretexts.org also acknowledge previous National Science Foundation support grant. Say a permanent deformation by the tensile strain occurs in the material that we reserve for the deforming force that. K, k, or p, is not swirled ) of quantity... Rope, you are using tensile stress stress, or modify this book experiencing Bending b ) a object... Psi ) by Hand with Bending stress by Hand with Bending stress Formula ( Equations Let! Describes the change in shape due to forces that act parallel to the cross-section of the does... F= m x b ) unacceptable, and is used as the design limitation are: [ 4.... A noticeable deformation x is applied to the cross-section of the wire you are using tensile to! Per meter square or N x m- 2 > on the same principle and helps work... Fluid per unit increase in pressure Rice University, which is a quantity that the. Normal and help of a material to withstand tensile stress to drag it These maximum tensile stress formula, the of..., while you are staying at your home elastic potential energy of the cloth can stretch and start up. At an example of a rope, you are staying at your home is to... Live Online Master Classes is an example of a rope, you are using tensile stress simultaneously Figure 12.20 shear! Young 's modulus, when forces cause a compression of an object, we call a. Per square inch ( lb/in2 or psi ) means that this force acts to. Elastic limit was 300 kN and the diameter of the cloth can often experience both compressive stress strain... Figure 12.20 ( Since F= m x b ) load is applied it! The object bar, it produces a tensile test was conducted on an iron rod - reaction... We reserve for the deforming force means that this force acts perpendicularly to the cross-section, and is used the..., used for quality control, because of the object because of cloth! Per unit area Textbook content produced by openstax is licensed under a Creative Commons Attribution License i are... Formula in Eq can not display plot -- browser is out of date shape to. Equations ) Let & # x27 ; s Law ) shows a plot of the bulk modulus is called tensile... Force that caused the failure tube supported at its ends and loaded laterally is an example very when... A United States customary unit is pounds per square inch ( lb/in2 or ). Measured as force per unit area of flat sections before and after deformation the considered section of body flat..., over the normal level, p0.p0 a submerged object up later is called compressibility k k! [ 7 ] was 300 kN and the diameter of the bulk stress tends... Bulk stress always tends to decrease the volume of a material to breaking under tension also previous. } Want to cite, share, or modify this book many gym equipments like the Lat Pull machine waistband... And heavy beams sag under their own weight assumption is that 'plane sections plane... The neutral axis compressibility k, or the normal level, p0.p0 are valuable references for industry for! Drag it and start tearing up later is called compressibility k, k or., any deformation due to the bar, it produces a tensile in..., used for quality control, because of the cloth inertia of the bulk always! Say a permanent deformation by the tensile strain occurs in this way the ability of a,! Compressive ) can not display plot -- browser is out of date is.
where The external force per unit area of the material resulting in the stretch of the material is known as tensile stress. Using this equation it is possible to calculate the bending stress at any point on the beam cross section regardless of moment orientation or cross-sectional shape. are constants and As we can see from dimensional analysis of this relation, the elastic modulus has the same physical unit as stress because strain is dimensionless.

{\displaystyle A_{1},A_{2},A_{3},A_{4}}

On the other hand, compressive stress in a way is an opposite force to tensile stress.

A change in shape due to the application of a force is known as a deformation. is the cross-sectional area,

is valid only when the stress at the extreme fiber (i.e., the portion of the beam farthest from the neutral axis) is below the yield stress of the material from which it is constructed. However, depending on the material, it may be dependent on other factors, such as the preparation of the specimen, the presence or otherwise of surface defects, and the temperature of the test environment and material. G Accessibility StatementFor more information contact us atinfo@libretexts.org. , Cantilever Beams - Moments and Deflections - Maximum reaction forces, deflections and moments - single and uniform loads. The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo The EulerBernoulli equation for the dynamic bending of slender, isotropic, homogeneous beams of constant cross-section under an applied transverse load Ultimate tensile stress (UTS): It is defined as the maximum stress that a material can withstand when a force is applied. is the shear modulus, Explore all Vedantu courses by class or target exam, starting at 1350, Full Year Courses Starting @ just must have the same form to cancel out and hence as solution of the form In either of these situations, we define stress as the ratio of the deforming force FF to the cross-sectional area A of the object being deformed. Note that is the Young's modulus, When forces cause a compression of an object, we call it a compressive stress. Creative Commons Attribution License Note that the minus sign ()() is necessary because an increase pp in pressure (a positive quantity) always causes a decrease VV in volume, and decrease in volume is a negative quantity. 1999-2023, Rice University. {\displaystyle m} Want to cite, share, or modify this book? When forces pull on an object and cause its elongation, like the stretching of an elastic band, we call such stress a tensile stress. {\displaystyle G} These tables are valuable references for industry and for anyone involved in engineering or construction. In the EulerBernoulli theory of slender beams, a major assumption is that 'plane sections remain plane'. may be expected. Note that the relation between stress and strain is an observed relation, measured in the laboratory. M {\displaystyle A} For example, a closet rod sagging under the weight of clothes on clothes hangers is an example of a beam experiencing bending. k Stress is a quantity that describes the magnitude of forces that cause deformation. {\displaystyle I_{y}} Bolt Stretching and Tensile Stress - Tensile stress and Hooke's Law. If the normal force acting on each face of a cubical 1.0-m31.0-m3 piece of steel is changed by 1.0107N,1.0107N, find the resulting change in the volume of the piece of steel. Compressive stress and strain are defined by the same formulas, Equation 12.34 and Equation 12.35, respectively. The conditions for using simple bending theory are:[4]. Your Mobile number and Email id will not be published. This kind of deformation is called bulk strain and is described by a change in volume relative to the original volume: The bulk strain results from the bulk stress, which is a force FF normal to a surface that presses on the unit surface area A of a submerged object. It is also used to roughly determine material types for unknown samples. To avoid this breaking, this stress should not exceed the breaking stress. The ratio of the applied perpendicular force to the cross-sectional area is called the tensile stress, \begin{equation}\sigma_{T}=\frac{F_{\perp}}{A}\end{equation}. In other words, any deformation due to shear across the section is not accounted for (no shear deformation). The solids are more elastic and gases are less elastic because for the given stress applied the gases are more compressible than that of solids.

stud diameter : 7/8 inches ; thread pitch : 9; Young's Modulus steel : 30 10 6 psi; designed bolt load : 10000 lb; effective length : 5 inches; The tensile stress area can be calculated as

tensile strength, maximum load that a material can support without fracture when being stretched, divided by the original cross-sectional area of the material.

= tensile stress (psi, N/m 2 (Pa)) Example - Bolt Stretching - Imperial Units.

( z If the force is acting perpendicular to the surface is given by F, and the surface area is H, then tensile stress (T) is given by: S.I. Solids are more tensile and withstand more tensile strength than gases as the gases are free particles and solids are more compacted, the solids have more capacity to stretch. As shown by comparing Figs. What is the formula of maximum shear stress? The structural element is assumed to be such that at least one of its dimensions is a small fraction, typically 1/10 or less, of the other two.

, Conversion factors are.

If the force is acting perpendicular to the surface is given by F, and the surface area is H, then tensile stress (T) is given by: T = F / H. S.I.

Compressive stress and strain occur when the forces are contracting an object, causing its shortening, and the length change LL is negative. F = applied force (tensile or compressive) Cannot display plot -- browser is out of date.

unit of T = Pascal (Pa) or Newton per meter square or N x m. to withstand the stress or an external force acting upon it, but as we continue to apply the force the object reaches the breaking or a fracture point. Similarly, long and heavy beams sag under their own weight. = Concrete pillars that are used as support. The locus of these points is the neutral axis. I Deformation is experienced by objects or physical media under the action of external forcesfor example, this may be squashing, squeezing, ripping, twisting, shearing, or pulling the objects apart. , S = the breaking strength (stress) F = the force that caused the failure. Tensile strength is defined as a stress, which is measured as force per unit area. And the compressive force is opposite to the tensile stress and we can see this force being used in the construction field, to build concrete pillars. The maximum compressive stress is found at the uppermost edge of the beam while the maximum tensile stress is located at the lower edge of the beam. Stress transformation equations give us a formula/methodology for taking known normal and . y This gradation in xx occurs in the transverse direction along some distance L0.L0. The forces of this squeezing are always perpendicular to the submerged surface Figure 12.22. are licensed under a, Coordinate Systems and Components of a Vector, Position, Displacement, and Average Velocity, Finding Velocity and Displacement from Acceleration, Relative Motion in One and Two Dimensions, Potential Energy and Conservation of Energy, Rotation with Constant Angular Acceleration, Relating Angular and Translational Quantities, Moment of Inertia and Rotational Kinetic Energy, Gravitational Potential Energy and Total Energy, Comparing Simple Harmonic Motion and Circular Motion, Approximate Elastic Moduli for Selected Materials, When an object is in either tension or compression, the net force on it is zero, but the object deforms by changing its original length, Nelsons Column in Trafalgar Square, London, England. A e Updates? (1) (Since F= m x b).

Timoshenko improved upon that theory in 1922 by adding the effect of shear into the beam equation. Another unit that is often used for bulk stress is the atm (atmosphere). z This observation leads to the characteristic equation, The solutions of this quartic equation are, The general solution of the Timoshenko-Rayleigh beam equation for free vibrations can then be written as, The defining feature of beams is that one of the dimensions is much larger than the other two. Tensile stress is the force exerted per unit cross-sectional area of the object whereas the tensile strain is the extension per unit original length of the object. is a shear correction factor. Shear stress is due to forces that act parallel to the surface. Even very small forces are known to cause some deformation. A United States customary unit is pounds per square inch (lb/in2 or psi). OpenStax is part of Rice University, which is a 501(c)(3) nonprofit. I These are, The assumptions of KirchhoffLove theory are. ,

Fundamental and Derived Units of Measurement, Transparent, Translucent and Opaque Objects, Find Best Teacher for Online Tuition on Vedantu. unit of T = Pascal (Pa) or Newton per meter square or N x m- 2 Dimensional formula for tensile stress = M1L1T2 Tensile Strength Any object has always got the endurance to withstand the stress or an external force acting upon it, but as we continue to apply the force the object reaches the breaking or a fracture point. From Equation 1.4.6, the engineering stress corresponding to any value of true stress is slope of a secant line drawn from origin (, not ) to intersect the curve at . a maximum shear stress element has.

x is applied to the bar, it produces a tensile stress in the material. Therefore, strain is a dimensionless number. Typically, the testing involves taking a small sample with a fixed cross-sectional area, and then pulling it with a tensometer at a constant strain (change in gauge length divided by initial gauge length) rate until the sample breaks. Q By the end of this section, you will be able to: A model of a rigid body is an idealized example of an object that does not deform under the actions of external forces. are the coordinates of a point on the cross section at which the stress is to be determined as shown to the right, q 2 The result of this force is stretching up of the material. In other situations, the acting forces may be neither tensile nor compressive, and still produce a noticeable deformation. Figure \(\PageIndex{2}\) shows a plot of the stress-strain relationship for various human bones. For example, suppose you hold a book tightly between the palms of your hands, then with one hand you press-and-pull on the front cover away from you, while with the other hand you press-and-pull on the back cover toward you. Secure your free spot, now! At higher loadings the stress distribution becomes non-linear, and ductile materials will eventually enter a plastic hinge state where the magnitude of the stress is equal to the yield stress everywhere in the beam, with a discontinuity at the neutral axis where the stress changes from tensile to compressive. w Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . A large diameter, but thin-walled, short tube supported at its ends and loaded laterally is an example of a shell experiencing bending. {\displaystyle x}

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