maximum tensile stress formula

Dimensional formula for tensile stress = [ M ^ -1 L ^ , 9 hours ago The Maximum Tensile Stress in the Bolt formula is defined as he maximum stress that a material can withstand when a force is applied. Every material has a theoretical ultimate strength and yield strength based on the properties of that material. Statement of Maximum shear stress theory: Maximum shear stress theory in three-dimensional loading: Maximum shear stress theory for biaxial loading: Yield surface for Maximum shear stress theory in biaxial loading: Maximum shear stress theory formula in form of axial stresses `(\sigma _{x}` and `\sigma _{y})`: Numerical on maximum shear stress theory: Conjugate beam method to find slope and deflection of beam, Wheel speed sensor vs ABS sensor Difference, Latent heat: Definition, Formula, Types, Diagram, Example, Calculate kinetic energy without velocity? Static Pressure Overview & Formula | What is Static Pressure? 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When external forces act upon a material they produce internal stresses within it which cause deformation. What is bending stress in beam? Bending Stress Equation Based on Known Radius of Curvature, See Also: University Templates Show details, 2 hours ago Maximum Shear Stress or Stress difference theory (Guests or Trescas Theory-1868)- Ductile Material The Tresca Criterion: Also known as the Maximum Shear Stress criterion. , where u is the acceleration due to gravity. Mechanics Of Materials Chapter 5 Stresses In Beams. What is maximum bending stress? Stress in this context is the ratio of force to area F/A, which appears on the right-side of the length change equation above. Barlow's Formula Calculator. Tensile testing is commonly used to determine the maximum load (tensile strength) that a material or a product can withstand. Elastic limit is the maximum stress to which a specimen may be subjected and still return to its original length upon release of the load. For example, when designing a bridge, it is important to know the compressive stress maximum that the materials can withstand. W = F/2 x m is stored as the elastic potential energy of the wire. We have grown leaps and bounds to be the best Online Tuition Website in India with immensely talented Vedantu Master Teachers, from the most reputed institutions. The formula for compressive stress is fairly simple and is derived by dividing compressive force (pounds) by area (in square inches). How do you calculate compressive strength from tensile strength? Take that value and multiply it by 60% (0.60). The result of the tensile strength is, when the force exceeds the tensile strength, it starts breaking up or tearing down. Multiwalled Carbon nanotubes have the highest tensile strength among all the materials. Whether you need help solving quadratic equations, inspiration for the upcoming science fair or the latest update on a major storm, Sciencing is here to help. For a member with a constant axial cross section, measure the cross section and calculate the cross-sectional area. A is the unit area of a solid body. Video advice: Tensile Stress & Strain, Compressive Stress & Shear Stress Basic Introduction. ScienceBriefss a new way to stay up to date with the latest science news! In a uniaxial tensile test, the principal stress at the yield point will be 1 = y, 2 = 0, 3 = 0 . An example of data being processed may be a unique identifier stored in a cookie. Yield strength is defined as the maximum stress that a solid material can withstand when it is deformed within its elastic limit. What is the formula of tensile stress? 2) Ultimate strength:-the maximum tensile stress a material can withstand or resist without breaking, . What is Max tensile load? Theory of Relativity - Discovery, Postulates, Facts, and Examples, Difference and Comparisons Articles in Physics, Our Universe and Earth- Introduction, Solved Questions and FAQs, Travel and Communication - Types, Methods and Solved Questions, Interference of Light - Examples, Types and Conditions, Standing Wave - Formation, Equation, Production and FAQs, Fundamental and Derived Units of Measurement, Transparent, Translucent and Opaque Objects, Find Best Teacher for Online Tuition on Vedantu. Therefore, if an engineer is designing a structural component, he can select the material and component dimensions based on the anticipated loads of the system. 2023 Leaf Group Ltd. / Leaf Group Media, All Rights Reserved. This theory is suitable for ductile materials. https://engineers.academyIn this video you will learn how to calculate the maximum allowable force on an engineering component. What will be the value of stress? 2mm of permanent deformation in a specimen with a gauge length of 100mm. Watch the units as you perform the calculations. See Also: Maximum tensile strength formula Show details. The dimensioning of the belt depends on this maximum stress. Which Teeth Are Normally Considered Anodontia. More about Kevin and links to his professional work can be found at www.kemibe.com. Tensile strength. What is the formula for tensile strength? Just a quick note, 0.2% of 25.25 is not 5.05, i.e. Beam stress deflection mechanicalc solved stresses in beams calculate the maximum tensile stress course hero beam bending stress formula calculation skyciv ed q find the maximum tensile . Tensile strength is defined as a stress that is measured as force per unit area. First, calculate the area A experiencing the force F of 1,400 N. This is given by multiplying the length L0 of the beam by its width: (8 m)(0.25 m) = 2 m2. How you can Calculate What Grade I Want around the Final, Responsibility disclaimer and privacy policy, Maximum tensile stress in the asphalt layer. This could cause the structure to collapse or the object to break apart. It is sometimes denoted by (the Greek letter sigma). It is the inverse proportion of the cross-sectional area of the body. The result of this force is stretching up of the material. Tensile or any other strength is simply maximum stress before the failure. Another simple example would be the following: If you have a 2-inch-by-2-inch post and you apply 8 pounds of force to the post, the amount of compressive stress would be 2 pounds. 1 Answer Sorted by: 2 To find the neutral axis of any section including the T section in your question, ( called T beam because its cross section is a T): one picks a horizontal axis parallel to x axis (or the axis they need to find the beam's neutral axis). Strain, on the other hand, is the ratio of the change in length L to its original length L, or L/L. The Breaking Stress of the Metal is 3 x 109 N / m2. Both EHEDG and the American 3-A Sanitary standards state a surface finish of 0. Stress is defined as the force per unit area. The maximum principal stress failure predictor (MPSFP) design rule (Samuel and Weir, 1999) states that if a component of brittle material is exposed to a multiaxial stress system, fracture will occur when the maximum principal stress anywhere in the component exceeds the local 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. Tug of war is another activity that is done based on the same principle. For an axial load material, the breaking strength (Ts) is given by: U = Force that causes the fracture or a breaking, S.I. Is higher tensile strength better? Now, by putting the values of `\sigma_{1}` and `\sigma_{2}` in equation of maximum shear stress theory we get, `(\frac{\sigma _{x}+\sigma _{y}}{2}+\sqrt{(\frac{\sigma _{x}-\sigma _{y}}{2})^{2}+\tau_{xy}^{2}})-(\frac{\sigma _{x}+\sigma _{y}}{2}-\sqrt{(\frac{\sigma _{x}-\sigma _{y}}{2})^{2}+\tau_{xy}^{2}})=\sigma _{y}`, `2\times \sqrt{(\frac{\sigma _{x}-\sigma _{y}}{2})^{2}+\tau_{xy}^{2}}=\sigma _{y}`, `\sqrt{(\sigma _{x}-\sigma _{y})^{2}+4\times \tau_{xy}^{2}}=\sigma _{y}`. Describe it. Tensile strain = + (/0)) Cable wires used in cranes, elevators also work on the same principle of tensile stress. Structural members that experience axial tensile loads need to be sized so that they do not deform or fail under those loads. Note:- Condition 1 is considered when values of `_{1}` and `_{2}` are different, while condition 2 or 3 are considered when `_{1}` and `_{2}` are same. Tensile strength is usually of a higher numerical value than the yield strength of a particular material. To use the compressive stress formula, you need to know the compressive force and the cross-sectional area of the object that is being compressed. For the tensile and compressive yield strength, the equations are written as. = F/A. Plus, get practice tests, quizzes, and personalized coaching to help you Susan Kristoff has been writing engineering content for 13 years. Material | Maximum Compressive Stress (psi) Concrete 10,000 Steel 40,000 Aluminum 12,000 Brass 25,000 Copper 15,000 As you can see from the table, concrete has a lower maximum compressive. Scientists Unlock Strategies of H-explosive device Element Einsteinium, Why Big Companies Struggle With Innovation. Video advice: Calculating maximum compressive and tensile bending stresses, How to calculate tensile strength What is the formula of tensile strength? Understand what compressive stress is, learn the compressive stress formula, and see how to calculate compressive stress. To view the purposes they believe they have legitimate interest for, or to object to this data processing use the vendor list link below. tensile strength, maximum load that a material can support without fracture when being stretched, divided by the original cross-sectional area of the material. The proof stress is measured by drawing a line parallel to the elastic portion of the stress/strain curve at a specified strain, this strain being a percentage of the original gauge length. The loading on the object has values `_{x}` = 120 Mpa, `_{y}` = 60 Mpa, `\tau_{\text{xy}}` = 30 Mpa while the yield strength of the material of the object is 300 Mpa. When the materials are pushed beyond UTS they experience cracking and is represented as tmax = Ptb/ ( (pi/4)*dc^2) or Maximum Tensile Stress in Bolt = Tensile force in bolt/ ( (pi/4)*Core Diameter of Bolt^2). How do I apply this. Is bending stress a normal stress? 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. It's a site that collects all the most frequently asked questions and answers, so you don't have to spend hours on searching anywhere else. Where is maximum tensile stress? Is ultimate tensile strength same as tensile strength? Log in or sign up to add this lesson to a Custom Course. For example, if you are using a press to compress a metal rod, the cross-sectional area would be the diameter of the metal rod. For example, 0. Right-click on 'Solution', hover your mouse on 'Insert' then hover your mouse on 'Stress Tool' as shown by the red arrow above. A force of 1,400 N acts on an 8-meter by 0.25-meter beam with a Young's modulus of 70 109 N/m2. Bending stress may be the normal stress that the object encounters when its exposed to some large load at a certain point that triggers the item to bend and be fatigued. To unlock this lesson you must be a Study.com Member. 2 in the EN specifications. Youngs modulus equation is E = tensile stress/tensile strain = (FL) / (A * change in L), where F is the applied force, L is the initial length, A is the square area, and E is Youngs modulus in Pascals (Pa). Compressive strength is defined as the maximum compressive stress that is experienced by the material before its breakdown. the elastic region once the working stress doesnt exceed the elastic limit, and also to be stressed within the plastic region once the working stress does exceed the elastic limit. Where, is the tensile stress; F is the force acting; A is the area; The formula is: s = P/a. tensile strength, maximum load that a material can support without fracture when being stretched, divided by the original cross-sectional area of the material. a servo cable with a structure of (4G2.5+ (21.5)C)C, should be used in a hanging application of 25m. Bending Stress Equation Based on Known Radius of Curvature . The tensile strength is decided from that curve (Refer to Fig. For a given component and a known tensile load, the maximum tensile stress is straightforward to calculate. Requested URL: byjus.com/physics/tensile-stress/, User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/103.0.5060.114 Safari/537.36. It indirectly tells us the ability of a material to withstand tensile stress. There are many causes of compressive stress. But I am unsure how I work out the maximum tensile and compressive bending stresses. S.I. It is important to note, however, that tensile strength is not necessarily the same as fracture strength.Let's consider the typical stress-strain curve of a ductile material, seen in Figure 1. Compressive stress is common in many well-known architectural elements, such as arches. Is higher tensile strength better? "Stress," in everyday language, can mean any number of things, but in general implies urgency of some sort, something that tests the resilience of some quantifiable or perhaps unquantifiable support system. Shear Stress Formula & Units | What is Shear Stress? \Delta L=\bigg(\frac{1}{Y}\bigg)\bigg(\frac{F}{A}\bigg)L_0, \frac{Delta L}{L_0}=\epsilon =\bigg(\frac{1}{Y}\bigg)\bigg(\frac{F}{A}\bigg)=\frac{\sigma}{Y}, \epsilon = (1/(70\times 10^9))(1400)=1\times 10^{-8}, \sigma = \frac{F}{A}=Y\epsilon = (70\times 10^9)(1\times 10^{-8})=700\text{ N/m}^2. Tensile & Compressive Stress Formula | What is Tensile Stress? The result of this force is stretching up of the material. Angular Acceleration Formula & Examples | What is Angular Acceleration? Maximum Tensile Stress in Bolt formula is defined as the maximum stress that a material can withstand when a force is applied. He has a B.A. 6 hours ago Tensile Stress Formula. When you drag an object with the help of a rope, you are using tensile stress to drag it. This is known as the yield strength of the material. It is denoted by the symbol . Ultimate tensile strength (UTS) is the maximum stress that a material can withstand while being stretched or pulled. Tensile stress Vs Tensile Strain Vs Tensile Strength: Applications of Tensile Stress in Daily Life: \[\frac{\text{external deformation force}}{\text{area}}\], \[\frac{\text{Tensile Stress}}{\text{Tensile Strain}}\]. The exam is created by gripping the ends of the suitably prepared standardised test piece inside a tensile test machine after which applying a constantly growing uni-axial load until such time as failure occurs. Tensile strengths have dimensions of force per unit area and in the English system of measurement are commonly expressed in units of pounds per square inch, often abbreviated to psi. Shear Strain Formula & Overview | What is Shear Strain in Physics? This can happen when an object is supported by a column or beam. The formula is: CS = F A, where CS is the compressive strength, F is the force or load at point of failure and A is the initial cross-sectional surface area. What is tensile strength in metal? Where, To Determine Yield & Tensile Strength of a Steel Bar. 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. Both the load (stress) and the test piece extension (strain) are measured and from this data an engineering stress/strain curve is constructed, Fig.3.From this curve we can determine: a) the tensile strength, also known as the ultimate tensile strength, the load at failure divided by the original cross sectional area where the ultimate tensile strength (U.T.S. How do you calculate minimum ultimate tensile strength? We see children playing whirligig and it is based on the principle of tensile stress. Stress is the relationship of force over a unit area, and it allows for the comparison of material strengths independent of cross-sectional area. Fracture strength The value of the stress in the material at the point of rupture. ), max = P max /A 0, where P . Extreme elasticity or Ultimate tensile strength (UTS): The value of the maximum pressure which can be exposed to the material on the application of power is known as the Ultimate tensile strength; Thankyou! S.I. Stress can be defined as the force which acts per unit area of a body or a material. These inner and outer edges of the specimen are called extreme fibers. Tensile stress acts along the axis of the object and stretches the object. Compressive stress is relevant in many engineering applications. shearing stress - stress that tends to shear the material - acts in plane to the stressed area at right-angles to compressive or tensile stress; Tensile or Compressive Stress - Normal Stress. The compressive stress maximum varies depending on the material that is being compressed. It is independent of the shape of the specimen. The formula is: = F/A Where, is the tensile stress F is the force acting A is the area. Compressive stress is also relevant in the field of geology. Tensile Stress: It is defined as the stress which occurs along the sides of the object in the direction of force which would increase the length of the material in the tensile direction but the volume will remain constant. For example, a member with a cross-sectional area of 2 in sq and an applied load of 1000 pounds has a maximum tensile stress of 500 pounds per square inch (psi). If maximum compressive stress is exceeded, the material will collapse. 1) as the maximum stress point in the curve during failure. The maximum shear stress theory says that failure will occur when the maximum shear stress exceeds the shear stress at uniaxial loading. Heres how. Experiments show the change in length L of a beam with an initial length of L0 subjected to a force F over a cross-sectional area A is given by the equation. A solid material's yield strength is the maximum tensile stress it can handle before permanent deformation occurs. The maximum compressive stress that an object can withstand varies depending on the material that is being compressed. This is called "maximum surface stress" and is typically represented by the sigma sign. I feel like its a lifeline. They calculate the TRS as MPa (lb/in^2) if you use the above units. An example of how to calculate stress would be the following: A metal rod is being compressed by a machine with a force of 200,000 pounds. It is defined as the amount of tensile stress a material can withstand before breaking and denoted by s. , See Also: Tensile strength calculation formula Show details. When the stresses exceed the yield point, the steel will not be able to bounce back. 2019 Daily-catalog.com. 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. Shear Strength. This information can help to ensure that the building is able to withstand the weight of the structure. Always ensure that the maximum permissible belt stress per is not exceeded. Best of all, you can't cause any construction workers any "stress" in the real world in so doing! The applied loads may be axial (tensile or compressive), or shear . Remember the units of stress are N/m^2 (newtons per meter squared) in metric or psi (pounds per square inch) in English units. The formula is: s = P/a Where, s is the tensile strength P is the force required to break a is the cross-sectional area. This defines the maximum permissible tensile force for standard cables with 15N/mm cross section of the sum of the main cores. The compressive stress maximum that a material can withstand before it breaks is known as the compressive strength of the material. Comment document.getElementById("comment").setAttribute( "id", "aeeb8fa131ec139806610768c1c6b5d6" );document.getElementById("ae49f29f56").setAttribute( "id", "comment" ); Save my name, email, and website in this browser for the next time I comment. It can only be produced when forces like compression and tension start to work on a body. Stress and strain Young's modulus and elastic modulus Elastic behaviour of solids 54,865 Tensile Stress Unit Following is the table explaining the units and dimensional formula: What is the difference between tensile and shear strength? A tensile test was conducted on an iron rod. This can also be used as the compressive strength formula as it is the limit at which the solid material deforms. Her articles have appeared on eHow.com, Suite101, her personal websites, and the websites of many ghostwriting clients. 3 hours ago Enter the ultimate force and the cross-sectional area into the calculator to determine the tensile strength. This formula will give you the ultimate tensile strength of that size and grade of bolt. Benjamin has a Bachelors in philosophy and a Master's in humanities. Calculating the maximum amount of stress a given structure or single beam can tolerate, and matching this to the expected load of the structure. In your example 0.2% proof is desired. Its worth emphasizing, that from the standpoint of developing understanding, memorizing their particular expression for $e$ is not all that useful. The cross-sectional area is the area of the object that is being compressed. This is the reason that the design calculations for fillet welds consider throat size calculation. Tensile stress: Tensile strength: It is defined as force per unit area which is associated with stretching and denoted by . Try refreshing the page, or contact customer support. Take the minimum tensile strength in psi of the ASTM grade, multiplied by the stress area of the diameter. Another way to measure compressive stress is with a schmidt hammer, also referred to as a rebound hammer. When stress is applied in a fillet weld joint, the throat will be the failure location if the load is exceeded the maximum load capacity. Maximum Shear Stress Theory & Formula | How to Find Maximum Shear Stress, Thermal Stress Equation & Units | How to Reduce Thermal Stress, Modulus of Elasticity Formula | Calculating Steel, Concrete & Aluminum, What Is Yield Stress? Divide the the applied load by the cross-sectional area to calculate the maximum tensile stress. For the components subjected to biaxial stresses, there are two planes on which the value of shear stress is zero. Two Blocks of Masses 2 kg and 3 kg are connected by a Metal Wire Going Over a Smooth Pulley. = L/L = (L - L)/L. Bridge Abutment Function, Parts & Types | What is a Bridge Abutment? The tensile strength (also called ultimate tensile strength) is the maximum stress that can be sustained by a structure in tension; if this stress is applied and maintained, the sample will fracture. We know that the maximum shear stress is given by max = ( 1 2)/2. unit of T = Pascal (Pa) or Newton per meter square or N x m ^ 2. The formula for compressive stress is force/area. Could someone please help identify which equation was used as well as why? Select one of the safety calculation methods. - Definition, Causes, Symptoms & Treatment, What Is Syncope? Tensile strength is indicated by the letter s and is defined as the maximum amount of tensile stress that a material can withstand before breaking. This device measures the amount of deformation that occurs in a material when a force is applied to it. What happens after ultimate tensile strength? It is defined as the amount of tensile stress a material can withstand before breaking and denoted by s. The formula is: = F/A. For a member with a variable cross section, select the smallest cross section. Mechanics (Physics): The Study of Motion. Its like a teacher waved a magic wand and did the work for me. Tensile strength is a value obtained by dividing the maximum load between the start of tensile test and breakage by the cross-section area of the specimen. Get unlimited access to over 84,000 lessons. We and our partners use cookies to Store and/or access information on a device. Tensile stress is one of the categories of normal stress. In materials science, the strength of a material is its ability to withstand an applied load without failure. The most commonly used units for stress are the SI units, or Pascals (or N/m 2 ), although other . 2 hours ago Statement of Maximum shear stress theory: The maximum shear stress theory says that failure will occur when the maximum shear stress exceeds the shear stress at uniaxial loading. When the materials are pushed beyond UTS they experience cracking is calculated using Maximum tensile stress = Tensile load /((pi /4)* Core Diameter ^2).To calculate Maximum Tensile Stress in the Bolt, you need Tensile load (P) & . The maximum stress, tensile or compressive, that can be applied to a metal without producing permanent deformation. 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. 2% deformation, RP0. Therefore the FOS by using the maximum shear stress theory is 3.53. Thus, the formula for calculating stress is: Where denotes stress, F is load and A is the cross sectional area. Compressive stress is an important aspect in many commonly seen architectural designs such as with an arch. The following formula is used to calculate a tensile strength. Tensile strength is maximum load that a material can support without fracture when being stretched. Chapter 5 Stresses In Beam Basic Topics. the first two steel beams for the freedom tower ro image by Gary from Fotolia.com. 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. For example, a member with a rectangular cross-section of 1 x 2 inches has a cross-sectional area of 2 square inches. TimesMojo is a social question-and-answer website where you can get all the answers to your questions. You would use compressive stress to hold the bridge together while it is being built. How do you find the maximum tensile load? The maximum tensile force for cables with copper cores is specified in VDE0298. Boundaries of region for tensile condition, `| \sigma _{1}-\sigma _{2} |= \sigma _{y}` (a), `| \sigma _{1}-\sigma _{2} |= -\sigma _{y}` (d). Thanks. All rights reserved. 1. noun. How do you find the ultimate tensile strength of Youngs modulus? This formula will give you the ultimate tensile strength of that size and grade of bolt. It is the resistance of a material to breaking under tension. It is helpful in determining the maximum pressure capacity a pipe can safely withstand. By using the formula for maximum shear stress theory for biaxial loading. What is tensile strength with example? At the inside of the bend, the stress will be at its maximum compressive stress, while at the opposite side the stress will be at its maximum tensile stress value. At os, the force is applied to compress and compact material. The force exerted by the column or beam on the object creates a compressive force that can cause the object to deform or collapse. Tensile testing is described, covering test specimen form, determination of the engineering stress/strain curve, and derivation of test results: ultimate tensile strength, yield point, elongation, reduction in area, Youngs modulus of elasticity and proof stress. This is an image showing the elongation from Lo to Length L, but there will be a decrease in the diameter of the rod, hence the decrease in the area as well. unit = Pascal or Newton per meter square or N x m, Difference Between the Tensile Stress and Tensile Strength, It is defined as the stress which occurs along the sides of the object in the direction of force which would increase the length of the material i. direction but the volume will remain constant. What is compressive strength and tensile strength? 3 hours ago Whereas, Tensile Strength is the maximum stress that a material can withstand while being stretched or pulled before failing or breaking. How do you calculate UTS? This physics provides a basic introduction into stress and strain. Eliminating the common term b from these two equations, we get that: If the minimum radius required to avoid breaking is k. 2. I would definitely recommend Study.com to my colleagues. What is yield strength formula? The yield strength formula is as follows: y min a = s yield. For example, here is an overview of the maximum compressive stress for some common materials: As you can see from the table, concrete has a lower maximum compressive stress than steel. What is the difference between tensile stress, tensile strength, and compressive stress? from Radboud University NijmegenGraduated 2002Lives in Lausanne, Switzerland2013present, Your email address will not be published. Common codes and standards that are followed for tensile testing are: ASTM E8/E8M, ISO 6891, JIS Z2241, ASTM D3039, ASTM D638, ASTM D828, ASTM D882, ISO 37, MPIF Test Standard 10, etc. This parameter applies to all types of materials such as wires, ropes, metal beams, etc. P a = 2 S y F d F e F t t / d o (3) . What are the stress and the strain? The method is not suitable in hydrostatic stress conditions. Necking, in engineering or material sciences, is a modality of tensile deformation where comparatively huge quantities of strain focalize disproportionality in a tiny region of the material. In order to calculate maximum surface stress, you must know the bending moment, the distance from the neutral axis to the outer surface where the maximum stress occurs and .

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