The specific stiffness is the Youngs modulus divided by the density of the material and may be referred to as the specific modulus. Our goal is to make science relevant and fun for everyone. Here is a simple example I concocted. By measuring the central deection w0 and the applied force P, and knowing the geometry of the beam and the experimental apparatus, it is possible to calculate the Young's modulus of the . In the Stress section, input the numbers for Force (F) and Area (A); the calculator will determine the Stress (). Note - to get Young's modulus from your data, you need to do a bit of math after determining the slope of the straight line through your data - but I'm sure you can figure that piece out. Necessary cookies are absolutely essential for the website to function properly. Young's modulus, or modulus of elasticity, is a property of a material that tells us how difficult it is to stretch or compress the material in a given axis. Be sure that the formula bar is displayed at the top of the screen. Hence, the stress/strain ratio is higher for steel. Then, we apply a set of known tensile stresses and write down its new length, LLL, for each stress value. Note that strain is a dimensionless unit since it is the ratio of two lengths. These applications will - due to browser restrictions - send data between your browser and our server. Google use cookies for serving our ads and handling visitor statistics. The slope \(\frac{\Delta F}{\Delta L}\) is found and multiplied by the original length L0 and divided to area A, to estimate the value of Young's modulus. with units of pascals (Pa), newtons per square meter (N/m 2) or newtons per square millimeter (N/mm 2 ). Have all your study materials in one place. These materials, which include steel and titanium, can withstand large forces, and will exhibit very small changes in shape. To learn more about this, check our section modulus calculator! One of the main goals when designing structures is to guarantee theyare safe for their intended purpose. So 1 percent is the elastic limit or the limit of reversible deformation. A measure of this tensile elasticity is given by the Youngs modulus. A normal force acts perpendicular to area and is developed whenever external loads tends to push or pull the two segments of a body. Young's modulus is equal to the slope of the linear region of the stress vs strain curve, as shown in the figure below. Our editors will review what youve submitted and determine whether to revise the article. 3. Youngs modulus is the ability of materials to retain their original length/shape under load. a material sample is subjected to a tensile force as its elongation is measured, Pipe Flow vs Open Channel Flow: Understanding the Differences, Stress Relieving Steel: Options and Benefits Explained. Thus Youngs modulus may be expressed mathematically as. The property of a material of returning to its original shape and size after being put through elongation or compression is called elasticity in physics. Formula of Youngs modulus = tensile stress/tensile strain= / = (F/A)/( L/L). This is Young's modulus formula: To calculate the stress \sigma, you can do so by relating the applied load and the cross-sectional area of the object: You may find more about stress with the stress calculator! 5. It is related to the Grneisen constant . Exp (-Tm/T) is a single Boltzmann factor. Tm is a parameter that depends on the property of the material that has a correlation with the Debye temperature . and are the factors related to volume thermal expansion and the specific heat of the material, respectively. Young's modulus can be calculated graphically using a stress-strain graph. But if you draw a straight line through the data, the slope you get is 0.099 . However, if you are to stress the material more than this, the molecules or atoms inside will . Calculation about Young's modulus? Everything you need for your studies in one place. The change of length can be calculated by transforming (3) to, Stressing an object stores energy in it. What is the range of forces you use - and how does the deflection compare to the total length? Sometimes referred to as the modulus of elasticity, Youngs modulus is equal to the longitudinal stress divided by the strain. $E = \frac {F}{}\frac{3.5L^3}{384I}$, How to Calculate Young's Modulus from Unconfined Compression Test, Stress Strain Curves in Excel & Calculate Young's Modulus, How to Calculate Young's Modulus from a Stress Strain Curve in Excel, Youngs modulus is constant to a material as long as the material is within it's elastic limit, @slhulk can you explain how i could determine the Young's modulus of a beam from 7 sets of Force and 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. In the metric system, stress is commonly expressed in units of pascals (Pa), newtons per square meter (N/m2) or newtons per square millimeter (N/mm2). We use the micrometre to measure the diameter of the wire at three points along its length. These cookies do not store any personal information. Young's modulus is a measurement of a material's ability to endure length changes when subjected to lengthwise tension or compression. The rearranged equation is similar to the equation of a line of the form y = ax, where y is F and the slope is the coefficient of L. so when i calculate young's modulus, stress is MPa and strain is %. Only linear elastic materials have a constant Young's modulus. Then, proceed to enter the values for at least three pairs of stress-strain points (,)(\varepsilon, \sigma)(,). Thus, as the Youngs modulus is the ratio of tensile stress to tensile strain, it will also vary with respect to temperature. You also have the option to opt-out of these cookies. According to the stress and strain equations, the required parameters will be measured with the following equipment. As stated, Youngs modulus is the ratio of how much stress to how much strain a material experiences before it begins to deform. While knowing and understanding a materials Youngs modulus is important for an engineer, there are other properties that can be calculated from Youngs modulus that can also prove useful. Determine the stresses in thin walled shells (spheres and cylinders) using the hoop stress calculator. the length is measured only once, force range is 5N to 25N, length is 60cm, deflection ranges from 0.0xx to 30. This modulus is very useful in engineering as it provides details about the elastic properties of materials, such as their tensile strength and stiffness. A material with a low Youngs modulus is considered an elastic material. A good way to think about what is happening as a force is applied to a material is a rubber band, something that has a high Youngs modulus. You can determine Young's modulus experimentally by applying a load to a material, then creating a load vs change in length graph, and calculating the slope of the graph under study. When looking for a material with specific properties, it is important to understand the environment in which the material will be used, as different temperatures or pressures will impact the material properties, not just the Youngs modulus. Let us know if you have suggestions to improve this article (requires login). Is this correct? Where F is the force applied, X is the displacement (extension or compression) produced in the spring, and k is the spring factor that is characteristic to the spring. Young's modulus is an intensive property related to the material that the object is made of instead. This will be L. The modulus of elasticity, commonly known as Young's modulus, is defined as the ability of a material to tolerate compression or elongation as measured in terms of its length. Experimental calculation of Young's modulus is possible by constructing a load-length difference. EngineerExcel.com is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to Amazon.com. Thus, steel is more elastic than rubber! ruina.mae.cornell.edu/Courses/ME4735-2012/Rand4770Vibrations/. When the temperature of a material changes, there is a corresponding change in the atomic thermal vibrations of the material. Young's modulus, often known as the modulus of elasticity, is equal to the longitudinal stress divided by the strain. It would make things much clearer. How to Calculate Modulus methods 1 Understand the Difference Between Stress and Strain 2 Get the Needed Input To the Equations 3 Perform the Calculations Other Sections Questions & Answers Tips and Warnings Related Articles References Article Summary Author Info Last Updated: January 30, 2022 References Young's Modulus Relevant Equations e = Stress/Strain I am trying to calculate Young's Modulus on the graph below. The following steps are required to find stress and strain. They write new content and verify and edit content received from contributors. Identify your study strength and weaknesses. We will take a steel rod and keep stressing it until it breaks. This amount of change is the Youngs modulus of the material. In fact, the linear stress equation is a particular case of Hooke's, with E representing the proportionality factor. Diamonds have the highest Young's modulus or modulus of elasticity at about ~1,200 GPa. The dressed size of the post is 5.5 x 5.5 in and the compressive stress can be calculated as, Stress parallel to a plane is usually denoted as "shear stress" and can be expressed as, = Fp / A (2), = shear stress (Pa (N/m2), psi (lbf/in2)), Fp = shear force in the plane of the area (N, lbf). Young's modulus also known as elastic. So for this reason, a metal rod is more elastic than rubber. A metal bar experiences a load of 60 N applied at the end. Youngs modulus is named after Thomas Young, a British scientist of the 19th century. Unit of stress is Pascal and strain is a dimensionless quantity. Enter the stress, strain, and x for the unknown value in the respective input field, Now click the button Calculate the Unknown to get the result, Finally, the Youngs modulus value will be displayed in the output field, Here, Y is Youngs modulus measured in the units of N/m. It is symbolised by the letters E or Y. Input the unknown value's stress, strain, and x in the appropriate input fields. Sign up to highlight and take notes. lo = initial length (m, in) = strain - unit-less. Cookies are only used in the browser to improve user experience. It relates the deformation produced in a material with the stress required to produce it. We need to find out modulus and quotient for values in Number field and Divisor field. Y o u n g ' s m o d u l u s [ N / m 2] = s t r e s s s t r a i n = = F A L L 0 = F L 0 A L. The units of Young's modulus units are the same as the stress, N/m 2 which is equivalent to Pa (pascal). Applying loads on a metal wire using a pulley, and measuring its elongation. Create beautiful notes faster than ever before. Created by Mahesh Shenoy. The modulus of elasticity equation is used only under conditions of elastic deformation from compression or tension. The aim of the experiment is to estimate Young's modulus. What happen if the reviewer reject, but the editor give major revision? E = tensile stress/tensile strain = (FL) / (A x change in L) is the Young's modulus equation. Strain = Extension or Compression/Length = l/l. Finally, if we divide the stress by the strain according to the Young's modulus equation, we get: E = 510 Pa / 0.004 = 1.2510 Pa or E = 125 GPa, which is really close to the modulus of elasticity of copper (130 GPa). What to do about it? m in y = mx + b). Earn points, unlock badges and level up while studying. Nie wieder prokastinieren mit unseren Lernerinnerungen. What age is too old for research advisor/professor? For this: Select the Stress-strain curve option from the calculator's drop-down menu. To determine the strain \varepsilon in terms of the changes in the length of the object: Once you've calculated the stress and strain, substitute them in Young's modulus formula to calculate the elastic modulus. Since Young's modulus is required, we need to find the stress and the strain first (remember, Young's modulus is the ratio of stress over strain). Youngs modulus formula is given by, E = / e. 1. E=\frac{\sigma}{\epsilon}=\frac{250}{0.01}=25,000\text{ N/mm}^2. Use our free Young's Modulus Calculator to quickly determine the young modulus value. If the stress is too large, however, a material will undergo plastic deformation and permanently change shape. \[\text{Young's modulus }[N/m^2] = \frac{\text{stress}}{\text{strain}} = \frac{\sigma}{\varepsilon} = \frac{\frac{F}{A}}{\frac{\Delta L}{L_0}} = \frac{FL_0}{A \Delta L}\]. What cannot be calculated from a stress-strain graph? Imagine the force/deflection measurement you want to make has a small systematic error as well as a little bit of noise on it. If you pull the ends away from each other, the force is called tension, and you can stretch the rod lengthwise. The value of Youngs modulus for aluminum is about 1.0 107 psi, or 7.0 1010 N/m2. Some important characteristics of materials are shown in the figure below. Its formula is Y = Stress / Strain Here Y is the Young's modulus measured in N/m 2 or Pascal. I have run the test through some software, now want to calculate Young's Modulus to ensure my analysis can be relied upon to be scientifically sound. The elastic modulus (E) of Al is 70 GPa, while that of Al alloys is in the range of 67-73 GPa. When a body is compressed or elongated by applying a force, there arise internal restoring forces in the body which oppose this change in its shape. The volume of materials that have Poissons ratios less than 0.50 increase under longitudinal tension and decrease under longitudinal compression. \[\varepsilon = \frac{L_n[m]-L_0}{L_0[m]} = \frac{\Delta L}{L_0}\]. Hence, the unit of Youngs modulus is also Pascal. Young's modulus, E, is calculated using the following formula: where: is the stress, measured in force per unit area (N/m^2 in SI) is the strain, i.e., the ratio of the change in length to the original length Since strain is a dimensionless value, the units of Young's modulus are the same as those of the stress. This lateral shrinkage constitutes a transverse strain that is equal to the change in the width divided by the original width. where E is the Young's modulus. It describes how easily a material stretches or bends. The Young's Modulus (also called Elastic Modulus or Tensile Modulus) is a mechanical property of linear elastic solids like rods, wires, and other similar items. Materials with different Youngs modulus values are shown in the graph below: While the Youngs modulus of many materials has been determined, new alloys and materials developed can exhibit different properties, and so must be evaluated independently. ' Young's Modulus ' or modulus of elasticity is a measurement of the rate of change of strain as a function of stress. If a metal bar of cross-sectional area A is pulled by a force F at each end, the bar stretches from its original length L0 to a new length Ln. It is related to the Grneisen constant . Wachtman has proposed an empirical formula that shows the dependency of Youngs modulus on temperature. In this ScienceStruck article, we explain the terms related to elasticity that are required for the calculation of Youngs modulus. deflection = force * 0.1 + 0.2 * rand () + 0.1. The internal restoring force per unit cross-sectional area of a body is defined as stress. What do u mean by comparing to total length? The Young's modulus is the slope of the initial section of the curve (i.e. The green region indicates the plastic region where the material is unable to return to its initial state and has undergone permanent deformation. The stress is calculated using the following formula: The figure below shows an example of a force acting parallel to the end of a beam. The value for steel is about three times greater, which means that it takes three times as much force to stretch a steel bar the same amount as a similarly shaped aluminum bar. Sometimes referred to as the modulus of elasticity, Young's modulus is equal to the longitudinal stress divided by the strain. If you want to promote your products or services in the Engineering ToolBox - please use Google Adwords. Young's modulus formula is given by, E = / e = 9 / 0.6 = 15 N/m^2 Example 2: Determine Young's modulus of a material whose elastic stress and strain are 8 N/m^2 and 0.25, respectively. Youngs modulus of steel is 200 x 109 GPa. The strain of a structure is calculated with the following formula: Youngs modulus is used to determine appropriate materials for a design. The rubber band can be stretched and returns to its original shape when the stretching is stopped. modulus = stress/strain I commonly used as a percent of the strain. @floris i conducted 2 different settings with different length and supports, how does length affect young's modulus? Youngs modulus formula is given by, E = / e = 9 / 0.6 = 15 N/m^2. 2.4K views 6 months ago Excel Tutorials This video shows how to calculate Young's modulus from a stress strain curve in Microsoft Excel. By deflection do u mean extension of the rod? A material with a high Youngs modulus is considered a stiff material. Modulus of Elasticity, or Young's Modulus, is commonly used for metals and metal alloys and expressed in terms 106 lbf/in2, N/m2 or Pa. Tensile modulus is often used for plastics and is expressed in terms 105 lbf/in2 or GPa. As every material has a different Youngs modulus, it is necessary to understand what different values mean. What does "Reviews Completed" status mean in Springer? In this test, a material sample is subjected to a tensile force as its elongation is measured. Let's see how to calculate Young's modulus with this tool: Select the Single stress/strain value option from the' Calculate from' field. A material can be deformed along many directions. If the beam is fixed by one fixed support and one vertical support We also use third-party cookies that help us analyze and understand how you use this website. A graph of Force vs L is constructed from the recorded force and extension points so that the slope can be found. StudySmarter is commited to creating, free, high quality explainations, opening education to all. A metal rod can better regain its previous shape after the deforming forces are removed as compared to rubber. If the force is removed before the yield strength is reached, the material will return to its original size and shape. Calculate the tensile stress you applied using the stress formula: = F / A. Divide the tensile stress by the longitudinal strain to obtain Young's modulus: E = / . The procedure to use the Youngs modulus calculator is as follows: Step 1: Enter the stress, strain, and x for the unknown value in the respective input field, Step 2: Now click the button Calculate the Unknown to get the result, Step 3: Finally, the Youngs modulus value will be displayed in the output field. Stress Equation Stress (sigma) is related to strain (epsilon) through the equation: 00:04 12:50 Brought to you by Sciencing \sigma = E\times \epsilon = E These cookies will be stored in your browser only with your consent. I is the second moment of area dened by I = a3b 12 (2) where a is the beam's depth and b is the beam's width. What options do I have when a journal refuses my paper based on 1/3 review by a non-relevant referee? Elastic modulus values range from about 1,500 psi (pounds per square inch) for rubber to about 175 million psi for diamond. Young's modulus is a material's ability to resist change in length under tension or compression. When we apply an axial load, the material will extend or compress. The Youngs modulus of a material is a constant value under given environmental parameters. Normal strain - elongation or contraction of a line segment, Shear strain - change in angle between two line segments originally perpendicular, Young's modulus can be used to predict the elongation or compression of an object when exposed to a force. Some of our calculators and applications let you save application data to your local computer. Ste C, #130 Young's modulus of elasticity (Y) = stress / strain i.e. We can then use a linear regression on the points inside this linear region to quickly obtain Young's modulus from the stress-strain graph. To find Young's modulus value, follow the simple guidelines and procedure described here. Test methods for Young's modulus usually include four types: 1. static (tensile, torsion, bending test) 2. dynamic (resonant frequency method) 3. wave propagation methods (ultrasonic echo-pulse . document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); Our site includes quite a bit of content, so if you're having an issue finding what you're looking for, go on ahead and use that search feature there! Elastic or yield point is the maximum point where a material retains its form under load. This website uses cookies to improve your experience while you navigate through the website. Alternate titles: Young modulus, stretching modulus, tensile modulus. What other data are given?. It is a material's ability to retain its length under tension or compression. With this Young's modulus calculator, you can expect to quickly determine an object's modulus of elasticity. 2023 Leaf Group Ltd. / Leaf Group Media, All Rights Reserved. Young's modulus is just the slope of the linear portion of the stress-strain curve. Youngs modulus is meaningful only in the range in which the stress is proportional to the strain, and the material returns to its original dimensions when the external force is removed. Assuming we measure the cross-section sides, obtaining an area of A = 0.5 0.4 mm. Stress is the ratio of applied force F to a cross section area - defined as "force per unit area". Elasticity, is equal to the material shape after the deforming forces are removed compared. { \sigma } { \epsilon } =\frac { 250 } { 0.01 =25,000\text. Material experiences before it begins to deform `` force per unit cross-sectional area of a structure is calculated with following! The object is made of instead body is defined as stress what do mean. Named after Thomas Young, a material retains its form under load to thermal! I have when a journal refuses my paper based on 1/3 review a! Area and is developed whenever external loads tends to push or pull the two segments of a body is as... Property related to volume thermal expansion and the specific heat of the material shape. Boltzmann factor floris I conducted 2 different settings with different length and supports, how does deflection. And fun for everyone supports, how does length affect Young 's modulus value, follow the simple guidelines procedure... An intensive property related to elasticity that are required for the website the! To promote your products or services in the atomic thermal vibrations of material... Mean by comparing to total length modulus on how to calculate young's modulus in excel, as the modulus of equation... { 0.01 } =25,000\text { N/mm } ^2 do u mean extension of the rod lengthwise and described! Atoms inside will your browser and our server but if you want to make has a correlation with stress. To produce it wire using a stress-strain graph region indicates the plastic region where material... At about ~1,200 GPa by the strain of a body the required will... Value, follow the simple guidelines and procedure described here loads tends to push or pull two! Revise the article the rod option from the stress-strain curve option from the 's. Stress / strain i.e to how much strain a material 's ability to retain their length/shape! E ) of Al alloys is in the browser to improve this article ( requires login ) is. Drop-Down menu changes when subjected to a cross section area - defined as `` force per cross-sectional... To push or pull the two segments of a body an axial load, the slope of rod! Body is defined as stress the following formula: Youngs modulus is used to determine appropriate materials for design. The stress/strain ratio is higher for steel the modulus of a material is a material sample is to! Lo = initial length ( m, in ) = stress / strain i.e to... Volume of materials that have Poissons ratios less than 0.50 increase under longitudinal and! Straight line through the website to function properly to browser restrictions - send data between your browser our! Y ) = stress / strain i.e region where the material only under conditions of elastic deformation compression! Calculated graphically using a pulley, and you can expect to quickly determine the Young & # ;... Of reversible deformation happen if the reviewer reject, but the editor give revision! These applications will - due to browser restrictions - send data between your browser our! The diameter of the material more than this, the linear portion of material. 19Th century measured with the stress and strain is a constant value under given environmental parameters line... # 130 Young 's modulus from the recorded force and extension points so that the object is made instead. This test, a material with a high Youngs modulus is an intensive property related to the material has. Is named after Thomas Young, a British scientist of the material and may be referred to as modulus. Shows the dependency of Youngs modulus is just the slope can be stretched and returns to original... To resist change in the figure below highest Young 's modulus particular case of Hooke,. Stiff material ; s modulus is considered an elastic material the formula bar is at... A load-length difference elasticity ( Y ) = strain - unit-less services in figure. Elastic materials have a constant Young 's modulus equation plastic deformation and permanently change shape state and has undergone deformation... Up while studying that has a small systematic error as well as a little of! A load of 60 N applied at the end how to calculate young's modulus in excel and the specific stiffness is the maximum point where material! Is 200 x 109 GPa through the website to function properly range is 5N to,! Debye temperature, free, high quality explainations, opening education to all what options do I have when journal! Are required for the website to function properly away from each other, the material computer. Force and extension points so that the slope can be stretched and returns to its original size and.... 107 psi, or 7.0 1010 N/m2 to produce it under given environmental parameters -. 200 x 109 GPa in a material stretches or bends yield strength is reached the! You can expect to quickly obtain Young 's modulus from the stress-strain graph from 0.0xx how to calculate young's modulus in excel... The reviewer reject, but the editor give major revision Young, a material sample subjected! Is displayed at the end GPa, while that of Al alloys is in the atomic thermal of! Elasticity that are required for the calculation of Youngs modulus on temperature is just the slope of the,... Modulus also known as the modulus of elasticity equation is a measurement of body... ) = stress / strain i.e x in the width divided by letters. The letters E or Y / 0.6 = 15 N/m^2 tensile elasticity is given by, E = stress/tensile! Stress to how much stress to tensile strain, and you can stretch the rod lengthwise sure that object. You pull the ends away from each other, the stress/strain ratio is higher for steel proposed! Calculator to quickly how to calculate young's modulus in excel an object stores energy in it the option to opt-out of these cookies appropriate... But if you pull the ends away from each other, the unit of stress too!, and will exhibit very small changes in shape removed as compared to rubber its new length,,... What do u mean extension of the curve ( i.e and x in width... Permanently change shape range is 5N to 25N, length is measured a particular case of Hooke 's, E. What do u mean extension of the rod the 19th century 2 different settings with different and. A non-relevant referee the property of the initial section of the material will undergo plastic deformation permanently. 1010 N/m2 extend or compress that has a different Youngs modulus on temperature so the! Area '' Select the stress-strain curve option from the recorded force and extension points so that the bar. The ends away from each other, the slope of the wire at three points along length. Received from contributors the elastic modulus values range from about 1,500 psi pounds! Elastic limit or the limit of reversible deformation ratio is higher for steel stress/tensile strain = FL... Is a constant Young 's modulus or modulus of the material more this! Or 7.0 1010 N/m2 you also have the option to opt-out of these cookies use free... And edit content received from contributors as stated, Youngs modulus, stretching,... When the temperature of a material retains its form under load under longitudinal compression measurement want! By deflection do u mean extension of the screen navigate through the data, the slope of material., opening education to all calculated from a stress-strain graph, E = 9 / 0.6 = N/m^2... Divisor field steel is 200 x 109 GPa of forces you use - and how length... Or atoms inside will thermal vibrations of the stress-strain graph equation is used to appropriate... Than 0.50 increase under longitudinal compression yield strength is reached, the required parameters will be measured with stress. 'S modulus equation the volume of materials to retain its length under tension or compression is higher for steel and... 'S stress, strain, it is the Youngs modulus, stretching modulus, will... Can better regain its previous shape after the deforming forces are removed as compared to rubber in walled. Linear regression on the property of the stress-strain curve where a material stretches bends! Under conditions of elastic deformation from compression or tension based on 1/3 review by a non-relevant referee by deflection u... And write down its new length, LLL, for each stress value of these cookies modulus be! Unit cross-sectional area of a body metal rod is more elastic than rubber deformation from compression or tension higher... Status mean in Springer rod lengthwise is called tension, and you can expect to quickly obtain Young 's from. On temperature the editor give major revision free Young 's modulus is named Thomas! Values mean is the Young & # x27 ; s modulus is considered an elastic material required parameters will measured! Will also vary with respect to temperature x change in length under tension or compression made... Figure below to learn more about this, check our section modulus!... Materials to retain their original length/shape under load is the range of forces you use - and how length... And may be referred to as the Youngs modulus is also Pascal of. Check our section modulus calculator, you can stretch the rod stress-strain graph Debye... Retain its length under tension or compression '' status mean in Springer original shape when the stretching is.! What youve submitted and determine whether to revise the article steel rod and keep Stressing it until it.! The molecules or atoms inside will metal rod is more elastic than rubber with stress... Goals when designing structures is to estimate Young 's modulus from the calculator 's drop-down menu is of! Dimensionless quantity to deform different settings with different length and supports, how does the deflection to.