Read more about us here. .bravenet-subscribe { Experience the full power of ClearCalcs with a 14 The shear center is outside the channel web. Analysis of FlangedAnalysis of Flanged SectionsSections If the neutral axis falls within the slab depth analyze the beam as a rectangular beam, otherwise as a T-beam. Help support us by using our affiliate links below. Y y_\textit{pna} The neutral axis is an axis in the cross section of a beam (a member resisting bending) or shaft along which there are no longitudinal stresses or strains. In our moment of inertia example: Once again, we can compare this result with that of the free moment inertia calculator to compare the results of both the centroid and moment of inertia, where both the centroid (216.29 in) and Moment of Inertia (4.74 x 10^8 in^4) match: Simple equations can also be used to calculate the Moment of Inertia of common shapes and sections. Now, use steel rod according to area of steel required as calculated above. Christian Science Monitor: a socially acceptable source among conservative Christians? Rriof Figure 1: Example of Truss Bride for Pedestrian - Pedestrian bridges are structures bulit over roads that require people to take longer, often inaccessible routes up and over many lanes of car traffic, without impeding the speed or movement of vehicular tratfic. The stress in a bending beam can be expressed as. 3) Conventional elastic-plastic material model hypothesis: It is directly related to the amount of material strength your section has. beam experiences the highest tensile stress, Wheel speed sensor vs ABS sensor Difference, Latent heat: Definition, Formula, Types, Diagram, Example, Calculate kinetic energy without velocity? b and } LEAN INTO EVERY RIDE: Smart Lean Technology, keeps you confidently grounded and in command of the road with 6-axis Bosch IMU, Dynamic traction control, ABS with cornering control, and Drag Torque Control. The thickness of the flange of T beam is equal to the thickness or depth of the slab forming the flange of the beam. Section Modulus Zyy (unit^3): S_x If that's not the case. Related Resources: material science Section Modulus Equations and Calculators Common Shapes. You can solve up to three sections before you're required to sign up for a free account - which also gives you access to more software and results. solved calculate the depth of neutral axis a beam size 450x300 mm use m2s grade concrete and 4 no fe 500 steel at bottom with clear cover solved calculate the depth of neutral axis a beam size 450x300 mm use m2s grade concrete and 4 no fe 500 steel at bottom with clear cover neutral axis in beam definition formula gate notes ultimate moment Find the moment of inertia of section I, rectangle, circle, triangle and all kinds of different shapes. regexPattern = "^[-!#$%&'*+./0-9=?A-Z^_`a-z{|}]+@[-!#$%&'*+/0-9=?A-Z^_`a-z{|}~. Strength of Materials | Beam Deflection and Stress. neutral layer are caused by axial force and the cross-section geometric center layer does not move. Similar to the elastic section modulus SSS, its plastic counterpart provides a relationship between stress and moment: The plastic moment refers to the moment required to cause plastic deformation across the whole transverse area of a section of the member. So the actual neutral axis will shift upwards i.e., n c > n as shown in Fig. Typically the most distant fiber is of interest. An example of data being processed may be a unique identifier stored in a cookie. The calculation of the plastic modulus can be easily formulated: Radius of gyration Radius of gyration R g of a cross-section, relative to an axis, is given by the formula: where I the moment of inertia of the cross-section around the same axis and A its area. Radius of gyration rxx (unit): B.M. As you can note, the transition from elastic to plastic is not uniform across the member, as some regions will reach the yield strength before others. Calculate deflection and slope of simply supported beam for many load cases, Fixed Beam Calculator The properties E, A, and Ix for other beam sections can be obtained from the ClearCalcs section properties library. Max. if (e.innerHTML != "") return false; } However, there are materials, such as cast iron . It is defined as: where The sign convention used for loading is (positive values shown): Distributed Loads are specified in units of force per unit length, kN/m or plf, along the beam, and can be applied between any two points. Connect and share knowledge within a single location that is structured and easy to search. Calculate the approximate steel requirements in relation. 2) Uniaxial state of stress hypothesis: Any point on the beam is uniaxial stretched or compressed when deforming occurs regardless of the effect of uniaxial force on the sec-tion size. BASIC FORMULAS I x = (B/3)*H3 - ( (H-t)3 / 3) (B - s) - F (H - y)2; I y = t*B3/12 + (H-t)*s3 / 12; A = t*B + s* (H-t); = Mx*y / Ix; y - distance from X axis to T-beam top. For materials with equal tensile and compressive yield stresses, this leads to the division of the section into two equal areas, Want to learn how to use specific calculators for your projects? padding: 5px 10px; } | e.innerHTML += 'Invalid email address'; S_y . This software will display the full report and worked example of reinforced concrete design calculations as per ACI, AS and Eurocode design standards. background: black; Step 3: Find Moment of Resistance. Test your knowledge on different topics of Civil Engineering, Statically Indeterminate Structures Definition and methods of solving, Truss Member Forces calculation Area of section (unit^2): Please use consistent units for any input. Assumptions. The previous formulas apply to materials that exhibit an elastic behavior and obey Hook's law. Let your friends know about it. Try it out for yourself and see the difference. The area A and the perimeter P of a tee cross-section, can be found with the next formulas: \begin{split} & A & = b t_f + (h-t_f)t_w \\ & P & = 2b + 2h \end{split}. Any content, trademark/s, or other material that might be found on the thathipsterlife.com website that is not thathipsterlife.com property remains the copyright of its respective owner/s. The author or anyone else related with this site will not be liable for any loss or damage of any nature. I_y = \frac{h_w t_w^3}{12} + \frac{t_f b^3}{12}. height: 35px; The location at which the pencil is balanced and does not fall off your finger would be the approximate location of the centroid of the pencil. Therefore the position of the neutral axis for the equilateral triangle is given by. Calculation tool for bending moment and shear force for Fixed Beam for many load cases, BM & SF Calculator for Cantilever Focusing on simple shapes only, the below diagram shows some of these equations: A centroid, also known as the 'geometric center' or 'center of figure', is the center of mass of an object that has uniform density. margin-bottom:10px; The polar moment of inertia, describes the rigidity of a cross-section against torsional moment, likewise the planar moments of inertia described above, are related to flexural bending. Multiply the last result by the thickness. Vw Jetta Sportwagen Accessories| See Moment of Ineria of a circle to learn more. 6. . The stresses in concrete and steel shall not exceed 5 N/mm2. } The section modulus is used by engineers to quickly predict the maximum stress a bending moment will cause on a beam. This tool calculates the properties of a T section. Home Depot Laguna Niguel| Calculate the Strength of Reinforced Concrete beam, Deflection & Slope Calculator This problem is not given enough attention in present publications. The location of neutral axis can be determined by applying the static equilibrium conditions. We can derive the section modulus formula for a rectangular section by dividing its second moment of area (bh/12) by the maximum distance from the neutral axis (h/2): The elastic section modulus formula of a square is S = a/6, where: We can derive the section modulus formula for a square section by dividing its second moment of area (a/12) by the maximum distance from the neutral axis (a/2): To calculate the plastic section modulus of an I-section, use the formulas: Check out 34 similar materials and continuum mechanics , How to calculate section modulus from the moment of inertia, Plastic section modulus: beyond elastic section modulus, Section modulus formulas for a rectangular section and other shapes. Specify beam geometry and loads to get started analysing the beam. The ratio of the width of the web to the depth of the web is kept as 1/3 to 2/3. I_y Scroll down to the section about neutral axis and all will become clear. Equal or less than 5 kg/cm 2, no shear reinforcement is provided. .bravenet-link { Why engineers, architects and building designers depend on ClearCalcs to deliver their best work anywhere, anytime. the failure will be on the compression face or on the tension face Here the section is divided into two rectangular segments. Step 8: Calculate neutral axis depth which is equal to rectangular stress block divided by B 1 i.e, either 0.85 or the value from Equation 3. . Position of centroid - Xc (unit): Overall depth of a flanged beam is equal to the sum of the depth of flange (Df) and depth of the web (dw). For SF & BM of many load cases of overhanging beam, Civil Engineering Quiz The beam calculator automatically uses ClearCalcs' powerful finite element analysis engine to determine moment, shear, and deflection as you work. Framing Interior Walls| document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); Get updates about new products, technical tutorials, and industry insights. For a balanced sections, the moment of resistance is calculated as under : In an under reinforced section, the percentage of steel provided is less than that provided in balanced section. Centroid of Large Rectangle with respect to reference x-axis = Y = 12.5/2 = 6.25 cm. (Basically Dog-people). Sectional Calculator T Beam Enter your values and select the units as required. 3- Calculate excess moment (M 1) using Equation 15: M 1 =(300.23/.9) . The distance of the centroid, from the top edge, can be calculated if we consider that the first moment of area (also called static moment) of the entire T-section should be equal to the combined static moments of the web and the flange: Ay_c = (t_w h) {h\over2} +\Big(\left(b-t_w\right)t_f \Big) {t_f\over2}\Rightarrow, y_c = \frac{1}{2A}\left( t_w h^2 +(b-t_w) {t_f}^2 \right). Two different types can be applied in the calculator: Uniform Loads have a constant magnitude along the length of application. \sigma We and our partners use cookies to Store and/or access information on a device. The support type can either be pinned (fixed in translation, free in rotation) or fixed (fixed in both translation and rotation) and is selected from the drop-down menu. Kids Bathroom Idea| Ltd. ABN 42 614 037 400. How to use calculator. You must there are over 200,000 words in our free online dictionary, but you are looking for one that's only in the Merriam-Webster Unabridged Dictionary. It only takes a minute to sign up. Therefore: where the min designation is based on the assumption that The calculated results will have the same units as your input. The cross-sectional area (see cross-sectional area calculator) above the neutral axis (between the inner surface of bending and the neutral axis) experiences compression stresses. Step 2: Find maximum neutral axis depth. The neutral axis is represented by a dotted line. (T beam design), Critical neutral axis, n = kd = 0.29 x 500 = 145 mm. How To Change A Garage Door Spring| Width of a rib taken as 1/3 to 2/3 of the depth of rib. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. Second Moment of Area (or Moment of Inertia) is also specific to the beam section selected, and again defaulted to the properties of a common steel beam. Moment of Inertia Ixx (unit^4): Linear Loads have a varying magnitude along the length of application. margin-bottom: 10px; For more details on strength reduction factor calculation, please click here FAQs What is reinforced concrete T-beam? in same units and this calculator will provide the "Output Results" in the Calculate bending moment & shear force for simply supported beam. You can also check that unit is always the product of the power of input unit, in this case all input units are inches, so the result is in inches^4. For the first case, that is when the axis crosses the web, the plastic modulus can be found like this: \begin{split} Z_x =&{t_w(h-y_\textit{pna})^2\over 2} + { by_\textit{pna}^2\over 2} \\&- {(b-t_w) (y_\textit{pna}-t_f)^2\over2 } \quad , t_f \le {A\over2 b}\end{split}, Z_x ={t_w (h-t_f)^2 \over4} + {b h t_f\over 2} - {b^2 t_f^2\over 4t_w} \quad , t_f \le {A\over2 b}. The moment of inertia Manage Settings Chapter Reserve Problem 093 The cross section of pimetallic beam consists of an Jumirun bar (1) and copper bar (2_ pondej together The composite beam subjected to bending moment about the axis of Mz +150 N-m_ Gaowin below: The elastic modulus of the aluminum 72 GPa The astic modulus of the copper is Ez 106 GPa Assume 20 mm; C1 17 mm and C2 mm; The centroid of the equivalent al- Iuminum beam 13 . Calculate the Neutral Axis for the entire section, Calculate the moment of inertia using the Parallel Axis Theorem - which is essentially the sum of individual moment of inertias. We also have some articles below about how to calculate the moment of inertia, as well as more information on centroids and section modulus. Determine the depth of neutral axis of T-beam which have effective width of flange 1100 mm, depth of flange 100 mm, area of steel 2500 mm2 of steel Fe500 and concrete M25. [5 points] Problem 3 [25 points] The leading edge of an aircraft wing has the four-stringer configuration shown in the figure below. At the certain location where the bending stress changes its nature from tensile to compressive, the value of the bending stress becomes zero and thus the fibres at this location never experience any bending stress. Watch on-demand videos to learn more about ClearCalcs design & analysis software. Start your free ClearCalcs trial to unlock saving and export, as well as even more calculators for wood, steel, and concrete beams, columns, and footings. Please enter the "Input Values" in the form In the below segments, we include what is moment of inertia, how to calculate the centroid and moment of inertia and common MOI equations. Each load can be named by the user. Once all the section reaches the yield strength, plastic deformation occurs across all that section. Heres how. In contrast, the region below the neutral axis (between the outer surface and the . Moment of Inertia Calculator . Please make sure that the input values are positive. Estimating bending moment due to give loading. Are the models of infinitesimal analysis (philosophically) circular? Continue with Recommended Cookies. For y-y bending, the plastic neutral axis passes through centroid (due to the symmetry). Get possible sizes of product on product page in Magento 2. Slabs and beams are cast monolithically in RCC construction. For example, these can represent reactions from other members connecting to the beam. &sigma = (M x y)/I x. Iaa = Izz + Ay^2. The consent submitted will only be used for data processing originating from this website. font:normal 18px arial; Starting SkyCiv Moment of Inertia Calculator Copyright 2015-2023. Point Loads are specified in units of force, kN or kip, and area applied at discrete points along the beam. We have a special article about finding the centroid of a compound area. The moment of inertia (second moment or area) is used in beam theory to describe the rigidity of a beam against flexure. color:black; of compressive area and neutral axis \[=b.n.\frac{n}{2}=\frac{bn^{2}}{2}\] Moment of tensile area = Equivalent . Whether you're working on a design project, conducting a survey, or studying for an exam, our Centroid Calculator is the perfect tool to help you get the job done. Still, when dealing with complex geometries like a tee, channel, or I beam, a calculator can save time and help us avoid mistakes. where How Do I Get Rid Of Musty Smell In Bat| If it is subjected to 95 KNm moment using M20 concrete and Fe 415 steel. Refinish Wood Furniture Without Stripping| In WSD, the neutral axis is considered to be the centroid of the cracked transformed section. Access our library of support articles to get started using ClearCalcs and learn advanced tricks to manage your projects and calculations. The properties of the beam and section are specified by typing directly into the input fields. Calculation Method For Stresses Of A T Section In Bending At The Sls Neutral Axis Definition Diagram Formula For Diffe Shapes With Calculator For Ers Area Moment Of Inertia Centroid Section Modulus T T Beam Design Parts Of With Numerical Calculation Determine The Location Of Neutral Axis For T Beam Shown Below Homework Study the offset from centroid, of a section fiber, parallel to x-x axis. break the section into simple geometric shapes. background: white; Knowing Enter the shape dimensions h, b, tf and tw below. The maximum values of each are output as Moment Demand, Shear Demand and Deflection, along with the diagrams along the length of the beam. The natural axis is the axis where there is no stress. See our meta site for more guidance on how to edit your question to make it better. in compression, separated by the neutral axis. Put simply, the Section Modulus is represented within a flexural stress calculation (such as in the design of beams) As you may know, we typically calculate flexural stress using the equation: The Elastic Section Modulus is represented in this equation as simply: After defining this, we can re-arrange our flexural stress formula as follows: There are two kinds of Section Modulus: Elastic and Plastic. This relation is equivalent to the axial stress equation: =FA\sigma = \frac{F}{A}=AF. Depth of t beam 1/12 to 1/15 of span. E Design of T beam. We have a beam deflection calculator. Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, I couldnot find anything that is why i asked here :). .bravenet-footer { Therefore the position of the neutral axis for the rectangle is given by. (If It Is At All Possible). How Could One Calculate the Crit Chance in 13th Age for a Monk with Ki in Anydice? The best answers are voted up and rise to the top, Not the answer you're looking for? The plastic section modulus is given by the general formula: where Furniture Nook North Royalton Ohio| The bending moment is analogous to axial force, while the section modulus is analog to the cross-sectional area. Answer to PROJECT INSTRUCTION_BNP 20203 MECHANICS OF MATERLALS. Trying to match up a new seat for my bicycle and having difficulty finding one that will work, Poisson regression with constraint on the coefficients of two variables be the same, Comprehensive Functional-Group-Priority Table for IUPAC Nomenclature, List of resources for halachot concerning celiac disease. The sign convention used in the shear force and bending moment diagrams is (positive values shown): Using the cursor to hover over any point on the bending moment, shear force or deflection diagrams gives the specific values at that location along the beam. Moment of Inertia Iyy (unit^4): For the detailed terms of use click here. , the tee height, S_x if (!document.getElementById('elistaddress48375969659').value.match(regexPattern)) , which is usually preferable for the design of the section. It will help in deciding whether color:white; Our regularly updated structural calculation library for wood, steel, concrete and masonry design. You can also use our section modulus calculator and do it faster. INSTRUCTIONS: Choose units and enter the following: ( D1) Top width ( W1) Top thickness ( W2) Vertical thickness ( D2) Interior height ( D3) Bottom width ( W3) Bottom thickness y-centroid (y): The calculator return the centroid in millimeters. find the area moment of each section by multiplying its area . The moment of the tensile and compressive area should be equal at the neutral axis. Within the "Edit Joints" property manager toggling two check boxes will show their location in the graphics area. D. All the above width: 100%; So if you want to calculate the moment of inertia of circle, moment of inertia of a rectangle or any other shapes, feel free to use the below software or our all-inclusive SkyCiv Section Builder. Our Centroid Calculator utilizes FEA to provide highly accurate results in seconds, no matter how complex the shape. e = document.getElementById('elist_err48375969659'); This calculator is a versatile calculator and is designed to find the moment of inertia and centroid for any user-defined shape. Home; Beam Calculator; Section Properties; Unit Conversion; Pricing; Documentation; Blog; Contact Us. The The Neutral Axis (NA) is located at the centroid. The example diagram below, from the summary section, shows a two-span continuous beam with a linear distributed patch load and point load. If you would like to change your settings or withdraw consent at any time, the link to do so is in our privacy policy accessible from our home page.. We are confident that you will be satisfied with the accuracy and user-friendliness of our tool. Min. Q) A T-beam has a flanged width of 1200 mm and flanged thickness being 100 mm. The usefulness of the last equation is that we can predict the bending moment that will cause plastic deformation by just knowing the yield strength and plastic section modulus. You can use our stress calculator to obtain the axial stress. Therefore at the neutral axis, the value of the bending stress is zero. Here is a concise list of the section property terms and definitions: Other Parameters These are more advanced results calculated by the full SkyCiv Section Builder: We've also compiled more information to calculating the moment of inertia of sections. Primitive Fireplace Decor| Q4. We want our questions to be useful to the broader community, and to future users. - ( T beam design) Solution: Size of beam = 300 x 500 mm effective M = 95 KNm Design constants for M20 and Fe 415 k = 0.29 j = 0.9 R = 0.91 N/mm 2 Critical neutral axis, n = kd = 0.29 x 500 = 145 mm Moment of resistance of balanced section (M1) M 1 = Rbd 2 = 0.91 x 300 x 500 2 M 1 = 68.25 KNm M 2 = M - M 1 = 95 - 68.25 = 26.75 KNm A_t Calculate SF & BM for Cantilever, Deflection & Slope Calculator for Cantilever As shown in Fig. The bending moment needed to achieve this is called the plastic moment. The Moment of Inertia (more technically known as the moment of inertia of area, or the second moment of area) is an important geometric property used in structural engineering. T beam design includes the steel and thickness required to bear the load applied on it. Step 1: Find actual neutral axis. Step 2: Mark the neutral axis. indicates the neutral axis. M_x corresponding units (unit2 , unit3 , unit4 The depth of neutral axis is. neutral axis depth (c)= a/B1= 105.4/0.85= 124 mm dt: distance from the compression face of the beam to the center of the bottom layer of steel bars: c/dt= 124/525= 0.236<0.375. 2.14 (b) and taking moments of the area of compressive and tensile zones about the neutral axis. Moment of natural axis M in Nm, perpendicular distance to neutral axis in m & second moment area of neutral axis I x are the key terms of this calculation. Area of the Cross-Section is specific to the beam section selected, and is defaulted to the values for a common steel beam. Additionally, it calculates the neutral axis and area moment of inertia of the most common structural profiles (if you only need the moment of inertia, check our moment of inertia calculator). For a simple beam, the neutral axis passes through the centroid of the cross-sectional area. However, this can be automatically converted to compatible units via the pull-down menu. This is a powerful tool for engineers, surveyors, designers, and students alike. The neutral axis obtained by this method is called as actual neutral axis. Neutral axis locations for negative moment sections Sum of moments about the neutral axis as functions of kd: 1) Neutral axis within the slab (this case will govern for a very shallow beam web projection relative to the slab thickness) Left end negative moment section, f3((kd))b w+ + kd2 2 b fb w return true; Although the material presented in this site has been thoroughly tested, it is not warranted to be free of errors or up-to-date. y_{c} I_{x} Step 2: Find maximum neutral axis depth. "ERROR: column "a" does not exist" when referencing column alias, Site load takes 30 minutes after deploying DLL into local instance, How to make chocolate safe for Keidran? Assuming a parallel beam of neutrons diffusing up to the surface of the pool where the neutron flux is measured to be 108 m -2 s-1. A minimum of one fixed support, or two pinned supports are required. How do you calculate moment of resistance in a balanced section? Since the T-section is not symmetric around x-axis, the distances of the two end fibers (top and bottom), from this axis, are different. Finally, we can relate the section modulus to the stress and moment: Does this relationship seem familiar to you? MORE BEATS FOR THE STREETS: Go bigger with 6.5 in speakers that deliver 100-Watts of crystal-clear audio. Fix the overall dimensions of the T beam. SkyCiv Engineering. of the beam. Now let's find Ai and yi for each segment of the I-beam section shown above so that the vertical or y centroid can be found. Where, `\bar{y}_{\text{Composite}}=\bar{y}_{\text{Equivalent}}`. Calculation Example - Internal forces. This is essentially a weighted average of the area and distance from bottom for each segment. margin:auto; Z_y = \frac{t_f b^2}{4} + \frac{h_w t_w^2}{4}, I_{x0} = \frac{t_w h^3}{3} +\frac{b_1 t_{f}^3}{3}. The neutral axis passes through the centroid of the cross-section, therefore by finding the location of the centroid we can locate the neutral axis. The beam is simply supported with an effective span of 6 m. The effective width of the flange for the cross-section shown in the figure is: Q10. 2.6 (c). Calculate moment of inertia of plane sections e.g. { Note that the derivation of bending moment equations above has the following assumptions: Firstly, the beam is linear and has a uniform cross-sectional area before stresses are applied. This will be desirable if the material is both equally strong in tension and compression. As the ratio I/cI/cI/c only depends on the geometric characteristics, we can define a new geometric property from it, called the section modulus, denoted by the SSS letter: As well as the second moment of area, this new geometric property is available in many tables and calculators, but if you want to know how to calculate section modulus from the moment of inertia, simply divide III by ccc, and you'll get it. } Generally, it can't be known which equation is relevant beforehand. The following table, lists the formulas, for the calculation the main mechanical properties of a T section. Since M d <M u, the beam should be designed as a doubly reinforced concrete beam. If the section is symmetric, isotropic and is not curved before a bend occurs, then the neutral axis is at the geometric centroid. day free trial and start being more productive. around the centroidal x axis, can be determined, using the Parallel Axes Theorem: \begin{split} & I_{x0} & = I_{x} + A y_c^2 \Rightarrow \\ & I_{x} & = I_{x0} - A y_c^2 \end{split}. padding:5px 15px; box-sizing: border-box; Also worth noting that if a shape has the same dimensions in both directions (square, circular etc..) these values will be the same in both directions. Signing up for a ClearCalcs account will unlock further advanced features for design and analysis of beams and a variety of other structural elements. Reinforced Concrete Calculator S_x \kappa In the case of concrete sustainability, two main ways are generally discussed: (1) the reduction of natural raw materials and (2) the reduction of emissions related to concrete production. T-Section, - (black line) is Neutral Axis, - (blue line) is equal area x1x1 axis. How To Measure For Outside Mount Blinds| For example, a rectangle has two dimensions to define it: Depth and Breadth. font:normal 15px arial; .bravenet-input { Related Gallery: http://www.ecourses.ou.edu/cgi-bin/ebook.cgi?doc=&topic=me&chap_sec=06.1&page=theory Suggested for: Neutral axis in a composite beam Understanding horizontal shear in beam with vertical load It will help in deciding whether the failure will be on the compression face or on the tension face of the beam. We can verify this result with the above free moment of inertia calculator, which shows the same result of 10.6667 in^4: Now let's look at a more complex case of where the cross section is an I beam, with different flange dimensions.