pipe bending moment calculator

Transverse metal area can be expressed as, Am = (do2 - di2) / 4 (3), External pipe or tube surface per ft of length can be expressed as, Ao = do / 12 (4), Ao = external pipe surface area (ft2 per ft pipe), Internal pipe or tube surface per ft of length can be expressed as, Ai = di / 12 (5), Ai = internal pipe surface area (ft2 per ft pipe), Transverse internal area can be expressed as, Aa = 0.7854 di2 (6), External circumference can be expressed as, Internal circumference can be expressed as. The above steel beam span calculator is a versatile structural engineering tool used to calculate the bending moment in a aluminium, wood or steel beam. By joining you are opting in to receive e-mail. Please let us know here why this post is inappropriate. Copyright 1998-2022 engineering.com, Inc. All rights reserved.Unauthorized reproduction or linking forbidden without expressed written permission. An additional purpose of the research was to determine the effect of technological deformations and internal stresses created in the plastic shaping of a round tube into a square section on selected bending parameters of a 25 25 2 mm square stee l pipe. Results of iteration cycle 2 are shown in Table 4.5. Click hereor follow the link below to download the Tube Section Modulus Calculator. Sagging bending moment is taken as (+be) sign and its result in developing tension in the bottom fibre and compression in the top fibre of the beam. Area Moment of Inertia Section Properties Don't want to hand calculate these, sign up for a free SkyCiv Account and get instant access to a free version of our beam software! The tube bending section modulus calculator allows you to input the tube specifications into an easy to use calculator. Examine how the principles of DfAM upend many of the long-standing rules around manufacturability - allowing engineers and designers to place a parts function at the center of their design considerations. Length of tube in a bend = CLR X DOB X .01745. or, to put it another way: L = (R X .01745) x Z, L is the length, R is radius of the pipe bend, Z is the angle of the bend. So my question is how can i get Bending Moment if I know SMYS because SMYS is a stress with units in MPa and Bending Moment units is in Kilo Newton Metre. Premium: PDF Reports and Custom Logo. simply supported? Determining the section modulus of the piece of tube or pipe you need to bend is important because it will allow you to knowbeforeyou bend if your equipment can successfully complete the bend. The tube bending section modulus calculator allows you to input the tube specifications into an easy to use calculator. As discussed in above section, the formula for calculating the bending stress in pipe is given below- b = E/R x y where, E is the Young's modulus of material R is the radius of bend or curvature y is the distance from neutral axis Use the correct formula to calculate the circumference of the bend. any wall thickness), it is considered acceptable . Together these two downloads are a powerful tool. Figure 1: Restrained and unrestrained parts of a Buried pipe. What you are trying to do cannot be done using a single formula such as wl^2/8. Pipe stress resulting from pipe-top tension is shown as: (21-34) Pipe stress due to hydrostatic pressure is compressive: (21-35) if you want to calculate solid bar Load (lbs) This is the force applied to your tube. Bending moment equations and formulas offer a quick and easy analysis to determine the maximum bending moment in a beam.. Below is a concise table that shows the bending moment equations for different beam setups. y = material's yield strength. Area Moment of Inertia Section Properties Tube/Pipe Calculator. Cookies are only used in the browser to improve user experience. (Units4), Radius of Gyration A. Bending moment (M) = 3000N-m = 3 10 6 N-mm Torque (T) = 10000 N-m = 10 10 6 N-mm ultimate tensile stress tu = 700 MPa = 700 N/mm 2 shear stress u = 500 MPa = 500 N/mm 2 Factor of Safety = 6 We know that the allowable tensile stress, t or b = tu / F.S = 700/6 = 116.7N/mm 2 and allowable shear stress = u / F.S = 500/6 = 83.3N/mm 2 However, existing methods cannot accurately estimate the bending moment in HDPE pipes due to neglecting the installation effect and the pipe-soil interaction under traffic loading. I = (d o 4 - d i 4) / 64 0.0491 (d o 4 - d i 4) (1) where . The calculator draws shear force and bending moment diagrams for a simple beam under the specified load. point? Finally, the material used in the beam is homogenous and isotropic. Articles that describe this calculator Internal forces diagrams for the two-support beam Shear force and bending moment in the two-support beam Distance between supports, m Load Items per page: Calculators used by this calculator Premium: Save Unlimited Models and Sections. Premium: Deflection and Stress Diagrams. Once a model with appropriate boundary conditions has been established, the maximum deflection or slope would be obtained using either double integra- bending moment and the bending curvature based on the results of experimental studies. Support Reactions. Only emails and answers are saved in our archive. Beam Deflection Calculators - Solid Rectangular Beams, Hollow Rectangular Beams, Solid Round Beams Enter value and click on calculate. Powerful hand calculation modules that show the step by step hand calculations (excluding hinges) for reactions, BMD, SFD, centroids, moment of inertia and trusses! Typically, structural engineers designing I beams or T beams calculate section modulus of the cross-sectional area of the beam to understand if the beam will support a particular load or repeated cyclic loading. The number of grids . Engineering Forum The load distribution of the element from node 20 to 50 can be seen in the right picture and it is a simple representation of the simplified analysis method for this segment of the pipe. *Eng-Tips's functionality depends on members receiving e-mail. Deflection for a given radius and length of deflecting pipe can be calculated as. Bending Moment at the fixed end is M = PL = 0.3 P N-m For a pipe with OD = 40 mm; ID = 30 mm, I = ( / 64) (OD 4 - ID 4) = ( / 64) (0.04 4 - 0.03 4) = 8.5910 -8 m 4 y = 40 mm / 2 = 20 mm = 0.02 m = M y / I = 0.3 P 0.02 / (8.59 10 -8) = 69,850 P Pascals moment through the thickness of a ring, see Fig. Section modulus is used in structural engineering to calculate the bending moment that will result in the yielding of a beam with the following equation: where. Wall Thickness (inches) Enter half of your O.D. inside diameter (in) - (default values: STD 4 inches - Carbon, Alloy and Stainless Steel Pipes - ASME/ANSI B36.10/19. I have forgottenStrength of Material Basics that I studied in 1st Yr. But I have read in a technical document, that for initial calculation Max Bending Moment can be estimated as 0.85 times SMYS. The term second moment of area seems more accurate in this regard. During cutting, because of the bending moment, excessive stresses build up at the cut tip and can cause plasticity. This engineering calculator will determine the section modulus for the given cross-section. E = Modulus of elasticity of pipe in N/m2 I = Moment of Inertia of pipe in m4 Note : Maximum bending stress of the pipe can be taken as 30% of allowable stress. Mx = RaLa - F1x1 - F2x2. deflection calculations to account for variations in the backfill. Beam length: 10.0 m. Second moment of area: 473.0 cm 4. Y is the distance between the X-X axis and the extreme fibre of the welded cross section, it is radius for the circular cross section. The shape factor relates pipe deflection to bending stress or strain and is a function of pipe stiffness, pipe embedment material and compaction, haunching, native soil conditions and level of deflection. If you want to promote your products or services in the Engineering ToolBox - please use Google Adwords. This is a printable handbook showing how to implement in four standardized steps the "forward mandrel" set-up for rotary-draw tube-bending machines and establish process control over the so-called black art.The procedure is based upon the guiding principle that the tools make the . Calculate the bending moment, shear force, reaction forces and deflection using real steel section properties. curved? Neverth. Make Shortcut to this Calculator on Your Home Screen. Learn methods and guidelines for using stereolithography (SLA) 3D printed molds in the injection molding process to lower costs and lead time. Training Online Engineering, Area Moment of Inertia Section Properties = I. It is able to accommodate up to 2 different concentrated point loads, 2 . As long as the round material number is higher than the non-round material, then that particular bender will be capable of bending your part shape. The reduced bending moment capacity of member BC is calculated and found to be 374 kNm, which is used in the next iteration cycle of analysis while the bending moment capacity of member AB remains at 515 kNm. if you enter an inside dimension for one input, enter an inside dimension for your other inputs. The bending moments calculator allows you to position one or two supports and up to six point loads along a straight beam and calculate the bending moments at any of the forces or supports entered. y'' = M / EIx y - beam deflection; y' - inclination angle. It's known you guys do the best work.". Create bending moment diagrams, shear force diagrams and measure deflection for an indeterminate beam span. Beams in bending experience stresses in both tension and compression. I = moment of inertia (in 4) d o = outside diameter (in) d i = inside diameter (in) Section Modulus All dimensions are entered in inches and all outputs will be in inches. Area Moment of Inertia Section Properties of Tube/Pipe Feature Calculator and Equations. What is bending stress? Bending Stress calculator uses Bending Stress = Bending Moment*Distance from Neutral Axis/Moment of Inertia to calculate the Bending Stress, The Bending Stress formula is defined as the normal stress that is induced at a point in a body subjected to loads that cause it to bend. Pipe outer surface stresses due to the bending moment loads can be calculated using the following formula: (21-33) where M is the moment, I is the moment of inertia for pipe section, and D is the pipe outer diameter. This beam deflection calculator will help you determine the maximum beam deflection of simply-supported beams, and cantilever beams carrying simple load configurations. Tackle any project with this powerful and fast beam software. Civil/Environmental engineering general discussion Forum, Low-Volume Rapid Injection Molding With 3D Printed Molds, Industry Perspective: Education and Metal 3D Printing. For example, if you calculate your pipe has an allowable moment capacity of 50kNm by limiting the maximum bending stress to 0.85 x yield stress that doesnt really help unless you know it needs to resist 400kNm. It then calculates the section area moment of inertia properties of common shapes. You can choose from a selection of load types that can act on any length of beam you want. **Albina takes no responsibility for the calculated results. Outside diameter of tube or bar (inches) Input your tube O.D. Based on linear elastic bending theory as indicated by Patswfc above. Engineering Videos Pipe Bending Revision 2.0 September 2014 1.0 Bending Processes for Pipe Fitting 1.1 Pipe and Tube Bending Pipe bending machines are typically human powered, pneumatic powered, hydraulic assisted, or electric servo motor. The analyses demonstrated that the shear locking is not significant for the passive pile embedded in soil. The pipe is connected to two pumps which are far away from each other. Setback = radius X tangent angle of bend. There are 5 main pieces of mandrel tube bender tooling needed to perform precise bends with a 2022 Tube Form Solutions All rights reserved. Effects of all parameters should be examined before generating the theory for a best solution. Formula MI for Solid Round Beams = (pi * (OD 4 - ID 4)) 64 Deflection = (length 3 * force) (3 * E * MI) Bending Stress = (force * length) (MI / (0.5 * height)) Where, MI = Moment of Inertia E = Modulas of Elasticity in psi A tube is a long hollow object that is usually round, like a pipe. Already a member? Youngs Modulus: 210.0 GPa. 3 can be modified with eq. 104.2 Curved Segments of Pipe (B) For ferrous material, when the radius of a bend is 5 nominal pipe diameters or greater, and the nominal wall thickness of the . The beam is subjected to a concentrated load F located at a distance a from the free end. You can target the Engineering ToolBox by using AdWords Managed Placements. Please read Google Privacy & Terms for more information about how you can control adserving and the information collected. Enter consistent dimensions(i.e. Even for axisymmetric stresses, the moment is balanced by the opposite moment at any other cross section. Enter consistent dimensions (i.e. DOB = Degree Of Bend. length with the help of mathematical calculation. This engineering calculator will determine the section modulus for the given cross-section. As a result of calculations, the bending moment M at point X is determined. Thanks Ussuri once again..Well I can understand lot of things are needed to be considered for accurate calculation. The bending stress is computed for the rail by the equation Sb = Mc/I, where Sb is the bending stress in pounds per square inch, M is the maximum bending moment in pound-inches, I is the moment of inertia of the rail in (inches)4, and c is the distance in inches from the base of rail to its neutral axis. Carbon, Alloy and Stainless Steel Pipes - ASME/ANSI B36.10/19. In the pipe bending operation the tube may be supported internally or externally to preserve the cross section of the pipe. Shape factor given below is for moderate to high compaction. M is the bending moment for the applied force. Some of our calculators and applications let you save application data to your local computer. Do not mix inside, outside, and centerline dimensions). For this reason, the analysis of stresses and deflections in a beam is an important and useful topic. Google use cookies for serving our ads and handling visitor statistics. (pi) = 3.1416 For example, if your die creates a 2.2" radius, and you need to create a 35 bend, your calculations would look something like this: to calculate one degree of bend 3.1416 (2x2.2) = 13.823/360 = 0.0384 to calculate CLR of 35 bend 0.0384 x 35 = 1.344" Offset Bend Calculation 3-Point Saddle Bend Calculation Thanks. Downloads Moment Diagram. The applied bending moment on your structure is a function of the applied loading. Also, the material composition determines the deforming of the tubing material past the given materials modulus of elasticity and into the yield strength of the material. Although less likely, a maxi-mum slope could be specified instead. Determining the correct tooling specifications for a tube bender can be difficult. Premium: Custom and Standard Sections or Materials. Discover how this hybrid manufacturing process enables on-demand mold fabrication to quickly produce small batches of thermoplastic parts. We don't save this data. Whether the pipeline is a pressure pipeline or a gravity main. The calculations are not valid past the beam end points. Please read AddThis Privacy for more information. I am sorry for asking such a fundamental question. I have implemented the method that you have advised !!! 1. The moment capacity for metallic pipes is a function of many Softening region parameters and the most common are listed below in arbitrary Linear limit sequence: Diameter over wall thickness ratio Material stress-strain relationship Material imperfections Welding (Longitudinal as well as circumferential) Initial out-of-roundness Join your peers on the Internet's largest technical engineering professional community.It's easy to join and it's free. Firstly, the beam is linear and has a uniform cross-sectional area before stresses are applied. Third, the beam is subjected to pure bending (bending moment does not change along the length). Is this a flexible pipe or a rigid pipe. Already a Member? Answer (1 of 2): Before answering this question I would like to have the material rhea-logy of the pipe in question. Area Moment of Inertia Section Properties of Tube/Pipe Feature Calculator and Equations. You need to calculate the section area moment of inertia for the round material and compare it to your non-round material. So, it is very simple to calculate it. Ya..I understand your point..but actually I am doing wall thickness calculation based on DNV-OS-F-101 ..In the spreadsheet, for load interaction, I need to put the value of ME (Maximum Bending Moment due to Environmental load)..I know I can get the exact value once I do Dynamic Pipeline Analysis..But initially I must assume certain value to put in the spreadsheet..as based on that spreadhsheet will give the result whether the assumed thickness is ok or not.. moment capacity of pipe = yield stress x elastic section modulus of pipe. Stringer Calculator. Engineering Toolbox STEP 2: Once those formulas have been resolved, the bending moment can be calculated at the nodes 20, 30 and 50. TESTIMONIALS. Engineering Calculators Calculate beam bending shear force, bending moment, slope and deflection for circular beams, semi circular beams, circular beam segments, and circular beam sectors. Cone Calculator. The term indicates a multiplier of Bending and Torsional stresses. Applications. However, section modulus can also relate to bending tubes. The analytical method can be by inspection, simple to complex hand calculations, or a . The magnitude and location of these loads affect how much the beam bends. Moment of Inertia. This Intensifier acts locally on a piping Component ( tees, elbows, bends, Olets, etc) and Its value depends on component geometry. We pretty much always calculate bending stress at a point along the beam where bending moment (and thus also stress) is highest. Table 4.5. h . If youve ever had to perform the calculations necessary to properly bend tube and pipe you know that while they are a vital part of the bending process, there is often a lot of information to juggle. Moment of inertia can be expressed as. 0.20 > K > 0.15 - A movable mandrel is required to bend the tube. Do not mix inside, outside, and centerline dimensions). The moment of inertia (second moment or area) is used in beam theory to describe the rigidity of a beam against flexure (see beam bending theory). If I have done my sums correctly that would equate to a 168.3 OD x 8.7mm WT pipe (almost). varying UDL? Based on these sign conservation we can write the equation of bending moment at that section x-x of the beam given above, Considering force on the left of section x-x. How do you know what bender will bend your square, rectangle, non-round shape? Enter beam length: Support Positions (from left-hand end): Help Using the finite element analysis program ABAQUS, a series of calculations on a cantilever beam, pile, and sheet pile wall were made to investigate the bending moment computational methods. So in the case of simply supported beam with force in the middle this point will be in the middle of the beam. Thanks Patswfc and Ussuri for your help. Many structures can be approximated as a straight beam or as a collection of straight beams. This ebook covers tips for creating and managing workflows, security best practices and protection of intellectual property, Cloud vs. on-premise software solutions, CAD file management, compliance, and more. It is a 6" subsea pipeline between Well Head Platform and Production Platform with risers installed at both ends. h = l 2 / (2 r) (3) where . When bending tube or pipe, the bender must have enough bend arm toque to overcome a materials section modulus to make a bend into the tube that is permanent. You also have options depending on . The selected tariff allows you to calculate the beam, frame or truss for 1 month without restrictions on the number of calculations. Schedule 30 gives a thickness of 8.382 mm. And you need to multiply this value by the distance from the neutral axis of bending stress. Pipe stress analysis is not an accurate depiction of the piping behavior, but it is a good approximation. I = (do4 - di4) / 64 0.0491 (do4 - di4) (1), S = 0.0982 (do4 - di4) / do (2). Promoting, selling, recruiting, coursework and thesis posting is forbidden. We don't collect information from our users. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework. Bending Stress is denoted by b symbol. . That is, for a predicted deflection of 3%, and a 2% variation, the actual deflection would be between 1% and 5%. partial UDL? Performing a bend incorrectly can lead to tube bulging, tube collapse, and other tube problems. Bending: Design for Strength, Stiffness and Stress Concentrations7/6/99 2 this would normally be a bound upon deflection v like . Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members. The installation of pipes generates an initial bending moment in the pipe, which should be included in the pipe bending moment calculation. In this formula, you need to divide the bending moment with the moment of inertia of the cross-section. Formula MI for Solid Round = (PI * Diameter4) / 64 Deflection = (Length3 * Force) / (3 * E * MI) Bending Stress = (Force * Length) / (MI / (0.5 * Height)) Where, MI = Moment of Inertia E = Modulas of Elasticity in psi How to calculate the deflection of a solid round beam? This engineering data is often used in the design of structural beams or structural flexural members. Shear Diagram. Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro .Add the Engineering ToolBox extension to your SketchUp from the SketchUp Pro Sketchup Extension Warehouse! The ROI Of Tube Bending Automation Calculator, Checklist for Specifying Tooling for a Tube Bender. The minimum value of the SIF is 1.0. These applications will - due to browser restrictions - send data between your browser and our server. When you click "Calculate Deflection" the tool will provide several engineering specifications such as the moment of inertia and yield strength to determine the deflection. I am not too sure exactly about the conditions. 2 to calculate maximum deflection for minimum radius to. Indeterminate / Continuous Beams. h max = l 2 / (60 d) (3b) where . It can also be used as an i beam load capacity calculator by using it as a bending stress or shear stress calculator. Calculation of total weight Total weight = weight of pipe (wp) + weight of fluid (wf) B. weight of pipe Pipe Strength Calculator (mass, buoyancy & stress). It then calculates the section area moment of inertia properties of common shapes. [2]. Bending Moment Diagram (BMD) Shear Force Diagram (SFD) Axial Force Diagram (AFD) Moment is positive, when tension at the bottom of the beam. Using The Deflection Calculator. A pipe is normally taken to mean a tube with a wall thickness greater than 1/10 th of the nominal radius.. Conversely, a tube is normally taken to mean a pipe with a wall thickness less than 1/10 th of the nominal radius.. Whilst the stress calculations in pipe are valid for pipe and tube (i.e. | Contact, Home Your pipe will have a limiting moment capacity but that doesn't help you if you dont know the moment it needs to resist. Weve created a tube bending calculator and tube bending formulas guide to help you navigate all of the calculations, variables, and prep work. Tube/Pipe Calculator, Inch (in.) To begin, choose a profile type and part number. The Euler Bernoulli beam equation is suitable for slender beams (it does not include the effect of shear), and for small angles ( < 0.5 rad). Bending Moment Equations for Beams. Load Condition Point Load Center 1/3 Load Even Distribution From there input a length and the expected profile load. Resultant stress () can be found out after weld stress analysis calculation by using the eq.5 as: = (s* s + b* b)=(31.78*31.78+63.69*63.69)=71.17 N . Reference: Acceptable ovality of a pipe should be determined by user, but as a guideline, 5% is a typical acceptance criteria, and ASME defaults to 8%. Therefore, prediction of the required moment for the proper bending process with low cost and shortened production time is needed. Hauch and Bai (2000) studied the bending moment capacity of metallic pipes subjected to bending and axial tension. Metric Conversion Calculator. "Your salesman provided a quick quote with an offer to explain things we should take into account. I = Moment of Inertia for unit length, m = t t / 12 t Stresses & Deflections in Beams. Pipe stress analysis is an analytical method to determine how a piping system behaves based on its material, pressure, temperature, fluid, and support. They can help you evaluate your current equipment, determine if you can accomplish a bend that a new customer or RFQ has requested, evaluate your current equipments capabilities versus a new piece of equipment, and ensure you have the correct calculations before you begin a bend. Because of a friction between pipe and soil, the buried pipe between points A and A' does not tend to move. Radius Calculator. Is it possible to determine or some more information is necessary ? The bending moment M applied to a cross-section is related with its moment of inertia with the following equation: (Units), Copyright 2000 - Thanks for the reply. FREE Tube-Bending Guide Download: A complete guide to the principles of the 4-Step set-up for tube-bending tools. Score: 4.1/5 (51 votes) . Login. The stress-free layer is positioned even further inside, it is the layer . This is so that building, bridges, and rail road tracks do not fail and have safety factors. S = section modulus. 2022, by Engineers Edge, LLC www.engineersedge.com For a contour method measurement of hoop stress, a radial cut is used. Roark's Formulas for Stress and Strain, Seventh Edition, Table 8.2 reference loading number 5M. This engineering data is often used in the design of structural beams or structural flexural members. The calculator is based on the piping formulas and equations below. h = deflection of pipe (m, in) r = radius of bending pipe (m, in) l = length of pipe from fixed position (m, in) Eq. Feedback Advertising Some of the most common shapes covered by the calculator are: Square Round Half rounds Triangles Rectangles Trapezoids Hexagons Octagons 0.000%. if you enter an inside dimension for one input, enter an inside dimension for your other inputs. And the ultimate bending moment subjected to combined pressure, axial tension and . The nature of soil conditions where the pipeline is perhaps buried. This is important because knowing if a bend will work before you perform it increases your efficiency, saves time, and saves material. . As with round tubes, we determine the feasibility and difficulty of the bend based on certain intervals of K-factor values: K > 0.20 - A fixed mandrel is sufficient for bending the tube. Reach out to the pipe manufacturer for short . In this calculation, a cantilever beam of length L with a moment of inertia of cross section Iy is considered. We have received your request and will respond promptly. Therefore, higher-order elements are not always necessary in the computation. continuous? AddThis use cookies for handling links to social media. I don't know in which category this would come. Unlimited Loads & Supports Add as many supports, loads, hinges and even additional members with SkyCiv paid plans. Example Length (Inches) = 15 Diameter (Inches) = 5 Force (Pounds) = 20 All rights reservedDisclaimer | A bending moment is measure of how much something is flexing. Moment Of Inertia Formula: I = L Where: L = Angular Momentum = Angular Frequency I = Inertia More Formulas: Finding moments of inertia may involve lots of complex calculations that are not easy to resolve every time. Click Here to join Eng-Tips and talk with other members! The developed elevation view shows the component in a flattened or unwrapped view. **Albina takes no responsibility for the calculated results. The formula for calculating the bending stress in pipe is same as that of beam. The degree of arc in plan relates directly to the overall run in developed elevation. Go to the bottom of the page for help with its use. Pipe Beam Bending Calculate beam bending shear force, bending moment, slope and deflection for pipe beams using the Euler Bernoulli beam equation. The lag factor should be included in deflection calculations to account for time dependent soil consolidation, with a minimum design recommended value of 1.5. But here we will be using formulas for some of the basic shapes. For example, the formula used when making a 90 bend is: Circumference = (pi*2*r) / (360/90).When bending, take into account the ability of the material to bend and sustain the bend. I would like to know bending moment for subsea pipeline as well as the riser. More than one. Calculator. Metric The calculator is based on the piping formulas and equations below. The minimum allowable bend ratio value for a pipe varies depending on the length of time the pipe needs to be bent (i.e., long-term vs. short-term). Metal 3D printing has rapidly emerged as a key technology in modern design and manufacturing, so its critical educational institutions include it in their curricula to avoid leaving students at a disadvantage as they enter the workforce. In particular, calculating the section area moment of inertia properties of common shapes for tube bending can be time-consuming and complicated.

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