Beam_Analysis_with_COSMOSXpress

SolidWorks Lesson Template for Teachers to Contribute Cover Sheet for Exemplary Lessons/Units Project Faculty Member Name: H Crosby Date: 6/26/06 Organization: University of Maine Title of Lesson/Unit: Determining Beam Stress and Deflection with COSMOSXpress _ Science, Technology, Engineering and Math) STEM Concepts Addressed: This lesson explores determining stress and deflection for a simply loaded cantilever beam We will first find the results by conventional analytical methods and then we will find them using COSMOSXpress (finite element analysis) We will also explore changing the cantilever beam geometry Length of instruction period: 50 minutes How many periods needed to implement lesson unit: Grade Level(s) for use: college Objectives: Learn to calculate maximum stress for a simply loaded cantilever beam Learn to calculate factor of safety for the same beam Learn to calculate maximum deflection for the same beam Learn to determine the same results using COSMOSXpress Learn to effects of changing beam dimensions Engineers often need to determine maximum stress in parts to find if they are safe Maximum stress is compared with material strength to determine factor of safety Engineers also need to determine maximum part deflection under load As an example, consider a simply loaded cantilever beam: P h” l b” The rectangular cross section cantilever beam is fixed at the wall and has a load P at the right end Maximum stress occurs at the wall at the top and bottom beam surfaces The top surface is in tension and the bottom surface is in compression Maximum beam deflection occurs at the right end of the beam We can calculate these values for the above case with the following equations: σ max = Fs = 6Pl b h2 σ yp σ max P l3 δ= E b h3 P = load appled at the end of beam, pounds l = beam length, inches b = beam base, inches h = beam height ( parallel to load ), inches Fs = factor of safety σ yp = material yeild strength , psi δ = deflection at end of beam, inches E = material modulus of elastisity , psi Note these equations are only valid for the case shown and for a steady load P Materials: SolidWorks, paper and pencil, calculator Procedures: First consider a cantilever beam 20 inches long with a base = inches and a height = 0.5 inches The beam is made from alloy steel and has a modulus of elasticity = 30,000,000 psi and a yield strength = 90,000 psi The beam is loaded with 200 pounds at the right end 200 pounds 0.5” 20” 2” Analyze the Cantilever Beam using Equations: • Determine beam maximum stress by the previous equation: σ max = Pl b h2 σ max = × 200 × 20 = 48,000 psi 2 × 0.5 • Fs = Fs = • Determine beam factor of safety with the specified alloy steel: σ yp σ max 90,000 psi = 1.9 48,000 psi Determine maximum beam deflection: δ= Pl3 E b h3 δ= × 200 × 20 = 0.85 inches 30,000,000 × × 0.5 • We will now draw the beam with Solid Works and solve for the above results using COSMOSXpress No calculations are needed with this finite element analysis program Draw the Cantilever Beam with SolidWorks: Click New on the Standard toolbar Click Part, and then click OK Click Options on the standard toolbar Click the Document Properties tab 5 Click Units Select IPS (inch, pound, second) and click OK Click Extruded Boss/Base on the Features toolbar The Front, Top, and Right planes appear Select the Right plane The display changes so that the Right plane is facing you The Sketch toolbar commands appear in the CommandManager, and a sketch opens on the Front plane Click Rectangle on the Sketch toolbar 10 Move the pointer to the sketch origin 11 Click the origin, and then move the pointer to create a rectangle approximately 2” wide by 0.5” high 12 Click again to complete the rectangle You not have to be exact with the dimensions; you will use the Smart Dimension tool to dimension the sketch 13 Click Smart Dimension on the Sketch toolbar 14 Click the bottom edge of the rectangle, and then click where you want to place the dimension 15 Be sure Smart Dimension is selected and click the right edge of the rectangle, then click to place its dimension 16 Double-click the base dimension The Modify dialog box appears The current dimension is highlighted 17 Set the value to 2, and then click OK 18 Double-click the height dimension and change its value to 0.5 19 Click Exit Sketch on the Sketch toolbar The Extrude PropertyManager appears in the FeatureManager design tree (left panel), the view of the sketch changes to trimetric, and a preview of the extrusion appears in the graphics area 20 In the PropertyManager, under Direction 1: Set Depth to 20 21 Click OK to create the extrusion 22 Click Zoom to Fit on the standard toolbar to center the sketch The cantilever beam should look as follows: Analyze the Cantilever Beam using COSMOSXpress: Click COSMOSXpress Analysis Wizard on the standard toolbar On the Welcome tab, you set the default system of units for COSMOSXpress Click Options The Options screen appears Set System of units to English (IPS) Check Show annotation for maximum and minimum in the results plots Click Next To assign Alloy Steel to the part: Click the plus sign next to Steel to see all materials in this class Select Alloy Steel Click Apply Click Next The Restraint tab appears To fix the left end of the cantilever beam: Click Next to continue Click Standard Views on the standard toolbar 10 Select Left The left face of the beam appears 11 In the graphics area, click the face of beam and click Next To apply the 200 pound force: 12 Click Next to continue 13 Under Standard Views select Dimetric 14 Select Force and click Next 15 Select the right beam end face and click Next 16 In the load dialog box, click Normal to a reference plane 17 Move the dialog box to the right and then select Top Plane on the Feature Manager Toolbar (Left side of screen.) 18 Check Flip direction 19 Enter 200 in the force value box and click Next 20 Click Next To analyze the part: 21 Click Yes (recommended) to accept the default mesh settings 22 Click Next 23 Click Run The analysis begins and a progress indicator appears A check mark appears on the Analyze tab and the Results tab appears The Results tab appears The first screen of the Results tab lists the minimum factor of safety of the model approximately as 1.9, in agreement with our previous analysis 24 On the Results tab, click Next 25 Click Show me the stress distribution in the model and click Next COSMOSXpress generates the stress distribution plot Note that the maximum stress, shown is red, is 47,390 psi, in close agreement with the calculated value of 48,000 psi The maximum stress also occurs at the wall on the top and bottom surfaces as predicted To view beam displacement: 26 On the Results tab, click Next 27 Click Show me the displacement distribution in the model and click Next COSMOSXpress generates the resultant displacement plot Note that maximum displacement is 0.834” at the right end of the beam, again in close agreement with the predicted value of 0.85” The previous cantilever beam equations are limited to a specific case, but COSMOSXpress works for more general and complex designs Analyze an Alternate Cantilever Beam using COSMOSXpress: Analyze the previous beam with the base is now 0.5” and the height is 2.0” All other properties are the same This is easily done by simply changing the base and height dimensions on the present drawing: Click close and no to save changes for COSMOSXpress Double click Extrude on the Feature Manage Toolbar (left side of screen Double click the 2” base dimension, change it to 0.5” and press enter Double click the 0.5” height dimension, change it to 2.0” and press enter Click Rebuild on the standard toolbar The beam now is redrawn on edge Click COSMOSXpress and repeat the above COSMOSXpress analysis The following results should appear: The Factor of Safety increases to 6.9, a 3.6 times increase, even though beam weight is the same as before Maximum stress decreases to 13,000 psi, a 3.6 times decrease Maximum deflection decreases to 0.0529”, a 16 times decrease Assessment: Change the beam cross section to 1” x 1” with all other properties the same Determine maximum stress and maximum deflection Bonus: Tubes are favored for lightweight designs such as bicycle frames Remove material from the beam cross section center to make a tube Increase outside dimensions to keep area and weight the same Analyze again for stress and deflection Factor of safety and stiffness should increase for a given beam weight, as this is a more efficient use of material Resources Used: SolidWorks Online Tutorials Copyrighted Materials: SolidWorks